We are always looking for ways to improve our students' math fluency. The constant lament that children cannot do times tables is a familiar one. The force feeding of number operations is both tiring and very time consuming. On the other hand students do need a degree of facility with numbers and if we as teachers can get there with a little slight of hand so be it. The following is not designed to be a panacea for all of our computational issues but merely a tool to get students thinking about numbers.
There are a number of "short cuts" that we can use that I have found children enjoy and handle with a certain amount of ease. One, I call, for lack of a better label, is the Power of 5. Very simply put, I ask a class of grade 5 or 6 students, what is the answer to 5 x 18. Usually the wheels start grinding and upon asking what is the process taking place inside their brains. I hear a variety of responses, such as, "I'm multiplying 5 x 10 and 5 x 8 and adding the two answers together". Many will tell you they are doing the traditional algorithm. This and other strategies are fine of course. However ask them what is half of 18. The answer 9 is quickly given. Place a zero after the 9 (0). Try 5 x 14, 5 x 16. Smiles ... as the solutions are found easily. This is the starting point. Odd numbers can be mastered with a bit of practice but a lesson in developing a facility with them is the second step in this strategy.
Move to more challenging questions 5 x 68 and 5 x 124. Now we do an interesting thing, I ask my students to read the number as they read a sentence from left to right. Now ask yourself what is half of each digit ... 6 > 3, 8 > 4, the answer 340. It is a real joy to see children who struggle with numbers tell you how easy it was to find half of 64 looking at the number this way. Now with 124, reading left to right. If the first digit is one join it with the second digit (12) and find half > 6, half 4 > 2, the answer is 620. Try a very large number 2 684 428. Students get a kick out of doing this without a calculator. The answer is 13 422 140. Now as a bonus you have then reading a very large number. And you will see the light come on for some of the students who find number operations a challenge. With today's access to worksheets programs it is easy to reinforce this concept.
Teachers and parents need to be aware that doing this gets students thinking about numbers in a non-traditional manner and that is always good!
The best results I have found with this is the use of short, maybe 15 minute teaching blocks 2 to 3 times a week to get students doing these automatically. Step 1 the multiplication of even numbers is mastered quickly, step 2 working with odd numbers will be addresses in the next article/blog. Be prepared to answer why we add zeros.
Initially this may seem to be a very simple or basic concept but having explored it in some depth we can take this a long way. Think, are not multiplication and division opposite operations? How does this apply to what we are doing? Also we can challenge students to see 25 or 75 can be connected to what we are doing, working with decimals is obviously a big part of what we are doing.
Sunday, July 27, 2014
Friday, July 18, 2014
Teacher "Tenure" --- A Myth
There was a recent lower court ruling against so-called "Teacher Tenure" here in California. The extent of the ruling is to be determined , but the general verdict is that "tenure" was unfair to providing an equal education for all students as called for by the State Constitution.
I believe the reading was faulty for a board range of reasons. First of all, teachers in California do not actually have tenure, at least not in the sense that professors get tenure.
When a professor has tenure they can be fired only for some gross negligence or breaking of the law. Poor teaching, poor research, or doing a shoddy job cannot lead to the loss of position under most university tenure rules. Of course, it takes much longer (typically 7 years) and a much more difficult process for professors to get that protection.
As for k-12 teachers in California we receive "Permanent Status." In a teacher's first two years (or more if they do not have have a permanent position contract) there is no due process-we can be rehired or not for the following year completely at the will and whim of the district. No reason need to given, and typically no reason given. After the probationary period, we receive "Permanent Status" within that district. If you move to a new district the process starts all over. But, by law, all teachers are evaluated by their principal or supervisor at least every 2 years. The law does not prevent then from being evaluated more frequently ( though occasionally local contracts may stipulate limits). If a teacher receives an unsatisfactory rating-a rating that is up to the principal of supervisor-then that automatically means they are in danger of losing their job. They are given the opportunity to show improvement, so there is a process. But, :tenure" for k-12 teachers does not in any way shape or form mean that they cannot be fired for poor teaching. The fact that poor teachers are not let go is completely a lack of principals and supervisors doing their job. In this area some principals work in elementary schools of up to 900 students with no assistant principal due to cutbacks.
Many states do not allow teachers to have the protection of due process (e.g. "tenure"). Charter schools, for the most part, do not give teachers such protections. Yet, there is no evidence that they get better outcomes for students. Charter schools do not outperform schools serving like students her in California or anywhere else. Nor do states without tenure outperform states that have tenure. Without even a correlation, much less a relationship shown between teacher "tenure" a student outcomes, to take away such protections claiming it is for the sake of student equity makes no sense at all,
What "tenure" protects is teachers being arbitrarily fired, or as is more often the case, fired for their views or being outspoken, "Tenure" is a form of due process. It just says the district must show cause in order to fire someone. One of my friends, lost his first teaching job, for instance, while still in the probationary period, even though he had all excellent teaching evaluations. What he did that was not so smart was openly express disagreement with some of the districts policies. As he was still probationary all they had to do was say, we are not asking you back next year. Even with the protection of due process, I have much more often seen principals and districts go after teachers for being "trouble makers" (i.e. expressing dissent as to school or district policies) than for poor teaching.
The solution to poor teachers is really four fold (at least). One is to attract better teachers. That means making the field more attractive not less. Lack of job security does not help attract people to the profession. Another is to continue to support teachers once in the field, something we do a poor job of. No teacher wants to be a bad teacher. And good teaching can be learned. Also many teachers teach under horrendous conditions. With proper support both in terms of teaching conditions and ongoing professional development, there would be very little poor teaching. We also need to support principals more in the process of both helping weak teachers, and helping them get rid of the bad
ones. Lastly, there probably does need to be a better system for figuring out what to do with those very few teachers who either are not cut out for teaching but somehow did get "tenure" or who have burned out and are no longer up to it, but cannot leave teaching because there are no other options for them economically.
The real agenda of the attack on teacher job security is really to reduce the power of teacher unions and an attack on public school teachers in general. Teacher unions are seen as a threat to the almost unrivaled power of the multibillionaires and corporate money in the American political arena. As it is they easily outspend unions 10-1, and seem to control the public discourse about most political issues are framed. Can you imagine their power once they completely decimate what little there is left of the unionized base in this country?
I believe the reading was faulty for a board range of reasons. First of all, teachers in California do not actually have tenure, at least not in the sense that professors get tenure.
When a professor has tenure they can be fired only for some gross negligence or breaking of the law. Poor teaching, poor research, or doing a shoddy job cannot lead to the loss of position under most university tenure rules. Of course, it takes much longer (typically 7 years) and a much more difficult process for professors to get that protection.
As for k-12 teachers in California we receive "Permanent Status." In a teacher's first two years (or more if they do not have have a permanent position contract) there is no due process-we can be rehired or not for the following year completely at the will and whim of the district. No reason need to given, and typically no reason given. After the probationary period, we receive "Permanent Status" within that district. If you move to a new district the process starts all over. But, by law, all teachers are evaluated by their principal or supervisor at least every 2 years. The law does not prevent then from being evaluated more frequently ( though occasionally local contracts may stipulate limits). If a teacher receives an unsatisfactory rating-a rating that is up to the principal of supervisor-then that automatically means they are in danger of losing their job. They are given the opportunity to show improvement, so there is a process. But, :tenure" for k-12 teachers does not in any way shape or form mean that they cannot be fired for poor teaching. The fact that poor teachers are not let go is completely a lack of principals and supervisors doing their job. In this area some principals work in elementary schools of up to 900 students with no assistant principal due to cutbacks.
Many states do not allow teachers to have the protection of due process (e.g. "tenure"). Charter schools, for the most part, do not give teachers such protections. Yet, there is no evidence that they get better outcomes for students. Charter schools do not outperform schools serving like students her in California or anywhere else. Nor do states without tenure outperform states that have tenure. Without even a correlation, much less a relationship shown between teacher "tenure" a student outcomes, to take away such protections claiming it is for the sake of student equity makes no sense at all,
What "tenure" protects is teachers being arbitrarily fired, or as is more often the case, fired for their views or being outspoken, "Tenure" is a form of due process. It just says the district must show cause in order to fire someone. One of my friends, lost his first teaching job, for instance, while still in the probationary period, even though he had all excellent teaching evaluations. What he did that was not so smart was openly express disagreement with some of the districts policies. As he was still probationary all they had to do was say, we are not asking you back next year. Even with the protection of due process, I have much more often seen principals and districts go after teachers for being "trouble makers" (i.e. expressing dissent as to school or district policies) than for poor teaching.
The solution to poor teachers is really four fold (at least). One is to attract better teachers. That means making the field more attractive not less. Lack of job security does not help attract people to the profession. Another is to continue to support teachers once in the field, something we do a poor job of. No teacher wants to be a bad teacher. And good teaching can be learned. Also many teachers teach under horrendous conditions. With proper support both in terms of teaching conditions and ongoing professional development, there would be very little poor teaching. We also need to support principals more in the process of both helping weak teachers, and helping them get rid of the bad
ones. Lastly, there probably does need to be a better system for figuring out what to do with those very few teachers who either are not cut out for teaching but somehow did get "tenure" or who have burned out and are no longer up to it, but cannot leave teaching because there are no other options for them economically.
The real agenda of the attack on teacher job security is really to reduce the power of teacher unions and an attack on public school teachers in general. Teacher unions are seen as a threat to the almost unrivaled power of the multibillionaires and corporate money in the American political arena. As it is they easily outspend unions 10-1, and seem to control the public discourse about most political issues are framed. Can you imagine their power once they completely decimate what little there is left of the unionized base in this country?
Friday, May 2, 2014
Reign of Error by Diane Ravitch
Dear readers,
Definitely go out and buy Reign of Error: The Hoax of the Privatization Movement and the Danger to Americas Public Schools by Diane Ravitch, which just has been launched with proper publicity. She is an amazing person-sending out a half- dozen of emails a day, three books in the last decade, and traveling to speak throughout the USA. Maybe changing your mind gives you energy, because my exhaustion comes (in part) from feeling it has been said before (including by me).
Reign of Error lays out step by step the relentless thirty year drive to either centralize the education of the young-on one hand-or divest it entirely into privatized hands on the other. Finally, the two sides have joined forces on a strategy that simultaneously does both. While this coalition has many old roots, in its current form it began with the fanfare around the publication of A Nation at Risk (1983). Ravitch was, at that time, a supporter of this bold statement that more or less accused America's teachers and school boards of a plot to undermine American health and welfare on the international scene. We were, said the signers, at risk of becoming a second rate nation if we did not take this crisis seriously. When asked AFT leader leader Al Shanker said he signed it because, "It's true our schools are not as bad as the report suggests, but we are entering a new period and they either have to change dramatically or what the report accuses them of will become true. We need a smarter citizenry."
The trouble is that crying "wolf" has never been a great way to make sensible policy. Sometimes there's no choice (like Pearl Harbor). But the continuous claims that our public education system is destroying our nation has almost entirely led to bad policy.
And in the past few years Diane's change of mind has been a particular blessing. She hasn't, as her preset opponents claim, done a complete switch at all-she was always pro-union, pro-public education and always for standards. Fairly traditional standards. She criticized progressive educators for abandoning standards, though this wasn't the case.
Then lo and behold: no one has pulled it all together better than Diane-over and over again in the past few years she has led the challenge to the corporate reformers-right, center and left. Her last two books Reign of Error and The Death and Life of the Great American School System (20100 pull it altogether.
In Reign of Error she spends the first 20 chapters laying out the case, and the last 13 offering some obvious and do-able responses to the oft-heard, "but what else can we do?" She's more supportive of the "way things were" than many other educators (like me) have been, relying subliminally perhaps on the fact that if we eliminate the scores of children in poverty on international tests, the USA does quite well. Yes, Massachusetts scores put it number one in the world, or close, if it were a nation (like Singapore?) rather than a mere state of the union. But I think neither of us is truly satisfied with what has passed for a good education in its highly regarded school districts, much less the districts that served the least advantaged schools. She also over estimates the degree to which Americans ever attended "common schools". That's another story which all this crisis talk leaves untouched-or as she ably documents, and where the promising fledgling progressive reforms of the 60s through 80s has focused on. Ted Sizer, author of a study of American high schools said, "using one's mind well" is the essential unexplored task facing the high schools for democracy. We have barely skimmed the surface of making either our schools or our democracy "belong" to everyone.\
Thank you, Diane. We all need to keep this book handy so we can whip out the citations to make our case for the kind of reform American really needs, in your own words: "to prepare citizens with the minds, hearts, and character to sustain our democracy into the future."
Best,
Debra
Definitely go out and buy Reign of Error: The Hoax of the Privatization Movement and the Danger to Americas Public Schools by Diane Ravitch, which just has been launched with proper publicity. She is an amazing person-sending out a half- dozen of emails a day, three books in the last decade, and traveling to speak throughout the USA. Maybe changing your mind gives you energy, because my exhaustion comes (in part) from feeling it has been said before (including by me).
Reign of Error lays out step by step the relentless thirty year drive to either centralize the education of the young-on one hand-or divest it entirely into privatized hands on the other. Finally, the two sides have joined forces on a strategy that simultaneously does both. While this coalition has many old roots, in its current form it began with the fanfare around the publication of A Nation at Risk (1983). Ravitch was, at that time, a supporter of this bold statement that more or less accused America's teachers and school boards of a plot to undermine American health and welfare on the international scene. We were, said the signers, at risk of becoming a second rate nation if we did not take this crisis seriously. When asked AFT leader leader Al Shanker said he signed it because, "It's true our schools are not as bad as the report suggests, but we are entering a new period and they either have to change dramatically or what the report accuses them of will become true. We need a smarter citizenry."
The trouble is that crying "wolf" has never been a great way to make sensible policy. Sometimes there's no choice (like Pearl Harbor). But the continuous claims that our public education system is destroying our nation has almost entirely led to bad policy.
And in the past few years Diane's change of mind has been a particular blessing. She hasn't, as her preset opponents claim, done a complete switch at all-she was always pro-union, pro-public education and always for standards. Fairly traditional standards. She criticized progressive educators for abandoning standards, though this wasn't the case.
Then lo and behold: no one has pulled it all together better than Diane-over and over again in the past few years she has led the challenge to the corporate reformers-right, center and left. Her last two books Reign of Error and The Death and Life of the Great American School System (20100 pull it altogether.
In Reign of Error she spends the first 20 chapters laying out the case, and the last 13 offering some obvious and do-able responses to the oft-heard, "but what else can we do?" She's more supportive of the "way things were" than many other educators (like me) have been, relying subliminally perhaps on the fact that if we eliminate the scores of children in poverty on international tests, the USA does quite well. Yes, Massachusetts scores put it number one in the world, or close, if it were a nation (like Singapore?) rather than a mere state of the union. But I think neither of us is truly satisfied with what has passed for a good education in its highly regarded school districts, much less the districts that served the least advantaged schools. She also over estimates the degree to which Americans ever attended "common schools". That's another story which all this crisis talk leaves untouched-or as she ably documents, and where the promising fledgling progressive reforms of the 60s through 80s has focused on. Ted Sizer, author of a study of American high schools said, "using one's mind well" is the essential unexplored task facing the high schools for democracy. We have barely skimmed the surface of making either our schools or our democracy "belong" to everyone.\
Thank you, Diane. We all need to keep this book handy so we can whip out the citations to make our case for the kind of reform American really needs, in your own words: "to prepare citizens with the minds, hearts, and character to sustain our democracy into the future."
