Encouraging students to visualise or summon up a mental image of something – seeing it in their mind – can help them to better understand it. An image may be a shape, graph or diagram, it may be a set of symbols or a procedure.

Once a student becomes comfortable visualising numeracy ideas and can consistently translate this thinking, you can then ask them to describe what they 'see' (quantities, actions, outcomes). When a student describes their thinking, they begin to recognise the relationship between language and actions. This helps them to apply the actions more easily.

You may need to provide modelling or scaffolding for some students initially. Use guiding questions such as:

- What was in your head when you were thinking of that?
- What do we do next?
- How would we get to the answer from here?

## Build numeracy vocabulary

When students can describe numeracy actions, you can begin to build their vocabulary and associate this language with symbols. For example, teach a student to say 'minus' instead of 'take away' when talking about subtraction or when using concrete materials. Have them draw or make the subtraction symbol (-) while they do this.

Gradually, students will think about these ideas in an abstract way and will be able read and represent numeracy ideas using just symbols instead of needing to explicitly link them to mental images or concrete materials.

This page uses Year 2 student Mahli as an example.

Mahli's teacher could use the following activities to teach Mahli how to read numbers up to 20.

## Teach students how to reason and think about numeracy concepts

Students need to be able to move between symbolic statements, word statements and quantities quickly and easily. All students, but particularly those with learning difficulties, need to be explicitly taught the language of numeracy and provided with opportunities to practise and consolidate this knowledge.

To form an understanding (and develop a more sophisticated understanding) of numeracy concepts, students need to think about them in particular ways. Students with learning difficulties may think about certain concepts in similar ways to younger students.

Until they develop their numeracy language and understanding these students will be unable to learn more complex numeracy knowledge and skills.

## Teach metacognitive strategies

Students with learning difficulties can find it challenging to reflect on their learning and direct their thinking. These metacognitive strategies need to be explicitly taught to help them to take ownership of their learning in numeracy and maths.

Teaching sentence stems will assist students to reflect on what they have learned (for example, 'I am learning about …' 'I didn't know …' 'I now know …' 'I will remember when doing … to …').

Encourage students to draw on these strategies at 3 separate points when working on a problem or learning activity.

At the beginning of the task: students interpret the problem using what they know and decide how it matches or doesn't fit with their existing knowledge. This includes planning how they will work through it.

While working through the task: students monitor their progress and have strategies prepared when they encounter obstacles or make errors and whether they need to change or reassess their approach.

After completing the task: students review what they have learned, acknowledging and making a note of their new understanding and how it adds to what they already know.

## Teach routines and provide opportunities for practise

Students will be most motivated when learning a new idea or skill for the first time. The aim is for them to eventually use this new knowledge or skill automatically. This is the result of learning, repetition and practise.

The more students practise and link this learning with what they already know, the more they will be able to use it with less effort and the more their numeracy will improve. For example, when multiplication becomes automatic through the memorisation of times tables, students use only a very small amount of their cognition allowing them to instead focus on how they need to apply the information or on other parts of the problem.

Being able to recall and use the names of written numbers, the names of the numbers in order, number facts, symbols and their meanings is crucial for all students and should form the basis of their numerical fluency.

To teach for fluency, provide tasks that are carefully graded for complexity and that ultimately require students to do more and more independently.

### Determine independence

Determining when a student is ready to demonstrate more independence and to what extent can be difficult. It is appropriate to give greater independence to a student when they consistently:

- identify and justify what word reading and/or comprehension strategies they will use to complete specific tasks
- demonstrate motivation or enthusiasm to engage in learning activities
- attempt (or express a desire to attempt) tasks by themselves and without assistance.

It's important to think carefully about the stages in which you will release responsibility for learning to a student and how you will monitor and record their progress. It can be easy to release too much responsibility too quickly and before students are completely ready.

For more information, visit Monitoring students' progress.

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