Relational and Instrumental Understanding

     I agree with the overall point of view Richard Skemp presents in his article regarding how there exists two types of understanding, relational and instrumental, and that the relational approach is the better of the two; however, I don’t share Skemp’s opinion that instrumental understanding isn’t really understanding at all but rather “rules without reasons.”  Though the relational approach provides a more complete “schema” of mathematical understanding for students, for many people the instrumental approach is the first step towards this relational understanding as this approach allows for an easier introduction of new math material than the relational method.

    I also think Skemp’s article downplays the effectiveness that the instrumental approach has towards helping students learn and understand mathematics.  For most people, learning math only occurs when they actually do math, ie, solve math problems.  In order to do this, there are at times certain rules that must be learnt first but once these rules are learnt, the theory behind where these rules come from, how they’re derived and why they work becomes much easier to understand.  It would be much more difficult for one to try to understand these explanations without having already learnt such rules.