I have written a number of entries regarding “understanding” in math. I have discussed various misunderstandings about understanding in math. There are two statements I haven’t addressed, which for me raise many questions.
I have heard many people express the thought that “Calculation is the price we used to have to pay to do math. It’s no longer the case. What we need to learn is the mathematical understanding.”
And often on the heels of this statement I will be told that they had done well in math all through elementary school, but when they got to algebra in high school they hit a wall. Or, similarly, they did great in high school, and hit a wall with calculus.
There is much information that we do not have from such statements.
- Was the education they received really devoid of any kind of understanding and all rote?
- Are there people who get A’s in math in high school who are really math zombies and cannot progress to the next level?
- Are these complaints limited to those
who were educated in the era of traditional or conventionally taught math?
- And of those, how much of what they experienced is due to concepts not explained well, emphasis on procedures only, and grade inflation?
- Are there gaps in their math education which compound on themselves?
- And to what extent are these problems the result of the obsession over understanding?
Considering these questions, I have listed some ideas for future studies based on communication I’ve had with people in math education:
- To what extent does success in high school math programs correlate with success in higher level math and science courses in college? (Differentiated by regular track vs AP/IB/honors track)
- For successful math students in high school, and college math what did they do that’s different than those who were successful in high school but did not do well in college math?
And a corollary of such a study would be:
- What percent of the student population has had math tutors, or been enrolled in learning centers?
- And for such students what are the basic teaching techniques used for math?
Finally, two more:
- What effect has the emphasis on understanding been on students who have been identified as having a learning disability?
- And a more difficult question, is there evidence that such emphasis has resulted in students being labeled as having learning disabilities?
I of course am interested in any studies you may know of that would shed light on these questions.