The “you have to be taught how” belief is the belief that you can’t do anything mathematical until someone shows you how. When I think about this belief, I wonder if it were true, how math would even exist to the extent it does today? Clearly, the mathematicians who have established the mathematics we teach our students, weren’t held back by this belief. That being said, I know that not every student that steps into my classroom will be a mathematician. Maybe none of them ever will, and that’s okay. I’m not in the business of generating math Phd’s, but rather, I hope my students can think critically and not be afraid to approach problems they might not yet understand. And, if students feel that they need to be taught how to do something before trying it, we have a big problem.
The “five minute” belief is believing that if you can’t figure out a problem in five minutes or less, you won’t be able to figure it out. I think it’s safe to say, that many people give it much less than five minutes. There are times where I wish students would just try it for five minutes. How often have students tried a problem and gave up after only a moment because it has become challenging? I see this belief every day I teach. […]