Support reasoning and deep thinking

Mathematics has been described by Zevenbergen, Dole & Wright (2004) as:

  • A way of thinking, seeing, and organising the world - organising and analysing information and events in a systematic way
  • A language - a precise way to communicate complex ideas
  • A tool - useful for efficiently solving problems and making wise decisions
  • A form of art - mathematics can be inherently beautiful
  • Power - a contributor to success, a social filter, a foundation for the powerful forms of knowledge.

Often, educators focus on mathematics as a tool for arriving at a correct answer and don’t provide students with the opportunity to appreciate the other facets of mathematics.

In order for students to appreciate the richness of mathematics, they need opportunities to experience these different ways of engaging with mathematics, and opportunities to reflect on how they use and value mathematics. It’s important to model to students that we value learning rather than performance (Sullivan et al 2020).

It is difficult to have a mathematically powerful classroom if the classroom is one that is predicated solely on finding answers as opposed to one that values noticing the process or structure so that students can reach the answer to the immediate problem, but also generalise what they have learned in order to be able to solve future problems.

(Day & Hurrell 2018)

 

Students can also confuse the speed at which they can solve a problem with mathematical proficiency and can struggle to persist when they struggle to find a solution. Clarke & Clarke (2003) reported that ‘students often believe that if they cannot solve a problem almost immediately, it is impossible.’ 

Key ideas to promote:

> The journey is as important as the destination

> Maths problems can have more than one answer

> There can be multiple ways to solve a maths problem

> Being able to produce a rapid answer doesn’t indicate the quality of mathematics reasoning

> Mathematical habits of mind are valuable and transferable

> Mathematical ideas are connected

 

Reflect

    • Do you provide all students with opportunities to explore the different facets of maths learning? Are less-confident students primarily focussed on skill-based activities?
    • In your teaching, how do you recognise and name mathematical skills and habits of mind?
    • How do you boost the maths status of students who struggle with maths?
    • How do you recognise different ways of approaching problems?

Try this

In your classroom

  • Select rich problems to use with students and focus on identifying patterns and problem-solving. Read more about designing mathematics investigations  
  • Focus on student thinking and explanations rather than single answers. For example, see these resources on transforming tasks
  • Model the struggle that is often involved in solving genuine problems
  • Identify the enabling prompts and scaffolds that will support students to make a start on solving problems
  • Use a range of representations and support students to move flexibly between representations. Support students to generate their own representations
  • Notice students’ maths skills and habits of mind, and recognise these in front of their peers
  • Incorporate open-ended tasks that encourage students to develop strategies, make use of mathematical tools and focus on explanations
  • Use maths tasks that are ‘low floor and high ceiling’ that can be approached in multiple ways
  • Provide opportunities for students to reflect on their mathematical journey, such as through journaling
  • Assess students’ workbooks regularly with a view to valuing students’ efforts in working mathematically
  • Link maths skills and mindsets to diverse future careers

In your school

  • In the school newsletter, share problems students have worked on in class, showcasing two or three work samples and explaining how students used different strategies to solve the same problem
  • In the school newsletter or on school social media, provide problems or puzzles for families to work on together. For example, check out these primary newsletter ideas