Language and communication in mathematics lessons can consist of words, images, diagrams, notations and other ways of communicating about mathematical objects, ideas, and practices.

For example, naming or labelling features of a diagram can be done using words, labels, notations, colours…. When names are attached to something mathematical, whether that is an object such as a number or angle, a relationship such as parallel or equal, or a process such as conjecturing or generalising, these names can be used to communicate about that object, relationship or process. Naming can also emphasise the importance of a particular action or object; for example, naming auxiliary lines highlights them as something mathematicians may use in a geometric image to work with that image.

The choice of the words we use in teaching can also influence the meaning that is being emphasised. For example, we can describe $LaTeX: \frac{2}{3}$ as two thirds, two out of three, two divided by three, two over three. Each of these conveys a different meaning, which may be more useful in some contexts than others. Two thirds emphasises the fractional structure, two of these things we call thirds, as well as the number it represents. Two out of three may be more useful in probability contexts where it emphasises the number of successful outcomes out of the total number of outcomes. Two divided by three emphasises the process involved, for example when converting to a decimal or when sharing or grouping. Two over three emphasises how we write this fraction.

When focusing on this dimension what is noticed may focus on what the teacher says or write, or what the students say or write, or a combination of these.

References

Ingram, J., Ward-Penny, R., Kimber, E., & Planas, N. (2024). Observations on naming and labelling practices in angle work with teachers: How might small language choices support mathematical activity? Proceedings of the Sixteenth ERME Topic Conference on Language and Social Interaction in Heterogeneous Mathematics Classrooms, Halle, Germany.

Lenz, K., Obersteiner, A., & Wittmann, G. (2024). Who benefits most from language-responsive learning materials in mathematics? Investigating differential effects in heterogeneous classrooms. Educational Studies in Mathematics, 116(2), 185–211. https://doi.org/10.1007/s10649-024-10321-9

Wilkinson, L. C. (2018). Teaching the language of mathematics: What the research tells us teachers need to know and do. The Journal of Mathematical Behavior, 51, 167–174. https://doi.org/10.1016/j.jmathb.2018.05.001

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