Opinion Piece on Math Education
I have written an opinion piece in math education that was published in the Lexington Minuteman on October 9, 2008 under the (slightly inaccurate) title "Math is key to success in the world economy". It seems to be no longer available on the Lexington Minuteman, so I've posted the original on scribed.
To Test or Not to Test
There has been a lot of debate on the issue of high-stakes testing that determines whether a student will be able to graduate high school and whether schools will be taken over by the state. In Massachusetts, this centers on MCAS (Massachusetts Comprehensive Assessment System), which was set up in response to the Massachusetts Education Reform Act of 1993. Since the adoption of the federal No Child Left Behind Act (NCLB) of 2001, similar assessment systems have been established nationwide.
The goals of the assessment system are laudable. Most observers agree that the public schools, particularly those in poor urban areas, have a history of failing their students. And it seems obvious to me that if a student cannot pass a fair test of basic skills, there is something wrong. I do not support granting diplomas to students who lack the most basic skills.
But as currently implemented there are big problems with MCAS. The importance of this test to schools has severely distorted priorities.
If a school is facing penalties unless they raise their MCAS scores, there is a tremendous incentive to transfer resources to those students who score in the lower ranks. There is no incentive to help student who are already scoring excellent.
Benefits for those students who MCAS and NCLB were designed to help are not clear either. High school drop out rates are up and anecdotal evidence as well as logic indicates that students who cannot pass MCAS after several tries are more likely to drop out. And since average scores will go up as more of these students drop out, schools have a disincentive to retain these students.
A personal communication by a community college science teacher reveals that most graduates of the Boston public schools who attend this community college place into a basic math course which begins at the third grade level. I asked how this could be possible, since these students have all passed the 10th grade Mathematics MCAS, which I regard as a reasonable test of high school math knowledge. The teacher replied,
I think the problem is analogous to that of car manufacturers that seek to improve the quality of their product. One way to improve quality is to devote more resources to inspecting the final product. A better way is to do what the Japanese have done and improve the process of car production. There will still be final inspections, but less defects will be found. In the same way, improvement in education must precede the institution of high-stakes testing.
The goals of the assessment system are laudable. Most observers agree that the public schools, particularly those in poor urban areas, have a history of failing their students. And it seems obvious to me that if a student cannot pass a fair test of basic skills, there is something wrong. I do not support granting diplomas to students who lack the most basic skills.
But as currently implemented there are big problems with MCAS. The importance of this test to schools has severely distorted priorities.
If a school is facing penalties unless they raise their MCAS scores, there is a tremendous incentive to transfer resources to those students who score in the lower ranks. There is no incentive to help student who are already scoring excellent.
Benefits for those students who MCAS and NCLB were designed to help are not clear either. High school drop out rates are up and anecdotal evidence as well as logic indicates that students who cannot pass MCAS after several tries are more likely to drop out. And since average scores will go up as more of these students drop out, schools have a disincentive to retain these students.
A personal communication by a community college science teacher reveals that most graduates of the Boston public schools who attend this community college place into a basic math course which begins at the third grade level. I asked how this could be possible, since these students have all passed the 10th grade Mathematics MCAS, which I regard as a reasonable test of high school math knowledge. The teacher replied,
... students who fail the MCAS tests are put into intensive "MCAS prep" programs. These are designed for one purpose only -- to get them past the test. I. e. it is "teaching to the test" in its purest form. Many students are indeed then able to pass the MCAS math test, and still be grossly deficient in math skills.
I think the problem is analogous to that of car manufacturers that seek to improve the quality of their product. One way to improve quality is to devote more resources to inspecting the final product. A better way is to do what the Japanese have done and improve the process of car production. There will still be final inspections, but less defects will be found. In the same way, improvement in education must precede the institution of high-stakes testing.
The Math Wars
The "Math Wars" have been framed as a debate between “traditionalists” and “reformers”. I don't take a side in this debate, but rather I think the debate is unproductive.
