Although the linguistic analysis in this probe study provides more information than is needed by classroom teachers, there are valuable points that would enable teachers to improve the ability of their students to give mathematical explanations.

Primary among these is to encourage their students to talk mathematics rather than just doing it. This advice is not new. It is an underpinning of the New Zealand Numeracy Project (Ministry of Education, 2004) as well as the NCTM Standards (2000) and several research projects (for example Khisty and Chval, 2002). Talking mathematics provides an opportunity for students to formulate their own understanding, explain it to their peers and explain their understanding to their teachers.

The major linguistic structures identified here, Premise, Consequence, and Conclusion, can be used in many types of mathematical discussion. This can be discussion among peers, with a teacher, and in writing. Evaluation of discussion in mathematics classes can be guided by seeing whether or not the appropriate elements are present. Teachers can guide students by asking them to explain in complete sentences, explain what they already know, what alternatives might eventuate, and what can be concluded from different outcomes. This structure can be applied to numerical investigations, algebraic comparisons, investigations involving statistics and probability, and geometric and measurement hypotheses and investigations. Not only are they useful for all strands of the curriculum, but for both primary and secondary students. Students taking the National Certificate of Educational Achievement will need to be able to write explanations including these components in order to achieve Excellence.

Primary school students need to be helped to tell the difference between a story appropriate for reading, writing or fantasy and one appropriate for mathematics. Many current pedagogical practices make this differentiation more difficult for children, for example calling equations “number sentences” and calling word problems “story problems”. This does not mean that fun and fantasy need to be removed from mathematics. Exercises in the size of a giant's hands or cloths are both fun and mathematically useful exercises in proportion. However, the subject of a mathematical explanation for this as well as for other mathematical tasks is a clear explanation involving stating a Premise, Consequence and Conclusion.