Best,
Debra
Friday, April 4, 2014
Follow the Money
I'm returning to my roots! Marx occasionally had it right. Along with Horace Mann, John Dewey, et al.
This whole "new reform" movement in education is being fueled (the $$$$) by ordinary greed. Or second-hand greed-seeing a chance to destroy the political power of an already waning labor movement by undermining the two teacher unions. This is being done by fooling folks who mistakenly saw their own longtime critique of the public bureaucracy in the "radical" sounding idea charter school being spread by corporate think tanks that went into building the "Charter Movement". Afraid of being part of the "status quo" some genuine school-based reformers provided cover for a shift in power quite the opposite of what they had in mind. Most of those genuine school and educational people, including of course Ravitch, have been that ship and returning to their roots.
Having failed time after time with vouchers-direct public funding of private schools, the new reformers saw a way around it. Their instincts also suggest that history favors reforms that make repeal difficult, almost impossible. So the motto is: move fast and thoroughly.
Reading back about the fall of the Soviet Union, the big question was what would happen to all the state-owned enterprises. It seemed a tough puzzle. But before one could seriously think it through they were all sold off-to friends and allies with money. Deed done. While I write this the same thing is happening to our public schools. This was not the plan in Minnesota which began the charter movement with the best of intentions, Nor the idea of Ted Sizer, or Deborah Meier who both started great little schools as charters. Or even Al Shanker who once proposed something he labeled charters-small schools under the initiative of teachers who wanted to try out some of their very different ideas, entirely under the aegis of the public system.
However, the idea of Charter Schools opened the eyes and ears of folks with quite different intentions. They saw that there was money to be made right and left and center. Buildings were "sold off" for nothing or nearly nothing. Public funds were used to start schools whose principals and leaders were paid a half million and more for being the "principal" or "superintendent". Publishing companies and private tech companies saw $$$$$ everywhere. By the time we wake up to what is happening we will no longer have a public education system in reality. Some charters will be legit-truly serving public purposes with public money and boards made up of educators, community members, etc. But most will be in the hands of the folks with no other connection to the school they "serve" than they have to anything else stockholders have-how much money can be made off this! Meanwhile...that their revolutionary ideas will have demonstrated no significant improvement in the situation facing America's poor children in terms of test scores will be just fine without them.
They did this with language resonating with the valiant words of "borrowed" from the civil rights movement. Except they seemed to have left out terms like "equal funding" or "integration." They did it despite the cost to teachers of color, to public unions which Martin Luther King Jr. died defending. And so on. They did this by adopting noble words (mea culpa) like choice and autonomy and self-governance and small scale and on and on. They did this by playing with data to confuse our judgement.
Shame on us for being duped.
Yet, I still believe-how can I not?-that some, if not many, of those who have gone along meant well, and were not influenced in any way by their moneyed interests. Sure, it's easier to believe what seems compatible with one's other interests. I've done that. And there are many others who have simply been naive, confused or not paying close attention.
Enough. We must fight this back quickly before they've bought out the whole shebang.
Some resources and organizations helping this fight:
The Network for Public Education
The Forum for Education and Democracy
This whole "new reform" movement in education is being fueled (the $$$$) by ordinary greed. Or second-hand greed-seeing a chance to destroy the political power of an already waning labor movement by undermining the two teacher unions. This is being done by fooling folks who mistakenly saw their own longtime critique of the public bureaucracy in the "radical" sounding idea charter school being spread by corporate think tanks that went into building the "Charter Movement". Afraid of being part of the "status quo" some genuine school-based reformers provided cover for a shift in power quite the opposite of what they had in mind. Most of those genuine school and educational people, including of course Ravitch, have been that ship and returning to their roots.
Having failed time after time with vouchers-direct public funding of private schools, the new reformers saw a way around it. Their instincts also suggest that history favors reforms that make repeal difficult, almost impossible. So the motto is: move fast and thoroughly.
Reading back about the fall of the Soviet Union, the big question was what would happen to all the state-owned enterprises. It seemed a tough puzzle. But before one could seriously think it through they were all sold off-to friends and allies with money. Deed done. While I write this the same thing is happening to our public schools. This was not the plan in Minnesota which began the charter movement with the best of intentions, Nor the idea of Ted Sizer, or Deborah Meier who both started great little schools as charters. Or even Al Shanker who once proposed something he labeled charters-small schools under the initiative of teachers who wanted to try out some of their very different ideas, entirely under the aegis of the public system.
However, the idea of Charter Schools opened the eyes and ears of folks with quite different intentions. They saw that there was money to be made right and left and center. Buildings were "sold off" for nothing or nearly nothing. Public funds were used to start schools whose principals and leaders were paid a half million and more for being the "principal" or "superintendent". Publishing companies and private tech companies saw $$$$$ everywhere. By the time we wake up to what is happening we will no longer have a public education system in reality. Some charters will be legit-truly serving public purposes with public money and boards made up of educators, community members, etc. But most will be in the hands of the folks with no other connection to the school they "serve" than they have to anything else stockholders have-how much money can be made off this! Meanwhile...that their revolutionary ideas will have demonstrated no significant improvement in the situation facing America's poor children in terms of test scores will be just fine without them.
They did this with language resonating with the valiant words of "borrowed" from the civil rights movement. Except they seemed to have left out terms like "equal funding" or "integration." They did it despite the cost to teachers of color, to public unions which Martin Luther King Jr. died defending. And so on. They did this by adopting noble words (mea culpa) like choice and autonomy and self-governance and small scale and on and on. They did this by playing with data to confuse our judgement.
Shame on us for being duped.
Yet, I still believe-how can I not?-that some, if not many, of those who have gone along meant well, and were not influenced in any way by their moneyed interests. Sure, it's easier to believe what seems compatible with one's other interests. I've done that. And there are many others who have simply been naive, confused or not paying close attention.
Enough. We must fight this back quickly before they've bought out the whole shebang.
Some resources and organizations helping this fight:
The Network for Public Education
The Forum for Education and Democracy
Friday, February 28, 2014
Early Childhood Education
I was recently asked to sign a petition to better fund early childhood education. I have to admit, though, that talk of early childhood education always raises mixed emotions in me. On the one hand, how could I not want to give disadvantaged youth the opportunity for quality early childhood education. And there is good research on the both how it can make a difference and on the real lack of it for many children.
But there in the rub. What is quality early childhood education? Over the past decade we have seen kindergarten turn into first grade. A place of worksheets and formal direct instruction. A place where children quickly learn whether they are "good" or "poor" students. Where they are put into the "fast" or the "slow" group.
Yes research after research study, as well as comparisons to other countries have shown that earlier is not better. Countries that start formal teaching of literacy later tend to actually do better at literacy over the years. Comparative studies of developmental early education versus formal instruction has shown similar results - developmental forms that do not stress formal teaching leads to better lasting results.
But when I heard of expanded early education, I see that in this county what that likely may mean is early formal instruction, early sorting kids into who is seen as good at school and those who are not, creating self-fulling prophesy, and taking away a time that should be for children to explore their world, and learn to socialize and play.
If early childhood education means a time kids received supportive opportunities to be involved in play, exploration of materials, exposure to wonderful stories and print, to interact with playmates in a safe and supportive environment, I am all for it.
If it means starting "first grade" at 3 or 4, then might we be doing more harm then good?
So it is with such fears that I hear talk of expanded early childhood education.
But there in the rub. What is quality early childhood education? Over the past decade we have seen kindergarten turn into first grade. A place of worksheets and formal direct instruction. A place where children quickly learn whether they are "good" or "poor" students. Where they are put into the "fast" or the "slow" group.
Yes research after research study, as well as comparisons to other countries have shown that earlier is not better. Countries that start formal teaching of literacy later tend to actually do better at literacy over the years. Comparative studies of developmental early education versus formal instruction has shown similar results - developmental forms that do not stress formal teaching leads to better lasting results.
But when I heard of expanded early education, I see that in this county what that likely may mean is early formal instruction, early sorting kids into who is seen as good at school and those who are not, creating self-fulling prophesy, and taking away a time that should be for children to explore their world, and learn to socialize and play.
If early childhood education means a time kids received supportive opportunities to be involved in play, exploration of materials, exposure to wonderful stories and print, to interact with playmates in a safe and supportive environment, I am all for it.
If it means starting "first grade" at 3 or 4, then might we be doing more harm then good?
So it is with such fears that I hear talk of expanded early childhood education.
Friday, February 21, 2014
Taking The Public Out Of Public Education
I recently talked to my old professor and mentor, Art Pearl. Art has been a political activist, writer and teacher, focusing on issues of democratic education for over four decades. Now in his 80s, he is still teaching, writing and acting on his beliefs. He talked to me about the attack on public schools, on unions, and the need for democratic education. In this column, I am going to use our discussion as a springboard for expanding my own ideas on the current attack on public education, on unions, and the unions representing public school teachers.
One can trace the beginning if this movement to a report, A Nation At Risk, written in 1983 by the National Commission on Excellence in Education, at the behest of then Secretary of Education, Bell. The report was really a call to arms to reframe the debate about education. It made a rhetorical claim that the mediocrity of our educational system put our nation at risk - equating it with an attack by a foreign country. No evidence was provided to support this claim. In fact, while every decade throughout the history of education, headlines have proclaimed that it is going to hell in a hand basket, and bemoaning the loss of the good old days, most evidence we have only points to continual progress, at least up to the 1990s (see The Way We Were? by Richard Rothstein, and The Manufactured Crisis by Bruce Biddle for extensive discussion and data on this topic).
One aspect of this effort to undermine public education has been to reframe the purpose of education as purely preparation for the workforce. In the past, public schools have been considered to have multiple purposes-socialization in its many forms, citizenship in its many forms, and providing students with a well rounded general education - cultural and "academic," meaning both individual potential aims as well as societal aims. Since that report, the public media discussion of education, including the U.S. Department of Education, has cast the purpose of education purely in terms of economic impact. They, as did the report, describe the threat of a failing educational system as a threat to our national economy. They sell education for its ability to get one a better job, a better income-using educational attainment to income correlation data. today, one virtually never hears mention of any other purpose for schools in the mainstream media or from government spokespeople.
Even if we accept that schools should be about job training, the economic argument used by the government and media is mostly based on lies and false information. The claim of A Nation at Risk, (one that has constantly been repeated since) is that our mediocre schools are leading to our economic downfall. However, there is not causal link in developed countries between schooling and the health of the economy (such a cause-effect link does exist in developing countries that do not already have a basically educated population). If there were such a link, why didn't we hear those same forces cheering what a great job our schools must have been doing when we had an economic boom in the 1990s? In fact, that the would have been the work force that was our public schools during the time to which A Nation At Risk referred. If this cause-effect relationship were correct, then our schools could not have been as bad as they claim.
In fact, the relationship between schooling and the economy in developed countries is mostly non-existent, or the reverse of that claimed. To some extent, schools do respond to the job market. For example, in the early 1990s almost nobody studied computer technology in school. The early dot-commers were often often self-educated in terms of technology. However, soon colleges and universities were establishing new programs in the computer sciences, quickly filling up with students. Then when the tech bust hit a decade later, the job market was flooded with these new graduates and the recently laid off workers.
However, for the most part, having an educated workforce neither creates nor destroys jobs. We now live in a global economy where such things have more to do with larger economic forces. Job loss in the U.S. has mostly been due to outsourcing, first manufacturing jobs, and lately other technical and professional jobs as well. The driving competitive force is that people in certain countries will work for less. The way we can compete with them in a free market economy is to take lower wages, less benefits, and accept other reductions in workplace quality and safety, as well as lowering environmental protections. Having better educated people to compete for these jobs will not bring them back to the U.S.
The only area the job market that is increasing (at least in numbers that are significant in terms of the size of the U.S. workforce) is in the service sector, jobs that actually require little in the way of schooling, and certainly not a college education. However, employers of such workers do want workers who are obedient, punctual and docile-just the sort of education that children in schools serving poor and minority children are receiving, even if they do get low test scores (Walmart, for instance, is one of the largest employers in the U.S.).
While getting a "good' education may make you as an individual, in a better position to compete for what jobs do exist, there is no evidence that a better-educated population would in any way lead to job creation. If however, schools are just job training sites, then while it is clear that I want my child to get the best education possible, it is less clear why the "public" should care or even want good schools for all. This may be especially true if all children getting a good education means they might out-compete my child for those scarce good jobs! This promotion of schools as the pathway to better jobs makes the free market and student as consumer mentality for schooling more appealing. I need to only concern myself with finding the best school for my child at a price I can afford.
However, thinkers as different as John Dewey and Horace Mann from the early days of public education, to recent thinkers as disparate as Deborah Meier, Ted Sizer, Diane Ravitch and E.D. Hirsh, have all argued that what and how children are taught in school matters for the survival of a democratic society, not just solely for how well trained for the workforce the students will be. Schools are the place where children move from the private sphere of the family to the public sphere of the larger society. If it is the habits and knowledge formed and developed in these public institutions that in part frame students' understanding of their larger place in society. When public schooling is about preparing students to be citizens for a democratic society, then clearly we all have a stake in what it means to be an educated citizen, in what habits and understandings are promoted there, in what knowledge is imparted there.
Another connected strand to this attack on public education is an attack on unions. We have lost a large segment of our skilled workforce to other countries, and we have had several Federal administrations unfriendly to organized labor. Due to these forces, the U.S. (once the leader in organized labor) now has among the lowest percentage of unionized workers compared to any other democratic industrialized nation. However, the one place where organized labor is still strong is in the public sector. The attack on public school is part of an attack of the last bastion of organized labor, the last place where workers can speak in a unified manner as a counterpoint to the powerful voices of corporate interests.
More and more, teachers and their unions are being blamed for the supposed failure of our public school system. It brought out in a way that connects to the general public's emotions and immediate experience. There is a lot of current fanfare in the media that incompetent teachers are hard to fire and teachers unions block reforms (both claims central to the premise of the movie "Waiting for Superman" for instance). Do they provide evidence? Very little. An easy way to check the validity of their claim would be to compare non-union states to union states, as many states don't allow teachers to unionize. There is either no connection or a positive correlation between states that have unions and academic success as measured by high school completion and test scores. In addition, most of the reforms that are touted as successful by the administration and think-tanks have taken place in cities with strong teacher unions.
