Systematic variation in examples in mathematics teaching

Mathematics teaching in Swedish compulsory school uses tasks and examples from which pupils can generalise. Studies have shown that which examples are chosen and how they are sequenced are of significance, since it can impede or enhance pupils’ learning. It has been suggested that a systematic variation within and between sets of examples is more likely to result in progress than unstructured sets. In this essay, we report on two studies in which systematic variation was built into examples used in two lessons about multiplication in Year 4 and two lessons about multiplication and division in Year 7. The aim is to describe how teachers in the two studies used systematic variation in and between examples. We show that in the first study, the variation used in the examples sheds light on mathematical strategies and structure, whereas in the second study, the variation illuminates conceptual understanding and mathematical structure. The implications for pupils’ learning of the implementation of systematic variation in and between sets of examples are discussed, and compared to the implications of teaching using sets of examples that have little systematic variation. It is argued that the use of systematic variation in and between carefully chosen sets of examples may provide pupils with greater opportunities for learning.