My thoughts on Richard Skemp's article on Instrumental and Relational Ways of Understanding Mathematics

The article written by Richard Skemp discusses Instrumental and Relational Mathematics, specifically how their differences can affect students' learning.

I was struck immediately when I read the part where only both Instrumental and Relational understanding were both considered 'Understanding' in the eyes of the learners. My experience in mathematical education can be traced from the east coast of the Eurasia to the west coast of America. The Shanghai math curriculum I studied from Grade 1 to Grade 7 offered a heavy instrumental methodology for any young student to be proficient in finding the correct answers during problem solving. Fortunately, some passionate and experienced teachers were able to bake in common theorems which can then be used in other topics (what we called use 1 example to produce 3 more 举一反三). When I began my Grade 8 education in BC, I was very complacent with the difficulty level. I thought I have full understanding by knowing every way and trick needed to achieve a perfect grade. However, when advancing through math courses, the allotted time allowed me to really think about the 'why' in the tricks I have learned by back in Shanghai. Spending my time re-learning these topics gave me a fresh perspective on the foundation theorems used which spiked my further interest in pursing a math related degree in UBC.  In a way, I was discovering the relational understanding of secondary math on my own.

I completely agree with Skemp's view on the critical role of relational understanding in our mathematics education. The issue of standardized grading, which produces students and teachers' urges in achieving correct answer through any means possible, is a difficult one to tackle, however, it instills fear and pressure into students than the good it does for our education system. In my tutoring / teaching in the past, I do emphasize the importances of deriving the underlying theorems with the students. This methodology has proven to effective for students to tackle any new problems involving the same theorem.