Inquiry Maths and Mixed Attainment Classes Andrew Blair

Inquiry Maths and Mixed Attainment Classes Andrew Blair Head of Mathematics, Haverstock School (Camden) www. inquirymaths. org @inquirymaths inquiry maths

Inquiry and mixed attainment 1 inquiry maths

Inquiry Maths lessons Learning Activity Communicating Thinking Ofsted reports* Inquiry lessons Discrete skills Conceptual understanding and connections Repetitive practice Teacher funnelling Routine application * Understanding the Score 2008; Made to Measure 2012 Regulating and reflecting Collaborative discussion (Re)solving conjectures and questions inquiry maths

Inquiry Maths and Mixed Attainment Classes • Devised and developed in mixed attainment classrooms. • Prompts promote learning at multiple levels. • Inquiry pathways involve students working on a common aim from different directions and at different levels of reasoning. • Students’ selection of an approach and mathematical level (guided by the teacher when necessary) ensures challenge and progress for all. • Inquiry unites the class in a mathematical process. • The unity of purpose promotes inclusiveness, cohesion and equity as all contributions add to the findings of the inquiry maths

Regulatory cards inquiry maths

Regulatory cards inquiry maths

Regulatory cards advantages • Self-differentiation: students choose point of access to the inquiry • Harmonisation of learning and concepts • Increases awareness of mathematical reasoning • Increases consciousness of own thinking • Increases constructive and critical agency inquiry maths

Levels of inquiry Questions Regulation Pathways Outcomes Structured Coconstructed Restricted by the teacher Guided Student-led Coconstructed Student-led teacher validation Student-led teacher instruction when required Student-led teacher assessed Open inquiry maths

Introducing Inquiry Maths 2 inquiry maths

What Inquiry Maths is not Discovery learning (investigations) Problem solving Students’ everyday interests or a ‘real life’ context Project-based learning inquiry maths

Inquiry maths model Polya: deduction completes induction We have discovered an interesting result but the reasoning that led to it was merely plausible, experimental, provisional, heuristic; let us try to establish it definitively by a rigorous proof. (How to Solve It, 1945) The result of the mathematician’s creative work is demonstrative reasoning, a proof, but the proof is discovered by plausible reasoning, by guessing. (Mathematics and Plausible Reasoning, 1954) inquiry maths

Inquiry maths model Students learn to § Ask questions and notice properties § Make conjectures § Plan, monitor and reflect on their activity § Explore ideas in collaboration § Identify when they need new knowledge § Ask the teacher for instruction § Explain their reasoning § Prove their results inquiry maths

Inquiry maths model Teachers aim to § Harness students’ curiosity § Connect concepts and procedures § Support student regulation § Co-construct open inquiries § Combine different forms of reasoning § Develop students’ initiative, independence and leadership inquiry maths

Starting an inquiry 2 inquiry maths

Inquiry Maths prompt Diagram Statement The sum of two fractions equals their product. Equation 24 x 21 = 42 x 12 “Less to it and more in it. ” inquiry maths

Inquiry Maths prompt 40% of 70 = 70% of 40 Alternatives 50% of 10 = 10% of 50 47% of 74 = 74% of 47 40% of 30% of 20 = 20% of 30% of 40 inquiry maths

Inquiry prompt 2 2 l +h =n inquiry maths

Orientation questioning and noticing inquiry maths

Regulatory cards inquiry maths