While it may be true that it isn't easy to fire poor teachers, no evidence is provided that too many poor teachers really is a major problem. Moreover, the principals I talk to all tell me that, while not being easy, they have always been able to get rid of the poor teachers they had. Is my sample of principals unrepresentative? Maybe-but then one could say that the problem is poor principal (though I hold them no more to blame than the teachers). When you make it easier to fire bad teachers, you also make it easier fire the good ones as well. What "tenure" provides is not a guarantee of a job for life, but that the teacher cannot be fired without cause, and puts the burden of proof for that cause on the employer. The question framed that way becomes, do we believe in due process? It is just such due process that teachers unions and the "tenure' process protect.
Charter schools and vouchers are currently the "reforms" of choice. Charter, private and parochial schools typically do not teacher unions. These schools also bypass publicly elected school boards that oversee their vision, mission and curriculum. They often also exclude unionized public employees for many other positions in schools-such as custodial and food services. The normal checks and balances of the democratic process are bypassed in the name of "efficiency" and the advantages of "market forces". These forces see charter chains, and private forms of education, which answer to their own private boards, as competing for the students. Parents and children are merely consumers of this commodity, and the more effective and efficient schools will get a bigger market share. The only thing left that will be public is that it is the public's money being used to pay for them.
This attack on the public nature of schools is in line with other current agendas of the free marketers-such as the privatization of Social Security and undermining public health care reforms. These are all part of a clear and premeditated mission to have this country run only by the dictates of the "free-market" economy (read as: run by transnational corporations and financiers). Schooling is just one of these fronts.
The only thing that can stand in their way is a truly democratic citizenry that takes action and speaks out. That means you!
One can trace the beginning if this movement to a report, A Nation At Risk, written in 1983 by the National Commission on Excellence in Education, at the behest of then Secretary of Education, Bell. The report was really a call to arms to reframe the debate about education. It made a rhetorical claim that the mediocrity of our educational system put our nation at risk - equating it with an attack by a foreign country. No evidence was provided to support this claim. In fact, while every decade throughout the history of education, headlines have proclaimed that it is going to hell in a hand basket, and bemoaning the loss of the good old days, most evidence we have only points to continual progress, at least up to the 1990s (see The Way We Were? by Richard Rothstein, and The Manufactured Crisis by Bruce Biddle for extensive discussion and data on this topic).
One aspect of this effort to undermine public education has been to reframe the purpose of education as purely preparation for the workforce. In the past, public schools have been considered to have multiple purposes-socialization in its many forms, citizenship in its many forms, and providing students with a well rounded general education - cultural and "academic," meaning both individual potential aims as well as societal aims. Since that report, the public media discussion of education, including the U.S. Department of Education, has cast the purpose of education purely in terms of economic impact. They, as did the report, describe the threat of a failing educational system as a threat to our national economy. They sell education for its ability to get one a better job, a better income-using educational attainment to income correlation data. today, one virtually never hears mention of any other purpose for schools in the mainstream media or from government spokespeople.
Even if we accept that schools should be about job training, the economic argument used by the government and media is mostly based on lies and false information. The claim of A Nation at Risk, (one that has constantly been repeated since) is that our mediocre schools are leading to our economic downfall. However, there is not causal link in developed countries between schooling and the health of the economy (such a cause-effect link does exist in developing countries that do not already have a basically educated population). If there were such a link, why didn't we hear those same forces cheering what a great job our schools must have been doing when we had an economic boom in the 1990s? In fact, that the would have been the work force that was our public schools during the time to which A Nation At Risk referred. If this cause-effect relationship were correct, then our schools could not have been as bad as they claim.
In fact, the relationship between schooling and the economy in developed countries is mostly non-existent, or the reverse of that claimed. To some extent, schools do respond to the job market. For example, in the early 1990s almost nobody studied computer technology in school. The early dot-commers were often often self-educated in terms of technology. However, soon colleges and universities were establishing new programs in the computer sciences, quickly filling up with students. Then when the tech bust hit a decade later, the job market was flooded with these new graduates and the recently laid off workers.
However, for the most part, having an educated workforce neither creates nor destroys jobs. We now live in a global economy where such things have more to do with larger economic forces. Job loss in the U.S. has mostly been due to outsourcing, first manufacturing jobs, and lately other technical and professional jobs as well. The driving competitive force is that people in certain countries will work for less. The way we can compete with them in a free market economy is to take lower wages, less benefits, and accept other reductions in workplace quality and safety, as well as lowering environmental protections. Having better educated people to compete for these jobs will not bring them back to the U.S.
The only area the job market that is increasing (at least in numbers that are significant in terms of the size of the U.S. workforce) is in the service sector, jobs that actually require little in the way of schooling, and certainly not a college education. However, employers of such workers do want workers who are obedient, punctual and docile-just the sort of education that children in schools serving poor and minority children are receiving, even if they do get low test scores (Walmart, for instance, is one of the largest employers in the U.S.).
While getting a "good' education may make you as an individual, in a better position to compete for what jobs do exist, there is no evidence that a better-educated population would in any way lead to job creation. If however, schools are just job training sites, then while it is clear that I want my child to get the best education possible, it is less clear why the "public" should care or even want good schools for all. This may be especially true if all children getting a good education means they might out-compete my child for those scarce good jobs! This promotion of schools as the pathway to better jobs makes the free market and student as consumer mentality for schooling more appealing. I need to only concern myself with finding the best school for my child at a price I can afford.
However, thinkers as different as John Dewey and Horace Mann from the early days of public education, to recent thinkers as disparate as Deborah Meier, Ted Sizer, Diane Ravitch and E.D. Hirsh, have all argued that what and how children are taught in school matters for the survival of a democratic society, not just solely for how well trained for the workforce the students will be. Schools are the place where children move from the private sphere of the family to the public sphere of the larger society. If it is the habits and knowledge formed and developed in these public institutions that in part frame students' understanding of their larger place in society. When public schooling is about preparing students to be citizens for a democratic society, then clearly we all have a stake in what it means to be an educated citizen, in what habits and understandings are promoted there, in what knowledge is imparted there.
Another connected strand to this attack on public education is an attack on unions. We have lost a large segment of our skilled workforce to other countries, and we have had several Federal administrations unfriendly to organized labor. Due to these forces, the U.S. (once the leader in organized labor) now has among the lowest percentage of unionized workers compared to any other democratic industrialized nation. However, the one place where organized labor is still strong is in the public sector. The attack on public school is part of an attack of the last bastion of organized labor, the last place where workers can speak in a unified manner as a counterpoint to the powerful voices of corporate interests.
More and more, teachers and their unions are being blamed for the supposed failure of our public school system. It brought out in a way that connects to the general public's emotions and immediate experience. There is a lot of current fanfare in the media that incompetent teachers are hard to fire and teachers unions block reforms (both claims central to the premise of the movie "Waiting for Superman" for instance). Do they provide evidence? Very little. An easy way to check the validity of their claim would be to compare non-union states to union states, as many states don't allow teachers to unionize. There is either no connection or a positive correlation between states that have unions and academic success as measured by high school completion and test scores. In addition, most of the reforms that are touted as successful by the administration and think-tanks have taken place in cities with strong teacher unions.
While it may be true that it isn't easy to fire poor teachers, no evidence is provided that too many poor teachers really is a major problem. Moreover, the principals I talk to all tell me that, while not being easy, they have always been able to get rid of the poor teachers they had. Is my sample of principals unrepresentative? Maybe-but then one could say that the problem is poor principal (though I hold them no more to blame than the teachers). When you make it easier to fire bad teachers, you also make it easier fire the good ones as well. What "tenure" provides is not a guarantee of a job for life, but that the teacher cannot be fired without cause, and puts the burden of proof for that cause on the employer. The question framed that way becomes, do we believe in due process? It is just such due process that teachers unions and the "tenure' process protect.
Charter schools and vouchers are currently the "reforms" of choice. Charter, private and parochial schools typically do not teacher unions. These schools also bypass publicly elected school boards that oversee their vision, mission and curriculum. They often also exclude unionized public employees for many other positions in schools-such as custodial and food services. The normal checks and balances of the democratic process are bypassed in the name of "efficiency" and the advantages of "market forces". These forces see charter chains, and private forms of education, which answer to their own private boards, as competing for the students. Parents and children are merely consumers of this commodity, and the more effective and efficient schools will get a bigger market share. The only thing left that will be public is that it is the public's money being used to pay for them.
This attack on the public nature of schools is in line with other current agendas of the free marketers-such as the privatization of Social Security and undermining public health care reforms. These are all part of a clear and premeditated mission to have this country run only by the dictates of the "free-market" economy (read as: run by transnational corporations and financiers). Schooling is just one of these fronts.
The only thing that can stand in their way is a truly democratic citizenry that takes action and speaks out. That means you!
Friday, February 14, 2014
Round, Square or Curly: Important Symbols in Mathematics
Parenthesis , Brackets and Braces
Important symbols in math
Parenthesis, Brackets and Braces
You'll come across many symbols in math. In fact, the language of mathematics is written is symbols and of course a little bit of text for clarification. This article focuses on parenthesis, brackets, and braces to provide clarification on their uses.
The parenthesis look like a typical bracket, on a keyboard, the will be found above the nine and zero and look like this: ( ) The parenthesis are used to group numbers or variables or both.
Examples of a parenthesis ( ):
When you see a question like this, you need to use the order of operations to solve it.
9 - 5 / ( 8 - 3) x 2 + 6
The parenthesis must be done first which means they can be removed when the operation is performed, in this case (8-3) becomes 5:
= 9 - 5 /5 -3 x 2 + 6
= 9 - 1 x 2 + 6
= 9 - 2 + 6
= 7 + 6
= 13
When you are asked to expand, it will mean doing everything within the parenthesis and then removing the parenthesis.
Parenthesis also means multiplication.
If the question is like this 3 ( 2 + 5), the parenthesis means to multiply, however, you won't multiply until you complete the operation which is 2 + 5, which will become 7 and then if would be multiplied by 3.
Examples of brackets [ ]:
Typically the brackets are found beside the p on the keyboard, above the brackets are braces. Brackets are used after parenthesis and are used to group numbers and variables as well. Typically, it would be the parenthesis first, the the brackets, then braces. Here's an example of brackets:
4 - 3[4 - 2(6 - 3) ] / 3
= 4 - 3 [ 4 - 2 (3)] / 3 ... do the operation in the parenthesis first, leave the parenthesis
= 4 - 3 [4 - 5] / 3 ... do the operation in the bracket
= 4 - 3[-2] /3 ... the bracket informs you to multiply the number within which is - 3 x - 2
= 4 + 6 / 3
= 4 + 2
= 6
Examples of braces { }
Braces are also used to group variables and numbers. Here is an example using parenthesis, braces and brackets which is also referred to as 'nested parenthesis' :
2 { 1 + [ 4 (2 + 1) + 3] } ... again, always work from the inside out
= 2 {1 + [4(3) + 3] }
= 2 {1 + [12 + 3] }
= 2 {1 + [15] }
= 2 {16}
= 32
These brackets are also used in sets {2, 3, 6, 8, 10...}
These three types of brackets are sometimes referred to as round, square and curly brackets. When working with nested parenthesis, the order from will always be: parenthesis, brackets, braces as shown: { [ ( ) ] }
You will encounter these parenthesis, brackets and braces more frequently in pre algebra and algebra.
Important symbols in math
Parenthesis, Brackets and Braces
You'll come across many symbols in math. In fact, the language of mathematics is written is symbols and of course a little bit of text for clarification. This article focuses on parenthesis, brackets, and braces to provide clarification on their uses.
The parenthesis look like a typical bracket, on a keyboard, the will be found above the nine and zero and look like this: ( ) The parenthesis are used to group numbers or variables or both.
Examples of a parenthesis ( ):
When you see a question like this, you need to use the order of operations to solve it.
9 - 5 / ( 8 - 3) x 2 + 6
The parenthesis must be done first which means they can be removed when the operation is performed, in this case (8-3) becomes 5:
= 9 - 5 /5 -3 x 2 + 6
= 9 - 1 x 2 + 6
= 9 - 2 + 6
= 7 + 6
= 13
When you are asked to expand, it will mean doing everything within the parenthesis and then removing the parenthesis.
Parenthesis also means multiplication.
If the question is like this 3 ( 2 + 5), the parenthesis means to multiply, however, you won't multiply until you complete the operation which is 2 + 5, which will become 7 and then if would be multiplied by 3.
Examples of brackets [ ]:
Typically the brackets are found beside the p on the keyboard, above the brackets are braces. Brackets are used after parenthesis and are used to group numbers and variables as well. Typically, it would be the parenthesis first, the the brackets, then braces. Here's an example of brackets:
4 - 3[4 - 2(6 - 3) ] / 3
= 4 - 3 [ 4 - 2 (3)] / 3 ... do the operation in the parenthesis first, leave the parenthesis
= 4 - 3 [4 - 5] / 3 ... do the operation in the bracket
= 4 - 3[-2] /3 ... the bracket informs you to multiply the number within which is - 3 x - 2
= 4 + 6 / 3
= 4 + 2
= 6
Examples of braces { }
Braces are also used to group variables and numbers. Here is an example using parenthesis, braces and brackets which is also referred to as 'nested parenthesis' :
2 { 1 + [ 4 (2 + 1) + 3] } ... again, always work from the inside out
= 2 {1 + [4(3) + 3] }
= 2 {1 + [12 + 3] }
= 2 {1 + [15] }
= 2 {16}
= 32
These brackets are also used in sets {2, 3, 6, 8, 10...}
These three types of brackets are sometimes referred to as round, square and curly brackets. When working with nested parenthesis, the order from will always be: parenthesis, brackets, braces as shown: { [ ( ) ] }
You will encounter these parenthesis, brackets and braces more frequently in pre algebra and algebra.
Friday, February 7, 2014
Fulfilling The Dream. . . If I Were In Charge Part Two
People sometimes ask me what I think what needs to be done with the schools. This is really a two part question for me. One part is the policy side - what should or should not be required. The other part of the question is what are my ideas of what a good school looks like, which does not imply I believe in mandating those ideas even if I could. In my previous blog, I addressed the first part of question. Now I will briefly tackle the second part.
A good test of schooling is whether one would send one's own children there. Those who have read my other blog entries know I favor progressive/constructivist pedagogy. That means that students have to be engaged in activities that matter to them in order to learn. The more those activities are connected authentically to the kinds of activities one engages outside of school, the more likely what they learn can and will be used beyond school. There is both the need of the student to follow their own personal interests and abilities, and expanding those interests.
One also needs to think about how the experience of school shapes both what a student learns about, and what kind of climate and culture they learn in it in. As psychologists such as Vygotsky, Bandura, Wenger and many others have shown, we learn more indirectly from how we experience the world, and watching how the adults in our world interact, as we do from any explicit instruction. Therefore, as much as possible the school should recreate the kind of culture, society we want our students to learn to be part of.
There is a built in tension of a democracy, between individual rights and pursuits, while recognizing that we are also a part of a larger society. Totalitarian and fascist states focus on the state over the individual, and so schools in such a culture would teach students to obey and focus on obedience to higher authority. In an anarchist or libertarian state is would focus on the rights and liberties if the individual. Would such a system even have public schooling, much less compulsory schooling?
