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Instrumental vs. Relational Understanding

When I was reading Skemp’s lengthy article, the first thing that triggered my thoughts  and got me stopped for awhile was the fact that I had never thought about understating math distinctively, and by reading the article, I realized that I did learn a lot about relational and instrumental understanding / mathematics and the difference between them, the two terms which were completely came  new to me at the beginning of the article. Soon I realized that; yes, there are in fact two different approaches to the teaching/learning mathematics. Although, I did not know much about the two understating before reading the article, the second thing that stopped me right away , and it even turned out to be a bit disturbing for me at first ,was remembering about my childhood mathematics studies! Having grown in Iran; the place that Math has been considered as the most important subjects of all, we were getting the mathematical lessons in more rational ways rather than the other! We were struggling with proving a lot of formulas before memorizing them, were being forced to know all the proof without taking a cheat sheet to the exam, and being punished for not knowing the proofs of the formulas! And that all was happening as early as  the  middle years of our schools. In addition to all, what stopped me again, were  all those pressures necessary in learning mathematics.Did I as a little middle schooler really need to know what was the mathematical concept behind an area of a circle? Did I really use that anywhere in my   life? or Did  I even really remember all the proofs up to today?...but then I also thought, some of my knowledge and understating are back to those days, and that what if those pressures were actually necessary and required?
Even-though, after reading the article I started questioning myself about my previous learning methods , I believe that having both rational and instrumental mathematics combined to teach to our students will not only  be necessary but  also be very beneficial to them. As a future math teacher, I would be combining these two understandings  in my classes to find out about the students’ learning abilities. To see who will be classified as relational learners who might be perusing their love to Math  whereas the instrumentally ones, who might never use math in their lives ever again.

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