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February 3, 2009

Dumbing Down Mathematics Part III

Nick Diaz

Across the country, the way mathematics is taught in the classroom and in textbooks has been changing notably in the past 20 years. Classrooms are often organized in small groups where students ask each other questions and the teacher is discouraged from providing information. Students may even take tests in groups, if they have tests at all.


The use of blocks and other manipulative objects has extended well beyond kindergarten and can now be found in many algebra classes.


While manipulatives can be powerful tools for leading students through a discovery process that reinforces mathematics, the haphazardly planned use of manipulatives can be destructive. An essential adjunct to "hands-on" mathematics is an effort to organize ideas and develop the capacity for mathematical thought and reason.


Experiments performed under the tutelage of unskilled guides can lead students into a chaotic jungle, one in which their minds become entangled in an underbrush of mismatched concepts to which these students, their parents, and their future teachers will be hard pressed to bring order.


Meanwhile, the students practice their fundamentals less and less. Time consuming projects and essays that involve very little mathematics are the rage. Calculator use is growing and taking away expectations for student learning.


Textbooks are full of color pictures and stories, but not full of mathematics. The books often don't even give explicit definitions or procedures. That would be "telling" and the new idea is for students to discover all of mathematics for themselves. Many of these programs don't even teach the standard algorithms for the operations of arithmetic. Long division is a devil that is to be beaten into extinction; if they manage that, multiplication will be next.


Along with the emphasis on non-traditional methods, we are offered a lot of rhetoric about higher order thinking and problem solving. There have been countless diatribes that rant about the evils of repeated practice and remembered facts and a steady stream of self-endorsements of the new directions. The selling of the so-called reform has been well rehearsed by its proponents over the last decade. Replete with glossy promotions, the new “new” math is long on salesmanship, but short on mathematics.


Perhaps the most viable criticism of traditional programs offered by the proponents of the new programs is that traditional students do not do as well on problem solving (meaning word problems) as they do on straight computation. An inspection of traditional texts will show that there are plenty of word problems.


There is some evidence to suggest that teachers assign a smaller proportion of word problems than computation problems, since the word problems are traditionally more difficult. In any case, the new programs seem to ignore the fact that basic computation skills are necessary in problem solving. If students lack the basic tools to yield correct results, concepts will not help. Consequently, the new programs do not appear to produce better problem-solving skills, as claimed.


Much criticism of the traditional programs, made by the proponents of these changes, seems to be entirely misplaced. The new programs are said to emphasize real-world problems more than traditional programs do.


Inspection of course materials, however, shows that the same real or, better yet, authentic topics appear in both, and some very unreal problems appear in the new textbooks.


Another claim is that traditional teachers are nothing but drill masters and unable to relate math to applied problems. This notion is necessary to discredit traditional teaching and teachers, and to complete the argument that teaching methods are to blame for inadequate achievement.


Although there are many variations in the methods of these new programs, they have one clear characteristic in common – they are all weak in mathematics.


The expectations for our students are seriously undermined; as the mathematics is leeched out of the textbooks, the opportunity for our students to learn is withering away.


This problem is not unique to elementary school mathematics, and it is not just confined to the four operations of arithmetic. The new methods and low content levels are present in many high school programs, and even in college math courses.


The deterioration in the curriculum materials has been quite dramatic over the past several years. It has also been accompanied by a deterioration in the mathematics achievement of incoming college students – those who will be the math teachers of tomorrow. The ever-increasing number of “developmental” non-credit math classes at community and four-year colleges demonstrate the validity of this assertion.


Now we are faced with an inadequate supply of teachers who are really qualified to teach mathematics, with new curriculum materials that lack the content our students need, and with poor achievement compared to our international competition – all wrapped in glowing rhetoric about the new directions in mathematics education.


There is a very real possibility that our children have been suffering, and will continue to suffer, as a result of these unverified curriculum designs. I’m afraid the pendulum has much further to go in that direction before it swings back to a saner, intellectually honest way.


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