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 questions
5. Give worksheets or problem sets that are from different sections to avoid compartmentalizing.
This summer has been a lot of work! Grad school is not a few hours a day of classes and then regular summer days. Classes take a long time, and we do A LOT every day. Then we usually have a few hours of homework every day. When we have take-home tests, we spend probably anywhere from 8-20 hours depending on the class and questions to finish it. It is a lot different than I expected, but I am loving getting to figure out and do hard math again! I'm so glad I'm doing it! I can definitely say that after 4 weeks of Grad school Calculus, I feel much more prepared to be able to teach Calculus or help students with Calculus.
On a side note, we're all a little annoyed that our Calculus Book is just called "Calculus 4th Edition." We think it should be called something like, "Hard Calculus." There was a whole chapter in our book titled, "Three Hard Proofs"...
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