Inquiry Maths

Ann MacdonaldAndrew Blair

(Longhill High School, Brighton & Hove)

www.inquirymaths.com

Inquiry Maths

• What is inquiry maths?• How do you get started?• How do you set (co-

construct) success criteria?

Aims of session

Inquiry Maths

• 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)

Why Inquiry Maths?Made to Measure (2012)

Inquiry Maths

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

Inquiry Maths

Inquiry Maths

Why Inquiry Maths?PRIMAS survey of inquiry-based teaching in the EU

Preconception of IBL compared with use of IBLORI: orientation towards IBLROU: routine use of IBLKND: IBL requires extensive content knowledgeMOT: 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

What shall we do next?

Inquiry Maths

Solving a Problem

Time (20 minutes)

STUDENT

Inquiry Maths

MATHEMATICIAN

Time (20 minutes)

Solving a Problem

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

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Getting started with inquiry

Inquiry Maths

• 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?

Getting started with inquiry

Inquiry Maths

• 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.

• 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

Your first inquiry

Establishing success criteria

Inquiry Maths

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.

OfSTED reports

Inquiry maths

Learning 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

Question Method Outcome

0 Verification given given given

1 Structured given given to be found

2 Guided given to be found

to be found

3 Open to be found

to be found

to be found

Levels of inquiry

Inquiry Maths