Group discussion on Skemp Article

 Following is what my group talked about in relation to the guiding questions on the Skemp article:

1. Are the two kinds of understandings distinct/separable?

In response to this question, we almost instantly and unanimously decided that yes the two kinds of understandings are indeed different. Instrumental and Relational understandings target different parts of students' brains. Instrumental's focus is on memorization, whereas relational encourages students to explore and come to their own conclusions. 

2. Is there a "best" order to teach them?

We thought that there is no right order to get a student to master a topic. This is a very case by case situation. It depends on the student's learning methods and interest in the subject matter. In a classroom, it would depend on the unit being covered. Sometimes, it is a good idea to provide the formula to get the ball rolling and then make relational connections at the end and witness students' surprise!

3. What kind of activities promote one or the other?

Instrumental understanding is mostly promoted my institutions such as Kumon where the priority is given to filling the pages. I once worked at a reward based math learning centre where students would get rewards for every five pages completed. Activities like this promote instrumental understanding. Relational understanding, on the other hand, is promoted by class group activities where students are required to research, class discussions, the teacher explaining the deeper connections of the material, and of course, real life examples.

4. How to assess understanding?

My group came up with some really cool ideas to assess understanding like - having a low stakes quiz, throwing them a curveball or asking trick questions and adding layers to the questions but the one that I brought up and relate to the most is having the students teach part of the lecture. I say this because my grandpa once said to me that "If you want to make sure to fully understand something, teach it to me." This is a practice that I utilized throughout my life and it has always worked for me (and everyone I recommend this to!)