How Do You Increase a Student’s Ability to Make Mental Leaps?
Want to get notified about new posts? Join the mailing list.
Perhaps counterintuitively, it’s not by actually increasing their mental “jumping” ability. Instead, it’s by helping them build knowledge “bridges” that reduce the distance to jump.
There’s a mountain of empirical evidence that you can increase the number of examples & problem-solving experiences in a student’s knowledge base, but a lack of evidence that you can increase the student’s ability to generalize from those examples (by doing things other than equipping them with progressively more advanced examples & problem-solving experiences).
As described by Sweller, Clark, & Kirschner (2010):
- "In short, the research suggests that we can teach aspiring mathematicians to be effective problem solvers only by providing them with a large store of domain-specific schemas. Mathematical problem-solving skill is acquired through a large number of specific mathematical problem-solving strategies relevant to particular problems. There are no separate, general problem-solving strategies that can be learned."
- -- Sweller, Clark, & Kirschner (2010) in Teaching General Problem-Solving Skills Is Not a Substitute for, or a Viable Addition to, Teaching Mathematics
Now, to be clear, this does NOT imply that students learn/generalize at the same rate.
Different students have different levels of generalization ability; you can give a group of students with similar background knowledge the same problem-solving experiences and some students will walk away with a more general understanding than other students.
It’s just that you can’t really train the implicit generalization ability so much as explicitly equip students with a larger underlying knowledge base.
Want to get notified about new posts? Join the mailing list.