June 28th, 2016 by Dan Meyer
The Hechinger Report asks, “Is it better to teach pure math instead of applied math?”:
In the report, “Equations and Inequalities: Making Mathematics Accessible to All,” published on June 20, 2016, researchers looked at math instruction in 64 countries and regions around the world, and found that the difference between the math scores of 15-year-old students who were the most exposed to pure math tasks and those who were least exposed was the equivalent of almost two years of education.
The people you’d imagine would crow about these findings are, indeed, crowing about them. If I were the sort of person inclined to ignore differences between correlation and causation, I might take from this study that “applied math is bad for children.” A less partisan reading would notice that OECD didn’t attempt to control the pure math group for exposure to applied math. We’d expect students who have had exposure to both to have a better shot at transferring their skills to new problems on PISA. Students who have only learned skills in one concrete context often don’t recognize when new concrete contexts ask for those exact same skills.
If you wanted to conclude that “applied math is bad for children” you’d need a study where participants were assigned to groups where they only received those kinds of instruction. That isn’t the study we have.
The OECD’s own interpretations are much more modest and will surprise very few onlookers:
- “This suggests that simply including some references to the real-world in mathematics instruction does not automatically transform a routine task into a good problem” (p. 14).
- “Grounding mathematics using concrete contexts can thus potentially limit its applicability to similar situations in which just the surface details are changed, particularly for low-performers” (p. 58).
BTW. I was asked about the report on Twitter, probably because I’m seen as someone who is super enthusiastic about applied math. I am that, but I’m also super enthusiastic about pure math, and I responded that I don’t tend to find categories like “pure” and “applied” math all that helpful. I try to wonder instead, what kind of cognitive and social work are students doing in those contexts?
BTW. Awhile back I wrote that, “At a time when everybody seems to have an opinion or a comment [about mathematics education], it’s really hard for me to locate NCTM’s opinion or comment.” So credit where it’s due: it was nice to see NCTM Past President Diane Briars pop up in the article for an extended response.
What is often overlooked in these kind of studies is the students who are enrolled in the various courses. The correlation between pure math courses and higher level math exists because higher achieving students are placed in the pure math classes, while lower performing students are placed in applied math.
Same thing is true for studies that claim that students who take calculus are the most likely to succeed in college. No duh! That is because those who are most likely to succeed in college take calculus.
The course work does not cause the discrepancy, the discrepancy determines the course work.