Assignment #2

In Skemp's article, he discusses the pros and cons of two types of mathematical learning; relational understanding, or the understanding of why something works and it's application, and instrumental understanding, or the understanding how to solve a problem. He says that both are valid means of teaching children math, but that the advantages of relational understanding are greater than those of the instrumental approach. The first of the four advantages of relational understanding is the fact that it can be applied to a broader range of problems. The importance of this fact is seen when looking at a disadvantage of instrumental understanding; that of if the problem is slightly different than the norm, the student will get it wrong because they only know how to solve things a certain way. The next advantage mentioned is that it is easier remember things taught relationally as opposed to instrumentally. This may seem contradictory because of the fact that with instrumental learning all you need to do is memorize a formula, but you have to memorize a formula for EVERYTHING instead of just learning how we obtain the formulas in a certain field of math and applying it. Moving on to the third advantage of relational understanding, and that is the fact that this form of learning can be a goal in and of itself; i.e. the reward of figuring out why a certain way of solving works is satisfying to the solvee. This point also leads us to one of the disadvantages of relational understanding, that of the time it takes to achieve the necessary understanding to apply said way of solving. The final advantage of relational understanding talked about is the fact that the satisfaction of discovery will lead others to more discoveries on their own. Now, the advantages of instrumental understanding such as simplicity of understanding and the immediate satisfaction of solving a problem are good, but when held up to those of relational understanding it is clear that relational understanding is the better way of learning.