For a context for this reflection, please read the previous two posts.
In this blog I have compiled a short list of the reasons why determining the complexity of a concept is so important for teachers. In subsequent blog posts I will unpick some of the discussions that we had when trying to solve this knotty, philosophical question.
Determining the complexity of a concept is important because…
1) … it makes you think about the order you do things in as a teacher.
In our discussions on Saturday we identified three broad stages each teacher needs to go through to help their students understand difficult concepts:
a) Map out their topic area into linked and ordered concepts.
b) Consider what barriers and difficulties students might experience in trying to understand a given concept…outside of the inherent difficulty of the concept.
c) Check for their students’ conceptual understanding…preempting and engaging with misconceptions.
2) … it helps you pitch work at the right level for your students.
If you work out how complicated a concept is, then you can work out how quickly your students might grasp it, what prior stage in their understanding they might need filling in, what they might need reminding of or, alternatively, what they might already find too easy.
3) … you can become more confident in sequencing units of work.
How do you order the concepts in your subject? Historically (as they were discovered), chronologically (as they ‘happened’), empirically (by working out what most people know vs what most people don’t know), in order of complexity (simple to complex) or spiralling (to repeat the most difficult of concepts several time)? Or a mixture of some/all of them?
4) … it identifies gaps in your own subject knowledge.
I remember being told at teacher training that if you can’t teach something to someone else, you probably don’t have mastery of it. Now while this might not be true in the completely literal sense, there is a grain of truth behind it at least: if you cannot break down complexity in your subject area in order to explain it to someone else, you probably need to do some more work getting to know the subject area! Mapping out your subject concepts is very useful for identifying these areas.
5) … it provides you with a diagnostic for correctly identifying your students’ misconceptions.
If a student doesn’t ‘get’ something, you can use your understanding of how the concepts within your subject area link together to identify dependent concepts that need to be taught prior to the student being able to ‘get’ the thing you were trying to teach them in the first place.
6) … it can help you pre-empt difficulties.
Mapping out complexity and considering why students might find something difficult means that you may be more likely to choose a more appropriate range of teaching techniques to suit the teaching of that topic. When you stop to ask yourself if a concept is counter-intuitive, or if it requires a lot of prior knowledge, or whether you have prepared sufficient examples to explain it, then you are more likely to have identified a difficulty that you can plan for.
7) … it involves identifying threshold concepts that probably take more time to teach.
Subject disciplines have paradigms particular to themselves. Some of these are counter-intuitive, others can be considered ‘troublesome’ because in understanding them, you subvert a preconceived notion or previously held knowledge. The idea that light can be considered a wave or a particle in physics. The idea that a reader constructs meaning in literature. The idea that cooking is all about energy transfer. These have been termed threshold concepts and may need more time devoted to them as they are so crucial. Once you grasp a threshold concept, it’s very difficult to forget; it shapes your understanding of the whole discipline. In future blogs I will look at some examples to see how this applies across the subject disciplines.
8) … it could help you work out an assessment structure.
In order to write an assignment with a metric of some sort, teachers encounter the need to devise a mark scheme or set of success criteria. Within each subject these are different depending on the stage that the pupil is learning at. This forces the teacher to determine the complexity of a concept because they have to find out at what point they can award a top mark, at what point they differentiate for complexity and how much of the complexity the students need to grasp at the given stage in their learning. By way of example: a top mark for an 11 year old’s essay about a piece of literature, would be less difficult objectively speaking than the top mark for an undergraduate analysing the same text.
These are some of the justifications for why this #touchpaper problem is worth deliberating further.