This course is separated into four modules of learning:
Module One: The Importance of Visual Representations
In this module, we’ll summarise what research tells us about the importance of using different representations in mathematics. We’ll look at the different types of representations that we can use to help deepen our pupils’ mathematical understanding and give them the tools they need to help them solve new problems.
We will see how representations fit into the five big ideas in the NCETM’s approach to mastery and the benefits, in particular, of using visual representations. We will also delve into cognitive load theory and how we can use visual representations to reduce cognitive load, freeing up the mental capacity for problem-solving and reasoning.
Module Two: Moving from the Concrete to the Abstract
We start module two with a consideration of abstraction and the challenges a novice learner faces when moving immediately into abstract concepts. We will explore how to combine concrete, pictorial and abstract representations and reflect on how we use these in our lessons now.
We will consider how conceptual development can be broken down into small steps and challenge ourselves to really unpick what this means for our next teaching block. Finally, we will go back to cognitive load theory and apply this to our practice and use of different representations throughout a lesson.
Module Three: Exploring the Bar Model
We will spend this module really getting to know the bar model, which has become a key visual representation in the mastery approach. We will look at why it is such a powerful visual representation and the contexts in which it can be used.
Once we’ve looked at the range of problems it can be used to represent, we will look at examples of addition and subtraction, multiplication and division, ratio and proportion. We have also included some useful resources that you can use immediately in your lessons.
Module Four: Using Visual Representations in Your Lessons
In this module, we’ll bring everything together and consider how you can apply your learning to your own lessons. We will discuss how many different models you should use and explore how to teach your pupils to use a new representation when you introduce it for the first time.
Many different representations can be used to understand the same problem, and we will look at how you can manage these different approaches to help your students get to the important features of each new concept. We will look at how we can use worked examples to reduce cognitive load and build up our pupils’ mathematical language through the systematic use of stem sentences.
Study time: 60 mins
