Our group discussion initially centered on relational and instrumental understandings being distinct, but group consensus definitely shifted toward the idea of a continuum, where students may move fluidly between relational and instrumental understanding depending on the concept or personal learning needs. I think this flexible view acknowledges the complexity of learning and could allow teachers to meet students where they are, helping them progress in a way that best supports their success.
We also considered whether it’s necessary for students to first develop instrumental understanding before moving toward a deeper, relational understanding. While many agreed that instrumental understanding could serve as a foundation (as it has for me), I recognized that this belief might stem from personal bias. Ultimately, I think I’ve concluded that rather than adhering to a strict progression, it's more beneficial to think of understanding as a continuum. This approach would seemingly allow a teacher to adapt their instruction to each student’s needs, encouraging both instrumental and relational understanding where appropriate.
I left the group discussion early before covering topics 3 and 4. However, I think that an instrumental approach might be helpful in teaching concepts where there is a single correct answer, such as multiplication tables or basic FOILing. These concepts can be assessed by evaluating a single answer or confirming that a specific rule was applied. Whereas, a relational approach might be more suited to having a student move from a concept to a concrete deliverable. Something like codifying logic inside a FOR loop in a programming class.
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