Skemp's article reflection

Relational Understanding and Instrumental Understanding

A reflection on Skemp's article

The first thing the author wrote that struck me was his differentiating the two ways in which students learn mathematics.  He maintained that there is an essential difference between the relational and instrumental approaches to mathematics.   I concede that these are definitely two different approaches to the way we study mathematics, but I never considered them separate entities altogether.  The author was successful, I think, in demonstrating that the instrumental approach to mathematics can be very limiting, and that it really should not even be called “mathematics” in the same way as is understood when we talk about relational mathematics.  The second thing that struck me was the author’s summary of the pros and cons of both approaches.  First, he talks about how “relational” mathematics is superior to “instrumental” mathematics.  However, there are some serious limitations in teaching mathematics relationally.  For example, this way of teaching might take a lot longer, and therefore might be impractical.  It made me wonder, where do we draw the line in terms of how much time should be sacrificed just so that we can teach in this way?  Finally, what struck me was the way in which the author radically separated the teaching of instrumental mathematics from the teaching of relational mathematics.  He seems to have a very black and white view.  I think that we have to consider these things more as a spectrum – our teaching will involve both instrumental and relational approaches.  We cannot teach everything intuitively, nor can we teach students only as though they were robots.  I think what the author failed to do was to see the gray area in which we can get the benefits from both ways of teaching math.