The article Relational Understanding and Instrumental Understanding brought forth many new ideas about the way I was previously taught and the way I may have taught math. I recall in high school frequently being told to just use what I was given and not try to understand why things worked in class, so as not to become confused. After reading this article I have begun to re-evaluate the way I may want to teach a math class and to give more thought to instrumental and relational understanding. I have chosen some quotes from his article that I found particularly interesting or insightful to discuss.
The first quotation “Instrumental understanding I would until recently not have regarded as understanding at all” (Skemp 2), I found surprising that someone would completely admonish one form of teaching over the other. While I have begun to think relational understanding may have more importance I believe that the two of them can be used together to teach effectively.
The next quotation I chose was, “there are two kinds of mathematical mis-matches which can occur. 1. Pupils whose goal is to understand instrumentally, taught by a teacher who wants them to understand relationally. 2. The other way about” (Skemp 4). These mis-matches made me think that, as teachers, we need to remember that every child learns differently. In order to effectively reach most of our students we should perhaps focus on using both types of understanding, instead of choosing one over the other, to try to avoid theses mis-matches.
The third quotation says, “I now believe there are two effectively different subjects being taught under the same name, ‘mathematics’” (Skemp 6). I found this quote hard to agree with, maybe because I am not as familiar or have not had as much time to think about the two types of understanding. It is an interesting idea, but as of now I am leaning towards seeing them as different teaching styles that we must learn to use and not actual subjects.
I found the next quote “Relational Knowledge can be effective as a goal in itself” (Skemp 10), and its subsequent explanation to be an exciting prospect. If this form of understanding can be self-motivating to the student, math can become more enjoyable to them and we as teachers can be more successful in our jobs. I would be interested in seeing how motivational or exactly what effects relational knowledge can have on a student or classroom.
The last quote I have chosen is “learning relational mathematics…can produce an unlimited number of plans for getting from any starting point within his schema to any finishing point” (Skemp 14). I felt these words to be inspiring. As a future teacher, by using relational understanding, I could provide my students with the tools to rely less on me and allow them to have a more in depth knowledge of what they are learning. I find it very interesting that this one type of understanding has the possibility to provide a student with an actual in depth understanding of their subject instead of memorization of formulas.
I thoroughly enjoyed this article and how it made me evaluate the way I have taught mathematics and how I can improve on them in the future. I will definitely try to incorporate both of the methods of understanding into my practice and learn more about relational understanding, which I am less familiar with.
References
1. Skemp, R.R.. “Relational Understanding and Instrumental Understanding.”First published in Mathematics Teaching 77 (1976) : 20-26
No comments:
Post a Comment