- Resources to support development of the Four Proficiencies -

The Four Proficiencies

The mathematical proficiencies – reasoning, problem solving, understanding and fluency – are closely intertwined, each one made stronger by the others.

Developing a capacity to reason, make sense of challenging problems, show deep conceptual understanding and mathematical fluency are key attributes assessed by the Trends in International Mathematics and Science Study) TIMSS and the Programme for International Student Assessment (PISA). The Organisation for Economic Co-operation and Development (OECD) deem these to be essential to the diverse array of maths-related situations that learners will encounter throughout their lives. They represent a mathematics passport to future employment, equipping Victorian learners to be critical and creative thinkers and productive citizens.

As a consequence, the resources offered here tap into the efforts of educational researchers and practitioners from Australia and around the world.

An experienced team has searched through, weighed up and assessed the tangle of resources available on the web and selected those that are accessible, research-informed, reliable and well-suited to Victorian teachers.  

These resources, which include a mix of shorter and longer papers, videos and illustrations of practice, have been organised according to different levels of need and readiness, with consideration of the time required to connect with and make sense of them. A number of reflective tools have been included to support sense-making and team dialogue.

Each linked resource includes a brief summary to help support selection.

Embracing the proficiencies means teaching young people to think and reason as they learn mathematics, stretching and challenging them to pose and solve meaningful problems, prioritising sense-making, patience and understanding over memorising, being quick or simply getting ‘right answers.’ Mathematics becomes more meaningful when the proficiencies become a focus of teaching and learning.

- Peter Sullivan -

An overview of the proficiencies

- Activities for professional learning -

Why focus on the proficiencies?

Start a conversation in Professional Learning Teams or other professional learning structures within your school context about the proficiencies of the mathematics curriculum by using this stimulus resource. 

After supporting your team to read through this stimulus, ask the following questions about what they noticed, reacted to or wondered:

The four proficiencies stimulus document:

  • What did you feel was the most compelling reason provided as to the need to consider the proficiencies?
  • Did this paper challenge your current thinking about teaching mathematics? If so, in what way?
  • To what extent are the proficiencies evident in your curriculum documentation?
  • How confident are you that you currently address the proficiencies in your teaching?
  • How will students benefit from a stronger emphasis on the proficiencies, do you think?
  • What impact will an emphasis on the proficiencies likely have on VCE attainment and choices?

You may wish to use one of these discussion protocols.

Opening up a conversation about the proficiencies and the current state of these in your school will support you, as a leader to develop a clearer picture of underlying belief systems of your teachers and how these impact on the readiness levels for them to take on changes to their practice.

Viviane Robinson's book "Reduce Change to Increase Improvement" (Corwin Press, 2018) provides some great advice around working with belief systems and Theories of Action. 


- Ideas for the questions to ask and resources to use at each stage of the Improvement Cycle -

Using the FISO Improvement cycle to support a focus on the proficiencies

Evaluate and Diagnose

To what extent are the proficiencies evident in the mathematics teaching and learning program in your school?

  • Use the provided resources to research each proficiency identifying the key features of each in practice (so that there is a shared understanding of what to look for).

    Analyse curriculum documentation for evidence of the proficiencies in the teaching and learning program and key tasks using the 'Reviewing and considering maths LEARNING, resources and apps' protocol.

  • Use the ‘reviewing and considering’ protocol or the checklist from MAV

    Collect information from your students as to how they experience mathematics teaching and learning in your school.

  • Student survey (When it comes to learning mathematics)

    With colleagues, reflect on the extent to which these proficiencies are emphasised in practice. Classroom observations of practice and Professional Learning Team reflections are a great way to do this. 

  • Classroom observation protocol

Prioritise and set goals

Analyse the data collected in the evaluate and diagnose stage to identify:

Where do your priorities for improvement in the enactment of the proficiencies need to be in order to most advance student learning?

Which proficiencies will you focus on in which classrooms?

Develop and plan

What changes will you implement? What new activities will you trial?

Who will you engage to work with you? What sources of support, expertise and leadership can you draw on?

Implement and monitor

Monitor your progress through ongoing collection of data and observations.

Discuss what is happening in classrooms in your PLT groups to identify whether improvement is occuring or if you need to revisit the goals and priorities you set to really improve student learning. 

Reflect on your progress and identify next steps using the data that you have collected and the observations that you made in earlier phases.

Re-evaluate to see if there are observable shifts in student or teacher behaviours and learning outcomes, as a result.

To support your investigation of the resources contained in this toolkit, this package of protocols and supports has been developed for you to draw on throughout each of these stages.

- Peter Burrows, Larrissa Raymond and Doug Clarke -

The verbs of the four proficiencies

This short paper outlines the various verbs that can be used for each of the four proficiencies. 

A very useful resource for planning questioning and lessons to highlight and develop the proficiencies in the teaching and learning of mathematics.

- A professional learning resource -

Exploring Learner Mindsets and Dispositions in Mathematics

This professional learning resource from the team at EdPartnerships provides all of the resources needed for schools, teams of teachers or individual practitioners to explore many of the barriers to student achievement in mathematics. It provides tools and scaffolds to support investigation of these barriers, develop strategies to overcome these and then test this with students. 
- Further resources and supports for a deep dive into each of the proficiencies -

The Proficiencies in Detail

Click on each of the links below to access more detailed information, guidance and advice as well as a range of professional learning and classroom support resources for each of the proficiencies:




Problem Solving