After discussion with my classmates, I have come to realize that incorporating both fluency (instrumental understanding) and meaning-making (relational understanding) is important to a student's learning. Both understandings are valuable in different situations for different individuals.
For example, as discussed in Skemp's article, when considering the area of a field whose dimensions are 20 cms by 15 yards, it is important to be fluent (successfully multiplying 20 by 15) and to understand the meaning (converting the units to be compatible).
It is important to understand that, while having concepts and a relational understanding of a particular topic in math is critical, that information has little use if a student lacks the mechanical and instrumental ability to manipulate those concepts.
It's almost like relational understanding is analogous to nouns in grammatical structure, and instrumental understand is analogous to verbs. A sentence is trivial without the utilization of both.
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