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(Longhill High School, Brighton & Hove)
Inquiry Maths Ann Macdonald Andrew Blair (Longhill High School, Brighton & Hove) Inquiry Maths
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Aims of session What is inquiry maths? How do you get started?
How do you set (co- construct) success criteria? Inquiry Maths
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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
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2014 National Curriculum: KS3 and KS4 Programme of Study
Why Inquiry Maths? 2014 National Curriculum: KS3 and KS4 Programme of Study Inquiry Maths
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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
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The sum of two fractions equals their product.
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What shall we do next? Inquiry Maths
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Solving a Problem STUDENT Time (20 minutes) Inquiry Maths
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Solving a Problem MATHEMATICIAN Time (20 minutes) Inquiry Maths
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Metacognition Declarative knowledge of: yourself as a thinker
academic tasks strategies to perform a task. Procedural knowledge: monitoring strategic decisions regulating thinking. Inquiry Maths
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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
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Regulatory cards Inquiry Maths
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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
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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
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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
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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
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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 *
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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
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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
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