Teaching challenge

Ms Smith has a clear sense of her learning goals and is confident at breaking the curriculum down into small, meaningful components. However, she struggles to know how quickly can she get pupils doing complicated thinking and when she should introduce more sophisticated tasks.

Key idea

Students must develop solid foundations of knowledge through carefully sequenced teaching and practice if they are to develop and apply sophisticated mental models.

Evidence summary

Mastering foundational knowledge and linking using core concepts

Ms Smith is already aware of the value of building her pupils’ subject knowledge, the risks of pupils’ misconceptions and the potential for knowledge gaps. She wants her students to solve problems and think critically, but they cannot do so if they have critical knowledge gaps and she has noticed that weak prior knowledge leads to misconceptions. This is because pupils use knowledge integrated in their long-term memory to learn more complex ideas and successfully apply what they have learned (Deans for Impact, 2015).

This implies that:

The sequence in which knowledge is introduced is crucial. For example, pupils are likely to struggle to evaluate the effectiveness of international aid if they are unclear about the challenges facing developing countries. They are likely to struggle to master algebra if their grasp of number is weak. This means Ms Smith needs to sequence the introduction of new ideas carefully so that foundational knowledge is introduced first. It also means she needs to check pupils have relevant prior knowledge before she introduces new ideas.
Ms Smith needs to highlight the link between past learning and new ideas to pupils – or help pupils to make those links themselves – so that they gain a deeper and better-organised understanding of the subject. Pupils learn new ideas with reference to what they already know (Deans for Impact, 2015), but Ms Smith cannot be sure they will make these links unprompted. Using core concepts help with these links.

Having broken down the knowledge she hopes pupils will gain and sequenced this carefully through one or more lessons, she can identify effective ways to introduce these ideas.

Teaching abstract ideas

Ms Smith needs to ensure pupils acquire foundational knowledge and core concepts successfully, and that she does not begin more complicated activities too soon. It’s easy for a relative expert in a topic – like Ms Smith – to grasp the abstract concepts and apply them. For example, she sees ongoing struggles over how much power ordinary people have throughout the political events of the nineteenth century; she uses symbolic representations of chemical reactions to understand what is happening in an (invisible) chemical reaction; and she can use the slope and intercept within a line graph to write an equation for that graph. However, for novices, abstract ideas can be particularly hard to grasp. If Ms Smith opens each of these topics with the abstract ideas, pupils may struggle to grasp them.

Concrete examples are much easier to understand (Willingham, 2009): in each case, pupils are likely to find it easier to first encounter the concrete example then to identify the underlying abstract principle. For pupils to be able to use both, Ms Smith needs to connect and integrate abstract and concrete ideas, and show the links between them (Pashler et al., 2007). An understanding of the abstract features allows pupils to successfully apply subject knowledge and concepts in new situations: for example, an understanding of the structure of a narrative can help them comprehend a new text.

Checking pupil understanding and offering opportunities for practice

Ms Smith needs to check pupil understanding before beginning tasks which ask pupils to apply their new learning. She could use diagnostic questions, presenting pupils with several options, working with colleagues to identify answers which are either correct or common misconceptions. pupils’ responses allow her to identify pupils who hold misconceptions and ensure they have grasped key ideas before continuing (Christodoulou, 2017). Ms Smith needs to ask herself, “how would I know pupils have acquired enough knowledge to practise successfully?”

Once pupils have enough knowledge, Ms Smith can ensure pupils practise applying it through meaningful tasks which promote their learning of new ideas (Willingham, 2009). Although pupils will initially have inflexible knowledge – knowledge which they struggle to apply to new contexts – through continued thinking and processing of new ideas, they will come to use this knowledge increasingly flexibly (Willingham, 2002).

Nuances and caveats

Ensuring pupils have mastered foundational knowledge and core concepts depends on first identifying what is core – fundamental to understanding the topic and discipline – which she will return to many times to ensure pupils have successfully acquired them.

Key takeaways

Ms Smith can help pupils to acquire and apply ideas by:

sequencing subject knowledge and concepts and linking them to pupil prior knowledge
modelling new processes and ideas, linking concrete and abstract models
checking pupil understanding before encouraging independent practice

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