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

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

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

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

PRIMAS survey of inquiry-based teaching in the EU 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

The sum of two fractions equals their product. Inquiry Maths

Inquiry Maths

What shall we do next? Inquiry Maths

Solving a Problem STUDENT Time (20 minutes) Inquiry Maths

Solving a Problem MATHEMATICIAN Time (20 minutes) Inquiry Maths

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

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

Regulatory cards Inquiry Maths

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

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

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

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

OfSTED reports Inquiry maths Learning Activity Communicating Thinking Discrete skills Conceptual understanding Activity Repetitive practice Regulating and reflecting Communicating Teacher funnelling Collaborative discussion Thinking Routine application (Re)solving conjectures and questions Inquiry Maths *

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

Levels of inquiry Open 1 2 3 Guided given to be found Question Method Outcome Verification given 1 Structured to be found 2 Guided 3 Open Inquiry Maths