Skemp : Mathematical Understanding

            As a future teacher, I totally agree with the issue Skemp has raised in this article about the instrumental understanding and relational understanding. There are three things that make me think about this, the role of Devil's Advocate, Theoretical formulation, and situational factors. 

First of all, the Devil's Advocate mentions three advantages of instrumental mathematical understanding. As a teacher, I am not going to deny the benefits of the advantages. In fact, the most of students and teachers both give priority to instant outcomes rather than the deep understanding of the math because of situational factors such as the there are limited questions going to be asked in examinations, over-burdened syllabi, and difficulty of assessment. As a result, students learn math for the short term. They do not think beyond it. They would give up the subject at some points due to instrumental understanding.

However, the four advantages of relational understanding are far more beneficial than instrumental understanding because of the theoretical formulation. I am thinking about how to encourage students and teachers both to give importance to learning relational mathematics rather than to stick with the fixed plan to learn mathematics. I believe that learning relational mathematics provides more flexibility with effective outcomes throughout students' school life. In other words, students can learn how to apply these concepts during learning math if they understand the foundation of math. They would like to pursue learning math with enthusiasm due to relational understanding.