Educational research is all over the place. There are a lot of books about teaching math, but they sometimes contradict each other. One book says it is better to use calculators to allow students to work with fractions if they don't really remember how to work with them themselves. Two days later, I read a book that talks about how hugely important it is that students are comfortable working with fractions because it prepares them for all sorts of important things in future math classes. I read an article over the weekend about problem solving in Calculus. It had some really good ideas about things teachers can do to help students get better at problem solving. A few of the ideas were: 1. Have students peer review 2. Assign multi-day problems so students don't think that problems should all be doable in 5 minutes 3. Ban pronouns! This will help students be more specific in their explanations and justifications 4. Have students come up with some of their own question