MAED 314A: Relational Understanding and Instrumental Understanding Reflection

MAED 314A: Relational Understanding and Instrumental Understanding Reflection
During the class, we have had a brief discussion about the relational and instrumental understanding in Mathematics. We have talked about the pros and cons to the two ways in teaching Mathematics. When I have started reading the article, “Relational Understanding and Instrumental Understanding”, I notice that Skemp is a firm believer in relational understanding. Reflecting back to the days I have started learning Mathematics, instrumental understanding has definitely helped me in learning at first.
By the end when I have read the whole article, I appreciate Skemp’s effort in presenting these two types of understanding by giving really good analogy. It makes me think deeply why instrumental understanding has been so effective for me. I realize that relational understanding is also part of the reason. For me, the instrumental methods are effective in learning the basic foundation; the relational methods allow for strong problem-solving skills. Therefore, I believe both methods are essential in Mathematics education.
5 Favorite quotes/statements from the article
1) Page 2. “You may think you understand, but you don’t really.” Skemp has made me ponder the meaning of ‘understand’. Is it ‘understand’ if a student can do a set of similar problems correct; but not a set of slightly modified problems?

2) Page 8, Number 2 in Devil’s Advocate. The point about students who described themselves as “thickos”; they need good marks to build up confidence. This speaks to me because I have experienced this all through high school and in university. Instrumental methods are definitely effective for achieving the desired good performance on tests.

3) Page 13. “At present most teachers have to learn from their own mistakes”. This is one of the advices that I appreciate. As a new teacher, lesson plans do not usually go well as planned. But we can definitely learn from our mistakes and try to improve it. The idea to gather all the teaching experience/knowledge for use by new teachers is great but it will not be that applicable if the actual experience is missing.

4) Page 14. “A person with a set of fixed plans can find his way from a certain set of starting points to a certain set of goals”.” Skemp’s analogy of getting to places strongly presents the importance of relational understanding. Everyone needs to be able to think critically. If we were so inflexible to change, then the world would be problematic.

5) Page 15. “The more complete a pupil’s schema, the greater his feeling of confidence in his own ability to find new ways of ‘getting there’ without outside help.” What a teacher can teach is limited; the students need to work hard themselves to achieve their own success. As a teacher, we can only present them the tools they need.