Effective mathematics teaching is the result of careful and purposeful planning. This blog post is the first in a series of three that will explore the key elements of purposeful planning in mathematics education, drawing on the insights of the Australian Association of Mathematics Teachers (AAMT) 2025 position on pedagogy in mathematics and Maths Australia’s ‘I-CRAVE Maths’ philosophy and methodology.
- Setting the Stage for Success: Clear Learning Goals and Success Criteria
Purposeful planning starts with a clear vision of what we want our students to achieve. While different educational frameworks might phrase it in various ways, the central idea is consistent: teachers need to establish clear learning goals and success criteria.
Maths Australia’s ‘I-CRAVE Maths’ emphasises the importance of students grasping the ‘why’ behind mathematical concepts. This aligns with setting learning goals by ensuring that students understand the purpose and expectations of their learning journey. Furthermore, ‘I-CRAVE Maths’ underscores the significance of students understanding the purpose of their learning, which corresponds to establishing success criteria by ensuring students know what they need to achieve.
By clearly defining learning goals and success criteria, teachers provide students with a roadmap for their learning, helping them understand their destination and how to recognise when they have arrived.
- Building Bridges: The Importance of Prior Knowledge
A vital aspect of purposeful planning is recognising and building upon students’ existing knowledge. Effective mathematics teaching acknowledges that students enter the classroom with a range of prior knowledge and experiences.
Maths Australia’s ‘I-CRAVE Maths’ training highlights the importance of understanding children’s developmental stages and considering their current level of mastery. This aligns with AAMT’s emphasis on building on prior knowledge by stressing the importance of understanding students’ developmental stages and prior learning experiences.
One effective way to build on prior knowledge is through a well-structured sequential framework of instruction. Such a framework involves building mastery upon mastery, understanding upon understanding. For example, this involves progressions like:
- Counting (0-9) to place value (0-9 hundreds, tens, units)
- Addition (single-digit static then with regrouping, then multi-digit static then regrouping)
- Subtraction (single-digit static then with regrouping, then multi-digit static then regrouping)
- Multiplication (single-digit then multi-digit)
- Division (single-digit then multi-digit)
- Whole number understanding — fractions, then fraction decimals, then fraction percentages, building strong links between each as a communication tool in different life settings.
By identifying mastery of broader maths concepts through sequential assessments and instruction of mathematical concepts, teachers can create a learning pathway that enables students to construct new knowledge on solid foundations.
3. Choosing the Right Tools: Intentional Task Selection
Purposeful planning also involves the intentional selection of tasks that will effectively support student learning. The tasks teachers choose should align with the learning goals and provide an appropriate level of cognitive challenge.
The ‘I-CRAVE Maths’ methodology demonstrates intentional task selection through its structured progression from concrete to representational to abstract. This aligns with AAMT’s recommendation to carefully choose tasks that align with learning goals and offer suitable cognitive challenges.
Moreover, ‘I-CRAVE Maths’ emphasises differentiating instruction and using varied tasks to cater to diverse learning styles and needs, further demonstrating intentional task selection. By offering a range of tasks, teachers can ensure that all students can engage with the material in a way that suits their individual learning needs.
4. Connecting the Dots: Making Connections to the Real World
Mathematics is not an isolated, abstract subject. Purposeful planning involves forging connections between mathematical concepts and the real world, helping students recognise the relevance and importance of their learning.
Maths Australia’s ‘I-CRAVE Maths’ indicates the importance of linking concepts to real-world applications, progressing a student only when it can be determined that the student can link life situations to abstract symbolic representations with confidence and accuracy. This aligns with AAMT’s practice of making connections by emphasising the importance of relating mathematical concepts to real-world contexts.
Additionally, the use of concrete manipulatives and visual representations can help students perceive the connections between concrete experiences and abstract concepts, reflecting AAMT’s emphasis on highlighting relationships within and across mathematical ideas. By establishing these connections, teachers can foster a deeper and more meaningful comprehension of mathematics.
Purposeful planning is fundamental to effective mathematics teaching. By establishing clear learning goals, building on prior knowledge, intentionally selecting tasks, and connecting to the real world, teachers can cultivate a dynamic and engaging learning environment that empowers students to develop a strong foundation in mathematics.
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