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January 6, 2009

Dumbing Down Mathematics Part 1

Nick Diaz

Since the 1980's, there have been substantial efforts nation wide to weaken mathematics education in America, and, unfortunately, these efforts have largely been successful.


This is not, however, a “Communist conspiracy.” It flows from an honest desire to help the less fortunate. This effort is based on the misguided notion that weaker mathematics will be helpful to the traditionally disadvantaged groups in our society. It is this effort, curiously known as reform, that is the root cause of what has come to be known as the math wars.


You won't find many reformers who will openly admit that they favor "dumbed-down" mathematics. In fact, the reform movement is characterized by a plethora of rhetoric to the contrary. The diatribes are extensive and frequent and are laden with phrases like "higher order thinking" and "conceptual understanding" and "real-world problems," while shy on terms like "arithmetic," "algorithm," “authentic.” Reformers have learned their scripts well, and the rhetoric comes gushing forth with little provocation.


The conditions that prompted this movement are obvious. Poor people and minorities are under-represented among those who reach high levels of mathematical achievement. Those who cannot master arithmetic and algebra are unlikely to achieve a decent college education. There is no question that the educational system in this country is not successful for a great many students, so the fix consists of making the mathematics easier.


This means less rigor, less emphasis on arithmetic and algebra, more reading and art and creative projects, less emphasis on correct answers, more calculators, and a host of other reform-minded solutions. Stylish pedagogical methods combined with rhetoric about higher order thinking, while downplaying or condemning outright both computation skills and mathematical proof, complete the package. This is reform mathematics education.


Sometimes dubbed “traditional” or “anti-reform” – notice how much better “reform” sounds than “traditional” or “anti-reform” – the second perspective has come in reaction to the first and is mainly supported by parents and mathematicians. This perspective holds out that the mathematics must not be "dumbed-down."


The key in this perspective is to increase achievement rather than to decrease expectations. Central to this position is that the traditionally less fortunate are not well-served by weaker mathematics and, in fact, should be insulted by it. The real key to success is real mathematics achievement, and every effort should be made to foster this achievement.


Ironically, the struggle to promote real mathematics education is left up to those outside of the field – mostly parents. The perspective is traditional in the sense that it seeks to prevent learning expectations from being further eroded away by “reform” efforts. Mathematics education in America has not been very successful; do not, however, look for relief in the “reform” notions. We would be better off if all the energy behind the “reform” was redirected toward clearly defined achievement goals, and we measured progress toward those goals frequently and objectively.


The reform designs open the door to claims of successfully teaching mathematics without really doing so. The reform writings and methods are many and varied, but a common feature is that they end up obscuring the failure to teach mathematics. In “reform” mathematics education, the goal of success for all is not supported by achievement, but rather by redefining success and, mostly, by obscuring failure. Some examples:


Group Learning and Group Tests – The story of Apollo 13 is used to promote group learning and group assessments with the argument that our students must learn to work together like people do in the real world. Never mind that people in the real world don't sit in groups doing algebra problems.


Group learning is plagued by inequities that most parents identify quickly – some do the work while others learn that they can "succeed" without learning the material and without effort. Group assessments effectively erase the ability to monitor individual achievement or to provide useful diagnostic information. Whether or not individuals are learning is obscured by these methods.


Calculators – Many argue that routine skills are out of date, and that technology has changed the mathematics that today's students need to know. The position includes multiplication and division, obviously. However, today's calculators can manipulate fractions and solve equations as well. Distancing students from these activities takes away the learning experiences that help form the foundation of mathematical understanding.


By far, most American parents want their children to be able to solve problems without calculators. The reliance on calculators allows “reformers” to claim success even when children do not learn the fundamental operations of arithmetic. Soon they will claim success in algebra for students who have not learned how to solve equations.


Projects – The reform programs are loaded with projects and activities, often called “investigations.” Part of the argument for these methods relates to ‘stimulating student interest.”


There are also claims of richer mathematics and the importance of context. Even a casual inspection of these activities will show that they tend to be very time consuming, while involving very little mathematics. Time for mathematics, both in class and at home, is seriously limited and must be used as efficiently as possible.


These activities are inefficient learning methods. But, beyond that limitation, they promote the evaluation of students on the basis of non-mathematical dimensions such as how artistic the display is or the writing style of the report or the social value of the application.


In my next installment, I’ll touch upon some other ways in which the “reform” advocates obscure failure and re-define success.


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