5 Strategies for Improving Student Reasoning

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?


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

5 Tasks for Strengthening Mathematical Reasoning  1. Incorrect solution 
2. What's the question 
3. Card sort 
4. Choose a group 
5. Always, sometimes or never

STRATEGY 1: Incorrect Solution

How it works:

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


STRATEGY 2: What's the question?

How it works:

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


  • 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:

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


  • 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:

  1. Present students with approximately 10 examples of a concept they are learning about.
  2. Invite them to identify two groups that they can place the 10 examples into
  3. 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.


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

STRATEGY 5: Always, Sometimes or Never?

How it works:

  1. 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’
  2. Present students with different mathematical students. For each one, students need to decide if it is Always, Sometimes or Never true.
  3. Invite discussion about students’ positions for each statement.


  • 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?


Five strategies for strengthening mathematical reasoning:

  1. Incorrect Solution
  2. What's the Question
  3. Card Sort
  4. Choose A Group
  5. 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.

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