The aim of education

Posted by Domenico, Uncategorized on Nov 2, 2015

After reading the article by Skemp, I chose to watch the video of Claxton because I think they both engage the public with an important question: what do we want from our students?


Whether we talk about understanding relationally, in the case of Skemp, or whether we talk about building a sceptical disposition towards the acceptance of knowledge, in the case of Claxton, according to them both, the kind of teaching that happens in class makes it impossible for the students to become really confident.


According to Skemp, the reason why so many children are only taught instrumental mathematics is because, within the current paradigm, the most important thing is to answer correctly a sufficient number of questions. Instrumental mathematics is much quicker to learn and better to pass the exams.

I believe this is generally true. But, is it really so straightforward?

Only in theory. In most of the cases, even this way of doing mathematics fails to engage the students. I am sure we all have experienced how, as soon as you change some how the context of the problem, students feel lost and make mistakes or make mistakes and feel lost.

I agree, the two kind of knowledge, relational and instrumental, seem so different that when applied to mathematics they could be regarded as different subjects. Could they be taught, for example, under the name of mathematics and applied mathematics? And would this, for instance, help teachers to see what students really struggle with?


Relational mathematics should be propaedeutic to instrumental mathematics. In other words, I first need to know why and then how. In this way students learn to make connections, to think outside of the box. The formula is the translation of a mathematical concept into terms that can be universally understood, but it is not the aim, it is the means.


Wandering within and beyond the fields of a subject, doing nothing and going nowhere, and in this process to see what of interest I might come upon. This is truly joyful and will help students to build up a mental map of the subject with all its connections and relationships with the real world. Individuals won’t feel lost if at some point they have made a mistake, they will feel more confident because they will be able to go back to their steps and possibly to find another route to get where they want. That is what enables learners to think with their own mind.


Is this what Claxton interpret as going beyond, or below, the content of the subject? I think so, and I agree with him, it is more important to see what is being transacted at a deeper level. One of the first aims of education should be to stretch your ability to empathize, to build disposition to ask sceptical, intelligent and respectful knowledge questions, to prepare patient problem solvers ready for the challenges of the 21st century. Of course we should be more interested to what is below the line. We want to educate people who can develop their own critical intelligence and do not accept everything they see through the media as truth. We can’t do this if we think of students as empty boxes to fill with prefabricated knowledge.


  1. rajchopra
    8 November 2015

    Dom, you are brave to make the statement: “he kind of teaching that happens in class makes it impossible for the students to become really confident.” It shows you have been thinking of what they said and this is your interpretation.
    I had to look up what ‘propaedeutic’ means and it is interesting that you consider relational teaching should come before instrumental.

    Also, you introduce several points to the the discussion.

  2. pepsmccrea
    9 November 2015

    Great to see you contrasting two powerful ideas, and looking at them critically and not accepting the simplicity of the arguments.

    Regarding your last sentence > do we need knowledge to be able to think critically?

    Strong thinkpiece. Keep making connections between the different ideas you have come across.

    • Dom
      22 November 2015

      Hi, thank you. It is a good question and I am not sure I can give an answer to it, yet. To be able to analyse, we might need some terms of comparison, so knowledge could come handy.
      My primary school teacher’s motto was, ‘those who are educated are free’. I believe he meant that by being knowledgeable, one is always able to make his own decisions and can avoid to be influenced by others. Therefore, my life started with me thinking that, I should know more.
      However, at some point, I learnt that ‘the ancient Oracle said that I (Socrates) was the wisest of all Greeks. It is because I alone, of all the Greeks, know that I know nothing.’ But this still implies knowledge.
      Personally, at the moment, I prefer to think that it is better if we keep our mind clear and with simple thoughts, as a way to evaluate what we come across with.

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