What struck me when reading Richard Skemp’s Relational Understanding and Instrumental Understanding was how easily I could relate to the two meanings of understanding. From my experience helping others in math, I found that a big difficulty for many was recalling what they had learned in previous grades or courses. It appears that they do not have the relational understanding explored in the article but only once had some instrumental understanding that has since disappeared. It is clear to me that their background of instrumental mathematics has led them to approach pretty much all mathematics problems with a similar way of thinking however, at higher levels of math, this becomes very difficult as to apply these new rules, they must remember some old rules which have fallen out of their memory. I feel like math to them seems like nothing more than memorizing a bunch of formulas and rules and to break this way of thinking is not an easy task. I’ve also felt at times a need to go back and help them relationally understand the basics but this proves to be a very, very time consuming task and I find it quite understandable why many who “miss a step” have trouble catching up. I think it is a very important task to have students understand relationally as much as possible starting from beginning because from my experience, memorizing is terribly unstimulating while having a true relational understanding can be fun and lead to further exploration.
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