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.
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