Entrance Slip #1: Richard Skemp's Article

Image source: http://www.davidtall.com/skemp/

In reading Richard R. Skemp’s article “Relational Understanding and Instrumental Understanding,” I’m not sure I am clear on the changed view on viewing relational and instrumental math as two separate subjects. From what I understand, using his music analogy, instrumental is like music theory, and relational is like playing music - they are connected but both have their individual value. If that is the case, I don’t agree that both are separate. In my view, closer to Skemp’s original view, I believe relational mathematics is a deeper and fuller understanding of math, while instrumental is more surface level. However, I also believe instrumental math is the first step into the world of mathematics for many people and should not be discounted as useful. I agree with Skemp’s observations on pages 11 and 12 about why instrumental math is often the focus in classrooms. In addition to these, I think gaps in learning are another thing that prevent many teachers from diving into a deeper understanding of mathematical concepts with their students. For example, if a high school teacher is trying to derive a formula but there are many students in their classroom who struggle with basic multiplication, division etc., it may confuse the students more than it aids them. Having a set of rules to memorize would make solving problems in class accessible, which feeds back into Skemp’s comment on page 8 that students can build their self-confidence.


Another thing that stood out to me in this article was the map analogy. I thought it was very clever! To take it a step further, knowing a town has the same layers as instrumental and relational math do in my point of view. Instrumental math would be the same as walking the streets, knowing where the essential stores are, and it’s enough to get by. However, relational math would be getting to know the people, history, economy, culture, and community that lives in that town on top of knowing the streets. While all these extra things are not essential to get by in town, they enrich the experience and provide a reason to have interest in or love the place. In my teaching, I definitely want to derive concepts so students have some history or culture to connect with. Understanding that there are road blocks, such as the ones Skemp has mentioned in his article, preventing full relational learning in the ideal way, I would strive to pick and choose the ones I felt were most useful to the students. In other words, regardless of if relational or instrumental math are two separate things or not, I think a classroom can only be taught either fully instrumental or with a mixture of instrumental and relational. I believe a mixture of instrumental and relational is a better approach because chances that more students may resonate with math are increased when different perspectives are introduced. In the analogy, this would be that it may be impossible to learn all facets of people, history, economy, culture, and community, but learning any combination of those could potentially strike a chord with students who believe learning maps for a town they don’t care about is useless.