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Pedagogy in Mathematics – how Maths Trek aligns with key research findings

Maths Trek 18/5/25

The Australian Association of Mathematics Teachers (AAMT) recently released their Pedagogy in Mathematics position paper, sparking considerable interest among educators across Australia. We unpacked its key findings and how they can be applied to teaching when using Maths Trek’s Foundation to Year 6 resources.

The report highlights the importance of using a variety of research sources and taking into account a teacher’s own judgement, tailored to the specific context of their classroom and students. Further, AAMT has translated these findings into actionable strategies, organised into three key practices.

Practice 1: Purposeful planning

Establishing clear learning goals and success criteria

‘When learning goals are clear to teachers, they can support students to understand what they are learning and why, enabling them to focus their efforts, monitor their progress, and take ownership of their learning.’

Every Maths Trek topic includes a succinct learning intention and success criteria so both teachers and students are clear on the outcomes of the lesson ahead. The lesson slideshow begins with a student-friendly summary, with the more detailed learning intention and success criteria readily available to the teacher in the lesson guide to use as a discussion prompt.

Building on prior knowledge

‘To do this effectively, teachers consider prerequisite knowledge and skills, common preconceptions and misconceptions, students’ prior experiences, and how current learning connects to future mathematical development.’

The Maths Trek Yearly Plans have been carefully curated to allow students to build on their knowledge effectively throughout the year and across the year levels. In Maths Trek, students are introduced to core concepts systematically and cumulatively, enabling them to comprehend new concepts more easily. This approach ensures a smooth progression from one concept to the next, facilitating the scaffolding of mathematical concepts and boosting students’ capacity and confidence in tackling new challenges.

Intentional task selection

‘Different types of tasks serve different purposes across a learning sequence, such as introducing new concepts, stimulating mathematical thinking and reasoning, making connections, developing understanding, building fluency and transferring learning.’

Maths Trek offers a rich variety of lessons, activities and tools to serve different purposes – from topic lessons used to teach core maths concepts, through to investigations that connect multiple topics through real-world contexts, to problem-solving lessons that foster critical thinking skills and provide a platform for important discussions and reasoning processes.

Making connections

‘Making connections involves deliberately highlighting relationships within mathematical concepts, across areas of mathematics, to other learning areas, and between mathematics and real-world contexts to deepen understanding. Connections don’t always happen automatically; teachers need to deliberately plan for them.’

The investigations in Maths Trek are fundamentally designed to allow students to make connections using mathematics in real-world contexts – from creating a map and directions to trek through Kakadu National Park, to investigating how much water is lost from a dripping tap and even developing a budget to spend at the local show.

Maths Trek has done the heavy lifting in designing investigations that incorporate content from previously learned topics and immerse students in unfamiliar, extended mathematical problems. This allows teachers to focus on facilitating rich discussions and helping students make connections to deepen their understanding.

Practice 2: Developing mathematical proficiency

Clear explanations

‘Teachers carefully consider both the amount of new information presented and how it is structured, using written, visual and verbal explanations strategically to manage students’ cognitive load.’

Maths Trek lesson slides have been carefully designed to step information out at a student-friendly pace using clear worked examples. The on-screen text is kept minimal to reduce students’ cognitive load, while the lesson guide provides teachers with extra detail and explanation prompts to support explicit teaching.

Representations and manipulatives

‘Engaging with multiple representations and manipulatives helps students access mathematical concepts, transition from concrete to abstract thinking, extend their reasoning, make connections between ideas and build a robust understanding.’

Maths Trek employs a variety of digital and physical manipulatives to help represent mathematical concepts. The suite of interactive tools, including a Hundreds chart, Place value chart, Spinner and Clock, is embedded in context within the lesson, or can be used for free practice when required. Concrete resources are specified for relevant lessons and investigations – teachers are informed in the Lesson Overview of exactly which resources are required and when they’ll be used. Alternatively, this information is conveniently collated under the Preparation and Planning section in the Weekly Resources Lists so teachers can plan ahead when sharing concrete materials between classrooms.

Mathematical dialogue and discussion

‘Through these discussions, students articulate and justify their reasoning, actively listen to others’ ideas, build on peer contributions, and participate in both whole-class and small group-settings.’

Maths Trek is brimming with opportunities for students to engage in mathematical dialogue and discussion. Teachers are supported to facilitate these discussions through problem-solving tasks and investigations, and what’s more, Maths Trek includes Critical Thinking lessons which help to explicitly teach cognitive verbs such as prove, justify or compare in mathematical concepts. Recognising and examining cognitive verbs helps provide students with structured road maps for giving well-reasoned and clearly articulated answers.

Maintaining appropriate challenge

‘Maintaining appropriate challenge fosters mathematical growth by ensuring all students are cognitively stretched, actively participate and feel capable and supported in their learning.’

On the surface, this strategy could be mistaken for providing differentiated instruction (we’ll go into that later), but its focus is more on ensuring the environment and classroom culture is nurtured in such a way that students are challenged but also supported.

