Discussion Reflection - instrumental + relational learning

At the end of today's class, we had the opportunity to enter into a small group discussion on Skemp's argument about instrumental and relational learning. 

1. Are the two kinds of learning distinct or separable?

    We defined them as two essential parts of the learning process that target and engage different parts of the brain. Of course, always facilitating a "plug and chug" mentality is contrary to the goal of math teachers (to develop a mathematical understanding or fluency); however, giving rules for simple ideas can be time-saving when necessary, and can also be a good way to mediate content for lower levels.

2. Is there a best order?

    We determined this to be a matter of preference, both for the students and the teacher, so a varied approach may be desirable. It might be an interesting "aha!" moment to determine the origin of a formula or topic after completing a unit, and contrarily, it's also exciting to feel as though you came to a foundational math concept on your own and get to use it right away.

3. What kind of activities promote the two types?

    Insofar as instrumental activities, these are the sort of math drills that I experienced in elementary school, where you had 1-minute to complete as many multiplication questions as possible and other related activities. Today's class where we engaged in class discussion would be an example of relational learning. Having students derive a formula before they use it (as mentioned above) and integrating models, visual representations, and real-life examples would be further methods.

4. How to assess understanding

    One thing our group had learned in another curriculum course was to evaluate often in a low-stakes environment, which would ease test anxiety and give regular check-ins on student progress. I also appreciate the "curveball" method where maybe a typical example from class is put on the test, but with an extra layer to consider. This method ensures that students aren't just mimicking class examples, but have a strong enough mathematical foundation to generalize theories and apply them to new scenarios. Another way to determine deeper relational understanding would be to have the students teach a concept to the class and answer their peers' questions.