5 Summary of Week 3

In Week 3 the focus has been on proportional reasoning and its link to multiplicative relationships. You have seen how the use of concrete objects can support early understanding of proportional reasoning, progressing to pictorial representations and, later, abstract mathematical notation as learners’ thinking becomes more sophisticated.

You have worked on a range of proportional reasoning problems, looked at examples of common misconceptions and considered how these could be addressed.

You should now be able to:

• define what is meant by proportional reasoning
• recognise when a learner is using additive reasoning or when they are using multiplicative reasoning
• use effective approaches for teaching proportional representations
• have an awareness of the common misconceptions which learners meet when working through proportional reasoning problems.

Next week you will study the first of two weeks on algebra, looking in particular about how the foundation of algebraic understanding is introduced and developed.

You can now go to Week 4.