Yorkshire Ridings Maths Hub - PowerPoint Presentation

Slide1

Yorkshire Ridings Maths HubReasoning Work GroupStrengthening Reasoning

Date:

15/06/16

Venue:

Harrogate Grammar SchoolSlide2

Aims of sessionRecognise the importance of Reasoning in the new curriculum and understand its implications for teaching approaches and Schemes of LearningKnow and be able to use some strategies for strengthening reasoning 2Slide3

WelcomeIntroduction to the project3Slide4

I

like

I don’t like

Reasoning

or not?

What mathematical thinking was happening just then?Slide5

What is reasoningWhat do we understand by ‘reasoning’Why is it important?5Slide6

The National Curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can

solve problems

by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

New National Curriculum aims

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Are there any aspects missing? Any that we didn’t just think about?Slide7

7

What if …Slide8

Assessment objectives from new GCSE (first teaching 2015) AO1

Use and apply standard techniques

40% Higher, 50% Foundation

AO2

Reason, interpret and communicate mathematically

30% H, 25% F

AO3 Problem solving

30% H, 25% F

8Structure of the key stage 2 mathematics test The key stage 2 mathematics test materials comprise: Paper 1: arithmetic (40 marks) Paper 2: reasoning (35 marks) Paper 3: reasoning (35 marks) Slide9

Strategies to provoke reasoningI like – I don’t likeVenn Diagram9Slide10

Numbers with a factor of 3

Multiples of 9

Even numbersSlide11

Venn diagramsHow might you use them with your students?How do they support the development of reasoning?What do you need to be wary of?Slide12

What is reasoningWhat do we understand by ‘reasoning’Why is it important?What does it look like in the classroom?Think of a (recent) lesson where you saw some high quality reasoningWhat provoked it?What qualities / behaviours were pupils showing?What teacher behaviours are a pre-requisite for this?12Slide13

"Put simply, the only point of asking questions is to raise issues about which the teacher needs information or about which the pupils need to think." [Wiliam and Hodgen, Working Inside the Black Box]

Plenty more on building classroom dialogue in the teacher handbookSlide14

“students learn to think mathematically by being in the presence of a relative expert who makes their thinking processes explicit.”[VYGOTSKY, L., 1978, Mind in Society: The Development of the Higher PsychologicalProcesses (London: Harvard University Press

), paraphrased

by John Mason]

14Slide15

What is reasoningWhat do we understand by ‘reasoning’Why is it important?What does it look like in the classroom?How do we develop good reasoning?15Slide16

nrich stepsStep one:  Describing: simply tells what they did.Step two: Explaining: offers some reasons for what they did. These may or may not be correct.  The argument may yet not hang together coherently. This is the beginning of inductive reasoning.

Step three

: Convincing

: confident that their chain of reasoning is right and may use words such as, ‘I reckon’ or ‘without doubt’. The underlying mathematical argument may or may not be accurate yet is likely to have more coherence and completeness than the explaining stage. This is called inductive reasoning

.

Step four

: Justifying

: a correct logical argument that has a complete chain of reasoning to it and uses words such as ‘because’, ‘therefore’, ‘and so’, ‘that leads to’

...Step five:  Proving: a watertight argument that is mathematically sound, often based on generalisations and underlying structure. This is also called deductive reasoning.

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Strategies to build progress in reasoningStep one:  DescribingStep two: ExplainingStep three: ConvincingStep four: JustifyingStep five:  Proving

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What can the teacher do to support progress through these stages?

Where does questioning and classroom dialogue fit in?Slide18

Questions to prompt reasoningWhat’s happening here?

Why do you think that?

How do you know?

Is that just a coincidence?

How is that possible?

What could you change? What effect would this have?

Is there another way to explain this?

Can you explain why that is right?

Will that always happen? Why?

Can we develop some that are more systematic?Slide19

Strategies to build progress in reasoningStep one:  DescribingStep two: ExplainingStep three: ConvincingStep four: JustifyingStep five:  Proving

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Can we develop question stems to help progress through each of these stages?Slide20

Strategies to provoke reasoningI like – I don’t likeVenn DiagramsChange one thing ….. …. so that the two fractions are equivalent

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What additional insight does this activity bring?Slide21

Strategies to Provoke ReasoningI like – I don’t likeVenn DiagramsChange one thing …..Concept Cartoons21Slide22
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Strategies to provoke reasoningI like – I don’t likeVenn diagramsChange one thing …..Concept CartoonsGive me an example ….

….. of a rectangle with perimeter 40cm

…..

and another

….. and another

….. now give me an interesting one

….. and now one that you think nobody else will have thought of 23What is the purpose of the last two questions?Slide24

Thank

you

m.stockton@easingwold.n-yorks.sch.uk

jrt@harrogategrammar.co.uk