1. Alison Borthwick & Alan Cross
BCME Reasons to Reason Reasoning in Primary Mathematics and Science
Alison Borthwick & Alan Cross

2. Mathematics and science are connected in many ways, but a particularly strong link is the extent to which they both use reasoning to work towards testing out conjectures and hypotheses.
We will explore:
definitions of thinking and reasoning;
understand how thinking and reasoning are similar yet different;
be able to begin to identify skills of reasoning;
the place of reasoning in mathematics.

3. Is this reasoning?

4. Is this reasoning?

5. Could reasoning be the currency of the future?

6. Do we reason in everyday life?   Choosing a birthday present for a friend? Selecting a new pair of shoes? Which route to take to work? 

7. Do we reason in mathematics. How. When. Why
Do we reason in mathematics?   How? When? Why? What do children look like when they are reasoning? Reasoning characteristics?

10. Is there a difference between thinking and reasoning?

11. Different theoretical view points of thinking and reasoning  Probably the single most important lesson is that being stuck is an honorable state and an essential part of improving thinking. (Mason, Burton and Stacey, 2010)   Reasoning is fundamental to knowing and doing mathematics. Reasoning enables children to make use of all their other mathematical skills and so reasoning could be thought of as the 'glue' which helps mathematics makes sense. (Pennant, Woodham and Bagnall, 2014)   Adaptive reasoning refers to the capacity to think logically about the relationships among concepts and situations. Such reasoning is correct and valid, stems from careful consideration of alternatives, and includes knowledge of how to justify the conclusions. (Kilpatrick, Swafford and Findell (2001)   .

12. Teachers views of thinking and reasoning  Thinking can be recalling facts. Reasoning is a form of thinking.   Thinking can be open-ended, abstract, no particular end point. Reasoning is trying to make sense of things; it is deeper than thinking.

13. but it is thinking in a logical purposeful, goal directed way
Reasoning is thinking,
but it is thinking in a logical purposeful, goal directed way
Thinking includes a whole range of cognitive activity.
Reasoning is purposeful, goal orientated and requires at least developing understanding of one or more concepts.

14. How do you reason in mathematics?
noticing
talking and listening
making sense
sharing insights
metacognition

15. How are you reasoning?
14 x 5 = ?
Use 5542 ÷ 17 = 326 to work out 326 x 18

16. Skills of reasoning What are they. Can we sort them. Organise them
Skills of reasoning  What are they? Can we sort them? Organise them? Which are more mathematical? Scientific?  

17. Web of reasoning
Pick to cards

18. When do you reason in mathematics
When do you reason in mathematics?   What types of tasks enable/encourage reasoning to take place? Task design Pedagogical choices

19. Do you spot opportunities for reasoning?
Why is the graph this shape? Why not a line? Why is it this steep?
Is this a pattern/ a trend?
What happened in the 1950’s?
What is happening now?
Can we extrapolate? Interpolate?
Doing all these – were you using them

20. Do teachers expect reasoning from children?
Is there a balance between…
thinking
doing
Take children from the active to the interactive

21. Why is it important to reason?
Reasoning allows us:
to use our knowledge and understanding;
identify gaps and shortcomings in our knowledge;
to improve our understanding;
deepen our understanding with:
- more complex ideas
links between ideas
increase our employability
Improve understanding – Boaler 4 year study – promotion of equality
Employability – Royal Society 2014 report

22. Possible frameworks for reasoning
NRICH 5 stages of reasoning
describing, explaining, convincing, justifying, proving
Bloom’s taxonomy
remember, understand, apply, analyse, evaluate, create
See, think, wonder
Using question stems Convince yourself, a friend, an enemy

23. Dodecahedron

24. Ideas for promoting reasoning
pupils
conjecturing atmosphere
encourage variation
celebrate being stuck
teachers
avoid proto typical examples
teach/model the vocabulary of reasoning
use reasoning questions e.g. why.. ? how many ways..? same different?

25. Table to record reasoning

27. Reasoning stickers

28. Chapters focus on: Introduction Frameworks EYFS Questioning Predicting
Pattern Seeking
Problem solving
Finding evidence
Creating a culture

29. A toolkit for reasoning
Reasoning skills
A reasoning survey
A reasoning rubric
A reasoning glossary
Examples of how to evidence reasoning
Developing a culture of reasoning

30. Reflections Reasoning is the golden thread
Reasoning is a life long skill, preparation for the future
Two subjects are better than one

32. Contact Details
Alison Borthwick Alan Cross