1. Brief thread about teaching methods (at object level) and about why I don't like steelmanning (at meta level). https://twitter.com/beyerstein/status/1361396735818534913

2. In math teaching, current practice everywhere I know is to require students to show their work, even if the final answer is one number.

3. This is good pedagogy. It means teachers and graders can spot where a student made a mistake and point it out.

4. This is especially good pedagogy if a teacher grades many answer sheets by the same student and notices patterns.

5. This is compassionate, because if a student makes a sign error but gets everything else right, I can give partial credit, maybe 8-9/10.

6. This helps defuse math anxiety, by telling students what they get right and what they need to work on, instead of just saying "wrong."

7. And because math anxiety is classed and gendered, good math pedagogy like this is automatically feminist and anti-racist.

8. The good = feminist/anti-racist bit isn't universal in education, e.g. I don't think it's true in didactics. But in math pedagogy, it is.

9. All of those effects are why showing your work is normalized in progressive education, with its emphasis on critical thinking and such.

10. (P.S. "progressive education" has a specific meaning and goes back to Dewey, this isn't some 2010s invention.)

11. Of course, there are best practices here. Most importantly: students can sometimes take different sequences of steps, and it's alright.

12. Also, be flexible with how students justify a step; if the step is right but the justification is wonky, say so, but don't grade down.

13. US high schools have an abomination called 2-column proofs, mechanizing the process. Don't do it; it's precision theater, not precision.

14. A student will answer many pset and test questions over a year that you'll grade, so you'll have many opportunities to catch errors.

15. Under no circumstances does this mean you should slack! But it does mean that you can be lenient in ambiguous cases.

16. Also, at somewhat meta level: be curious! Singapore, for example, is an ESL nation; you can learn from it even if it's anti-progressive.

17. You may notice that showing your work also underpins curricular rigor, which in US politics is a center-right catchphrase.

18. But this shouldn't surprise! Math anxiety is such that good pedagogy has higher impact on girls and low-SES students.

19. So a rational teacher who dgaf about equity, and a rational teacher who only cares about equity, will teach math in similar ways.

20. Now, let's circle back to the Equitable Math screencap. It says asking students to show their work is racist against ESL students.

21. This is a horrible claim. It's wrong. It's harmful, because it recommends against something that *helps* ESL students do better.

22. And that's why I don't steelman: one could come up with guidelines for how to avoid common pitfalls, but Equitable Math doesn't do that.

23. One could (and @matthematician does) say "insisting on rigid styles like 2-column is bad and you should be more compassionate."

24. But this is not what Equitable Math says. What it says is "requiring students to show their work is teacher-centered and racist."

25. Someone who says such a thing isn't interested in solving problems in pedagogy about how to teach more flexibly.

26. Were a political party in Berlin to advocate for adopting Equitable Math here, I'd vote against it, because this is a bad proposal.

27. Steelmanning in this context would mean pretending that Equitable Math is a more competent pedagogy and ignoring its harms.

28. Let's go back to the original topic, since math pedagogy is cool and talking about cool things > talking about boring things.

29. I think it's crucial to understand how central math anxiety is as a barrier at all levels up to about the middle of bachelor's degree.

30. The upshot, knowing who math anxiety affects the worst, is that there is no culture war over values here.

31. There might be political values issues about *didactics* (what's more important to teach, calculus or discrete math?). But not pedagogy.

32. Good pedagogy requires teachers to devote time behind the scenes to evaluating pset and test answers, to offer good feedback.

33. This is absolutely student-centered, and, through personal feedback, has elements of personalized tutoring.

34. This has political implications, but none of them is a culture war - they're about funding levels, including class size and salaries.

35. So please, before you turn everything into an online culture war, follow good pedagogy and provide sufficient resources for it. /end