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

Regulatory cards inquiry maths After posing questions / making observation, students invited to participate in structuring / directing lesson. At same time cards suggest types of activities that are consistent with the discipline of mathematics (induction and deduction). Also include s ‘social’ cards on how to inquire. Change sets of cards depending on experience of class with inquiry (e.g. use the pack of 6 cards for less experienced inquirers). inquiry maths

Regulatory cards inquiry maths After posing questions / making observation, students invited to participate in structuring / directing lesson. At same time cards suggest types of activities that are consistent with the discipline of mathematics (induction and deduction). Also include s ‘social’ cards on how to inquire. Change sets of cards depending on experience of class with inquiry (e.g. use the pack of 6 cards for less experienced inquirers). 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

Restricted by the teacher Levels of inquiry Questions Regulation Pathways Outcomes Structured Co- constructed Restricted by the teacher Guided Student-led Open Student-led teacher validation Student-led teacher instruction when required Student-led teacher assessed (Optional) 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) Polya: deduction completes induction IM aims to combine two forms of mathematical reasoning identified by Polya: “deduction completes induction”; procedures used and practised in service of exploration (e.g. 24 x 21 = 42 x 12). Differences between inquiry and investigation: http://www.inquirymaths.com/posts/thedifferencesbetweeninvestigationsandinquiries 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 Connect concepts and procedures 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

“Less to it and more in it.” 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 50% of 10 = 10% of 50 Alternatives Choosing a prompt, a teacher cannot just take one ‘off the shelf’ from the website. Should think about setting the prompt JUST ABOVE level of class, so involves a feature that is FAMILIAR (gives students confidence to question and observe) and UNFAMILIAR (intriguing). Example, one department with sets in year 8 changed the percentages prompt on the website to present the right balance of familiarity and intrigue for classes with different levels of attainment. inquiry maths

Inquiry prompt l + h = n 2 2 inquiry maths

Orientation questioning and noticing inquiry maths

Regulatory cards inquiry maths