25 Teaching point 1
Introducing a new topic
CLT effects to consider:
When introducing a new topic it is important to be aware of both the element interactivity effect and the isolated elements effect.
The teacher needs to avoid asking pupils to process content that is too detailed and complex too early on in the new topic or lesson. If they offer complex information at the outset, the element interactivity may be too high.
Moreover, by breaking the content down into manageable chunks, and teaching it accordingly, the teacher is instead promoting the isolated elements effect, which will help to avoid overloading working memory.
26As a reminder, it is important to remember that the principles of CLT only apply to domain-specific biologically secondary knowledge. The ‘rules’ also only apply to the limitations in working memory which occur when the pupil is a novice, with very limited knowledge of a given topic. Their schema is, in effect, empty.
Element interactivity effect
Given this premise, let’s take the example of a teacher who is preparing to teach the topic of polygons to a class of novice learners.
What would potentially be wrong with presenting the topic as shown in Figure 1.2 on page 27?
The answer to this question is that, in CLT terms, the problem is one of high element interactivity. Whilst it is still an example of a schema, there is too much detail in this resource for the novice learner to cope with, meaning working memory would be overwhelmed.
The focus of the learning is polygons. However, the relevant information is effectively hidden from the novice learner. It sits within a sea of content. The other information – angles, averages, fractions, decimals and percentages – will be relevant to pupils as they progress through the maths curriculum, but at the moment represents too much irrelevant detail for the novice.
There is also no apparent coherence within this resource – at least not for the novice learner. For example, pupils would have no sense of any common features, groupings or relationships between various polygons. The teacher (i.e. the expert) would clearly see this coherence, but the novice learner simply could not.
It is absolutely crucial to remember that the teacher would certainly want the pupils to know and understand all of this material at the end of the topic (and CLT recognises this). Pupils being able to recall and demonstrate precise and accurate understanding of the content in this schema is, of course, the ultimate goal. In the terminology of CLT, we’d call this the ‘automation of schemas’.27
28One of the issues with schemas like this example is that they are written by the expert but not seen through the eyes of the novice.
Therefore, in CLT terms, it would be highly erroneous to start with this.
Isolated elements effect
Let’s now approach this topic in a CLT-friendly way.
For the novice learner, it would be more effective if the content on polygons was instead designed in the way shown in Figure 1.3 on page 29.
The question is, why?
This second option promotes the isolated elements effect, and is therefore desirable. Essentially, the teacher would deal with each element in turn. Through direct instruction the pupils would learn everything they need to know about the properties of these polygons.
The experienced teacher who is introducing the topic of polygons would probably start with the four-sided shapes. Of these, the square would be the first, as it contains the least number of variables (i.e. the sides are the same length, all the angles are the same and there is minimal variation of numbers – e.g. the length is the same as the width).
The teacher would offer direct instruction about the properties of the square first and promote understanding, perhaps through worked examples. They would not only ensure that pupils have understood but would also try to obtain a high success rate – indicated, for example, by correct answers to informal assess...
