Two Types of Mathematics

Posted by KK on Nov 3, 2015

TASK 2 –


It seems there is an agreement among mathematicians, businesses and teachers alike that the way mathematics is taught in most schools is a bit short sighted and mostly driven by examination results. Just like Dan Meyer and Ken Robinson in Task 1, Richard Skemp, in Relational and Instrumental understanding, has systematically analysed our education system and pointed out the disadvantages of status quo.

A lot has been said about the advantages of introducing relational mathematics in schools instead of depending on instrumental way of teaching. The fact that relational mathematics demands a lot of time to introduce to students, and definitely much more time to older students who have only known instrumental way as the norm, would not sit well with the expectations of school boards and head teachers alike whose standards are mostly assessed and measured by their students grades attained at GCSE and A levels. Relational understanding would require patience and as such could be appropriate for introduction to year 7s and upper primary school students who have not been spoilt with the quick fixing methods and have ample time to experiment and learn. If only government’s objectives were adapted to allow a smooth introduction to this type of learning, by reducing the amount of exams taken to remove the result driven attitude and all fears that come with it, then progress could be within reach. That means the way examinations are set would need to change. Group projects, achievements and continuous individual assessment throughout the years could form a bigger part of the examination process. This way, teachers would not waste much time on short term solutions but expend their energy on teaching visible mathematics that really makes sense.

Therefore, timing would be of utmost importance before introducing relational understanding in schools, especially where instrumental way of teaching and learning has deep roots.

One fact that we can all agree on, is that students do not teach themselves instrumental methods of problem solving. Unfortunately, it is teachers who introduce it to them. This could be due to pressure from above to complete syllabi and to ensure that students pass their national exams. Or it could also mean that the production line of teachers has problems in itself.

Since an introduction to a new way of learning and teaching would definitely meet resistance from its recipients, among others, then an appropriate system of effective feedback and formative assessment, that is forward looking and which does not detain students’ development must be put in place (Dylan Wiliam). An assessment can be doctored in a way that it provides information that can be used as a feedback for teachers to modify and adapt teaching and learning activities (Black and Wiliam 1994).

To summarise, it is clear that there is a political and social will to embrace relational understanding, especially in mathematics, but there is also a lot of resistance within. I don’t know if the recent approval to open a grammar school in the south of England has got anything to do with the current discussion. But what I know is that relational mathematics learning and teaching does go hand in hand with effective way of feedback and all aspects of formative assessment which stresses on the knowledge of where the learner is, where they are going and how to get there. This ensures that all students are totally engaged in the topic, thereby allowing the teacher to respond appropriately to students’ needs for further development ( Dylan Wiliam).


  1. Glen
    7 November 2015

    I really enjoyed reading this KK, I liked the way you do eloquently laid out your rationale and argument throughout. You say we should attempt to implement relational understanding around year 7, but do you not feel this is still to late? Surely to implement relational understanding from the very start would be more prudent, however I do believe should we attempt this then as you suggested it would take a long time to do so we might need to overhaul the system entirely!

    Great article!

  2. Rhys
    8 November 2015

    I really enjoyed reading this KK. I thought you raised some good points and also i liked how you managed to link back to Task 1 as well. Good use of a summary paragraph, it sums everything up in your piece nicely.

  3. pepsmccrea
    9 November 2015

    A very considered and pragmatic analysis of Skemp’s ideas. Also great to see you exploring connections with current events in the world of education (eg. grammar schools).

    In future thinkpieces, I’d like to see you make more links with ideas from previous thinkpieces.

  4. Kkay
    9 November 2015

    Thanks guys for the comments and yes I will try to link with ideas from past tasks

  5. asreall
    29 December 2015

    I enjoyed reading your article and wholeheartedly agree with the reduction
    of standardized testing and your whole school career should contribute towards your final grade. Much like your actual career when you leave school.

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