I submitted a comment to the blog post rebuttal of Barbara Oakley’s NY Times op-ed. It has been four days and it is still under moderation, so rather than keep people in suspense, here is the comment I submitted:
In your post you state: “It is true that traditional ways of teaching mathematics have been shown to be harmful for all students, and even more harmful for non-dominant populations, including girls. This phenomenon has been widely documented by professors of mathematics education such as Rochelle Gutierrez, Jo Boaler, and others.”
What research has shown this to be true for ALL students as you state? You cite Boaler who has gone on record as saying that learning times tables can be injurious to students. She believes that memorization does harm and undermines “understanding”. You also you cite Gutierrez who claims that minorities and girls don’t do well in math because of the way it’s taught. Even if we agree with Gutierrez’s claim, that would say that not all are injured, but just minorities and women.
I wrote an article some time ago about traditionally taught math and showed data
from the Iowa Tests of Basic Skills (for grades 3 through 8 ) and the ITED (high school grades) from the early 40’s through the 80’s for the State of Iowa. (See https://www.educationnews.org/education-policy-and-politics/traditional-math-the-exception-or-the-rule/)
The scores (in all subject areas, not just math) show a steady increase from the 40’s to about 1965, and then a dramatic decline from 1965 to the mid-70’s. One conclusion that can be drawn from these test scores is that the method of education in effect during that period appeared to be working. And by definition, whatever was working during that time period was not failing. And this was at a time when traditional math teaching was the mainstay.
It is true that traditionally taught math can be done poorly. It can also be done well, and there have been many people who have benefitted from such instruction. Regarding memorization, I suggest you read “Memorable Teaching” by Peps McCrea which is an exploration of how memorization is an essential part of the learning process. (https://www.amazon.com/Memorable-Teaching-Leveraging-learning-classroom/dp/1532707797) I also suggest you read some of the papers and articles written by a group of cognitive scientists who call themselves “The Learning Scientists”. Their website is here: http://www.learningscientists.org/