Last summer, I took an online Stanford OpenEdX course taught by Jo Boaler, a professor of mathematics education at Stanford University, entitled How to Learn Math: For Teachers and Parents. I found it an incredibly valuable experience, and interested parents and educators might wish to avail themselves of this great resource while it is being offered again this summer.
While the course covered some pedagogical strategies that were more geared towards educators (e.g. "important factors in the teaching of algebra"), there was plenty of material valuable for parents. One of the major themes of the class was about developing a family or classroom culture of an open (anyone can learn mathit just takes perseverance) vs. closed (you are either born with a good "math mind" or not) mindset. I realized that I was subtly contributing to a closed mindset by doing innocent things like telling my daughter to go see her dad about a question on her math homework, stating: "he's the math guy" (and therefore also feeding the stereotype that women aren't as good at math as men).
A couple of other key takeaways for me that the course dives into:
The importance of making mistakes to brain development. Kids are under a lot of pressure to perform and get perfect grades. The course describes the research behind the benefit of brain connections made through the processing and correcting of mistakes, yet students are afraid to make them. Based on what I learned in the course, now when we review my kids' returned work with mistakes, I try to really emphasize that it's an opportunity to build more brain connections and to really cement in the knowledge through the process of re-working the problem.
Embracing mistakes as part of encouraging risk taking. If parental or teacher praise is on the performance ("you are so smart!") versus the processes ("you really worked hard through the problem and stuck with it!"), students can become timid about risk taking least they lose the "smart" label. (This is also a theme of Carol Dweck's book, Mindset, that Boaler incorporates into the course.) If we aren't seeing some mistakes, the work may be too easy and the students are being cheated of learning opportunities.
When students work together, they succeed. Boaler cites research that suggests that when students work together as part of a study group, they have much more positive outcomes. When looking at why that helps, the research suggests that the process of reasoning out loud and needing to describe to others why an answer makes sense helps solidify the concept. In college, my husband had a group of buddies who met at the library for a study group for all of their math and business classes, and I'd occasionally join their table. Somewhere between the juvenile jokes at each other's expense, they did just what the research described; they had to analyze each other's approaches to the problem and justify their own. In the end, they each mastered the material and all of them were highly successful students. It is hard to replicate this type of group study opportunity outside of school with busy schedules, but I encourage my kids to call and talk through homework problems with their friends.
If the $125 cost of the course is a bit too steep, some of the key learnings I found most valuable can also be found in Jo Boaler's book What's Math Got To Do With It? that is available at the Menlo Park library.