1. Inquiry Maths Andrew Blair and Emma Rouse
Haverstock School (Camden) and Brittons School (Rainham)
@inquirymaths @Emmaths1618
Inquiry Maths

2. Introducing Inquiry Maths1
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3. Inquiry Maths website
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4. Inquiry Maths and Mixed Attainment Classes
Devised and developed in mixed attainment classrooms.
‘Prompts’ promote learning at multiple levels.
Inquiry pathways involve students working on a common aim from different directions and at different levels of reasoning. 
Students’ selection of an approach and mathematical level (guided by the teacher when necessary) ensures challenge and progress for all.
Inquiry unites the class in a mathematical process.  
The unity of purpose promotes inclusiveness, cohesion and equity as all contributions add to the findings of the inquiry.
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5. KS3 Programme of Study (from September 2014)
Inquiry Maths is getting more interest at the moment because of the KS3 PoS. Difference between inquiry / enquiry: ‘enquiry’ might be defined as a short task; ‘inquiry’ is a pedagogical approach that might stretch over 4 hours or more – includes all elements in one process, e.g. questioning, exploring, conjecturing, generalising, justifying, proving.
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6. 9-1 GCSE Assessment Objective
AO2 (reasoning, interpreting and communicating) in 9-1 GCSE all features of IM (weighting H: 30%, F:25%) GCSE did not have an AO specifically for reasoning – “select and apply of methods in a range of contexts” 25-35%
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7. Inquiry Maths lessons 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
* Understanding the Score 2008; Made to Measure 2012
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8. What Inquiry Maths is not
Discovery learning (investigations)
Problem solving
Students’ everyday interests or a ‘real life’ context
Project-based learning
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9. Inquiry Maths model Polya: deduction completes induction
We have discovered an interesting result but the reasoning that led to it was merely plausible, experimental, provisional, heuristic; let us try to establish it definitively by a rigorous proof. (How to Solve It, 1945)
The result of the mathematician’s creative work is demonstrative reasoning, a proof, but the proof is discovered by plausible reasoning, by guessing. (Mathematics and Plausible Reasoning, 1954)
Polya: deduction completes induction
IM aims to combine two forms of mathematical reasoning identified by Polya: “deduction completes induction”; procedures used and practised in service of exploration (e.g. 24 x 21 = 42 x 12). Differences between inquiry and investigation:
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10. Inquiry Maths model Vygotsky: self-regulation
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. (Thinking and Speech, 1934/1987)
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11. Inquiry Maths model Students learn to
Ask questions and notice properties
Make conjectures
Plan, monitor and reflect on their activity
Explore ideas in collaboration
Identify when they need new knowledge
Ask the teacher for instruction
Explain their reasoning
Prove their results
Main features of IM: (1) inquiry starts with asking questions and making observations (noticing properties) and (2) students plan and monitor the inquiry, so involved in directing (co-constructing the direction of) the inquiry.
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12. Inquiry Maths model Teachers aim to Connect concepts and procedures
Harness students’ curiosity
Connect concepts and procedures
Support student regulation
Co-construct open inquiries
Combine different forms of reasoning
Develop students’ initiative,
independence and leadership
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13. Starting an inquiry 2
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14. “Less to it and more in it.”
Inquiry Maths prompt
Diagram
Statement The sum of two fractions
equals their product.
Equation x 21 = 42 x 12
IM prompt is a diagram, statement or equation. Stripped back to a minimum, piques students’ curiosity (a property that is intriguing) and loaded with the potential for open inquiry. As a HoM said when describing a prompt, “less to it and more in it.”
“Less to it and more in it.”
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15. Inquiry Maths prompt 40% of 70 = 70% of 40 50% of 10 = 10% of 50
Alternatives
Choosing a prompt, a teacher cannot just take one ‘off the shelf’ from the website. Should think about setting the prompt JUST ABOVE level of class, so involves a feature that is FAMILIAR (gives students confidence to question and observe) and UNFAMILIAR (intriguing). Example, one department with sets in year 8 changed the percentages prompt on the website to present the right balance of familiarity and intrigue for classes with different levels of attainment.
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16. Inquiry Maths prompt
Optional
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17. Orientation questioning and noticing
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18. Regulatory cards Inquiry Maths Emma: participants select a card
After posing questions / making observation, students invited to participate in structuring / directing lesson. At same time cards suggest types of activities that are consistent with the discipline of mathematics (induction and deduction). Also include s ‘social’ cards on how to inquire. Change sets of cards depending on experience of class with inquiry (e.g. use the pack of 6 cards for less experienced inquirers).
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19. Regulating inquiry 3
Andrew
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20. Regulatory cards
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21. Regulatory cards Inquiry Maths
After posing questions / making observation, students invited to participate in structuring / directing lesson. At same time cards suggest types of activities that are consistent with the discipline of mathematics (induction and deduction). Also include s ‘social’ cards on how to inquire. Change sets of cards depending on experience of class with inquiry (e.g. use the pack of 6 cards for less experienced inquirers).
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22. Regulatory cards Schoenfeld
Student
Explaining origin of regulatory cards:
– link to explanation of diagrams on website.
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23. Regulatory cards Schoenfeld
Mathematician
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24. 4 Inquiry pathways Inquiry Maths
Participants follow direction of cards - after mins of exploration, participant from each table (identified and asked during the exploration phase) presents their working / findings.
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25. How could the inquiry develop?
Inquiry pathways
How could the inquiry develop?
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26. Inquiry Maths prompt
Optional
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27. Curriculum and prompt
Optional
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28. Assessment guided poster
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29. From Emma’s classroom 5
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30. Prompt 40% of 70 = 70% of 40 Inquiry Maths
Emma presents an example(s) from her classroom
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31. Students’ inquiry Inquiry Maths
Emma presents an example(s) from her classroom
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32. Students’ inquiry Inquiry Maths
Emma presents an example(s) from her classroom
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33. Students’ inquiry Inquiry Maths
Emma presents an example(s) from her classroom
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34. Inquiry display Inquiry Maths
Emma presents an example(s) from her classroom
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35. Summary
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36. What do students say?
“I ask lots more questions in maths after doing inquiry lessons. Last week I made up my own inquiry on enlargements.” (year 8)
“What’s different is that I feel I have a say in what we do. That makes me work harder.” (year 10)
“I benefited from an inquiry lesson as I could show how I proved my answer was correct using algebra.” (year 8)
“When I ask a question, I want to answer it more.” (year 9)
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37. What do teachers say?
“I really liked the way the inquiry allowed the students to ‘roam free’ with ideas and concepts. Allowing the students to explore and express their thoughts was a real eye opener and was very rewarding to see as a teacher.”
“I ran my first inquiry lesson with year 7 today. It was professionally invigorating.”
“Using Inquiry Maths over this year for my year 7 class has made my students into active learners who are fearless and methodical when attacking a problem.”
“The process gave the students the experience of being real mathematicians, something which is far too rarely the case in schools. They loved it and I felt that I learned much more about their strengths than I had in the preceding lessons.”
“The students’ responses were inspiring, amazing, and truly beyond any of my expectations.”
“I was pleased with the students’ enthusiasm and very proud of their first attempt at Inquiry Maths.”
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38. Questions
inquiry maths