Developing concepts of ratio

06 May 2021

What does research suggest about developing concepts of ratio?

• Ratio is a well-researched but complex representation which may be best considered as overlapping with other representations of proportion, such as fractions, and is linked to multiplicative thinking, equivalence, scaling and similarity
• Ratio can be used and interpreted in different ways, including part-whole, whole-whole or part-part relations
• Providing opportunities for students to explore the difference between using natural and rational numbers supports teaching and learning about ratio
• Careful variation in contexts of ratio tasks, moving through stages of multiplicative thinking and using technology, supports the development of student understanding of ratios
• Considering possible misconceptions, often arising out of applying additive strategies, can support teachers in effective teaching of ratio
• Some strategies may support proportional reasoning more strongly than others; for example, the “unit value” method
• Double number lines, ratio tables and other models may be useful to teachers and students