The reformers actually represent the educational establishment, and their position has been the official position of the National Council of Teachers of Mathematics (NCTM) for over 20 years. They believe in learning by discovery, cooperative work in small groups, and an emphasis on communicating one's thinking. Their philosophy of education is constructivism, and although the word constructivism does not appear in the Principles and Standards for School Mathematics, it is clearly a constuctivist document. The traditionalists, who include many parents and a large number of university mathematicians and scientists, have developed as a reaction to what they see as the excesses of the reformers and a perceived decline in the abilities of college students. A more informal movement, their position seems to be well stated by the Mathematically Correct movement. Traditionalists stress the importance of individual competence, ability to instantly recall number facts, and the ability to perform important algorithms. Although I have not seen them espouse a theory of education, from their prescriptions they implicitly adopt behaviorism and cognitivism.
There is a hidden but clear political dimension to the math wars. The NCTM Principles and Standards states "All students should have the opportunity and support necessary to learn significant mathematics with depth and understanding. There is no conflict between equity and excellence." I see no evidence that the traditionalists agree with this, and my conversations with traditionalists indicate that most believe that mathematics teachers need to put forth a challenging curriculum, and essentially serve those students that are able to rise to the challenge. They also contend that the reform agenda has put equity far ahead of excellence.
My belief is that traditionalism and reformism are not as diametrically opposed as they seem, and that the future will see a convergence in these movements. I think that most reformers now see that students must spend a substantial amount of time on rote learning. For example, the number of high-school graduates who struggle to make change without electronic assistance is disturbing. Without the instant recall of basic number facts, such as the single-digit multiplication table, students are severely handicapped in trying to solve more complex problems. And I think that most traditionalists see value in the goals of the reform movement. I think we can both do a better job of education the top 20% of students who we need as a technological elite and the bottom 80% who will have to find jobs that are increasingly more quantitative and will also need to be informed citizens in a world that depends more and more on numerical analyses.
Those who care about mathematics education need to move beyond the math wars and work together to improve the quality of the teachers and schools that provide this education.
The reformers actually represent the educational establishment, and their position has been the official position of the National Council of Teachers of Mathematics (NCTM) for over 20 years. They believe in learning by discovery, cooperative work in small groups, and an emphasis on communicating one's thinking. Their philosophy of education is constructivism, and although the word constructivism does not appear in the Principles and Standards for School Mathematics, it is clearly a constuctivist document. The traditionalists, who include many parents and a large number of university mathematicians and scientists, have developed as a reaction to what they see as the excesses of the reformers and a perceived decline in the abilities of college students. A more informal movement, their position seems to be well stated by the Mathematically Correct movement. Traditionalists stress the importance of individual competence, ability to instantly recall number facts, and the ability to perform important algorithms. Although I have not seen them espouse a theory of education, from their prescriptions they implicitly adopt behaviorism and cognitivism.
There is a hidden but clear political dimension to the math wars. The NCTM Principles and Standards states "All students should have the opportunity and support necessary to learn significant mathematics with depth and understanding. There is no conflict between equity and excellence." I see no evidence that the traditionalists agree with this, and my conversations with traditionalists indicate that most believe that mathematics teachers need to put forth a challenging curriculum, and essentially serve those students that are able to rise to the challenge. They also contend that the reform agenda has put equity far ahead of excellence.
My belief is that traditionalism and reformism are not as diametrically opposed as they seem, and that the future will see a convergence in these movements. I think that most reformers now see that students must spend a substantial amount of time on rote learning. For example, the number of high-school graduates who struggle to make change without electronic assistance is disturbing. Without the instant recall of basic number facts, such as the single-digit multiplication table, students are severely handicapped in trying to solve more complex problems. And I think that most traditionalists see value in the goals of the reform movement. I think we can both do a better job of education the top 20% of students who we need as a technological elite and the bottom 80% who will have to find jobs that are increasingly more quantitative and will also need to be informed citizens in a world that depends more and more on numerical analyses.
Those who care about mathematics education need to move beyond the math wars and work together to improve the quality of the teachers and schools that provide this education.
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