I would like to deal with several comments that have been made about our critique of Rowser-Koontz article in the Mathematics Teacher.
We have made several points, which we still stand by. The first is that it is harmful to associate certain learning styles with a particular racial or ethnic group. While the authors do use the expression "many African Americans," we wonder what "many" can mean. If it means only a small percentage, then what's the point of making the statements; if it means a large percentage, then we can certainly associate the particular behavior with African Americans. One can only assume that the authors meant the latter. In the context of the article, and especially, in the context of its title, the word "many" can only amount to an effective stereotype. Furthermore, Goldenberg says nothing to enlighten us as to what standards are used to determine who is African American. This sort of determination would open up a discussion of race, genetics, appearances, culture etc. Are we prepared to carry such a discussion through all its details? And to what end?
The truly distressing thing is that all of the nonsense is unnecessary. As we point out: "Had the authors simply stated that various students learn and reason in various ways, and that teachers must proceed with this knowledge and use diverse teaching teaching techniques, they would have been merely restating a widely proclaimed and accepted fact." Why the need to mention African American or any other group? The same holds for so-called "IQ." Why do research to correlate IQ with race? Why not with eye-color or height? There is more variation WITHIN "racial" or ethnic groups than BETWEEN these groups. We must address the individual and the individual's needs. There are two main reasons for the proliferation of classification by race. The truely malignant one is to prove notions of racial superiority (Shockley, Herrnstein, Murray, et. al.). The other reason is to have a leg up in getting grants and having papers published...
We agree with Judy Roitman about the use of different teaching techniques. In addition to our statement just quoted, we also say: "[we must] start the educational process from where each student is situated" and "the authors are right in asserting that this help [in sharpening reasoning and computation skills] must come in varying formats." Goldenberg certainly overlooked these statements.
Goldenberg chides us for failing to appreciate how Koontz and Rowser distinguish between inferential and inductive reasoning. In fact, they don't. Here is what they say. (1) "An inference is a judgment made from observations or evidence." (2) "Inductive reasoning forms generalizations from many specific cases." This reminds me of the distinction between capitalism and communism: "Under capitalism, man exploits man, whereas under communism the reverse is true." If there is any important distinction here, it escapes us. None of our dictionaries give us any further clue. Perhaps Goldenberg can enlighten us. We quoted Koontz and Rowser that inferential reasoning "must not be thought of as inferior." Would Goldenberg care to defend this statement?
When we face a student who is weak in mathematics, we must try to find out why, and then address that student's needs. Perhaps the student has had bad teachers, or is unduly influenced by negative peer attitudes. Perhaps the student is specifically math-phobic or learning disabled, or has never reached the stage of intellectual development necessary for abstract thought. Sometimes we can intervene intelligently, or make a shot in the dark... or maybe just wait. For some, group learning is helpful, for others, counterproductive. Does it help to know that the student is African American, Nigerian, Israeli, Chinese or rich? If the student is African American, do we say: Aha! You probably "prefer novelty, freedom and personal distinctiveness"? If the student is Asian, do we say: You are obviously an underachiever? This is a very dangerous road to go down.