InquiryInquiry mathsmaths

Andrew Blair

www.inquirymaths.com @inquirymaths

inquiry maths

www.inquirymaths.com

inquiry maths

KS3 Programme of Study (from September 2014)

inquiry maths

inquiry maths

PRIMAS survey of inquiry-basedlearning in the EU – 12 countries

Preconception of IBL compared with use of IBLORI: orientation towards (would like to implement) IBLROU: routine use of IBLKND: IBL requires extensive content knowledgeMOT: IBL motivates students(strongly 1: disagree, 2: disagree, 3: agree, 4: strongly agree)

PRIMAS survey of inquiry-basedlearning in the EU – 12 countries

Problems with implementation of IBLCLA: classroom managementRES: resourcesSYS: systems restrictions(strongly 1: disagree, 2: disagree, 3: agree, 4: strongly agree) inquiry maths

What is inquiry maths?

inquiry maths

X Discovery learningX Problem solving (open middle) Co-constructed exploration Student regulation Development of independent inquirers Connected concepts and procedures Inductive and deductive reasoning

QuestionConcepts and procedures

Outcomes

1 Verification given given given

2 Structured given given to be found

3 Guided given to be found to be found

4 Open to be found to be found to be found

Levels of inquiry

inquiry maths

Prompt diagram, statement or equation

l2 + h2 = n inquiry maths

inquiry maths

Orientationquestions and comments

inquiry maths

Regulatory cardsestablishing aims and planning actions

Stage

Read

Ana lyse

Exp lo re

Plan

Implement

Ver i f y

1 5 10 15

Time (20 minutes)

STUDENT

inquiry maths

Regulatory cardsSchoenfeld

S t a g e

Read 1 2

Ana lyse 34 5

Exp lo re 6 7

Plan 8 9 10

Implement 11

Ver i f y 1 5 10 15

MATHEMATICIAN

Time (20 minutes)

inquiry maths

Regulatory cardsSchoenfeld

Declarative knowledge of

• yourself as a thinker

• academic tasks• strategies to

perform a task.

Procedural knowledge of

• monitoring strategic decisions

• regulating thinking.

inquiry maths

Regulatory cardsmetacognition

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 cardsLev Vygotsky

Exploration

inquiry maths

Proof

inquiry maths

(Level I) List the attributes• rectangular lattice• subject of the formula (number of squares, lines)• length and width• 3 and 6 (double/half, triangular numbers)

(Level II) Modify the attributes by asking "What-if-not?"• what if the lattice is not rectangular?• what if the subject is not the number of lines?• What if the formula did not involve the length and width?• What if the length and width are not triangular numbers?

(Level III) Pose questions(Level IV) Analyse the questions

Changing the prompt

inquiry maths

inquiry maths

Further inquiry

Length, height l2 + h2 l(h + 1) + h(l + 1) Number of lines

3, 1 9 + 1 6 + 4 10

6, 3 36 + 9 24 + 21 45

10, 6 100 + 36 70 + 66 136

15, 10 225 + 100 165 + 160 325

Prove l2 + h2 = l(h + 1) + h(l + 1) when l and h are consecutive trianglar numbers.

inquiry maths

Further inquiry

Further inquiry

inquiry maths

inquiry maths

Questions

• How do you plan a lesson for Ofsted or an observation? • How do you decide what the success criteria or lesson

objectives are going to be? • How do you manage the regulatory cards? • How do you decide if the prompt is appropriate for a class?• How does inquiry work with mixed ability? • Can you expect students in bottom sets to take part in inquiry

lessons? • Are students mature enough to be given this level of

responsibility?• Can you expect students to inquire into topics without being

given 'content' knowledge beforehand?inquiry maths

Questions

Setting the level of the prompt

Inquiry Maths

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

inquiry maths

Inquiry maths

Level Concept Method Harmony

Objective-led lesson

1 Determined by teacher

Determined by teacher (through task)

Unpredictable

Investigation 2 To be discovered by student

Determined by teacher (empirical induction)

Possibleno mechanism to overcome disharmony

Inquiry 3-4 Suggested by prompt

Agreed in co-construction

Likely mechanism of joint regulation to ensure harmony

Inquiry mathsharmonising method and content

inquiry maths

InquiryInquiry mathsmaths

Andrew Blair

www.inquirymaths.com @inquirymaths

inquiry maths