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Peter Sullivan
Planning, Teaching & Assessing: Six Key Principles for Effective Maths Instruction
When planning your mathematics program, it’s essential to align your teaching with evidence-based strategies. In my book Teaching Mathematics: Using research-informed strategies (2011), I outline six key principles that provide a strong framework for effective mathematics lessons.
1. Articulating Goals
Start by identifying the big mathematical ideas your class needs to learn and making them visible for students. Planning becomes far more targeted when you clearly communicate to students the learning goal and how they will engage with it.
2. Making Connections
Successful maths lessons build on what students already know — both their mathematical understanding and their experiences. Establishing links to prior learning, real-world contexts, and cultural knowledges helps students see relevance and deepen understanding.
3. Fostering Engagement
Engagement must go beyond worksheets. Use rich, open-ended tasks, games, collaborative talk and multiple representations (concrete, visual, symbolic) to allow students to explore, make decisions and develop mathematical thinking.
4. Differentiating Challenges
Students come with varied levels of readiness, and your planning must include strategies both to support those who need reinforcement and to challenge those ready for extension. Targeted teaching groups, thoughtful questioning, meaningful feedback and collaborative tasks help meet this diversity.
5. Structuring Lessons
A well-planned lesson sequence is critical: introduction of the goal, development of ideas, opportunities for students to explore and apply, teacher summarisation and consolidation. Also include explicit teaching, multiple exposures, and design for all learners (e.g., through a Universal Design for Learning lens).
6. Promoting Fluency and Transfer
Fluency is more than speed. It involves automaticity of basic skills, purposeful practice, and most importantly transfer of learning into new contexts. Spaced, interleaved and retrieval practice strategies support retention; metacognitive strategies empower students to reflect on and regulate their own learning.
Why this matters for your planning
When you embed these six principles into your planning you ensure that your lessons are not just activities, but purposeful sequences of learning. You move beyond “we’ll do this page today” to “we’ll work toward this goal, build on what students know, engage them meaningfully, challenge appropriately, structure the flow, and support transfer.” For you as the teacher, this means planning with clarity and intention; for students, it means purposeful, connected and engaging mathematics.
Peter Sullivan, Teaching Mathematics: Using research-informed strategies (2011). These principles draw on work from a range of researchers in this field, including Good, Grouws and Ebmeier (1983); Hattie (2009); Swan (2005); Clarke and Clarke (2004); and Anthony and Walshaw (2009)