Getting Started

Students who experiment with new concepts prior to formal explanations understand new concepts more quickly, develop more connected understanding and retain what they have learned.

We know it works, because we check every year...

Improving Learning Rates on Standardised Testing Through a Balanced Teaching Cycle: A Tale of Three Schools
pp.10-17 of Teaching Mathematics April 2023, QAMT

Check out the rest of our research, including our latest PAT Maths and NAPLAN results, at the bottom of this page.

Why Back to Front Maths Works

Back to Front Maths is a balanced teaching approach formed by combining multiple high-impact strategies, rather than simply a set of resources. It is this combination of strategies, underpinned by our unique developmental sequence, that results in such reliably high students gains.

In our teaching cycle, students:

  1. Start by experimenting with unfamiliar concepts to develop new ideas. This process also guides the teacher to uncover misconceptions, addressing them with our conceptual-change questioning process.
  2.  Students make and test conjectures, exploring new ideas and connecting them with more familiar maths.
  3. Next, learning is formalised into mathematical principles, including algorithms and formulae.
  4. Principles are extended, transferred and generalised to other areas of the curriculum, linking concepts by way of flexible strategies.

Teacher support

Teachers are supported, not only with a flexible work-program that helps build connections between seemingly unrelated areas of maths, but also with lesson plans that include detailed questioning, flexible strategies and differentiation across multiple year levels. Assessment criteria sheets and moderation tasks provide strong guidance for reporting. 

Over 40 hours of videos provide professional learning on important content areas, pedagogical approaches and even advice on difficult to manage situations. Teachers who struggle with their own confidence find these an invaluable tool, both to build their own mathematical understanding, and to support their class.

Our Teaching Cycle

Over the course of a topic, you will use several different types of lessons.

Experimental problem 

Experimental problems introduce new learning, encouraging students to make and test conjectures, and creating the opportunity for us to observe any misconceptions. Questioning provides guidance for how to confront misconceptions during the lesson, and differentiation suggestions enable adaptation over multiple year levels. During this lesson it is not important to end up at the right answer… try to delay the “summary” phase until the start of the next lesson to encourage students to think about it over night.

Explicit teaching of flexible strategies

Start by asking students to edit or review their work from the previous lesson. Next, ask specific students to share strategies that you want to encourage others to use. As they explain their process, summarise their thinking into clear steps and outline them on the board, re-explaining or adding more detail as needed. Add your own strategy as well, being sure to focus on strategies that are efficient, flexible, appropriate and accurate. Use the questions within the lesson to focus on the underlying connections and help students to understand what they are doing. Each question builds in complexity and asks students to identify the pattern. The final few are great for extension. Provide as many practice questions as necessary, but remember that spacing these out over time is more effective.

Extend and generalise

These lessons focus on determining when, where and in which circumstances the steps will work. They extend student thinking using non-routine questions that require working backwards or manipulating a formula. These kinds of lessons also include real-world connections, investigations or modelling tasks.

Interleaved and spaced retrieval for fluency

Encourage retrieval and retention by requiring students to complete questions that they have forgotten how to answer, and by ensuring that the same strategy cannot be used to answer multiple questions in a row. 

Why subscribe?

Developmental work program

  • Content aligns week-to-week across all year levels from Foundation to Year 6 
  • Every 5th week is kept free for flexible teaching
  • 3 content lessons + 1 interleaved retrieval lesson + 1 flexible lesson each week
  • Flexible strategies link number concepts to non-number concepts each term 
  • Investigations, extension tasks and modelling are built in to the program for easy access

Assessment criteria

Assessment criteria for F-8 and 11-12 Essential Maths embed both the content and proficiency requirements from the Achievement Standard. Further depth is added to the A and B levels using the content descriptors and elaborations.

Moderation tasks for problem solving, reasoning and understanding provide a single-lesson point of calibrating for overall judgement.
Click here to download a sample task for year 6

Diagnostic testing and tracking

Our proprietary stage testing and tracking sequence enables teachers to track the progress of students across their whole schooling. It is designed to be used with either groups, or whole classes rather than requiring individual testing.


Professional learning videos

We have over 40 hours of professional learning videos embedded on the website. This video demonstrates how to use an array strategy for multiplication and division, and how to extend the strategy for measurement, algebra and probability.

Our research

Not only does our approach work, it works exceptionally well and reliably. Every year we collect data on PAT M and NAPLAN results from schools working in projects with us. Here is some of our latest data, along with how our schools progressed during the pandemic, and a selection of our peer-reviewed research data.

What happens within the first year? 

This graph shows the combined growth rates from all schools with an ICSEA under 1000 that worked with us on a targeted improvement project at any time between 2018 and 2023. The black line shows one year of growth, measured according to the ACER PAT M 50% figures. Growth rate improved by 37% (P<0.05).

The red is the growth from the year before our project began. The blue shows the added growth made by students after a single year.

What happens over three years?

This graph shows the combined growth rates from students that we could track across 4 successive PAT tests in a three-year long project with three primary schools, together with the 50th percentile figures from ACER. Student progress on PAT M improved by 75% across the schools (P<0.05).

Download the paper here:
Improving Learning Rates on Standardised Testing Through a Balanced Teaching Cycle

What happens in a pandemic?

13 schools worked with us on projects with us throughout the peak of the pandemic. Whereas nationally NAPLAN results experienced a dramatic decline, our schools improved, closing the gap to Australian schools entirely by 2023.

2021: Our schools’ growth rate on PAT M increased by 40% (P<0.05). The graph below shows results for 2935 students across 16 schools compared to their baseline year.

2022: 77% of schools working with us on projects throughout 2021 and 2022 had their highest ever NAPLAN results. 

2023: This graph shows the results for every teacher working with us on an open project during 2023, with the 50th percentile curve added for context.

Here are some of our peer-reviewed papers