Inquiry Maths Ann Macdonald Andrew Blair (Longhill High School, Brighton & Hove)

1. Inquiry Maths Ann Macdonald Andrew Blair (Longhill High School, Brighton & Hove) www.inquirymaths.com Inquiry Maths

2. Aims of session • What is inquiry maths? • How do you get started? • How do you set (co-construct) success criteria? Inquiry Maths

3. Why Inquiry Maths? Made to Measure (2012) • Problem solving is rarely integral to learning; instead, tended to be an activity that occurred towards the end of topic – did not place students in position of thinking deeply about how to solve the problem (69) or of drawing on their previous knowledge, and grappling with applying it in a new, unusual or complex context. (71) • In the best schools, topics are introduced by presenting a suitable problem and inviting students to use knowledge in innovative ways. (103) Inquiry Maths

4. Why Inquiry Maths? 2014 National Curriculum: KS3 and KS4 Programme of Study Inquiry Maths

5. Why Inquiry Maths? PRIMAS survey of inquiry-based teaching in the EU Preconception of IBL compared with use of IBL ORI: orientation towards IBL ROU: routine use of IBL KND: IBL requires extensive content knowledge MOT: IBL motivates students (strongly 1: disagree, 2: disagree, 3: agree, 4: strongly agree) Inquiry Maths

6. The sum of two fractions equals their product. Inquiry Maths

8. Inquiry Maths

9. What shall we do next? Inquiry Maths

10. Solving a Problem STUDENT Time (20 minutes) Inquiry Maths

11. Solving a Problem MATHEMATICIAN Time (20 minutes) Inquiry Maths

12. Metacognition Declarative knowledge of: • yourself as a thinker • academic tasks • strategies to perform a task. Proceduralknowledge: • monitoring strategic decisions • regulating thinking. Inquiry Maths

13. Vygotsky 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. Inquiry Maths

14. Regulatory cards Inquiry Maths

16. Getting started with inquiry • Will all students learn (make progress)? • Will the students be challenged? • Will the students be engaged? • Will the students choose their regulatory card for the ‘wrong’ reason? • How does an inquiry lesson meet the school’s requirements re: learning objectives? Inquiry Maths

17. Getting started with inquiry • Students’ fractions assessments showed good progress – lower ability students did better then expected. • Algebraic fractions were explored by some students. • I am learning how to monitor choices. • Increased engagement. • Lesson study into establishing success criteria. Inquiry Maths

18. Your first inquiry • Students should write down any questions that occur to them during feedback session rather than interject. • Have resources ready in case students decide they need to consolidate a skill. • Don’t worry if students cannot suggest possible ways to move forward initially. • Remember an inquiry is not the same as an investigation. Be prepared for the lesson to go in a different direction than you may have predicted. • Prepare to extend (or cut short) the time allocated for the inquiry depending on the class’s response. Inquiry Maths

19. Establishing success criteria Lesson objective • Reasoning during inquiry: notice, conjecture, reason, generalise, prove. • Specific mathematical procedure. • Suggest concepts that link to prompt. Independent inquirers • Aims teacher structure, teacher guidance, co-constructed, independent. Inquiry Maths

21. Inquiry Maths

22. Planning an INQUIRY: phases (a) Orientation to the prompt (b) Establishing aims and planning actions (c) Exploration (d) Teacher exposition (e) Solving (f) Presenting results (g) Reflecting and evaluating Inquiry Maths

23. Levels of inquiry Inquiry Maths