38 votes
Accepted

Students confusing "object types" in introductory proofs class

I personally use terms like "type disagreement" and "type error". This agrees with the notion of types within computer science (https://en.wikipedia.org/wiki/Type_system). When I ...
  • 3,463
26 votes

Is patching up a student's poor solution better than providing a good solution?

As Besicovich once said, the reputation of a mathematician is determined by the number of their badly written papers (the pioneering work is often clumsy and follows the route far from the shortest ...
  • 1,269
14 votes

Is patching up a student's poor solution better than providing a good solution?

A lot of studies in math education have found that mathematical confidence is an important mediator of success - that is, students who aren't confident in their ability to do math are less likely to ...
9 votes

Is patching up a student's poor solution better than providing a good solution?

I've had foreign language teachers distinguish between learning a grammatical form either "for production" or "for recognition". The former means the student can produce a sentence ...
5 votes

Students confusing "object types" in introductory proofs class

For me, I use "type error" or "typing error". I would avoid "type disagreement" because it suggests that you actually have types that disagree. But that's not correct; ...
  • 2,388
5 votes

Is patching up a student's poor solution better than providing a good solution?

One problem with mathematics for many students is that is perceived as something complete that one learns, rather than an activity one does. On one hand, you do want to present nice and elegant ...
  • 5,064
2 votes

Is patching up a student's poor solution better than providing a good solution?

There is usually more than one solution to every problem - so, if student took a less efficient way of doing it, they would benefit from both: knowing how to get through using this method and how to ...
2 votes

Is patching up a student's poor solution better than providing a good solution?

It's a judgment call, but I think you are probably right, especially with very bad solutions. I agree that it's important for people to try first (even if bad). Makes them learn more than seeing the ...
2 votes

Students confusing "object types" in introductory proofs class

I don't think the three examples are instances of the same error. 1. In a proof that a function f:A↦B is onto, a student will say "Let x∈f" instead of "Let x∈B" Whatever ...
2 votes

Students confusing "object types" in introductory proofs class

These are examples of metonymy. "Let x∈f" instead of "Let x∈B"." This is totum pro parte synedoche. And aspect of the function (the range) is being confused with the function ...

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