In the opening paragraph, Kilpatrick says that the title of his article is a play on the title of a different article called "The Unreasonable Effectiveness of Mathematics". I have not read "The Unreasonable Effectiveness of Mathematics", but I am assuming Kilpatrick chose to name his article about research in math education in a similar way because the effectiveness of mathematics is not necessarily because the research in mathematics education in effective itself.
The article was about how research in math education is ineffective for several reasons. The ways to improve research in math education are to create more of a community that includes practicing teachers, a theoretical construct for viewing the work, and the ability to recognize the limits and complexities of the researchers' domain.
The article mentioned how using research to solve a math problem is like a technology problem whereas using research to solve a math education problem is quite the opposite since it now becomes about dealing with people. This differentiation between humans versus technologies is so interesting to me when thinking of teaching math or of just the school system in general. There are so many things going on in a mathematics classroom when considering just the teacher, but add the students in there and the school environment, and the picture becomes even more complex. It is nice to read research articles on math education because they can be very insightful, but what may work for one teacher in a certain school may not even come close to working for a different teacher in even the same school.
Thanks for your thoughtful response. I totally agree that different things work differently for different teachers, and also for different students. I think the value of math research is finding multiple ways to present concepts to students. I know when I'm teaching a new concept, I usually have two of three ways of explaining it to different students - as the year goes on I get a pretty good idea of which approach will work best for an individual student - It certainly would be interesting to have a more formal understanding of why this is and how to best approach different learners - maybe even some sort of streaming of classes based on learning styles.
ReplyDeleteReading the last paragraph of your response reminded me of some reading I've done recently, from the work of Ted Aoki. He distinguishes between "curriculum-as-plan" and "curriculum-as-lived-experience." He states exactly what you say: that a curricuolum in one classroom with a particular group of unique faces, may not be effective for a new group of students with completely different faces, life experiences, and views on school. Somehow, within mathematics education, we need to be aware of the life experiences of our students. Many would argue that math is not a value-free discipline, as many others state the opposite, and this may be part of the problem. Some are viewing the mathematics classroom as a technology, free of values and human interactions, when in reality, mathematics may be far from.
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