In my school, build on the foundation of democratic principals, students work not just individually, but also with others who are both alike and different from themselves. That in itself is one of the most important skill that I see any citizen needs. Most of what we do in life is in collaboration with others, in both the work and civic spheres. Humans are, by nature, social animals. The way a school and its curriculum is organized takes that into account. It means assessments that are part of the learning process and that mimic or are actual real like products or performances for the most part.
Long term projects would be at the center of most learning activities, activities that require students to integrate a variety of skills and abilities across disciplines. This mimics the kind of activities and work people engage in for the most part outside of school. Real learning takes place when we work at real tasks that matter. The more in depth the project is, the deeper the learning will be, and the more likely it will stay with us. Such learning takes time.
Students would stay with the same teacher for a minimum of two years. Deep learning takes deep relationships, and when teachers and students only work together for one year, those deep relationships are hard to build, with the family as much as with the student. If you are changing whom you work with too often, it gets hard to put in the investment in the relationship.
The school would be run collaboratively among the faculty. While it is important for all members of the school community to have a say, how much would vary depending on the kinds of decisions. Major curricular decisions would be the purview of the teaching faculty.
Another aspect is school size. Most of the above is hard to implement in a large school. The larger the numbers of people the more such institutions must make decisions based on expediency and smooth running of the institution rather on the educational needs of the students. Additionally, the number of people needs to be small enough so that the school can be a community where all members actually can get to know each other over time.
Some people claim such schooling is only appropriate for the gifted, or is not practical, and could not work in the real world. However, as I have documented in earlier blogs the evidence is quite strong that it does work, and that actually such practices are probably more important for the disadvantaged than the advantaged, since the advantaged get so many of these advantages outside of school.
From personal experience I know these ideas are challenging but they do work. What do you think are the elements that make good schools?
A good test of schooling is whether one would send one's own children there. Those who have read my other blog entries know I favor progressive/constructivist pedagogy. That means that students have to be engaged in activities that matter to them in order to learn. The more those activities are connected authentically to the kinds of activities one engages outside of school, the more likely what they learn can and will be used beyond school. There is both the need of the student to follow their own personal interests and abilities, and expanding those interests.
One also needs to think about how the experience of school shapes both what a student learns about, and what kind of climate and culture they learn in it in. As psychologists such as Vygotsky, Bandura, Wenger and many others have shown, we learn more indirectly from how we experience the world, and watching how the adults in our world interact, as we do from any explicit instruction. Therefore, as much as possible the school should recreate the kind of culture, society we want our students to learn to be part of.
There is a built in tension of a democracy, between individual rights and pursuits, while recognizing that we are also a part of a larger society. Totalitarian and fascist states focus on the state over the individual, and so schools in such a culture would teach students to obey and focus on obedience to higher authority. In an anarchist or libertarian state is would focus on the rights and liberties if the individual. Would such a system even have public schooling, much less compulsory schooling?
In my school, build on the foundation of democratic principals, students work not just individually, but also with others who are both alike and different from themselves. That in itself is one of the most important skill that I see any citizen needs. Most of what we do in life is in collaboration with others, in both the work and civic spheres. Humans are, by nature, social animals. The way a school and its curriculum is organized takes that into account. It means assessments that are part of the learning process and that mimic or are actual real like products or performances for the most part.
Long term projects would be at the center of most learning activities, activities that require students to integrate a variety of skills and abilities across disciplines. This mimics the kind of activities and work people engage in for the most part outside of school. Real learning takes place when we work at real tasks that matter. The more in depth the project is, the deeper the learning will be, and the more likely it will stay with us. Such learning takes time.
Students would stay with the same teacher for a minimum of two years. Deep learning takes deep relationships, and when teachers and students only work together for one year, those deep relationships are hard to build, with the family as much as with the student. If you are changing whom you work with too often, it gets hard to put in the investment in the relationship.
The school would be run collaboratively among the faculty. While it is important for all members of the school community to have a say, how much would vary depending on the kinds of decisions. Major curricular decisions would be the purview of the teaching faculty.
Another aspect is school size. Most of the above is hard to implement in a large school. The larger the numbers of people the more such institutions must make decisions based on expediency and smooth running of the institution rather on the educational needs of the students. Additionally, the number of people needs to be small enough so that the school can be a community where all members actually can get to know each other over time.
Some people claim such schooling is only appropriate for the gifted, or is not practical, and could not work in the real world. However, as I have documented in earlier blogs the evidence is quite strong that it does work, and that actually such practices are probably more important for the disadvantaged than the advantaged, since the advantaged get so many of these advantages outside of school.
From personal experience I know these ideas are challenging but they do work. What do you think are the elements that make good schools?
Thursday, January 30, 2014
The Dream For A Better School System ...If I Were In Charge
People sometimes ask me what I think needs to be done with the schools. This is really a two part question for me. One part is the policy side-what should or should not be required. The other part of the question is what are my ideas of what a good school and teaching look like, which doesn't imply I believe in mandating those ideas even if I could. For this blog I will look at the former, and discuss the latter in a future blog.
What I would change is the mandating of curriculum (so called Standards). The mandating of standards for education in a democracy can only be justified in the case of an overwhelming consensus on such standards. There's no evidence for such a consensus, and lots of evidence that there is considerable controversy over both what such a curriculum should look like and whether there should be one at all. While I have my own views on what I think all children should learn, I do not see it as my, or anyone else's place to impose those beliefs on others, much less an entire nation.
Along with that is we need to get rid of high stakes mandated standardized testing. Standardized tests have so many problems, not the least of which is that they impose a standardized curriculum. If a certain test is required, and there are high stakes for how one does on that test, then teachers must teach to it, and students must gear themselves to it as well. That means standardized curriculum. Standardized tests are also, by definition, culturally biased-they have to be normed, which means an automatic bias to the dominant group. That is just a fact of psychometrics. And, as the test makers have admitted, their reliability for individuals is not all that great, and yet they are used to judge individual students. I also do not accept their validity for much more than a test taking skills, school skills, and one's zip code.
What I do support is a strong public school system. One thing such a system needs is at the very least equalized funding, and really more funding is needed for those who live in poverty and have other strikes against them in life to at least equalize some of the built in advantages those that are well to do and of the dominant culture can give easily to their kids without schools.
I also would not allow schools supported with public funds to select students. The only selection that can be justified is to balance in terms of demographics to more equally represent the community. Such balances do matter. It does matter that we are raised and schooled with those that represent the larger society. Schools of choice are great if the choice is the choice of the students and parents and not of the schools. One way charter schools often get around this is counseling students out with such phrases as, "Your child would/does not fit here". I would ask of anyone stating that, "Do you have a better school for my child than this one?" If they cannot honestly find a better fit for that child, one that all parties agree to, then they have no place making such statements.
I would give local schools and localities autonomy over what and how to teach. But they would have to publicly justify their decisions, allow for public input and make their results public. What kind of results would vary, but again, they need to justify why they think the results they have used demonstrate a well educated democratic citizen. There would need to some sort of democratic governance, but that can look different in different places.
These are the main things I see that are justifiable at the national or state level. Others you can think of? The second part of the question is what do I think good teaching and schooling look like, which I will explore in a future blog.
What I would change is the mandating of curriculum (so called Standards). The mandating of standards for education in a democracy can only be justified in the case of an overwhelming consensus on such standards. There's no evidence for such a consensus, and lots of evidence that there is considerable controversy over both what such a curriculum should look like and whether there should be one at all. While I have my own views on what I think all children should learn, I do not see it as my, or anyone else's place to impose those beliefs on others, much less an entire nation.
Along with that is we need to get rid of high stakes mandated standardized testing. Standardized tests have so many problems, not the least of which is that they impose a standardized curriculum. If a certain test is required, and there are high stakes for how one does on that test, then teachers must teach to it, and students must gear themselves to it as well. That means standardized curriculum. Standardized tests are also, by definition, culturally biased-they have to be normed, which means an automatic bias to the dominant group. That is just a fact of psychometrics. And, as the test makers have admitted, their reliability for individuals is not all that great, and yet they are used to judge individual students. I also do not accept their validity for much more than a test taking skills, school skills, and one's zip code.
What I do support is a strong public school system. One thing such a system needs is at the very least equalized funding, and really more funding is needed for those who live in poverty and have other strikes against them in life to at least equalize some of the built in advantages those that are well to do and of the dominant culture can give easily to their kids without schools.
I also would not allow schools supported with public funds to select students. The only selection that can be justified is to balance in terms of demographics to more equally represent the community. Such balances do matter. It does matter that we are raised and schooled with those that represent the larger society. Schools of choice are great if the choice is the choice of the students and parents and not of the schools. One way charter schools often get around this is counseling students out with such phrases as, "Your child would/does not fit here". I would ask of anyone stating that, "Do you have a better school for my child than this one?" If they cannot honestly find a better fit for that child, one that all parties agree to, then they have no place making such statements.
I would give local schools and localities autonomy over what and how to teach. But they would have to publicly justify their decisions, allow for public input and make their results public. What kind of results would vary, but again, they need to justify why they think the results they have used demonstrate a well educated democratic citizen. There would need to some sort of democratic governance, but that can look different in different places.
These are the main things I see that are justifiable at the national or state level. Others you can think of? The second part of the question is what do I think good teaching and schooling look like, which I will explore in a future blog.
Friday, January 24, 2014
Problem Solving Strategies in Mathematics
Learning how to solve problems in mathematics is knowing what to look for. Math problems often require established procedures and knowing what and when to apply them. To identify procedures, you have to be familiar with the problem situation and to be able to collect the appropriate information, identify a strategy or strategies to use the strategy appropriately. If you use the steps below you too can be a successful problem solver.
Problem solving requires practice! The more you practice, the better you get.
Practice, practice, practice!
1. Clues:
* Read the problem carefully.
* Underline clue words.
* Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
* What did you need to do?
* What facts are you given?
* What do you need to find out?
2. Game Plan:
* Define you game plan.
* Have you seen a problem like this before?
* Identify what you did.
* Define your strategies to solve this problem.
* Try out your strategies. Using formulas, simplifying, use sketches, guess and check, look for a pattern, etc.
* If your strategy doesn't work, it may lead you to an "aha" moment and to a strategy that does work ( often
the most powerful learning, is learning from our mistakes).
3. Solve:
* Use your strategies to solve the problem.
4. Reflect:
* This part is critical. Look over your solution.
* Does it seem probable?
* Did you answer the question?
* Are you sure? Prove it!
* Did you answer using the language in the question?
* Same units?
Clue words (vocabulary):
When deciding on methods or procedures to use to solve problems, the first thing you will need to do is look for clues which is one of the most important skills in solving problems is mathematics. If you begin to solve problems by looking for clue words, you will find that these "words" indicate an operation.
For Instance:
Clue Words for Addition
* sum
* total
* in all
* perimeter
Clue Words for Subtraction
* difference
* how much more
* exceed
Clue Words for Multiplication
* product
* total
* area
* times
Clue Words for Division
* share
* distribute
* quotient
* average
Although clue words vary a bit, you'll find that there will be consistency with them to guide you to the correct operation. This is the number one reason students have difficultly with problem solving and word problems they do not know the clue words i.e. vocabulary.
Also use your textbook, many texts have a list of problem solving strategies in the back of the book. They will state the strategy, when to use it, give an example and have practice problems.
Problem solving strategies that are helpful in solving word problems.
* Draw a diagram
* Try, check, revise
* Look for a pattern
* Make a table
* Solve a simpler problem ... often called sub-problems
* Use logical reasoning
* Work backward
Problem solving requires practice! The more you practice, the better you get.
Practice, practice, practice!
1. Clues:
* Read the problem carefully.
* Underline clue words.
* Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
* What did you need to do?
* What facts are you given?
* What do you need to find out?
2. Game Plan:
* Define you game plan.
* Have you seen a problem like this before?
* Identify what you did.
* Define your strategies to solve this problem.
* Try out your strategies. Using formulas, simplifying, use sketches, guess and check, look for a pattern, etc.
* If your strategy doesn't work, it may lead you to an "aha" moment and to a strategy that does work ( often
the most powerful learning, is learning from our mistakes).
3. Solve:
* Use your strategies to solve the problem.
4. Reflect:
* This part is critical. Look over your solution.
* Does it seem probable?
* Did you answer the question?
* Are you sure? Prove it!
* Did you answer using the language in the question?
* Same units?
Clue words (vocabulary):
When deciding on methods or procedures to use to solve problems, the first thing you will need to do is look for clues which is one of the most important skills in solving problems is mathematics. If you begin to solve problems by looking for clue words, you will find that these "words" indicate an operation.
For Instance:
Clue Words for Addition
* sum
* total
* in all
* perimeter
Clue Words for Subtraction
* difference
* how much more
* exceed
Clue Words for Multiplication
* product
* total
* area
* times
Clue Words for Division
* share
* distribute
* quotient
* average
Although clue words vary a bit, you'll find that there will be consistency with them to guide you to the correct operation. This is the number one reason students have difficultly with problem solving and word problems they do not know the clue words i.e. vocabulary.
Also use your textbook, many texts have a list of problem solving strategies in the back of the book. They will state the strategy, when to use it, give an example and have practice problems.
Problem solving strategies that are helpful in solving word problems.
* Draw a diagram
* Try, check, revise
* Look for a pattern
* Make a table
* Solve a simpler problem ... often called sub-problems
* Use logical reasoning
* Work backward
Friday, January 17, 2014
Poverty and Education
I read an article by Michael Petrilli of the Fordhanm Foundation in EdWeek. He claims that poverty is not the issue.
Pertrilli made these statements about children living in poverty.
*"Most were born to single mothers, and their fathers have been absent from the start, or by the time they turn two or three.
*Most of their mothers were teenagers or in their early 20s when they gave birth.
*Most of their mothers have very little education - a high school diploma or less, and thus few marketable skills.
*Many of their mothers suffer from mental illness or addiction or both;
If we give these families more money...will it erase the huge gaps...between these kids and their age-mates born into two-parent families? With highly-educated mothers and fathers? To believe so you'd have to put as much faith in cash transfers and social services as some reformers put in schools. You'd have to believe in miracles."
In response, I would say that tackling poverty and creating full employment and tackling society's inequalities would actually help solve these too. Fathers are absent because they cannot support their families. Young motherhood is often a symptom of hopelessness, as is drug addiction. Petrilli shows data that America's poverty is not really that much worse than other countries (though still worse even by his figures), so the problem cannot really be poverty (since he also accepts data purporting that they do better academically). What he leaves out is that even if it's true, those other countries do a better job of providing the supports for the poor that he derides as useless-housing, medical care, food, pre- and post-natal care- than the U.S. It may be those supports that keep fathers at home, create less single motherhood, and provide the supports needed for those who are single mothers.
