Reflection on Skemp’s article “Relational Understanding and Instrumental Understanding”

       While I am reading the article, few times I stopped and reread. The first time, I stopped at the mismatching “football” between two teams. This example recalled my experience on the term before and after immigrant to Canada. The second time, I stopped when the pupil responds “because area is always in square centimetres”. This example reminds me of my students when they were not fully understanding the meaning of units and area. They just instrumentally copy the examples in class without identifying the different meaning. The third time, I stopped after Skemp discussed the ground of instrumental teaching, because I believe there should be more reasons than he listed, such as the limited pupil’s foundation skill and knowledge level. I also stopped a few more times for the rest article, his opinion raised my interesting and encouraged me to relate with my experience.

       Overall, I agree with him on the part of the discussion about advantages on both sides. Relational mathematics is the desired way to teach students; however, the reality of educational environment might limit the teacher’s choice. As secondary math teachers, there should be various level students in our classroom. The most capable students can easily get the relational expression within the limited class time and move forward. The average student might struggle on it and can only make minimal amount of connection with the relational understanding. Some students might have limited foundation knowledge which brought from their elementary education and tries to avoid to learning math. For the weakest student, if they could understand and support with the easier instrumental understanding, they can cumulatively build up their confidence, and motivation to work more on math. Based on student centre education, I would like to stand on that, no one method can math all student’s needs. Math teacher has to be more adoptive on choosing the right way to facilitate student’s learning.