Inquiry Maths model of teaching

1. InquiryInquiry mathsmaths
Andrew Blair
www.inquirymaths.com
@inquirymaths
inquiry maths

2. www.inquirymaths.com
inquiry maths

3. KS3 Programme of Study
(from September 2014)
inquiry maths

4. inquiry maths
PRIMAS survey of inquiry-based
learning in the EU – 12 countries
Preconception of IBL compared with use of IBL
ORI: orientation towards (would like to implement) 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)

5. PRIMAS survey of inquiry-based
learning in the EU – 12 countries
Problems with implementation of IBL
CLA: classroom management
RES: resources
SYS: systems restrictions
(strongly 1: disagree, 2: disagree, 3: agree, 4: strongly agree) inquiry maths

6. What is inquiry maths?
inquiry maths
X Discovery learning
X Problem solving (open middle)
 Co-constructed exploration
 Student regulation
 Development of independent inquirers
 Connected concepts and procedures
 Inductive and deductive reasoning

7. Question
Concepts 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

8. Prompt
diagram, statement or equation
l2
+ h2
= n
inquiry maths

9. inquiry maths
Orientation
questions and comments

10. inquiry maths
Regulatory cards
establishing aims and planning actions

11. Stage
Read
Analyse
Explore
Plan
Implement
Verify
1 5 10 15
Time (20 minutes)
STUDENT
inquiry maths
Regulatory cards
Schoenfeld

12. S t ag e
Read
∇1 ∇2
Analyse
∇3∇4 ∇5
Explore
∇6 ∇7
Plan
∇8 ∇9 ∇10
Implement
∇11
Verify
1 5 10 15
MATHEMATICIAN
Time (20 minutes)
inquiry maths
Regulatory cards
Schoenfeld

13. 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 cards
metacognition

14. 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
Lev Vygotsky

15. Exploration
inquiry maths

16. Proof
inquiry maths

17. (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

18. 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

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

20. Further inquiry
inquiry maths

21. inquiry maths
Questions

22. • 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

23. Setting the level of the prompt
Inquiry Maths

24. 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

25. 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)
Possible
no mechanism to
overcome
disharmony
Inquiry 3-4 Suggested
by prompt
Agreed in co-
construction
Likely
mechanism of joint
regulation to
ensure harmony
Inquiry maths
harmonising method and content
inquiry maths

26. InquiryInquiry mathsmaths
Andrew Blair
www.inquirymaths.com
@inquirymaths
inquiry maths