Relational & Instrumental Understanding

    When Skemp defined the two different kinds of understanding, there was an instant connection in my mind to how I've approached mathematics over the years.  When I'm learning, I quickly gain instrumental understanding, but in order to feel good about the subject I need to reach relational understanding.  I find that one of the best ways to do this is to try to explain it to someone else- thus my tutoring over the years has pushed my relational understanding.  Skemp's descriptions of potential mismatches between students and teachers also caught my eye- although in high school, all my teachers looked for was instrumental understanding, university finals caught me off guard with questions that pushed beyond exactly what we had been taught and it forced me into relational understanding if I wanted to succeed.  One last thing that arose for me during reading was about the BC curriculum.  Although I don't know too much about it yet, I believe that a teacher I worked with last semester mentioned that they had switched from having content expectations to having "curricular competencies" where they are able to do all sorts of things like explaining and reasoning as opposed to knowing specific content.  However, she also mentioned that this made it a bit of a struggle, since the content is so closely tied to the competencies.

    Overall, I agree with Skemp that relational understanding serves us better.  Understanding the material instead of simply regurgitating rules not only helps making connections within math class, but also might help students think about math out in their own lives and to be able to apply lessons they've learned.  Many students don't continue in math past high school, but it can still help them adapt to whatever is happening in their lives.  While a certain level of instrumental understanding makes math speedy, relational understanding gives a much more complete picture.