While most critics of our current economic system and I think giving the poor more money and supports is a good idea, we do not see it as the solution either, but rather a band-aid. What is needed is a society that can provide meaningful employment for its citizens, that can provide decent housing, food, medical care, etc. It needs a society organized for a more equitable distribution of the resources.
A better education for the poor helps the individual student succeed, but it does not create more jobs nor reduce the overall rate of poverty nor solve the issues of inequality in a developed country such as ours. It does not change the number of winners and losers, though it just might even the odds a bit.
As John Dewey noted almost a century ago, a certain type of better education, i.e. one that helps students participate and understand democracy and develop certain habits of the mind, can be one of the aspects to creating a society, but alone it cannot do the job. And most of the reforms that Pertrilli supports- more testing and top-down "accountability" based on that testing - actually create a less, not more democratic culture in schools, especially schools for the poor.
Pertrilli made these statements about children living in poverty.
*"Most were born to single mothers, and their fathers have been absent from the start, or by the time they turn two or three.
*Most of their mothers were teenagers or in their early 20s when they gave birth.
*Most of their mothers have very little education - a high school diploma or less, and thus few marketable skills.
*Many of their mothers suffer from mental illness or addiction or both;
If we give these families more money...will it erase the huge gaps...between these kids and their age-mates born into two-parent families? With highly-educated mothers and fathers? To believe so you'd have to put as much faith in cash transfers and social services as some reformers put in schools. You'd have to believe in miracles."
In response, I would say that tackling poverty and creating full employment and tackling society's inequalities would actually help solve these too. Fathers are absent because they cannot support their families. Young motherhood is often a symptom of hopelessness, as is drug addiction. Petrilli shows data that America's poverty is not really that much worse than other countries (though still worse even by his figures), so the problem cannot really be poverty (since he also accepts data purporting that they do better academically). What he leaves out is that even if it's true, those other countries do a better job of providing the supports for the poor that he derides as useless-housing, medical care, food, pre- and post-natal care- than the U.S. It may be those supports that keep fathers at home, create less single motherhood, and provide the supports needed for those who are single mothers.
While most critics of our current economic system and I think giving the poor more money and supports is a good idea, we do not see it as the solution either, but rather a band-aid. What is needed is a society that can provide meaningful employment for its citizens, that can provide decent housing, food, medical care, etc. It needs a society organized for a more equitable distribution of the resources.
A better education for the poor helps the individual student succeed, but it does not create more jobs nor reduce the overall rate of poverty nor solve the issues of inequality in a developed country such as ours. It does not change the number of winners and losers, though it just might even the odds a bit.
As John Dewey noted almost a century ago, a certain type of better education, i.e. one that helps students participate and understand democracy and develop certain habits of the mind, can be one of the aspects to creating a society, but alone it cannot do the job. And most of the reforms that Pertrilli supports- more testing and top-down "accountability" based on that testing - actually create a less, not more democratic culture in schools, especially schools for the poor.
Friday, January 10, 2014
The 5 Steps to Setting SMART Goals
What are Smart Goals?
S.M.A.R.T. is an acronym for the 5 steps of specific, measurable, achievable, relevant, and time-based goals. It is a simple tool used by businesses to go beyond the realm of fuzzy goal-setting and into an actionable plan for results. I have adapted the idea to use in an educational setting and you will find a copy of the specific goal setting handout that I use with my students at the end of this article.
Specific: Great goals are well-defined and focused. I want to earn an A in history. That's fuzzy and a long term goal. You want to write a long term goal and short term goals. The short term goals are the steps that you are going to do the reach your long term goal. For instance, you would defined the long term goal as - I will earn an A in history. The short term goals are the steps which could include - I will reach my goal by studying for 10 minutes every night in addition to doing my regular history homework assignment. I will join a study group to study for exams. I will do all the extra credit assignments. I will write class notes and revise them after class to add more details. I will make flash cards and put them in my back pocket and review them while I wait for the school bus. I will talk to my teacher to find out what are the things he/she recommends to earn an A.
Measurable: A goal without a measurable outcome is like a sports competition without a scoreboard or score keeper. Your scores on assignments will let you know if your on track. And you can make yourself a checklist to keep in your daily planner to keep you focused.
Attainable: Far too often students get goals beyond reach. This can happen when you set too many goals and I recommend no more than 2-3 goals. Once you achieve one goal you can then focus on another one.
Relevant: This is something that each individual must identify for himself/herself. Knowing and learning take on importance only when we are convinced that it matters or makes a difference.
Time-Based: Goals just don't get done when there is no time frame tied to the goal setting process. I will achieve my goal by________________(date).
SMART GOAL SHEET TUTOR: LEARNER:
Today's Date: Target Date for Goal to be Achieved:
Start Date: Date Achieved:
GOAL:
Specific: What exactly will you (the learner) accomplish? Think narrow, not broad.
Measurable: How will you know when you reach this goal? What is the proof?
Attainable: Is achieving this goal realistic with effort and commitment? Have you got the resources to achieve this goal? If not, how will you get them?
Relevant: Why is this goal significant to your life?
Time: When will you achieve this goal? (Set flexible but specific target dates.)
I will achieve my goal by (date)
GOAL-SETTING
1. What do you (the learner) hope to accomplish as a result of accomplishing your goal?
2. Why is it important to you to accomplish this?
3. What are the first three steps you need to complete in order to achieve your goal?
4. Of these three, which is the most important to you and why?
5. What aspects of reading, writing, or math will you need to build or strengthen in order to meet
your goal?
6. What knowledge, skills and strategies do you already possess that will help you reach your goal?
7. List any concerns or potential obstacles you have that may stand in the way of achieving your
goal.
8. Create an action plan to work towards your answer to question number 4 or 5.
1st step by
2nd step by
3rd step by
4th step by
This goal is important because:
The benefits of achieving this goal will be:
Take Action:
Potential Obstacles Potential Solutions
Who are the people you will ask to help you?
Specific Action Steps: (Short term goals i.e. what steps need to be taken to achieve your goal?
1st step Deadline
2nd step Deadline
3rd step Deadline
4th step Deadline
It's important to periodically review your goals and make adjustments if necessary. If a specific task and/or activity isn't working develop a different one.
Goal setting is an essential tool for success. It is a life-long habit that you can use to both in school and out of it! Remember in the end to be SMART. Also, celebrate your success!
S.M.A.R.T. is an acronym for the 5 steps of specific, measurable, achievable, relevant, and time-based goals. It is a simple tool used by businesses to go beyond the realm of fuzzy goal-setting and into an actionable plan for results. I have adapted the idea to use in an educational setting and you will find a copy of the specific goal setting handout that I use with my students at the end of this article.
Specific: Great goals are well-defined and focused. I want to earn an A in history. That's fuzzy and a long term goal. You want to write a long term goal and short term goals. The short term goals are the steps that you are going to do the reach your long term goal. For instance, you would defined the long term goal as - I will earn an A in history. The short term goals are the steps which could include - I will reach my goal by studying for 10 minutes every night in addition to doing my regular history homework assignment. I will join a study group to study for exams. I will do all the extra credit assignments. I will write class notes and revise them after class to add more details. I will make flash cards and put them in my back pocket and review them while I wait for the school bus. I will talk to my teacher to find out what are the things he/she recommends to earn an A.
Measurable: A goal without a measurable outcome is like a sports competition without a scoreboard or score keeper. Your scores on assignments will let you know if your on track. And you can make yourself a checklist to keep in your daily planner to keep you focused.
Attainable: Far too often students get goals beyond reach. This can happen when you set too many goals and I recommend no more than 2-3 goals. Once you achieve one goal you can then focus on another one.
Relevant: This is something that each individual must identify for himself/herself. Knowing and learning take on importance only when we are convinced that it matters or makes a difference.
Time-Based: Goals just don't get done when there is no time frame tied to the goal setting process. I will achieve my goal by________________(date).
SMART GOAL SHEET TUTOR: LEARNER:
Today's Date: Target Date for Goal to be Achieved:
Start Date: Date Achieved:
GOAL:
Specific: What exactly will you (the learner) accomplish? Think narrow, not broad.
Measurable: How will you know when you reach this goal? What is the proof?
Attainable: Is achieving this goal realistic with effort and commitment? Have you got the resources to achieve this goal? If not, how will you get them?
Relevant: Why is this goal significant to your life?
Time: When will you achieve this goal? (Set flexible but specific target dates.)
I will achieve my goal by (date)
GOAL-SETTING
1. What do you (the learner) hope to accomplish as a result of accomplishing your goal?
2. Why is it important to you to accomplish this?
3. What are the first three steps you need to complete in order to achieve your goal?
4. Of these three, which is the most important to you and why?
5. What aspects of reading, writing, or math will you need to build or strengthen in order to meet
your goal?
6. What knowledge, skills and strategies do you already possess that will help you reach your goal?
7. List any concerns or potential obstacles you have that may stand in the way of achieving your
goal.
8. Create an action plan to work towards your answer to question number 4 or 5.
1st step by
2nd step by
3rd step by
4th step by
This goal is important because:
The benefits of achieving this goal will be:
Take Action:
Potential Obstacles Potential Solutions
Who are the people you will ask to help you?
Specific Action Steps: (Short term goals i.e. what steps need to be taken to achieve your goal?
1st step Deadline
2nd step Deadline
3rd step Deadline
4th step Deadline
It's important to periodically review your goals and make adjustments if necessary. If a specific task and/or activity isn't working develop a different one.
Goal setting is an essential tool for success. It is a life-long habit that you can use to both in school and out of it! Remember in the end to be SMART. Also, celebrate your success!
Friday, December 13, 2013
Finals - Don't Panic - Follow These Tips
Tips for how to study for finals.
6. Adopt efficiency measures. The single most important thing you can do if you have more finals than any human can manage is to work efficiently. First thing, don't waste your time on things that do not really advance your preparation for the test: things like copying over your notes, doing all the reading again. Much better is to do targeted activities that get you ready for the actual problems that will appear on the final: things like writing out study questions with problem-solution guides, doing extra problems from the book, website, or handout, or marking up your notes for issues that will likely come up on the test, and many students like making flash cards, color coded mind maps, etc. Many teachers have review sessions before or after school. This is the single most efficient strategy, since teachers or TA's go over problems very similar to those the will appear on the final, in the best case, drop hints about questions that will actually appear on the exam.
7 .Set a study schedule. You won't have to decide each time when - and whether - you're gonna study if you've calendared your study schedule before exam week. And, if you set the times - and mean them - you will overcome the single biggest impediment to preparing for finals: PROCRASTINATION!
8. Avoid "interleaving". Many students divide their study sessions into parts for each subject: 30 minutes for science, 40 minutes for math, 60 minutes for English, and so on. But you'll study better - and retain the material better - if you devote the entire study session to one subject. That's because you will get less confused, and you'll build up steam, if you're working in one thing. Also (in the best case), you won't feel compelled to take a break after each subject, which will also save you time. A good rule of thumb. 45 minutes of uninterrupted study time = 1 break. 1 break = 10 minutes.
9. Turn off the media. "Nuff said.
10. Tell 'em to "cut you a break". Many students will have a much easier time studying for finals if they jettison a few commitments. If you work, tell your boss you absolutely, positively, 100 percent have to work fewer hours the week before exams and during exam week itself. Tell your parents and/or kids that you're not going to be at their beck and call during this high-pressure fortnight. And as for your church or synagogue, your sports, or clubs - well, you know what I'm going to say.
11. If you learn better working in a group, then by all means do so. Be sure to carefully choose who you are going to work with as time is a commodity not to be wasted.
If you follow these tips you will lessen your stress and of course do well on your exams.
Best of luck with your finals, and have a happy 2014!
1. Develop good study habits. For example, I have my students make flash cards, mind maps, and study their class notes, etc. four days a week for 10 minutes. This saves time in the long run because if you are studying regularly you are transferring the concepts into long term memory and when you go to study for the final you will find that you already know the material.
2. I make finals for my students. Then I teach them how to do this. I use their textbooks, class notes, previously taken tests, and often the textbooks have websites with practice test. However, I think that teaching students how to write test questions and having them make problem solution guides is a better way to help students learn the concepts. Join a study group and suggest this method and you will be surprised at how affect it is. When I was a classroom teacher, I had my students work in groups to create test questions and problem solution guides. This method was so successful that I often didn't give them an actual test because they had learned the material. The students always told me that they learned more this way. Learning how to write a test question is a life long learning tool that I found my students using all the time, it became a habit. Another benefit in learning how to write test questions with multiple choice answers is that it teaches students how tests are structured and they become better test takers in general.
3. Unbeknownst to some students, many schools have a procedure for dealing with an overload of finals on the same day. If you have, say 3 finals on the same day, the school will arrange for one of the teachers to move her/his final to a different day. Find out if your school has this policy.
4. Most students begin studying for final the week before. But if you have lots of finals, you'll do better to start studying for some of them a few weeks before or better yet, if you study regularly like I suggested in #1 for all subjects the extra time will give you plenty of time to go over the material that may be more challenging. If you need to do extra reading or get a term paper done earlier this will relieve any stress. But the extra time for preparation - and the sense that you have plenty of time for all your finals - will make the added planning and effort worthwhile.
5. A major mistake - that you should avoid - is planning to spend equal time studying for each of your finals. It is better to apportion your study time unequally to your different finals. Things to ask yourself: Is this a class I'm acing already, or that is in real grade trouble? Am I pretty much guaranteed a certain grade in this class, or is the grade in the balance? What percentage of the course grade does the final count, anyway?
3. Unbeknownst to some students, many schools have a procedure for dealing with an overload of finals on the same day. If you have, say 3 finals on the same day, the school will arrange for one of the teachers to move her/his final to a different day. Find out if your school has this policy.
4. Most students begin studying for final the week before. But if you have lots of finals, you'll do better to start studying for some of them a few weeks before or better yet, if you study regularly like I suggested in #1 for all subjects the extra time will give you plenty of time to go over the material that may be more challenging. If you need to do extra reading or get a term paper done earlier this will relieve any stress. But the extra time for preparation - and the sense that you have plenty of time for all your finals - will make the added planning and effort worthwhile.
5. A major mistake - that you should avoid - is planning to spend equal time studying for each of your finals. It is better to apportion your study time unequally to your different finals. Things to ask yourself: Is this a class I'm acing already, or that is in real grade trouble? Am I pretty much guaranteed a certain grade in this class, or is the grade in the balance? What percentage of the course grade does the final count, anyway?
6. Adopt efficiency measures. The single most important thing you can do if you have more finals than any human can manage is to work efficiently. First thing, don't waste your time on things that do not really advance your preparation for the test: things like copying over your notes, doing all the reading again. Much better is to do targeted activities that get you ready for the actual problems that will appear on the final: things like writing out study questions with problem-solution guides, doing extra problems from the book, website, or handout, or marking up your notes for issues that will likely come up on the test, and many students like making flash cards, color coded mind maps, etc. Many teachers have review sessions before or after school. This is the single most efficient strategy, since teachers or TA's go over problems very similar to those the will appear on the final, in the best case, drop hints about questions that will actually appear on the exam.
