After reading this article, I found myself relating to Skemp in a way that as an educator, I too have been guilty of prioritizing and having a bias in favour of relational understanding in mathematics. It wasn't until I started my job as an educator at an institution in Vancouver that I was made aware of the two types of understandings that Skemp mentions. I remember being called into my manager's office to discuss the goals of a new student. Upon looking into the student's file, we decided that not focusing much at all on deeper understanding of concepts would be the best way to go in his case and in all honesty, I felt frustrated and wanted to push my student's limits. It took some self control on my part not to do that and the results were outstanding. The student made it through math with a decent enough grade and was able to prioritize other things that truly interested him and he was happy!
As a product of the Indian high school system though, where grades and mindless memorization are given priority over relational understanding of any material, I was not surprised that I needed to pause and think about the concepts Skemp mentions in his article that I too was made to understand in an instrumental way. As for where I stand on the issue Skemp raises, I believe that as an educator, you really have to talk to your student about their goals and find the balance between instrumental and relational understanding. They may be interested in learning about fractions in a relational way but not Areas. Engaging with the student and being proactive in setting goals together would make this easier.
I wonder, in a class full of 30 students, how difficult it must be to balance understanding each student's goals and adapting your teaching approach to meet their individual needs. How do you manage to strike that balance between instrumental and relational teaching when working with such a diverse group?
ReplyDelete