Instrumental versus Relational

Posted by Senay on Nov 1, 2015

The key ideas being explored in the article Relational Understanding and Instrumental Understanding by Richard Skemp and the clip by Robert Bjork called Desirable Difficulties are; the different kinds of understanding and how we often attach conflicting values to words, the two different kinds of understanding that exist in mathematics (instrumental vs relational), which of these types of understanding (if any) is superior, the conflicting meanings of the word “mathematics” itself, the strong case for the superiority of relational mathematics for the long term benefit of the student, in spite of this the good reasons why some students are only ever taught instrumental mathematics during their time at school and (in the interview clip) further supporting evidence for the superiority of relational mathematics in the “desirable difficulties” theory.


In my own experience of learning at school at a young age (particularly in the classroom setting) I can now clearly understand that I was largely achieving only instrumental learning. Education in my country of origin is very exam driven (even more so than in the UK in my opinion) and after considering the article and clip above it is now very apparent to me that the teachers I had were first and foremost concerned with getting us ready for and through our exams. This was the case in all of my lessons but especially in mathematics. It was only as I got older that I achieved any kind of relational understanding. Mostly through independent study and approaching my teachers outside of the normal class/homework routine. I think this became easier as I got older and is undoubtedly linked to the development of me as a person and my general understanding of everything.


Clearly relational understanding is what we should all be striving for when learning and teaching. This is understanding in the true sense of the word. I like the analogy of the foreign/strange city. It is okay to teach a student how to get from point A to point B if this is all they need to get them through an exam. The problem is in real life if there is a reason why the route from A to B is not straightforward then a student with only instrumental understanding could soon experience difficulty. For this reason, any level of relational understanding that can be achieved most be seen as a positive. In practical terms education today is dominated by syllabi and exams and unless a drastic change in this system occurs (unlikely for the time being in my opinion) then instrumental understanding has to be a priority. Teachers simply do not have the luxury, in such limited circumstances, with students of various abilities and backgrounds to invest large amounts of time in the kind of free, independent learning that increases relational understanding. This having been said there is a strong argument that this may have better long term benefits for students and lead to better results – the calculation any teacher has to make  is whether they can take this risk with the next assessment, exam or inspection around the corner.


  1. Stephen
    6 November 2015

    I think its great that you have seen the reason why people end up being taught instrumental maths, especially with your experience in school in your home country. Do you think that the relational mathematics that Skemp talks about is similar to the idea that Dan Meyer puts forward about the importance of maths logic and problem solving for students lives ater school? I wonder how we can assess relational understanding when Skemp suggests that its use may make getting the right answer harder.

  2. Glen
    7 November 2015

    I found this piece really insightful Senay! I like the link you made between your own learning and the topic. You argue that as teachers we should be promoting a relational understanding in our classrooms, but how do you believe teachers can go about this? With obligations to teach students to pass exams do you feel teachers hands are tied?

  3. pepsmccrea
    9 November 2015

    Great to see you reflecting on how the ideas you have come across fit with your own experiences as a learner. Also, good to see you exploring the limitations and reality of Skemp’s suggetions. I was hoping to hear some more about your thoughts on desirable difficulties and how that fitted in with Skemp’s ideas.

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