7 .Set a study schedule. You won't have to decide each time when - and whether - you're gonna study if you've calendared your study schedule before exam week. And, if you set the times - and mean them - you will overcome the single biggest impediment to preparing for finals: PROCRASTINATION!
8. Avoid "interleaving". Many students divide their study sessions into parts for each subject: 30 minutes for science, 40 minutes for math, 60 minutes for English, and so on. But you'll study better - and retain the material better - if you devote the entire study session to one subject. That's because you will get less confused, and you'll build up steam, if you're working in one thing. Also (in the best case), you won't feel compelled to take a break after each subject, which will also save you time. A good rule of thumb. 45 minutes of uninterrupted study time = 1 break. 1 break = 10 minutes.
9. Turn off the media. "Nuff said.
10. Tell 'em to "cut you a break". Many students will have a much easier time studying for finals if they jettison a few commitments. If you work, tell your boss you absolutely, positively, 100 percent have to work fewer hours the week before exams and during exam week itself. Tell your parents and/or kids that you're not going to be at their beck and call during this high-pressure fortnight. And as for your church or synagogue, your sports, or clubs - well, you know what I'm going to say.
11. If you learn better working in a group, then by all means do so. Be sure to carefully choose who you are going to work with as time is a commodity not to be wasted.
If you follow these tips you will lessen your stress and of course do well on your exams.
Best of luck with your finals, and have a happy 2014!
Friday, November 22, 2013
Math Anxiety . . . What it is~Where it comes from~How to overcome it!
I have a student that knows the math content being presented in class but always hesitates when he is solving problems and lacks self-confidence. It made me think about what is math anxiety, what causes it, and most importantly how to overcome it.
What is Math Anxiety?
Math anxiety or fear if math is actually quite common. Math anxiety is similar to stagefright. Why does someone suffer from stagefright? Fear of something going wrong in front of a crowd? Fear of forgetting the lines? Fear of going completely blank? Fear of being judged poorly? Math anxiety conjures fear of some type. The fear that one won't be able to do the math or the fear that it's too hard or the fear of failure which often stems from having a lack of confidence. For the most part, math anxiety is the fear about doing the math right, our minds draw a blank and we think we'll fail and of course the more frustrated and anxious our minds become, the greater the chance for drawing blanks. Added pressure of having time limits on math tests and exams also cause the levels of anxiety to grow for many students.
Where Does Math Anxiety Come From?
Usually math anxiety stems from unpleasant experiences in mathematics. Typically math phobics have had math presented in such a fashion that it led to limited understanding, Unfortunately, math anxiety is often due to poor teaching and poor experiences in math which typically leads to math anxiety. Many of the students I've encountered with math anxiety have demonstrated an over reliance on procedures in math as opposed to actually understanding the math concepts. When one tries to memorize procedures, rules, and routines without much understanding, the math is quickly forgotten and panic soon sets in. Think about your experiences with one concept - the division of fractions. You probably learned about reciprocals and inverse. In other words, "It's not yours to reason why, just invert and multiply". Well, you memorized the rule and it works. Why does it work? Do you really understand why it works? Did anyone ever use pizza or math manipulatives to show you why it works. Did anyone ever make the connection to the commutative or distributive laws? Or did they relate the algorithm to whole numbers? It not, you simply memorized the procedures and that was that. Think of math as memorizing all the procedures - what if you forget a few?
Therefore, with this type of strategy, a good memory will help, but, what if you don't have a good memory? Understanding the math is critical. Once students realize they can do the math, the whole notion of math anxiety can be overcome. Teachers and parents have an important role to ensure students understand the math being presented to them.
Myths and Misconceptions - None of the following are true!
You're born with a math gene, either you get it or you don't.
Math is for males, females never get math!
If the logical side of your brain isn't your strengtht, you will never do well in math.
Math is a cultural thing, my culture never got it!
It's hopeless, and much too hard for average people.
There's only one right way to do math.
Overcoming Math Anxiety
1. A positive attitude will help, positive attitudes come with quality teaching for understanding which often isn't the case with many traditional approaches to teaching mathematics.
2. Ask questions, be determined to "understand the math". Don't settle for anything less during instruction. Ask for clear illustrations and for demonstrations or simulations.
3. Practice regularly, especially when you are having difficultly.
4. When total understanding escapes you, hire a tutor or work with peers that understand the math. You can do the math, sometimes it just takes a different approach for you to understand some of the concepts.
5. Don't just read over your notes - do the math. Practice the math and make sure you can honestly state that you understand what you are doing.
6. Be persistent and don't over emphasize the fact that we all make mistakes. Remember, some of the most powerful learning stems from making a mistake.
Find out more about the myths of doing math and you too will overcome math anxiety. And, if you think making mistakes it a bad thing, look again. Sometimes the most powerful learning stems from making mistakes!
What is Math Anxiety?
Math anxiety or fear if math is actually quite common. Math anxiety is similar to stagefright. Why does someone suffer from stagefright? Fear of something going wrong in front of a crowd? Fear of forgetting the lines? Fear of going completely blank? Fear of being judged poorly? Math anxiety conjures fear of some type. The fear that one won't be able to do the math or the fear that it's too hard or the fear of failure which often stems from having a lack of confidence. For the most part, math anxiety is the fear about doing the math right, our minds draw a blank and we think we'll fail and of course the more frustrated and anxious our minds become, the greater the chance for drawing blanks. Added pressure of having time limits on math tests and exams also cause the levels of anxiety to grow for many students.
Where Does Math Anxiety Come From?
Usually math anxiety stems from unpleasant experiences in mathematics. Typically math phobics have had math presented in such a fashion that it led to limited understanding, Unfortunately, math anxiety is often due to poor teaching and poor experiences in math which typically leads to math anxiety. Many of the students I've encountered with math anxiety have demonstrated an over reliance on procedures in math as opposed to actually understanding the math concepts. When one tries to memorize procedures, rules, and routines without much understanding, the math is quickly forgotten and panic soon sets in. Think about your experiences with one concept - the division of fractions. You probably learned about reciprocals and inverse. In other words, "It's not yours to reason why, just invert and multiply". Well, you memorized the rule and it works. Why does it work? Do you really understand why it works? Did anyone ever use pizza or math manipulatives to show you why it works. Did anyone ever make the connection to the commutative or distributive laws? Or did they relate the algorithm to whole numbers? It not, you simply memorized the procedures and that was that. Think of math as memorizing all the procedures - what if you forget a few?
Therefore, with this type of strategy, a good memory will help, but, what if you don't have a good memory? Understanding the math is critical. Once students realize they can do the math, the whole notion of math anxiety can be overcome. Teachers and parents have an important role to ensure students understand the math being presented to them.
Myths and Misconceptions - None of the following are true!
You're born with a math gene, either you get it or you don't.
Math is for males, females never get math!
If the logical side of your brain isn't your strengtht, you will never do well in math.
Math is a cultural thing, my culture never got it!
It's hopeless, and much too hard for average people.
There's only one right way to do math.
Overcoming Math Anxiety
1. A positive attitude will help, positive attitudes come with quality teaching for understanding which often isn't the case with many traditional approaches to teaching mathematics.
2. Ask questions, be determined to "understand the math". Don't settle for anything less during instruction. Ask for clear illustrations and for demonstrations or simulations.
3. Practice regularly, especially when you are having difficultly.
4. When total understanding escapes you, hire a tutor or work with peers that understand the math. You can do the math, sometimes it just takes a different approach for you to understand some of the concepts.
5. Don't just read over your notes - do the math. Practice the math and make sure you can honestly state that you understand what you are doing.
6. Be persistent and don't over emphasize the fact that we all make mistakes. Remember, some of the most powerful learning stems from making a mistake.
Find out more about the myths of doing math and you too will overcome math anxiety. And, if you think making mistakes it a bad thing, look again. Sometimes the most powerful learning stems from making mistakes!
Sunday, November 17, 2013
What is Wrong With Charter Schools?
There are two local school districts considering charter schools and there have been discussions about instituting a voucher system. Recently a local newspaper published a column written by one founders of one of the proposed charters and a letter written to the editor by a parent. Both articles are riddled with misinformation.
There are many innovative public schools all around the country. I personally have had the good fortune to have taught in such schools and have worked with many progressive educators. As nice as independent schools are, and I have visited many, they cannot afford to serve the poor to more than a token extent, and so are therefore, elitist. And I do not agree that you should be free to educate students however you want. I believe in public responsibility, and how you educate children matters to society as a whole not just to you or the child. That's where I align myself with thinkers like John Dewey; there is a balance in a democratic society between the freedom of the individual and responsibility to society. Where to draw the line is complex, but it needs to exists. Drawing that line is part of the democratic process.
The rhetoric behind vouchers is that if everyone had vouchers parents could select the best school for their child instead of being forced to go to "government schools".
Where does such logic fall apart? There are two main logistical reasons it is really a false promise. One is economic and the other is the question of who gets to choose.
The private schools that the elite send their children to cost tens of thousands of dollars a year to attend. I looked up a few private schools and tuition ranged from $20,000 to well over $30,000, more than many private colleges. And the actual amount they spend per pupil is well over the tuition since they raise lots of extra money from alumni. They also tend to pay their non-unionized teachers significantly less than public schools.
Since at best the voucher proposals I have seen only pay a small fraction of that, these vouchers will leave the recipients with few real choices without putting out a lot more money. I do not think the public is going to go for vouchers of $20,000+ and have never even heard such figures discussed. It they did, the public education budgets would soar. And those already in private schools would and should claim they should get the subsidies too. What it would do in effect, at the rates being proposed, is subsidize the middle class and the rich to abandon public schools and send their children of private schools, and while leaving such choices out of reach financially for the poor.
The other issue is who chooses. Most private schools have selective admission, and limited space. Since unlike public schools they get to choose their students, even if the voucher fully paid for them (which of course it will not), they would still most likely cream the easiest students to teach, leaving the more difficult to teach children to the public schools.
These two factors in combination would end up subsidizing private schools and the middle and upper class families at the expense of public schools and the poor that are left in them. This would further segregate our schooling system into the haves and the have-nots.
Since I have never heard voucher proponents either suggest that vouchers should be at the levels necessary to have them cover the full cost of most private schools, nor to force private schools to take those children, I find their arguments disingenuous.
Charter schools, in theory at least, get around both of the above limitations. There is no tuition; schools receive the same funding as other public schools, and (at least in California) schools cannot select the students. (In reality, though, they often find ways of using other means to "encourage" and "discourage" certain types of students) So, is this not a solution?
Why I still do not favor even this is that it fundamentally changes the purpose of public schools. Traditionally we have considered the education of the next generation to be a concern of society as a whole. In fact, virtually every society has considered this to be true throughout history. For this reason, locally elected school boards have governed our public schools.
Charter schools and voucher systems make schooling a private consumer choice. In the charter and voucher systems consumers choose among the choices offered them, but have no guaranteed right to have a say about the schooling other than making that choice. Those who do not have children in school have no say at all. Private schools are run privately, and do not have to answer to the public. Charter schools usually have to answer for test scores and financial responsibility, but even there it is to the state and not in any direct way to the local public. While charter schools have governing boards, they select their own members of those boards. This gives control of the content of schooling to those who run the schools, often for-profit concerns, but even if not, private concerns of some sort. While our government is not perfect, should I really trust those who have private agendas and do not have to answer to the public to decide the how and what of our next generation's schooling? Public school boards are elected, and have open meetings: private schools do not have to. Even if the charters do have open meetings, they are often run by national organizations and so are inaccessible and would probably just say, "Don't send your child here if you don't like our agenda".
Charters and vouchers are about redefining the public as consumers rather than citizens, which is part of a larger corporate agenda to destroy public institutions and limit the power of the public.
For the above (and other) reasons, I see truly public schools as the only answer for those committed to a democratic society.
Read between the lines the implication that anything government does must be poor quality. Yet since parents in the suburbs and rich areas are perfectly happy with their public schools, why is it only the public schools that poor kids go to that seem to be failing? "Government" schools for the rich and middle class are fine it seems-as long as they do not have to share them with the poor.
There are many innovative public schools all around the country. I personally have had the good fortune to have taught in such schools and have worked with many progressive educators. As nice as independent schools are, and I have visited many, they cannot afford to serve the poor to more than a token extent, and so are therefore, elitist. And I do not agree that you should be free to educate students however you want. I believe in public responsibility, and how you educate children matters to society as a whole not just to you or the child. That's where I align myself with thinkers like John Dewey; there is a balance in a democratic society between the freedom of the individual and responsibility to society. Where to draw the line is complex, but it needs to exists. Drawing that line is part of the democratic process.
The rhetoric behind vouchers is that if everyone had vouchers parents could select the best school for their child instead of being forced to go to "government schools".
Where does such logic fall apart? There are two main logistical reasons it is really a false promise. One is economic and the other is the question of who gets to choose.
The private schools that the elite send their children to cost tens of thousands of dollars a year to attend. I looked up a few private schools and tuition ranged from $20,000 to well over $30,000, more than many private colleges. And the actual amount they spend per pupil is well over the tuition since they raise lots of extra money from alumni. They also tend to pay their non-unionized teachers significantly less than public schools.
Since at best the voucher proposals I have seen only pay a small fraction of that, these vouchers will leave the recipients with few real choices without putting out a lot more money. I do not think the public is going to go for vouchers of $20,000+ and have never even heard such figures discussed. It they did, the public education budgets would soar. And those already in private schools would and should claim they should get the subsidies too. What it would do in effect, at the rates being proposed, is subsidize the middle class and the rich to abandon public schools and send their children of private schools, and while leaving such choices out of reach financially for the poor.
The other issue is who chooses. Most private schools have selective admission, and limited space. Since unlike public schools they get to choose their students, even if the voucher fully paid for them (which of course it will not), they would still most likely cream the easiest students to teach, leaving the more difficult to teach children to the public schools.
These two factors in combination would end up subsidizing private schools and the middle and upper class families at the expense of public schools and the poor that are left in them. This would further segregate our schooling system into the haves and the have-nots.
Since I have never heard voucher proponents either suggest that vouchers should be at the levels necessary to have them cover the full cost of most private schools, nor to force private schools to take those children, I find their arguments disingenuous.
Charter schools, in theory at least, get around both of the above limitations. There is no tuition; schools receive the same funding as other public schools, and (at least in California) schools cannot select the students. (In reality, though, they often find ways of using other means to "encourage" and "discourage" certain types of students) So, is this not a solution?
Why I still do not favor even this is that it fundamentally changes the purpose of public schools. Traditionally we have considered the education of the next generation to be a concern of society as a whole. In fact, virtually every society has considered this to be true throughout history. For this reason, locally elected school boards have governed our public schools.