Maths Trek assists teachers to foster this all-important learning environment. Lessons in the program follow the Gradual Release of Responsibility model of I do, We do, You do. When all students are explicitly taught the concepts, followed by a class collaboration in applying the concept in practice, it sets them up in a supportive environment to go on and attempt further activities independently.

As a part of this process, topic lessons include open-ended and targeted question prompts that enable students to actively participate in the learning, which can also provide a confidence boost in a safe and supportive environment.

Practice 3: Adapting to and supporting all learners

Differentiated teaching

‘When implemented effectively, differentiated teaching enables all students to engage meaningfully with challenging mathematical content, make progress in their learning and achieve their potential as mathematical learners.’

The findings encourage teachers to remain flexible and responsive in their differentiated teaching, rather than placing all students on the same pathway for every lesson. Teachers should consider the broad array of resources and tools they can draw from for differentiated instruction and continuously evaluate when and how the resources should be best used.

Every topic in Maths Trek includes differentiation tasks to further support or extend students. Topics from Year 2 upwards also include an extra challenge for fast finishers. Daily Number Practice is an interactive tool that helps build fluency in maths, with eight levels of progression for each of the four operations. Problem-solving strategies include two to three Your turn tasks that increase in difficulty so teachers can instruct more capable students to complete all three, while working with students who require support on the first task. Investigations include an Inquiry question to further extend students who benefit from an extra challenge.

Strategic questioning

‘Effective questioning begins with careful planning, where teachers design questions to align with learning goals and consider how to pose them effectively.’

For teachers using Maths Trek, purposeful and contextual questions are provided throughout the program, saving valuable time and providing opportunities to develop mathematical understanding through discussion.

The open-ended and targeted questions in lesson slides not only serve as discussion prompts, but the ongoing act of questioning in maths lessons also helps students develop their communication and reasoning skills, while fostering a safe and collaborative learning environment.

Guiding and focus questions are also included as part of the teacher notes for every investigation. Questions like What information do you need to collect? to Were you able to include everything from your wish list in your final budget? Why/Why not? and What mathematical language did you use in your instructions? are conveniently at your fingertips when the opportunity for strategic questioning arises.

For each problem-solving strategy, taught from Y1 upwards, there is a stepped-out Work together problem that uses targeted questioning to unpack and then solve the problem as a class before students attempt to solve other problems independently.

All problem-solving practice units also feature a question related to the main problem to extend thinking and generate discussion about how students would approach the question.

Practice and consolidation

‘Other consolidation strategies include collaborative group work, classroom discussion, peer teaching, and transferring learning to new or unfamiliar contexts.’

Maths Trek offers targeted practice of lesson content, but what truly sets it apart is its investigations. These investigations provide additional reinforcement of mathematical concepts through collaborative group work, classroom discussions, peer teaching and applying learning to new or unfamiliar contexts. The introductory lesson for each investigation provides an opportunity to discuss, learn or revise any important words in the context of the investigation. Students complete a mix of individual, paired and group activities using online and print resources. These activities provide opportunities for problem-solving, questioning, discussion and critical thinking, helping students build independence and grow in confidence.

From Year 1 upwards, Maths Trek also has dedicated problem-solving practice units which challenge students to choose from previously learned problem-solving strategies and apply them to unfamiliar problems. Explanatory notes and solution working images support teachers to lead a discussion about how the problem can be solved and encourage students to share alternatives.

Effective feedback

‘By gathering evidence throughout a learning sequence, teachers monitor progress and adapt their teaching to better meet students’ needs.’

In order to provide feedback, teachers require resources and tools that allow them to monitor progress. Maths Trek provides a range of formative methods to assess student understanding. A revision lesson is conducted every few weeks – this allows teachers to easily identify which topics students have grasped and which topics may require revisiting. Leading up to Maths Trek’s termly summative tests, this frequent formative check-in ensures feedback is given to students in a timely manner. Maths Trek also provides Problem-Solving Checklists with a date and comments section to record feedback prompts. Investigations come with a Cover sheet or Investigation report that includes a formative assessment checklist section to provide specific feedback.

Framework for action – professional learning is key!

Underpinning the key findings and recommendations, the report acknowledges that when it comes to teaching mathematics, educators should be flexible to suit their specific circumstances. The focus should be on ‘building professional expertise rather than prescribing particular approaches’. Its recommended framework for action strongly encourages schools to provide opportunities for their educators to expand their teaching capabilities through professional learning and peer collaboration.

Schools can take advantage of Maths Trek’s free professional learning workshops, with workshop offerings including:

• Delivering Impactful Lessons with Maths Trek
• Enhancing your Student’s Critical Thinking Skills in Numeracy

Congratulations to the AAMT for creating such a valuable and accessible report on best practices in mathematics pedagogy. We’re sure educators across the country are finding it as useful and insightful as we have.

Firefly Education would like to acknowledge the kind permission of the Australian Association of Mathematics Teachers (AAMT) to write this article based on their Pedagogy in Mathematics position paper. Firefly Education is not associated with AAMT and copyright for the position paper belongs to AAMT. To access the position paper, please visit https://go.aamt.edu.au/2025Pedagogy.

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