Response to the Richard Skemp article

Instrumental Understanding vs. Relational Understanding

It is my experience as a tutor, that most students prefer instrumental understanding versus relational understanding and most math teachers are in favor of the former. Instead of trying to solve a given problem, students with instrumental understanding are focused on getting the solution right, rather than using logical reasoning. I have seen students do the calculations of the values of a function perfectly but getting stuck at graphing the function because they don't see the biger picture. Many of these students have an amazing speed and accuracy at computation but are lacking in understanding even the basic principles of Mathematics. This ability at computation gives them an advantage over students who use relational understanding, students who have a deeper understanding of principles but are lacking in computational skills. These students know how to figure out the solution to difficult “mindbenders”, but, often make errors and are a lot slower in performing computations.

I find it unfortunate that most students in our school systems are taught instrumentally. This might be due to the structuring of a one year curriculum into one semester, this way teachers have to rush trough material making sure they finish it by the end of the semester. It is hard to accommodate students whose goal is to understand relationally since the majority of each classroom are students who understand instrumentally. Most teachers also prefer students with computational abilities and are not willing to change their teaching style in order to accomodate relational understanding. Even most regional and provincial level individual Mathematics competitions are designed to fit the learning style of those who understand instrumentally. In team competitions though, where higher level critical thinking is required, students with relational understanding thrive, they have a great advantage over the former group of students.