Reasoning With Primary Aged Children Thinking Out Loud Reasoning With Primary Aged Children Debbie Streatfield and Faye Heath

Objectives for the workshop: Understand the importance of developing children’s reasoning skills in primary schools; Know a range of ways to develop children’s reasoning skills within the primary mathematics curriculum. Thinking Out Loud

The importance of reasoning ‘Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement in mathematics’ ‘Mathematical reasoning is learning to reason about the underlying relations in mathematical problems they have to solve.’ ‘In the context of time pressures, more time should be allocated to developing children’s reasoning, than to practising calculation skills.’ From: Development of Maths Capabilities and Confidence in Primary School Terezinha Nunes Peter Bryant Cathy Sylva and Rossana Barros 2009 Thinking Out Loud

Talk Vocabulary Correct use of vocabulary Speaking in complete sentences Opportunities to talk Modelling and scaffolding Thinking Out Loud

Thinking Out Loud It is … because … It could be … because … Promoting the vocabulary of reasoning:   It is … because … It could be … because … It can’t be … because … It won’t work because … If … then … It would only work if … If … is … then … is … I know … because … I notice that … We could try … Thinking Out Loud

Putting reasoning at the heart of maths learning Pupils need to understand that they are expected to: think before doing notice things make decisions based on what they notice, know and understand. From: NCETM Primary and Early Years Magazine No. 93 Thinking Out Loud

Thinking before doing Put the boxes in order How spread out are the marbles? Put the newspapers in order What other approaches do you use that support your children to think before they do? Thinking Out Loud

Noticing things NCETM Video Thinking Out Loud

Noticing the student [need to] asks themself what is similar about the questions and what different, what it is about the context which enables the technique to work, what sorts of difficulties might the technique encounter in different situations, etc. From: John Mason Asking Mathematical Questions Mathematically 1998 Thinking Out Loud

8 + 5 Grid pairs such as those shown below, or other (correct) variations on them, were produced by different pupils: Either or or

Making decisions based on what they notice and understand True or False? 3999-2999=4000-3000 3999-2999=3000-2000 Explain your reasoning. Write three more pairs of equivalent calculations using 2741-1263=2742-1264 as a starting point. Year 5 example from NCETM – Teaching for Mastery Questions, tasks and activities to support assessment Thinking Out Loud

The importance of planning effective questions Questions can be invitations to pupils to do something, say something or suggest something What is important is the thinking that the questions generate e.g. reasoning about what the child is being asked to do; on choices to be made; on representations that support understanding (theirs or others); in order to justify the answer Thinking Out Loud

Cuisenaire/number rods If the dark green is a half, which rods could you use to make one and a quarter? If the yellow is a half, which rods could you use to make one and a half? Which rods would you choose to represent a half, and why? Can you create your own effective questions? Thinking Out Loud

Supporting Fluency Reasoning about what is already known in order to work out what is unknown will improve fluency From: NCETM Primary and Early Years Magazine No. 93 Thinking Out Loud

Progression in reasoning Step 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. 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. 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. From: Reasoning: The Journey from Novice to Expert (Article) Nrich website Thinking Out Loud

NCETM developing opportunities and ensuring progression in the development of reasoning skills +COUNTING Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number   count backwards through zero to include negative numbers interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero use negative numbers in context, and calculate intervals across zero count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward count from 0 in multiples of 4, 8, 50 and 100; count in multiples of 6, 7, 9, 25 and 1 000 count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 given a number, identify one more and one less find 10 or 100 more or less than a given number find 1 000 more or less than a given number Spot the mistake: 5,6,8,9 What is wrong with this sequence of numbers? True or False? I start at 2 and count in twos. I will say 9 What comes next? 10+1 = 11 11+1= 12 12+1 = 13 …….. 45,40,35,25 I start at 3 and count in threes. I will say 13? 41+5=46 46+5=51 51+5=56 …… 50,100,115,200 38 is a multiple of 8? 936-10= 926 926 -10 = 916 916- 10= 906 ……. 950, 975,1000,1250 324 is a multiple of 9? 6706+ 1000= 7706 7706 + 1000 = 8706 8706 + 1000 = 9706 177000,187000,197000,217000 When I count in 10’s I will say the number 10100? 646000-10000= 636000 636000 –10000 = 626000 626000- 10000 = 616000 -80,-40,10,50 When I count backwards in 50s from 10 I will say -200 The temperature is -3. It gets 2 degrees warmer. The new temperature is -5? Thinking Out Loud

Diamond 9 Thinking Out Loud

Reflection Thinking Out Loud What elements of developing effective reasoning do you see used most frequently and effectively in your school? What would you like to develop? How might you go about developing this? Thinking Out Loud