# Uncovering learning and misunderstandings

Being able to talk about these operations seems to be important in thinking about and doing these operations (see for example Anna Sfard (2001)). If the child is unable to talk about and model these ideas (e.g. on a number line) then their understanding may be operational and not relational (Skemp 1976), they may be parroting not thinking. There is a great deal more vocabulary that must be secure before moving onto multiplication and division.

Unless a child can talk about their ideas how can teachers assess their ideas and how can they both know what is needed next? Helping the child to use appropriate language to express their own learning is a vital part of teaching. It is not enough for the teacher to use the language, the child must be able to as well (Lee 2006).

Discussion must form a part of mathematics lessons, if the only discourse used is between teacher and child, the children will see mathematical language as something apart from them. They must use that language between themselves if they are to take ownership of the learning. Asking pupils to discuss "what is the same and what is different?" or to be ready with a reason "why?" immediately increases the language use by the pupils and begins to encourage a conjecturing atmosphere Mason et al (2005).

## References

- Lee, C. (2006) The role of language in the learning of mathematics, assessment for learning in practice. Buckingham, Open University Press
- Mason, J., Jonhnston-Wilder, S. & Graham, A. (2005) Developing Thinking in Algebra. London, Sage (Paul Chapman).
- Sfard, A. (2001). There is More to Discourse than Meets the Ears: Learning from mathematical communication things that we have not known before. Educational Studies in Mathematics, 46(1/3), 13-57
- Skemp, R. (1976) Relational Understanding and Instrumental Understanding Mathematics Teaching, 77, 20–26.