The idea of teaching instrumental vs relational mathematics made me rethink how I was taught when I was in high school. I feel that I was taught instrumentally and for that reason I knew the algorithms behind the mathematics but not why those algorithms worked. I think it is important to teach relationally so we can help develop our students critical thinking skills and help them overcome the idea that mathematics is the act of memorizing algorithms and repeating them on assessments. I also thought the idea of teachers teaching beyond the simple “here is an example, now practice” was interesting, to tackle teaching instrumentally we must take an inquiry-based approach in the classroom. Students learn best by doing and figuring out things for themselves, if we as teachers fall into the routine of just showing students how to do the problems, they will never grow their critical thinking skills. Another point in the article that made me stop was student’s response of “because area is always in square centimeters,” (Skemp, 1978) I too remember stumbling on that thought when I was in school because the concept of area was never truly explained to me. Helping students understand where concepts come from is crucial to their learning.
I agree with the
issue Skemp raises because it is important to help students understand why
mathematics works. Even though the students may not understand in the moment
why we are talking about concepts not necessarily related to the topic at hand,
they will understand in the future when they understand why mathematical
concepts work. I speak from experience when I say, learning instrumentally hindered
my ability to understand mathematical concepts at the university level. How can
we expect a student to write a proof in their real analysis class when they don’t
even understand why differentiation works? I think we need to implement relational
learning in every mathematics classroom starting from a young age, the younger we
start truly explaining concepts to our students, the greater their understanding
will be overall!
Works Cited
Skemp, R. R. (1978). Relational Understanding and
Instrumental Understanding.
Hello Nandini, I appreciate the question you raised about mathematical proofs. It can indeed be challenging for students to write proofs in a real analysis class when they don't fully grasp differentiation. Educators can employ strategies and approaches to support their learning and bridge these gaps in understanding. I'm curious about the strategies you might implement to facilitate learning in such situations?
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