Our group consists of Raymond (me), Jacob, Krystal, Mark, Andy, and Jasmine. Below are snippets of our discussion.
1) Are the two kinds of understanding distinct / separable?
For question 1, all of us agreed that the 2 understandings are distinct and separable. We all came up with examples on the differences.
2) Is there a ‘best’ order to teach them?
For question 2, we went back and forth on whether if relational or instrumental should be first. Our conclusion is that the order can vary depending on the topic or level of the student.
3) What kinds of activities promote each one?
For question 3, we came with examples like teacher giving 50 to 100 arithmetic questions for students to practice the mechanism of subtraction. This type of activity promotes instrumental understanding. Another example is using language to articulate the thought process of problem solving. While difficult for some student, this would promote relational understanding.
4) How to assess understanding?
For question 4, we agreed that assessment of instrumental understanding requires students to solve problems in similar formats to the ones used in class and exercise. Vice versa, assessment of relational understanding should ask students to solve questions which are thought provoking and out-of-norm compared to the typical classroom exercises.
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