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Critical Thinking to solve maths problems

To request the Powerpoint Chris talks about in this piece please email

I work in a range of challenging schools and most often with year 11 students who have had a poor mathematics background. Many have them have been switched off from maths and I am interested in finding a set of questions that will strip away a lot of wording and will challenge critical thinking to solve problems and encourage students to think for themselves.

I want to change the students’ attitude and involvement in thinking about mathematical problems and to make them feel that they can use skills that they have previously learned to help them problem solve.
One of the things I have found, in working with a lot of year 11 students, is that they are often afraid to commit to answering in case they are wrong.

I want them to feel that they are able to understand and discuss questions without that fear.

It is important to make them feel successful and understand that there may be different ways of solving problems and that sometimes there is not just one correct way.

I hope that by discussing in pairs or 3s will help them and let them feel that they can share their ideas with the rest of the class.

Many of the questions will be diagrams with little information that hopefully will capture the students interest and therefore involvement.

The danger here is that they will think that they will know the answer without reading the question properly when it comes to examinations. I will therefore need to make sure that the types of questions are well balanced to make sure that this does not happen.

I had a few ideas about the approach to take;

  • show diagrams and ask the students what they think the problem could be.
  • ask what maths they know that they could use to solve the problem
  • give them a problem with a little information and give them time to think about the different skills they might use.
  • Get students to recall knowledge that they already have so that they can carry out methods proficiently
  • Let them try to solve the problems in two or threes. To enable them to reason with growing confidence.
  • Discuss the possible solutions with the whole group for a greater understanding by talking through the thinking that might lead me to a solution.

I decided to look at 3 levels of questioning for Foundation, intermediate and Higher Tier students, initially selecting six to ten questions for each level.

I wanted to see if other schools would be willing to learn and contribute to the project and have a set of questions that they could use, adapt and give me some feedback so I approached a couple of local schools, where I have worked with their year 11 students and they have expressed an interest in trialling it.

I set about writing questions and at the same time including teacher prompts that could be used if necessary, with the intention of adding to these as situations arise to make them more complete.

The main challenges:

  • To get year 11 students involved in the tasks and staying on task.
  • To ensure that the level of the “questions” is applicable for the students.
  • To make the tasks interesting so that the students would want to be involved.
  • Getting them to talk to each other about the problems.
  • Aim to get the students processing questions in a systematic manner.
  • Working in pairs or groups of 3 to encourage discussion.
  • To get students to recognize what they know and what they need to learn or revise.
  • Determine which tasks were relevant to which grade/tier.
  • Some will need challenge through greater depth whilst others will need support and even intervention.

Changes that were made
This will be an ongoing project and I envisage that the changes and developments will be too. I am very open to comments and suggestions that will improve this work, if it is to enhance students thinking to solve problems.

  • I decided to change the questioning to include an intermediate group of students and used the crossover type of questions that appear on both Higher and Foundation tier.
  • I extended this to include more groups within the schools this to make it a larger pilot scheme.
  • I included more teachers to cover this in other schools
  • Because some of the basic skills were lacking, I had to teach those skills before completing the questions
  • We also had to undertake some intervention for skills that needed revision

 What made the real difference?

  • Students being able to talk about maths and learn from each other.
  • Confidence was boosted
  • Groups arguing and discussing to justify their ideas and coming to a shared decision about solving the problems
  • Students modifying their thinking to solve problems
  • Students being prepared to tackle “unknown” problems using the mathematical skills that they had.

Questions for the teachers

  1. Were the students interested in this as a project?
  2. Did they get involved?
  3. Were they willing to discuss their ideas?
  4. Were they able to discuss in a sensible but passionate manner?
  5. Were they worried if their answer was not correct?
  6. Did they work in pairs or groups?
  7. How did they resolve differences?
  8. Did any of them modify their strategy midway?
  9. Did they change their answers? Why?
  10. Were they able to justify their answers?
  11. How much did you have to prompt them?
  12. Were the prompts useful?
  13. Do you feel that this has helped them to make progress?
  14. Diid their confidence with Mathematics improve as a result?
  15. Do you have any further comments to make?

2 Replies to “Critical Thinking to solve maths problems”

  1. Fiona Bray says:

    I would like to take part and trial these questions.

  2. Nexus Education says:

    Hello Fiona, thank you for the comment. I will email the documents across to you now. Don’t forget to also visit our homepage and subscribe to our newsletter for more great resources like this!! Thanks, Rhiannon

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The author

Chris is a Freelance Education Consultant, and senior leader, with a Leadership and Mathematics Specialism. She support Leadership teams in Teacher training, accelerating attainment, behaviour management and Mathematics in primary and Secondary schools.

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