The aim of education
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.