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.
Friday, February 28, 2014
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.
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