Mathematics is an interesting case because it uses three ways of making meaning: language, visuals and the symbolic (ie equations). Understanding mathematics is understanding all these three aspects, but here, we would like to focus on the **patterns of language**.

For example, what are the patterns in a command such as:

*Find the area of a triangle with base 10 cm and height 5 cm. *

This example is typical of mathematical commands: it has a **command** (*Find*) at the front which expresses a mathematical operation and the rest is a **dense noun group**.

The noun group itself has patterns: it starts with a mathematical concept (area) which is followed by providing a real-life situation (a triangle of a certain size) and then finishes with some data needed to carry out the mathematical operation.

Similarly:

*Calculate the sine of angle φ in the right-angled triangle ABC where AB is 8cm and BC is 16 cm. *

To understand this, a student would understand they have to ‘calculate’ (*Find, Solve, What is* …) some mathematical concept and, in this case, it is ‘sine’, and then, they consider the following questions:

- What do I have to find? (sine of angle
*φ*) - Where is angle
*φ*? What is the specific situation? (in the right-angled triangle ABC) - What do I need to calculate the sine value? This is the ‘invisible’ mathematical operation being tested (opposite length over hypotenuse length).
- What are the lengths of those sides? (8 cm and 16 cm respectively)

As we can see, our questioning is based on **the structure of the noun group**.

So, the issue is not remembering the list of technical terms but **the teacher and students engaging with developing a strategy for understanding the problem** — an appropriate pedagogical strategy would be the Teaching and Learning Cycle discussed in other articles.

While engaged in using the strategy, the technical terms are used over and over again and, if the students are given opportunities to say the words, then they engage in a process where concept and words collaborate so that learning happens and vocabulary development is a part of that.