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I’ve heard a lot of the following kind of comment when I discuss curricular issues with people, whether in real life or in the blogosphere: “Sure, we’d love to teach [insert math topic here] to these kids, but they’re just not ready for that.” It came up in the comments on this post about putting geometry before algebra I in the K-12 curriculum (“Students aren’t ready to do abstract reasoning when they’re in the 7th grade”), and it’s come up in discussions I’ve had with colleagues about our freshman math offerings (we were discussing putting some treatment of Polya’s problem-solving heuristic in Calculus and giving students more difficult problems to solve, and the objection was that freshmen “just aren’t ready” for that).
I’m aware that there are psychological theories that establish how children attain different cognitive levels at different times of their lives, so there could be some basis for this idea. But a lot of the time when the “they’re not ready” argument comes up when talking about teaching, it’s just sounds like low expectations and a desire to rationalize the student-faculty non-agression pact. What do you think? Is “they’re not ready” is a valid curricular design principle or just a cop-out?
Update: Alright, so the last question above is loaded. Let’s try it a little more fairly: When is the “they’re not ready” approach valid, and when is this just a cop-out? For example, obviously students who haven’t had algebra I aren’t ready to learn algebra II. But if someone says, for example, that freshmen aren’t ready for proofs, is that psychology talking or is it just low expectations? I’ve heard that last example in the form of “freshmen aren’t emotionally ready” to handle lots of difficult problems, and I strongly suspect that that’s not based on sound cognitive psychology. But I could be wrong.