We get students to think hard and explore new concepts before the teacher gives the formal explanations.
This helps the maths to stick better, builds new connections in the
- Download our published research – this shows PAT M growth of 12-18 months higher than annual expectations for the lowest 20% of students – presented in Auckland, 2018
- New paper on the nature of questioning in challenging tasks presented in Ireland, 2019
How it works:
Back to Front Maths is a teaching approach rather than a set of resources. In this approach, students:
- Start by experimenting with unfamiliar concepts to develop new ideas. This process also guides the teacher to uncover and confront misconceptions.
- Students explore their new ideas and connect them with more familiar maths.
- Students formalise their findings into mathematical principles, including algorithms and formulae.
- Students extend and generalise the new mathematical principles that they have learned to other areas of the curriculum.
Evidence: PAT Maths and NAPLAN Improvements
In 2018, Tierney Kennedy published a peer-reviewed journal article showing an effect size of 0.7 above the yearly expectations in PAT Maths over a two-year project: Kennedy – Intervention using challenging tasks and conceptual change
Our NAPLAN results also show statistically significant higher cohort growth than similar schools:
Here are some graphs of our PAT M improvement rates, combined from all our projects in 2020 and 2021.
2021 Project Update:
On average, schools in projects with us in 2021 have improved their PAT M growth by 40% on their baseline year. The red lines below show the average baseline growth and the blue lines show 2021. In addition, 46% of schools in projects with us have achieved their highest ever NAPLAN results. Well done everyone!
The lowest 20% of students progressed on standardised testing at the rate of 3 times government expectations.
The growth resulted in a relative gain of 9% in percentile rankings for students.
What can subscribers access?
This section enables users to download, print and use any activity from any grade with their students. These lessons cover every requirement from the Australian Curriculum, including the proficiency strands, from Foundation to year 7.
Lesson plans for the Journal problems clearly explain how to implement problem-based teaching, with misconceptions, leading questions and suggestions for differentiation included for every problem.
Printable activities include Journal problems for introducing new concepts through problem-solving and diagnosing misconceptions, and Blast activities for using questioning to build the deep understanding necessary to develop mathematically.
- Sample – Developmental sequence for fractions for year 3
- Sample – Year 1 lesson on two-digit numbers
- Sample – Fluency activity: Make ten dominoes
- Free trial offer – download sample activities from each different grade here.
Assessment in Back-to-Front Maths is based on the proficiency strands, just like in the achievement standards. This section clearly and simply explains what is means to receive an A, B, C, D or E and what to look for to make these judgements. This includes a range of criteria sheets, assessment schedules and explanations provided in both teacher and parent-friendly language.
Moderation tasks are also included for taking base-line, mid-year and end-year standardised measurements. These tasks are designed with deliberately low-level content, but with very non-standard thinking, to more accurately pinpoint growth in problem-solving, reasoning and understanding.
Eight investigations for each year level from 3-7 have been included in this section. Each investigation is designed to cover concepts from across at least three year levels. These real-life tasks vary in length from a few hours to a whole term, and list journal problems and blast activities used to support the investigation.
Alignment tables and term planners enable teachers to quickly and simply design units of work for their students using Microsoft WORD documents. Detailed explanations of how to fit everything in, and how to provide differentiation for both support and extension students are also included in this section.
What would you like to find out next?
- How the program and resources work
- How to plan your year program
- What I need to know about the Australian Curriculum
- Booking Professional Learning
- Upcoming Training Events
- Read about Our Consultants