Alison Borthwick & Alan Cross BCME 2018 Reasons to Reason Reasoning in Primary Mathematics and Science Alison Borthwick & Alan Cross

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.

Is this reasoning?

Is this reasoning?

Could reasoning be the currency of the future?

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? 

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?

Is there a difference between thinking and reasoning?

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)   .

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.

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.

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

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

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?  

Web of reasoning Pick to cards

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

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

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

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

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

Dodecahedron

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?

Table to record reasoning

Reasoning stickers

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

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

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

Contact Details Alison Borthwick alisonborthwick@me.com 07879402898 Alan Cross alan.cross@manchester.ac.uk 07984714378