Inquiry Maths Andrew Blair and Emma Rouse Haverstock School (Camden) and Brittons School (Rainham) www.inquirymaths.org @inquirymaths @Emmaths1618 Inquiry Maths

Introducing Inquiry Maths 1 Inquiry Maths

Inquiry Maths website 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

KS3 Programme of Study (from September 2014) Inquiry Maths is getting more interest at the moment because of the KS3 PoS. Difference between inquiry / enquiry: ‘enquiry’ might be defined as a short task; ‘inquiry’ is a pedagogical approach that might stretch over 4 hours or more – includes all elements in one process, e.g. questioning, exploring, conjecturing, generalising, justifying, proving. Inquiry Maths

9-1 GCSE Assessment Objective AO2 (reasoning, interpreting and communicating) in 9-1 GCSE all features of IM (weighting H: 30%, F:25%). 2010 GCSE did not have an AO specifically for reasoning – “select and apply of methods in a range of contexts” 25-35% Inquiry Maths

Inquiry Maths lessons Ofsted reports* Inquiry lessons 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

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 Vygotsky: self-regulation Students learn to regulate their own thinking when their behaviour is regulated by collaborators in social activity and when they regulate the thinking of others. (Thinking and Speech, 1934/1987) 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 Main features of IM: (1) inquiry starts with asking questions and making observations (noticing properties) and (2) students plan and monitor the inquiry, so involved in directing (co-constructing the direction of) the inquiry. 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 IM prompt is a diagram, statement or equation. Stripped back to a minimum, piques students’ curiosity (a property that is intriguing) and loaded with the potential for open inquiry. As a HoM said when describing a prompt, “less to it and more in it.” “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 Maths prompt Optional Inquiry Maths

Orientation questioning and noticing Inquiry Maths

Regulatory cards Inquiry Maths Emma: participants select a card 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

Regulating inquiry 3 Andrew Inquiry Maths

Regulatory cards 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 Schoenfeld Student Explaining origin of regulatory cards: http://www.inquirymaths.com/home/Regulatory-cards/why-do-maths-students-need-self-regulation – link to explanation of diagrams on website. Inquiry Maths

Regulatory cards Schoenfeld Mathematician Inquiry Maths

4 Inquiry pathways Inquiry Maths Participants follow direction of cards - after 10-15 mins of exploration, participant from each table (identified and asked during the exploration phase) presents their working / findings. Inquiry Maths

How could the inquiry develop? Inquiry pathways How could the inquiry develop? Inquiry Maths

Inquiry Maths prompt Optional Inquiry Maths

Curriculum and prompt Optional Inquiry Maths

Assessment guided poster Inquiry Maths

From Emma’s classroom 5 Inquiry Maths

Prompt 40% of 70 = 70% of 40 Inquiry Maths Emma presents an example(s) from her classroom Inquiry Maths

Students’ inquiry Inquiry Maths Emma presents an example(s) from her classroom Inquiry Maths

Students’ inquiry Inquiry Maths Emma presents an example(s) from her classroom Inquiry Maths

Students’ inquiry Inquiry Maths Emma presents an example(s) from her classroom Inquiry Maths

Inquiry display Inquiry Maths Emma presents an example(s) from her classroom Inquiry Maths

Summary Inquiry Maths

What do students say? “I ask lots more questions in maths after doing inquiry lessons. Last week I made up my own inquiry on enlargements.” (year 8) “What’s different is that I feel I have a say in what we do. That makes me work harder.” (year 10) “I benefited from an inquiry lesson as I could show how I proved my answer was correct using algebra.” (year 8) “When I ask a question, I want to answer it more.” (year 9) Inquiry Maths

What do teachers say? “I really liked the way the inquiry allowed the students to ‘roam free’ with ideas and concepts. Allowing the students to explore and express their thoughts was a real eye opener and was very rewarding to see as a teacher.” “I ran my first inquiry lesson with year 7 today. It was professionally invigorating.” “Using Inquiry Maths over this year for my year 7 class has made my students into active learners who are fearless and methodical when attacking a problem.” “The process gave the students the experience of being real mathematicians, something which is far too rarely the case in schools. They loved it and I felt that I learned much more about their strengths than I had in the preceding lessons.” “The students’ responses were inspiring, amazing, and truly beyond any of my expectations.” “I was pleased with the students’ enthusiasm and very proud of their first attempt at Inquiry Maths.” Inquiry Maths

Questions inquiry maths