Learning rules! or learning rules?

Posted by Glen on Nov 1, 2015

The work written by Skemp puts forward the idea of faux understanding in a mathematical concept, two different types of understanding, relational understanding and instrumental understanding. Skemp goes on to argue that the dichotomous relationship between the two presents a dynamic that can be detrimental to teaching, when students hold an instrumental understanding, and just want rules, not caring for the why, especially when the teacher presents a learning session through relational understanding. After reading through this article, I looked back at my own education, and feel like I would have been an instrumental learner mathematically, but not because I wanted rules to apply to constrain mathematics, but because that was the manner in which I was taught. Going back to Dan Meyer’s talk, the concept of mathematics, as with any subject should be openly explored and challenged in a classroom dynamic, and not constrained by drills we serve to teach children, drills that answer the example, and when students are presented with the a problem where the rule can be applied, but it isn’t obvious students get it wrong. I believe that the work by Skemp does serve to isolate that the impatient problem solving attitude set out by Meyer, and attempt to provide further reasoning behind it, however I also believe that the work conducted by Willingham on the idea of different learning styles could also be applied here. Willingham argues that the idea of learning styles while incredibly present in schooling is something that after rigorous academic investigation has been proven to be nothing more than the ability to adapt to different learning scenarios.

What do us as academics and as teachers to be do about this however? If the emphasis was placed solely on one’s ability to retain information in a particular manner, one would assume that teaching through learning style would be more prudent. Whereas in reality we know this not to be true or to exist, we do know (thanks to Skemp) that teachers as well as students can be seen to be either instrumental or relational thinkers, and as such that is far more important in my opinion than the individual’s capability to be able to interpret information. Rather ironically last week I argued that more freedom should be allowed into the curriculum, that teachers should have the capability to promote education and learning for the pursuit of knowledge, not the pursuit of a job, however after reading Skemp’s work, I find myself arguing that we need to promote teacher training around relational understanding, and not instrumental understanding. Not solely for the purpose of teachers having a passion for the knowledge that permeates the curriculum, but because how can we be expecting students to learn in relational understanding manner, when we as teachers are not conveying it ourselves? The growing trend I feel throughout Meyer, Robinson, Skemp and Willingham is that teachers need to be able to promote education in a way that not only engages students of all ages/demographics but also in a manner that makes them appreciate the subject more than it just being a stencil to apply to real world problems.


  1. marcus
    5 November 2015

    I was really interested to read about your ideas in this think-piece, Glenn. I found your thoughts on the importance of learning styles quite intriguing… You suggest that the way in which teachers and students think is more important. However I wonder if learning styles are just as significant? In order to change the mindsets of our students, shouldn’t we be considering their learning styles to be just as or maybe even more important?

  2. Senay
    8 November 2015

    I really enjoyed reading this Glen. You have made your points very clearly, especially the importance of learning styles to the instrumental vs relational debate. I also liked the link you made between Skemps and Dan Meyer (“The concept of mathematics – subjects should be openly explored and challenged!”) I think the word “explore” is critical and that students should be given time to think around the subject because in the long term this develops more profound understanding. The question is if the government/state has to make judgements about what the next generation should be learning and what the country’s economy’s needs will be in the future (which is in effect what a curriculum is) how can this be married with the concept of “free” learning which could take the student in a direction away from the curriculum?

  3. pepsmccrea
    9 November 2015

    Great to see you reflecting on how this fits with your own educational experiences. Good links back to Willingham’s & Meyer’s ideas that are helping you pull things together and make sense of a complex practice.

    It might be helpful to try to be even clearer about some of your key messages in your next thinkpiece.

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