Relational or Instrumental? A Commentary on Skemp's Article

For our first MAED314A assignment, we were asked to write a short commentary on an article by Richard Skemp on instrumental and relational understanding of mathematics. As well, we were asked to choose 5 quotes from the article and comment on them.

Commentary:

In reading Skemp’s article, Relational Understanding and Instrumental Understanding, I was able to fully realize concepts that I had encountered in my own time of learning mathematics. Skemp makes note of two ways of understanding mathematics and says that both ways of understanding have merits. I’m inclined to agree with Skemp in so far as both types of understanding are necessary to be able to effectively teach mathematics. I feel that a compromise between the two schools of thought are necessary to cater to the minds of each learner in the classroom. I would like to say, however, that I would much rather prefer the relational way of understanding mathematics because I have always felt that, in the long run, it is simpler and more useful. Given that, instrumental learning and understanding of mathematics has its merits and I believe that Skemp has covered those merits quite well in his article. I agree that it is faster, simpler, and provides immediate satisfaction than its relational counterpart. As such, I am inclined not to simply dismiss this way of learning. The bottom line is that I agree with most of what Skemp has said in his article and that I, myself, have learned quite a bit through reading and digesting the ideas inside it.

Quotes:

“That he is a junior teacher in a school where all the other mathematics teaching is instrumental.” (11)

In some merits, Skemp is right. A junior teacher will find it difficult to apply a different teaching style in a school where the vast majority of teachers support a certain style. But my question is, why would it be difficult? Why can’t the junior teacher be a catalyst for change? There isn’t really a concrete reason why the junior teacher should teach a certain way. Unless maybe his or her job depended on it.

“From the marks he makes on paper, it is very hard to make valid inference about the mental processes by which a pupil has been led to make them”(12)

From the meagre amount of marking that I’ve done, I am inclined to agree. While it is easy to spot a mistake that a student can make and correct it, it isn’t always clear to see what the student was thinking while writing down the solution to a problem.

“So far my glowing tribute to mathematics has left out a vital point: the rejection of mathematics by so many, a rejection that in not a few cases turns to abject fright.”(12)

I hear this all the time from other students. “Math I hard. Math is scary.” Partly the reason I wanted to get into teaching was to help prevent this sort of mentality.

“At present most teachers have to learn from their own mistakes” (13)

I don’t yet know whether or not I should agree or disagree with this statement. I am inclined to disagree given the amount of support that a teacher has at his or her disposal. Besides, a teacher can learn from other teachers’ mistakes too.

5. “…nothing else but rational understanding can ever be adequate for a teacher.” (11)

I wholeheartedly agree with this statement. As discussed in the article, instrumental understanding is generally superficial and a teacher with superficial understanding of the given material, regardless of subject matter, cannot effectively teach.