Thank you for this great post. I would like to comment on a particular part:
“Besides, even in the technical classes, forgetting is the near-universal outcome, and the long-term benefits are mostly conceptual — for if you don’t use these skills continuously for the rest of your life, you’re almost certainly going to lose them. Maybe more than once.”
This seems strongly like throwing the baby out with the bathwater. At least for math, it is, as you say, very clear that skills build on top of each other, and that weak students struggle greatly because they lack the foundational skills. I used to tutor friends and used to be regularly shocked by how much they forgot: how to divide by fractions, summation with exponents, just basic stuff. So the following is pretty likely:
1)If you don’t understand old concepts in math, you will not understand many new concepts
We should be making sure they remember this material not in 20 years, but in 2 years if and when we make them struggle through calculus (unless one has a realistic plan for how to let the majority of underachievers in math just drop out of advanced math classes). This gives mediocre students a fair chance of actually building deeper understanding of what is going on on a conceptual level, and underachieving students a chance to get acceptable grades so that they do not become dejected and apathetic.
For math, students get assigned homework anyway. I see no reason why that homework should not include an automatically generated exercise aimed to repeat an old concept. Of course, multiple-choice flashcards would be a failure mode.
I recall reading someone who applied spaced repetition principles to the math homework they assigned. Instead of doing the normal thing where each week would introduce new content and have homework on that content, the homework for each week was 1⁄3 that week’s content, 1⁄3 previous week’s content, 1⁄3 content from any of the previous weeks. Claimed that it significantly boosted people’s retention and exam scores.
I don’t see as much disagreement between us as you might be thinking. Precisely because I agree with your numbered points 1 and 2, I suggested it could be beneficial to compress most of our 12 years of math instruction down to a more intensive 2-3 years. That doesn’t mean we couldn’t instill useful basic arithmetic in lower grades. If we chose a smaller set of core basics, it could be quite practical to retain them over long summers and breaks—at least for the students who stay in our system for the long haul.
I’m also glad you brought up the fact that spaced repetition doesn’t have to involve software. I should have done more to remind readers of this. I weave the spacing and testing effects into the fabric of my course in many ways that have nothing to do with software.
Carefully engineered homework assignments are great if you have motivated students. Take-home SRS could even work for that. Those students are usually fine, though. It’s the apathetic middle I have to fight for, and they won’t do homework regardless of how I try to incentivize it.
Moreover, I don’t feel good about assigning to students who would hate to do it. School is already prison for those kids. I don’t want to send prison home with them. As both a child and a parent, I have been too familiar with the toxic effects homework—especially math homework—can have on family relationships. Let kids have a light at the end of the daily tunnel, I say.
Is homework vital to a successful math program? I don’t know. But I’m glad I don’t teach math.
Thank you for this great post. I would like to comment on a particular part:
“Besides, even in the technical classes, forgetting is the near-universal outcome, and the long-term benefits are mostly conceptual — for if you don’t use these skills continuously for the rest of your life, you’re almost certainly going to lose them. Maybe more than once.”
This seems strongly like throwing the baby out with the bathwater. At least for math, it is, as you say, very clear that skills build on top of each other, and that weak students struggle greatly because they lack the foundational skills. I used to tutor friends and used to be regularly shocked by how much they forgot: how to divide by fractions, summation with exponents, just basic stuff. So the following is pretty likely:
1)If you don’t understand old concepts in math, you will not understand many new concepts
2) many students forget old concepts
3)Spaced Repetition (not necessarily software!) ensures remembering
We should be making sure they remember this material not in 20 years, but in 2 years if and when we make them struggle through calculus (unless one has a realistic plan for how to let the majority of underachievers in math just drop out of advanced math classes). This gives mediocre students a fair chance of actually building deeper understanding of what is going on on a conceptual level, and underachieving students a chance to get acceptable grades so that they do not become dejected and apathetic.
For math, students get assigned homework anyway. I see no reason why that homework should not include an automatically generated exercise aimed to repeat an old concept. Of course, multiple-choice flashcards would be a failure mode.
I recall reading someone who applied spaced repetition principles to the math homework they assigned. Instead of doing the normal thing where each week would introduce new content and have homework on that content, the homework for each week was 1⁄3 that week’s content, 1⁄3 previous week’s content, 1⁄3 content from any of the previous weeks. Claimed that it significantly boosted people’s retention and exam scores.
Is this the post you’re thinking of ?
Looks like it, thanks! I’d have had no idea of how to re-find it.
I don’t see as much disagreement between us as you might be thinking. Precisely because I agree with your numbered points 1 and 2, I suggested it could be beneficial to compress most of our 12 years of math instruction down to a more intensive 2-3 years. That doesn’t mean we couldn’t instill useful basic arithmetic in lower grades. If we chose a smaller set of core basics, it could be quite practical to retain them over long summers and breaks—at least for the students who stay in our system for the long haul.
I’m also glad you brought up the fact that spaced repetition doesn’t have to involve software. I should have done more to remind readers of this. I weave the spacing and testing effects into the fabric of my course in many ways that have nothing to do with software.
Carefully engineered homework assignments are great if you have motivated students. Take-home SRS could even work for that. Those students are usually fine, though. It’s the apathetic middle I have to fight for, and they won’t do homework regardless of how I try to incentivize it.
Moreover, I don’t feel good about assigning to students who would hate to do it. School is already prison for those kids. I don’t want to send prison home with them. As both a child and a parent, I have been too familiar with the toxic effects homework—especially math homework—can have on family relationships. Let kids have a light at the end of the daily tunnel, I say.
Is homework vital to a successful math program? I don’t know. But I’m glad I don’t teach math.