Content, Concepts and Skills

The IB has a focus on conceptual understanding (it is one of their Approaches to Teaching) but also recognises the importance of developing content knowledge and skills. In a recent CPD session we discussed what the breakdown of these three were in our own teaching and what we thought the IB emphasised.

First we were asked to draw a pie chart showing how much time we spend teaching each of content, concepts and skills. Mine looked something like this.

Then we were asked to do the same thing in a departmental group but for the IB course we taught, and how much emphasis the IB placed on each of these within the curriculum. We focused on the Mathematical Studies course, and came up with this.

Within doing this we had a discussion about what we meant by each of these terms, and in this post I want to share a little about my thoughts on this topic.

Disclaimer: - this is how I interpret the terms content, concepts and skills in the context of Mathematics, and that does not mean everything I say will make sense in other subjects. I am sure some of it is common, but, as we all know, each subject is very different to others.

Disclaimer 2: - these are very much ideas of mine, and not really based on research or reading. This post is really just a bit of a chance for me to write out my initial thoughts on the distinction.

So what do I understand by the terms?

Content - what we "know" and teach our students to "know". This is the facts. This is learned through repetition and recall.

E.g. knowing that gradient is the steepness of the line

Skills - what we can "do" with our knowledge. This is the applications of the facts to solving problems. This is learned through repeated practice.

E.g. being able to calculate the gradient of a line

Concepts - what we can "understand" about the subject. These are the big picture ideas that go across different topics and allow us to interpret results. This is learned through (self-)explanations.

E.g. the concept of gradient being the rate of change

When we started this discussion, my initial response was that we need content before we can develop skills or conceptual understanding. I still stand by this, but I think there is more nuance to it than that. All three aspects are closely linked to each other, and having one will help develop the other two. I see it as a kind of cycle, as shown below (I sketched this out whilst walking home after the session).

So what are the connections?

Content <-> Skills

We obviously need to know the formula for finding gradient to be able to do this, but do you need to know that gradient is the steepness of the line? I don't think so. I have taught students who can do the skill before they know what it means. It could even be argued that doing the skill successfully leads to you learning the content better.

What about in, say, History. Here the skill might be to write a PEEL paragraph, but can this be done without content? We need some content to be able to write the paragraph for sure, but through writing the paragraph, can students also learn more content?

Content <-> Concepts

You definitely need to know what gradient is to be able to fully understand. But can it work the other way round? Well, I think it can be argued that it is very hard to know something if you do not understand the basic principle. Can you know that gradient is the slope of a line, if you do not understand what slope is?

Let's think about Geography, and the concept of migration. This is a big concept to understand, though it is easy to identify the basic premise. Through different case studies (content) students can further develop their conceptual understanding of migration, but having a starting point on the concept allows them to access the case studies to begin with.

One danger in this connection is the idea that if we understand the concept, then we know the facts. This is just not necessarily true. I often have students who say they understand from the explanation, but are then unable to recall the content (or indeed be able to apply the concept to some skill), so clearly understanding in the moment is not enough. But it is a good starting point. Could the problem be concerned with familiarity with the idea in the moment leading to a false sense of understanding?

Concepts <-> Skills

Many people would argue that you need to be able to understand something in order to apply it to solve problems. But I think it is also completely possible to be able to do the skill which develops the understanding. Many students only truly grasp what gradient is when they meet calculus, and at this stage they have been finding gradients for at least 2 years.

Towards the end of the CPD session I put out the question "Do skills and concepts become content when you have expertise?" I.e. Once you have applied the skill of finding the gradient of a line many time, it becomes knowledge to you that you can draw on without much thought. And similarly, when you understand the concept of gradient as a rate of change, this becomes knowledge that you don't need to think about.

Or, as another example, consider the concept of splitting what we say into pieces that go together. This is the concept behind the use of full stops and commas (among others). Once you have practised this often, it becomes automatic, and the concept now becomes knowledge. Or does it? This was my speculation. And this comes from the idea of linking concepts with understanding. If you just think of concepts as the bigger picture, then this makes less sense.

But if you consider concepts as conceptual knowledge and skills as procedural knowledge, then we can think of these as just different types of (content) knowledge. Does this work in other subjects? I think the idea of skills in other subjects is very different to Mathematics.