I teach two different classes with a similar (if not identical) mix if students: college algebra and accelerated probability and statistics. I have been using problem solving in college algebra as a basis for our classroom discussions and I like the material I’ve chosen. However, it didn’t seem as though the college algebra students were developing those patient problem solving skills as much as I’d hoped. Most were working hard, but many of them were stopping when they hit a snag and then waiting for the “smart” kids to come up with the formula or equation.
The aha moment came when I gave a problem to my accelerated prob and stat students that was similar to that of the college algebra class: there were multiple entry points, many solving methods and a high ceiling. I noticed that as the problem progressed, more of the students in the stats class were still working on formulating a solution than would normally be doing the same in college algebra. The students in stats valued all of the methods as productive in some way, whereas in college algebra, many students reject ‘guess and check’ as it doesn’t seem like ‘real math’ to them. I realized why this was: they didn’t have a concrete formula they were searching for. They truly had to discover it on their own. Having accepted that there was no formula, they then trudged onward toward a solution that made sense. I made an assumption, that my college algebra students confirmed that in algebra, they have always been told that they need to set up an equation, find the right formula, or pick the right method. So when problems get hard, they know they can wait for the smart kid to figure out the formula and they can then apply it to a similar scenario next time. And advanced kids are very good at repeating a process, as long as it’s easy to figure out which specific process applies.
Don’t get me wrong, these are VERY smart, hard-working, awesome kids. I am just struggling with how to get them to, well, struggle, a little bit longer.