Relational Understanding and Instrumental Understanding

The article “Relational Understanding and Instrumental understanding” written by Richard R. Skemp made me reflect on my ways of approaching the subject content. I really liked the term “Relational understanding and the instrumental understanding” he used for different levels of understanding. I have been using both approaches depending on the different situations during my school life. Although I firmly believe, it is essential for the students to know the concept behind the rules of their routine actions. If a teacher is accustomed to using the instrumental style of teaching then it would be detrimental for the students who want to have relational understanding. I remember one of my history teachers would deduct marks if we did not answer her exam questions as written in the textbooks. I believe such practices will impoverish the creative minds of students. 

In addition to this, I found it interesting, how a student good in instrumental math understanding can do better in the other subjects where math is required. I believe along with knowing the instrumental ways, one must have deep knowledge in order to solve the problems with much more understanding. The example he uses to explain the importance of having a “cognitive map” of town instead of just knowing the directions to final positions encourages me to take teach math by making connections with interrelated topics so that students have the whole essence of the concept.  A relational understanding of math gives us ample freedom to approach problems in comparison to instrumental understanding which constraints us to solve problems using a certain set of rules.

Going further the contrast discussed between relational mathematics and instrumental mathematics intrigued me to think more about it. Skemp also raises the question about considering relational math and instrumental math as two different subjects or different approaches to the same content. I find the latter more relevant. From my past experience of tutoring math, I have experienced that math made more sense to my students if they were taught the underlined concepts of the problems( for instance -4 -5 = -9 can be taught with the help of number line rather than just telling them the rule of adding and putting a negative sign Infront), hence, they will feel more confident in solving the difficult questions themselves. The substantial difference between the approaches of the types of math can make a significant difference in the student’s core understanding and learning outcomes. Although, I understand, in actual practice, teachers and students are constrained by the time, exam pressures, content completion deadlines which can overlook the relational understanding,. Therefore, we as educators must reflect on our ways of understanding and on our pedagogy in order to induce a relational approach in our students wherever possible.