I want to talk about why students forget so much of what they learn.

Endless exercises, worked examples & precise definitions aren't enough. So, what’s missing?

**Reasoning.**

It's the glue that holds maths learning together.

Students need regular opportunities to:

- explain,
- justify,
- compare, and
- reflect on new learning.

When they do this, students can then actually *trust* that the maths they’re doing isn’t just some process to be memorised, but that it makes purposeful, meaningful sense.

But, what does this look like in practice?

Here are *five easy-to-implement task types *that together invite students to think critically about what they are doing – and, ultimately, become stronger and more confident in maths:

## 5 Strategies for Strengthening Mathematical Reasoning

### STRATEGY 1: Incorrect Solution

How it works:

- Present students with the solution to a problem that is incorrect in some way, but that offers us something valuable to think about.
- Ask students: Why might I like this solution?
- Then: How would you help this student with a similar problem next time?

Examples:

### STRATEGY 2: What's the question?

How it works:

- Take a standard problem from the topic students are learning about.
- Present students with only the answer to that problem, and ask: What's the question?
- Invite students to solve one another’s questions.

Examples:

- The total is 11.
- The area is 48 square metres.
- The expression simplifies to 9ab.
- The average age is 11.

### STRATEGY 3: Card Sort

How it works:

- Choose 5-10 standard problems from the topic students are learning about.
- For each problem, create 3 cards showing different representations of that problem, e.g. diagram, table, answer, question, working out.
- Present students with the cards to match up.
- For an extra challenge, make a couple of the cards blank. Students then need to decide what the missing information is.

Examples:

- Match up a multiplication (e.g. 3 x 15) with its product and an array
- Match up linear equations with their graph and table of values.

### STRATEGY 4: Choose a Group

How it works:

- Present students with approximately 10 examples of a concept they are learning about.
- Invite them to identify two groups that they can place the 10 examples into
- Ask: Can you come up with a name to describe each of your two groups? Now, add two more examples that can fit into each of your groups.

Examples:

- 10 different angles diagrams
- 10 different algebraic expressions
- 10 different collections of dots.

### STRATEGY 5: Always, Sometimes or Never?

How it works:

- Make a space in the room where students can stand along a continuum. One end represents ‘Always’, the other end represents ‘Never’ and in the middle is ‘Sometimes’
- Present students with different mathematical students. For each one, students need to decide if it is Always, Sometimes or Never true.
- Invite discussion about students’ positions for each statement.

Examples:

- Can you A/S/N divide a number by 2?
- Is the perimeter of a rectangle A/S/N less than its area?
- Does subtracting A/S/N make a number smaller?

## SUMMARY

Five strategies for strengthening mathematical reasoning:

- Incorrect Solution
- What's the Question
- Card Sort
- Choose A Group
- Always, Sometimes or Never

### What can you expect from these strategies?

Your students will:

- Reflect on & make sense of their learning,
- Better remember what they learn, and
- Build confidence in themselves.

As a teacher, you will:

- Help your students to think for themselves,
- Get formative data & rich insights into what your students know, and
- Have quick strategies for going helping students go deeper in their learning.