Response to Skemp Article

One thing I found interesting while reading was the part where Skemp discusses, instrumental understanding and how sometimes it is described as “rules without reason”. This particular part of the article reminded me of when I first started working at a tutoring company. I was explaining multi-digit multiplication to a student. I first showed the student an example of one question where I went over all steps and one of the steps was to place a zero under the one’s place. My employer had overheard this and asked the student do you know why the zero goes there and the student had said no. I then realized my mistake that I shouldn’t have just given the student the steps on how to answer these questions. Instead, I should explain the reasoning and why things were done the way they were to help the student have a clear understanding of the concept. Another thing that made me “stop” while reading this piece was the part about the area of the field where two different units were used and students answered the question without really understanding it. I found it interesting that the article mentioned this because this also reminded me of my experience while tutoring. A lot of times students would look at similar questions and instead of reading what the question was asking, they would be quick to use the same method to solve all questions resulting in getting a few of the questions wrong. Another thing that made me “stop” while reading this piece was when Skemp uses the example of having fixed routes to get around town versus creating a cognitive map of the town. I found this interesting because it was a  simple and unique way to demonstrate instrumental and relational understanding. I agree with the article on how by creating this mind map of the town, one is able to form these different connections and paths that they wouldn’t be able to if they only had a fixed route. 

I think Skemp raises many good points on learning for both instrumental mathematics and relational mathematics. I think relational mathematics is beneficial to use in a classroom because it allows to students to form connections and it allows for long-term learning. I think once relational understanding is established students will remember it for longer and may perhaps use this knowledge to build on other things they’re taught. I also think that instrumental mathematics has a place in the classroom as well. At times when first introducing a topic, it can be easier to explain the concept without providing the why behind it. The article mentioned that relational understanding in math may take longer. I think that perhaps at times there may not be enough time to focus on the relational understanding. This is where instrumental understanding comes along as it is easier to use during a short amount of time. I think that both relational and instrumental understanding should be used in a class. This is because at times it may be beneficial to use relational mathematics and for other topics, instrumental mathematics may be more beneficial.