Charter schools and voucher systems make schooling a private consumer choice. In the charter and voucher systems consumers choose among the choices offered them, but have no guaranteed right to have a say about the schooling other than making that choice. Those who do not have children in school have no say at all. Private schools are run privately, and do not have to answer to the public. Charter schools usually have to answer for test scores and financial responsibility, but even there it is to the state and not in any direct way to the local public. While charter schools have governing boards, they select their own members of those boards. This gives control of the content of schooling to those who run the schools, often for-profit concerns, but even if not, private concerns of some sort. While our government is not perfect, should I really trust those who have private agendas and do not have to answer to the public to decide the how and what of our next generation's schooling? Public school boards are elected, and have open meetings: private schools do not have to. Even if the charters do have open meetings, they are often run by national organizations and so are inaccessible and would probably just say, "Don't send your child here if you don't like our agenda".
Charters and vouchers are about redefining the public as consumers rather than citizens, which is part of a larger corporate agenda to destroy public institutions and limit the power of the public.
For the above (and other) reasons, I see truly public schools as the only answer for those committed to a democratic society.
Read between the lines the implication that anything government does must be poor quality. Yet since parents in the suburbs and rich areas are perfectly happy with their public schools, why is it only the public schools that poor kids go to that seem to be failing? "Government" schools for the rich and middle class are fine it seems-as long as they do not have to share them with the poor.
Friday, November 8, 2013
When Will I Ever Use This Stuff?!
When will I ever use this stuff?!
I have been in education for forty years and the statement I hear over and over again with regards to math is something I'm sure you have heard too. It I've heard it once, I've heard it thousands of times: "When will I ever use this stuff".
All too often, students who make this statement are referring to the actual concept they are learning; whether it be Pythagorean's Theorem, long division, multiplication of polynomials, properties of polygons, the Power Rule, or what have you, their comment is usually based on the specific math topic. I related what they are learning to "real- life" examples, and or course, I tell them they are also actually applying and deepening many life long skills that will benefit them for the rest of their lives. Skills that include but are not limited to: analyzing, making connections, problem solving, looking for patterns, proving, thinking, understanding and persistence. Math is an opportunity gateway, it opens doors and without it, it often closes doors. However, if in fact math isn't for you and you have a goal or career that doesn't require university math, here's some of the everyday math that you'll need, hence this article is for you.
Everyday Math
First of all, before I generate this list of what I believe to be helpful math for everyone to know for day to day living, it's only my opinion and may differ from the opinions of others.
Percent
Percent is a concept that is used regularly. What is the percent of deductions of your gross pay? This helps you calculate your net pay or potential pay. Sales are often based on percent, what is 20, 30, or 40 percent of a number? Percent is used in loans, investment and mortgages. You need to understand enough about percent to use a calculator correctly. Percent is used to calculate simple and compound interest. Percents are used in services to calculate sales tax and tips. You should be able to use mental math for some percent computations and the calculator for others.
Four Operations
The four operations refers to adding, subtracting, dividing, and multiplying and are sometimes referred to as arithmetic. I think this concept is self explanatory. We use the four operations for mental math in grocery stores, bill payment, recipes, etc. You should know the basic multiplication facts and you should know when and how to add, subtract, divide and multiply fluently mentally and with a calculator.
Measurement
Understanding the various units of measure that we are exposed to each day is vital to making decisions based on this information. When you go into the carpet store to consider a purchase and the store clerk tells you the carpet is 4.50 per square yard, you need to have an understanding of what your room measurements of 12 feet by 16 feet means in terms of the unit of measure, square yards. Think in terms of following a recipe. If you do not understand the various units of measure for dry goods such as flour, then you can make a mess out of baking. Measurement recognition and understanding is a daily occurrence. Even if you need an online converter or calculator for conversions, a basic understanding of measurement is helpful.
Estimation
Estimation is a basic skill we use so much in our daily lives that we never think about it. Estimation is not a guess; it is a calculation based upon specific information and often referred to as an "educated guess".You estimate what time you have to get up in the morning to do all the tasks needed before you head off to school or work. You estimate how long it will take you to your homework. I'm sure you can think of countless examples.
Charts, Graphs and Data
Visual representation of information is commonplace in modern living. Graphs and charts are used to reduce the amount of textual explanation that many comparisons require. With the advent of the internet, it's imperative that we have the ability to look at a graph and see the weight of the data points individually while having an idea as to the trend the data exhibits. Basic to extremely complex information can be portrayed using charts such as scatter plots in terms we understand. It's helpful to be able to interpret pie charts, and line bar graphs.
Problem Solving
Problem solving is a daily skill. Being able to use the basic math mentioned here and apply it to problem solving situations is key. In other words, knowing what math to use to solve basic problems. Examples of this are in doubling a recipe, halving a recipe, calculating how much tile is needed id a room of various sizes, balancing check books, calculating time lapses and distances for trips along with various money situations/financial literacy.
It can be difficult to determine the daily math one needs in everyday life and much depends on ones responsibilities in life, however, having a grasp on the above certainly helps. And, taking steps to improve your math skills is always a great idea. Knowing math helps us understand the world and empowers our ideas.
I have been in education for forty years and the statement I hear over and over again with regards to math is something I'm sure you have heard too. It I've heard it once, I've heard it thousands of times: "When will I ever use this stuff".
All too often, students who make this statement are referring to the actual concept they are learning; whether it be Pythagorean's Theorem, long division, multiplication of polynomials, properties of polygons, the Power Rule, or what have you, their comment is usually based on the specific math topic. I related what they are learning to "real- life" examples, and or course, I tell them they are also actually applying and deepening many life long skills that will benefit them for the rest of their lives. Skills that include but are not limited to: analyzing, making connections, problem solving, looking for patterns, proving, thinking, understanding and persistence. Math is an opportunity gateway, it opens doors and without it, it often closes doors. However, if in fact math isn't for you and you have a goal or career that doesn't require university math, here's some of the everyday math that you'll need, hence this article is for you.
Everyday Math
First of all, before I generate this list of what I believe to be helpful math for everyone to know for day to day living, it's only my opinion and may differ from the opinions of others.
Percent
Percent is a concept that is used regularly. What is the percent of deductions of your gross pay? This helps you calculate your net pay or potential pay. Sales are often based on percent, what is 20, 30, or 40 percent of a number? Percent is used in loans, investment and mortgages. You need to understand enough about percent to use a calculator correctly. Percent is used to calculate simple and compound interest. Percents are used in services to calculate sales tax and tips. You should be able to use mental math for some percent computations and the calculator for others.
Four Operations
The four operations refers to adding, subtracting, dividing, and multiplying and are sometimes referred to as arithmetic. I think this concept is self explanatory. We use the four operations for mental math in grocery stores, bill payment, recipes, etc. You should know the basic multiplication facts and you should know when and how to add, subtract, divide and multiply fluently mentally and with a calculator.
Measurement
Understanding the various units of measure that we are exposed to each day is vital to making decisions based on this information. When you go into the carpet store to consider a purchase and the store clerk tells you the carpet is 4.50 per square yard, you need to have an understanding of what your room measurements of 12 feet by 16 feet means in terms of the unit of measure, square yards. Think in terms of following a recipe. If you do not understand the various units of measure for dry goods such as flour, then you can make a mess out of baking. Measurement recognition and understanding is a daily occurrence. Even if you need an online converter or calculator for conversions, a basic understanding of measurement is helpful.
Estimation
Estimation is a basic skill we use so much in our daily lives that we never think about it. Estimation is not a guess; it is a calculation based upon specific information and often referred to as an "educated guess".You estimate what time you have to get up in the morning to do all the tasks needed before you head off to school or work. You estimate how long it will take you to your homework. I'm sure you can think of countless examples.
Charts, Graphs and Data
Visual representation of information is commonplace in modern living. Graphs and charts are used to reduce the amount of textual explanation that many comparisons require. With the advent of the internet, it's imperative that we have the ability to look at a graph and see the weight of the data points individually while having an idea as to the trend the data exhibits. Basic to extremely complex information can be portrayed using charts such as scatter plots in terms we understand. It's helpful to be able to interpret pie charts, and line bar graphs.
Problem Solving
Problem solving is a daily skill. Being able to use the basic math mentioned here and apply it to problem solving situations is key. In other words, knowing what math to use to solve basic problems. Examples of this are in doubling a recipe, halving a recipe, calculating how much tile is needed id a room of various sizes, balancing check books, calculating time lapses and distances for trips along with various money situations/financial literacy.
It can be difficult to determine the daily math one needs in everyday life and much depends on ones responsibilities in life, however, having a grasp on the above certainly helps. And, taking steps to improve your math skills is always a great idea. Knowing math helps us understand the world and empowers our ideas.
Friday, November 1, 2013
Online Resources: There are a number of websites that provide help with mathematics
This week I am sharing some links to excellent websites that provide help with math.
Online Resources:
* http://kahnacademy.org - this site contains hundreds of topic specific videos and example problems.
* http://www.purplemath.com
* http://math.com
* http://mathforum.org/dr/math
* http://nlvm.usu.edu/en/nav/vlibrary.html - National Library of Virtual Manipulatives
Online Resources:
* http://kahnacademy.org - this site contains hundreds of topic specific videos and example problems.
* http://www.purplemath.com
* http://math.com
* http://mathforum.org/dr/math
* http://nlvm.usu.edu/en/nav/vlibrary.html - National Library of Virtual Manipulatives
Friday, October 18, 2013
The Importance Of Relationships
I communicate regularly with my students teachers, and I know my middle school and high school students much better than their teachers do. And the more I think about education and learning, the more I see relationships as the key to what really matters. If I think about all the movies I have seen about "great teaching" both fictional and those "based on a true story", while the actual teaching going on in them varies enormously, what they all have in common is a teacher that builds caring strong relationships with their pupils, from "To Sir With Love", "Up The Down Staircase" of the 60s, to more recent movies such as "Mr. Holland's Opus" and "Dangerous Minds." But of course that portrayal could just be the license of the writers and directors.
But I would say I have found the same in my experience as a teacher and now a tutor. I worked with teachers with many different pedagogical approaches. If you have read my previous columns, you will see it's clear I have strong beliefs about which are more effective. However, the most consistent thing that I noticed of teachers that appeared to me as more effective was that those teachers all had strong relationships with their students. The students knew their teacher expected them to learn, and was there to help them succeed in doing so.
It was really much for this reason that I decided to move to elementary school after teaching middle and high school for 17 years. It is really difficult to build those relationships when every hour you have a new group of students. I often asked other teachers to keep an eye an a specific student in the hopes that one of us could connect with them. And I consequently worried that there where students that had no one to advocate for them and that someone would slip through the cracks. With elementary school kids I had the same ones all day long. It is also a reason I have never liked "regrouping" with other teachers - I never saw the trade off as worth the loss in knowing my students fully.
One anecdote. At one place I taught, we were using the Reading Recovery program for our struggling first and second grade readers. Reading Recovery is a strongly researched based program giving intensive support to the lowest readers in the first and second grades, based on some of the best research of learning to read, with a strong research record of its own, and all the practitioners of it have to be credentialed teachers who have gone through an intensive training in the model. One year I taught third grade and my struggling readers did not qualify. So instead we used instruction assistants, who had a rudimentary training in more traditional phonics approaches to work with them. I would argue that third graders who are still struggling with reading are probably more difficult candidates, as they have a longer history of failure to overcome.
Yet, in decidedly non-random and small sample that this consisted of, my instructional assistant succeeded with every one she worked with. The same cannot be said of the Reading Recovery program that had about a two-thirds success rate with our students. I attribute it to the strong relationship she built with each of them-letting them know that she believed they each would and could learn to read.
This, maybe, is what worries me most about many of the past educational reforms. They make those relationships more difficult. Scripted curriculum, larger classes and school consolidation, use of technology for instruction, and worst of all, the tactics of fear-trying to scare teachers and students into doing a better job. Each if these, in a different way, makes it slightly more difficult for teachers and students to develop strong relationships.
I will be following the implementation of the Common Core Standards as they are designed to foster more teacher and student engagement and allow teachers the opportunity to develop their own units of study that incorporate the required standards.
I have been offered a job to teach an all on-line teacher education course. I haven't made a decision yet, but I am curious to know to what degree this mode allows for and interferes with such relationships.
If you or any one you know teaches on-line, or for that matter, if you have taken on-line classes, I would be interested in hearing about your experience. What kinds of relationships does on-line learning foster?
Debra
But I would say I have found the same in my experience as a teacher and now a tutor. I worked with teachers with many different pedagogical approaches. If you have read my previous columns, you will see it's clear I have strong beliefs about which are more effective. However, the most consistent thing that I noticed of teachers that appeared to me as more effective was that those teachers all had strong relationships with their students. The students knew their teacher expected them to learn, and was there to help them succeed in doing so.
It was really much for this reason that I decided to move to elementary school after teaching middle and high school for 17 years. It is really difficult to build those relationships when every hour you have a new group of students. I often asked other teachers to keep an eye an a specific student in the hopes that one of us could connect with them. And I consequently worried that there where students that had no one to advocate for them and that someone would slip through the cracks. With elementary school kids I had the same ones all day long. It is also a reason I have never liked "regrouping" with other teachers - I never saw the trade off as worth the loss in knowing my students fully.
One anecdote. At one place I taught, we were using the Reading Recovery program for our struggling first and second grade readers. Reading Recovery is a strongly researched based program giving intensive support to the lowest readers in the first and second grades, based on some of the best research of learning to read, with a strong research record of its own, and all the practitioners of it have to be credentialed teachers who have gone through an intensive training in the model. One year I taught third grade and my struggling readers did not qualify. So instead we used instruction assistants, who had a rudimentary training in more traditional phonics approaches to work with them. I would argue that third graders who are still struggling with reading are probably more difficult candidates, as they have a longer history of failure to overcome.
Yet, in decidedly non-random and small sample that this consisted of, my instructional assistant succeeded with every one she worked with. The same cannot be said of the Reading Recovery program that had about a two-thirds success rate with our students. I attribute it to the strong relationship she built with each of them-letting them know that she believed they each would and could learn to read.
This, maybe, is what worries me most about many of the past educational reforms. They make those relationships more difficult. Scripted curriculum, larger classes and school consolidation, use of technology for instruction, and worst of all, the tactics of fear-trying to scare teachers and students into doing a better job. Each if these, in a different way, makes it slightly more difficult for teachers and students to develop strong relationships.
I will be following the implementation of the Common Core Standards as they are designed to foster more teacher and student engagement and allow teachers the opportunity to develop their own units of study that incorporate the required standards.
I have been offered a job to teach an all on-line teacher education course. I haven't made a decision yet, but I am curious to know to what degree this mode allows for and interferes with such relationships.
If you or any one you know teaches on-line, or for that matter, if you have taken on-line classes, I would be interested in hearing about your experience. What kinds of relationships does on-line learning foster?
Debra
Tuesday, October 8, 2013
Improving Math Skills by Improving Your Note Taking
When studying for math, we often use exercises, worksheets and sample problems to work through in order to prepare of an upcoming test, exam, or review. However, as in most other subjects, note taking and journaling is also very effective and very important to help with the understanding of specific math concepts. Whether you dictate your notes and have them available for audio, or write your notes to review them visually, the strategies and tips here will help you prepare for math quizzes and tests. Effective notes will help you to remember important concepts taught in class and they will guide you through various math problems.
Taking Notes
I prefer to use the two column approach in my notes and I also prefer pencil. To use the two column approach, your actual notes will be on one side and the examples of theorems/formulas will be on the other. There is usually more than one method of solving a problem, use your notes to document this. Be sure to include examples that you believe will help you later. Math is often about making connections as so many concepts interrelated, be sure to record the connections you make. Areas where you have concerns of believe to be your greatest weakness are also the areas you should emphasize. To emphasize you may wish to use a highlighter and attach a few stickies. Personally, I prefer to date my notes as well, I also include the text pages for handy reference.
Format
I've already mentioned that it is helpful to keep audio notes, however, it is difficult to record examples of exercises in audio. Audio is better when you are reviewing postulates, procedures, and formulas. The more you hear the explanations, the greater chance you will retain the information. However, you may also wish to record your notes on your computer. Microsoft One Note is quite effective. There's an add-in that allows you to perform calculations, and to plot graphs and it contains an extensive collection of mathematical symbols and structures to display expressions and has a pretty good equation gallery. Two others are La-Tex, and Math Symbols. Although I like La Tex, it is not my first choice for taking notes. Math Symbols is great for creating exercises and it allows you to create your equations quickly (newer versions has handwriting recognition) but you'll still need another application to integrate it with. A lot of my students prefer One Note because it's where they keep all of their notes. But, everyone is different and you'll need a strategy that works best for you.
Tips for Improving Your Note Taking Skills
* Listen carefully to your instructor and jot down the key points about solving problems, proving theorems or using a procedure. Write everything you think that will help you when you return to this concept later.
* Don't get too wordy, keep your notes to the point and simple to understand.
* Use logical organization, jumping around from concept to concept will only be confusing. Make sure your examples have key points in your notes.
* Explain your reasoning. This component is key, keep it short and sweet but explain the logic behind the application or procedure.
* Record alternate methods, as I mentioned earlier, there is usually more than one way to solve a problem,
be sure to record the alternative method.
* Yes, it's a lot of work but a great way to learn . . . recopy your notes. Highlight and add or delete
information/
When taking notes in math, look at your textbook. What do you like about it? What don't you like about it? Think of your notes as a set of cheat notes for you to review. Make them look like a text that you find easy to follow.
In summary, most important of all is the review your notes in a timely way. Make review part of your routine. We are all guilty of cramming before tests and exams but a little review along the way will better equip you to
see greater success in math. If journaling works better for you, you may wish to read my up-coming posts about strategies for effective math journaling.
Taking Notes
I prefer to use the two column approach in my notes and I also prefer pencil. To use the two column approach, your actual notes will be on one side and the examples of theorems/formulas will be on the other. There is usually more than one method of solving a problem, use your notes to document this. Be sure to include examples that you believe will help you later. Math is often about making connections as so many concepts interrelated, be sure to record the connections you make. Areas where you have concerns of believe to be your greatest weakness are also the areas you should emphasize. To emphasize you may wish to use a highlighter and attach a few stickies. Personally, I prefer to date my notes as well, I also include the text pages for handy reference.
Format
I've already mentioned that it is helpful to keep audio notes, however, it is difficult to record examples of exercises in audio. Audio is better when you are reviewing postulates, procedures, and formulas. The more you hear the explanations, the greater chance you will retain the information. However, you may also wish to record your notes on your computer. Microsoft One Note is quite effective. There's an add-in that allows you to perform calculations, and to plot graphs and it contains an extensive collection of mathematical symbols and structures to display expressions and has a pretty good equation gallery. Two others are La-Tex, and Math Symbols. Although I like La Tex, it is not my first choice for taking notes. Math Symbols is great for creating exercises and it allows you to create your equations quickly (newer versions has handwriting recognition) but you'll still need another application to integrate it with. A lot of my students prefer One Note because it's where they keep all of their notes. But, everyone is different and you'll need a strategy that works best for you.
Tips for Improving Your Note Taking Skills
* Listen carefully to your instructor and jot down the key points about solving problems, proving theorems or using a procedure. Write everything you think that will help you when you return to this concept later.
* Don't get too wordy, keep your notes to the point and simple to understand.
* Use logical organization, jumping around from concept to concept will only be confusing. Make sure your examples have key points in your notes.
* Explain your reasoning. This component is key, keep it short and sweet but explain the logic behind the application or procedure.
* Record alternate methods, as I mentioned earlier, there is usually more than one way to solve a problem,
be sure to record the alternative method.
* Yes, it's a lot of work but a great way to learn . . . recopy your notes. Highlight and add or delete
information/
When taking notes in math, look at your textbook. What do you like about it? What don't you like about it? Think of your notes as a set of cheat notes for you to review. Make them look like a text that you find easy to follow.
In summary, most important of all is the review your notes in a timely way. Make review part of your routine. We are all guilty of cramming before tests and exams but a little review along the way will better equip you to
see greater success in math. If journaling works better for you, you may wish to read my up-coming posts about strategies for effective math journaling.
Friday, October 4, 2013
The History of Standards-Based Education
Currently in education there is a lot of talk about the new Common Core State Standards and the need for high standards. I will discuss in this column where that concept came from and how it has been distorted from its original use.
The idea of a standards-based educational system came from the work of Ted Sizer (1932-2009). In the early 1980s he was involved in a nationwide study of high schools that resulted in his book Horace's Compromise (and later Horace's School and Horace's Hope). In Horace's Compromise, Sizer describes the work of a typical teacher, and how no matter how willing, well-meaning, and hardworking, the teacher cannot meet the needs of the over hundred students she sees everyday, and how students by the same token cannot do deep quality work while jumping from one subject to another each with a different teacher and mostly sitting there being expected to soak up facts and concepts. In other words, the lack of real quality learning going on in schools was not the fault of teachers or students, but the design of the institution and the compromises teachers and students made with each other to survive in such an institution.
Sizer proposed that instead of students being rewarded for successfully passing a certain number of courses, and being in school for a certain amount of time, they be required to demonstrate the knowledge and abilities of a successful high school student through some sort of performance assessment where students actually showed they could apply what they had learned. He also posited certain attributes tat schools would need in order to carry out such an education.
What came out of that directly from Sizer and likeminded educators was an organization, the Coalition of Essential Schools, which holds a set of ten common principles that schools doing such work adhere to. This organization supports schools trying to make the changes to move toward applying these ideas. According to Sizer, how schools would measure this success, and how each school would carry out those principles in practice, needed to be locally decided.
This idea of Sizer's that students should graduate by being measured against a set of standards rather than just seat time became popularized in the 1990s. However, in many ways the concept got turned on its head. For one thing, the term "standards" took on a new meaning from its usual everyday meaning of a level of quality. Instead "standards" became a laundry list of facts and concepts, both broad and discrete, to be learned, as well as levels of performance. This standards, rather than being locally decided as Sizer proposed, have been mandated by National and State authorities.
The other distortion is that meeting these standards is measured by standardized tests. Performance has come to mean not what Sizer had in mind-the ability to carry out real world tasks that used the knowledge and abilities that schools decided were important-but how one "performs" on a standardized tests. These standardized tests are designed to test students' recall random sample of what is on that laundry list of facts and concepts. High standards have come to mean high scores on such tests.
Sizer's idea was that graduation by standards should free up schools to look and act differently, and free up students to demonstrate their knowledge in a variety of ways. The current practice of "standards" has meant that the standardization of curriculum, pedagogy, and assessment of the students, as well as their teachers, schools, districts, and states by the use of standardized tests. So far there's no evidence that the current use of standardized curriculum and the high stakes use of standards has improved the quality of education. The achievement gaps these so called reforms were to solve are as great of greater than before these changes. Graduation rates are overall no better, and we do not hear high school teachers claiming that students are coming in more prepared than they used to be. So far the only response the educational establishment has to offer to lack of results is that we need more standardization, a Common Core of facts and concepts, more tests, and higher stakes.
On the other hand, Sizer's ideas of standards without standardization have also been tried out, at times with astounding success. One of the first schools to implement Sizer's ideas was Central Park East School (CPESS) a public school of choice in New York's East Harlem. Deborah Meier, building on her work at Central Park East Elementary School, collaborated with Ted Sizer on how to meld his ideas and hers to develop a secondary school on the Coalitions principles. They came up with a school where students studied fewer topics, and worked with fewer teachers more intensively. All faculty and administrators worked as advisors who stayed with students over time and met with their advisory group daily. Students took part in internships in real world professional settings. The standards of the school were upheld through a series of portfolios and defenses of those portfolios in front of a committee. Students graduated, not after a prescribed number of years or prescribed number of completed courses, but when they had successfully passed and defended those portfolios. The standards of Central Park East were built around certain "Habits of Mind" that the faculty believed were important in all facets of life and in all disciplines. To a large extent, the demonstration of the use of those habits was the rubric used to decide if the portfolio or defense of the work met the schools standards. The students of CPESS had success at graduating high school and going on to, as well as succeeding in, college and far beyond their demographic equivalents in other public high schools in New York (see David Bensman's fascinating book Central Park East and its Graduates which documents his study of CPESS alumni).
After CPESS, such schools sprung up all over New York City, and to some extent nationwide. Schools such as Urban Academy, the International High Schools, the Met Schools, High Tech High, and Boston Arts Academy, to just name a few, continue if this tradition of high standards without standardization, of depth of knowledge over coverage, and of the importance of relationships with students as essential to successful education. While each of these schools looks very different, in each school one will see students who are passionately following their own interests while being held to a common set of high standards in a non-standardized curriculum. These schools have shown that they help students beat odds in terms of graduation and getting into college. Even more importantly, these schools produce graduates with positive attitudes toward learning and their ability to shape their own futures and contribute to the larger society.
When I attended a forum recently on the Common Core, many concerns were voiced. True positive educational reform with high expectations/standards can be achieved - there are models (I just described a few) to learn from and we, citizens, must be activity engaged in the process. Educate yourself, volunteer at your child's school, go to school board meetings (remember they are elected politicians) and remember that everything a teacher can or cannot do in her classroom is determined by a politician.
The idea of a standards-based educational system came from the work of Ted Sizer (1932-2009). In the early 1980s he was involved in a nationwide study of high schools that resulted in his book Horace's Compromise (and later Horace's School and Horace's Hope). In Horace's Compromise, Sizer describes the work of a typical teacher, and how no matter how willing, well-meaning, and hardworking, the teacher cannot meet the needs of the over hundred students she sees everyday, and how students by the same token cannot do deep quality work while jumping from one subject to another each with a different teacher and mostly sitting there being expected to soak up facts and concepts. In other words, the lack of real quality learning going on in schools was not the fault of teachers or students, but the design of the institution and the compromises teachers and students made with each other to survive in such an institution.
Sizer proposed that instead of students being rewarded for successfully passing a certain number of courses, and being in school for a certain amount of time, they be required to demonstrate the knowledge and abilities of a successful high school student through some sort of performance assessment where students actually showed they could apply what they had learned. He also posited certain attributes tat schools would need in order to carry out such an education.
What came out of that directly from Sizer and likeminded educators was an organization, the Coalition of Essential Schools, which holds a set of ten common principles that schools doing such work adhere to. This organization supports schools trying to make the changes to move toward applying these ideas. According to Sizer, how schools would measure this success, and how each school would carry out those principles in practice, needed to be locally decided.
This idea of Sizer's that students should graduate by being measured against a set of standards rather than just seat time became popularized in the 1990s. However, in many ways the concept got turned on its head. For one thing, the term "standards" took on a new meaning from its usual everyday meaning of a level of quality. Instead "standards" became a laundry list of facts and concepts, both broad and discrete, to be learned, as well as levels of performance. This standards, rather than being locally decided as Sizer proposed, have been mandated by National and State authorities.
The other distortion is that meeting these standards is measured by standardized tests. Performance has come to mean not what Sizer had in mind-the ability to carry out real world tasks that used the knowledge and abilities that schools decided were important-but how one "performs" on a standardized tests. These standardized tests are designed to test students' recall random sample of what is on that laundry list of facts and concepts. High standards have come to mean high scores on such tests.
Sizer's idea was that graduation by standards should free up schools to look and act differently, and free up students to demonstrate their knowledge in a variety of ways. The current practice of "standards" has meant that the standardization of curriculum, pedagogy, and assessment of the students, as well as their teachers, schools, districts, and states by the use of standardized tests. So far there's no evidence that the current use of standardized curriculum and the high stakes use of standards has improved the quality of education. The achievement gaps these so called reforms were to solve are as great of greater than before these changes. Graduation rates are overall no better, and we do not hear high school teachers claiming that students are coming in more prepared than they used to be. So far the only response the educational establishment has to offer to lack of results is that we need more standardization, a Common Core of facts and concepts, more tests, and higher stakes.
On the other hand, Sizer's ideas of standards without standardization have also been tried out, at times with astounding success. One of the first schools to implement Sizer's ideas was Central Park East School (CPESS) a public school of choice in New York's East Harlem. Deborah Meier, building on her work at Central Park East Elementary School, collaborated with Ted Sizer on how to meld his ideas and hers to develop a secondary school on the Coalitions principles. They came up with a school where students studied fewer topics, and worked with fewer teachers more intensively. All faculty and administrators worked as advisors who stayed with students over time and met with their advisory group daily. Students took part in internships in real world professional settings. The standards of the school were upheld through a series of portfolios and defenses of those portfolios in front of a committee. Students graduated, not after a prescribed number of years or prescribed number of completed courses, but when they had successfully passed and defended those portfolios. The standards of Central Park East were built around certain "Habits of Mind" that the faculty believed were important in all facets of life and in all disciplines. To a large extent, the demonstration of the use of those habits was the rubric used to decide if the portfolio or defense of the work met the schools standards. The students of CPESS had success at graduating high school and going on to, as well as succeeding in, college and far beyond their demographic equivalents in other public high schools in New York (see David Bensman's fascinating book Central Park East and its Graduates which documents his study of CPESS alumni).
After CPESS, such schools sprung up all over New York City, and to some extent nationwide. Schools such as Urban Academy, the International High Schools, the Met Schools, High Tech High, and Boston Arts Academy, to just name a few, continue if this tradition of high standards without standardization, of depth of knowledge over coverage, and of the importance of relationships with students as essential to successful education. While each of these schools looks very different, in each school one will see students who are passionately following their own interests while being held to a common set of high standards in a non-standardized curriculum. These schools have shown that they help students beat odds in terms of graduation and getting into college. Even more importantly, these schools produce graduates with positive attitudes toward learning and their ability to shape their own futures and contribute to the larger society.
When I attended a forum recently on the Common Core, many concerns were voiced. True positive educational reform with high expectations/standards can be achieved - there are models (I just described a few) to learn from and we, citizens, must be activity engaged in the process. Educate yourself, volunteer at your child's school, go to school board meetings (remember they are elected politicians) and remember that everything a teacher can or cannot do in her classroom is determined by a politician.
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