developing Reasoning - Camden Primary …

1 IntroductionDuring the academic year 2013-14, a group of teachers met several times after school to examine how to place Reasoning at the heart of calculation teaching in Reasoning ? Why now?Problem solving, fluency and Reasoning : these are the key aims of the New National Curriculum and we want these to be strong threads that weave together in our mathematics teaching. However, although the New Curriculum is clear about the end of year expectations for children s calculation, there is no explicit guidance about how to build a culture of Reasoning in the will we assess children with no levels?.. through our questions!With the departure of curriculum levels, assessment will and should be based on teachers questioning; life after levels is all about the questions we ask! Levels were for tracking children s progress and attainment but true assessment is embedded in questioning.

2 With the aims of developing Reasoning in children, and developing questioning in teachers in mind, we developed a resource to help teachers ask questions that develop Reasoning within calculation is Reasoning so important? Reasoning is the magic ingredient that gives mathematics purpose, direction and depth. If a child can reason, they can justify, generalise, prove, explain and explore; in essence, they can make sense of mathematics. The New Curriculum aims to be a mastery curriculum: all the children should be on the boat before setting sail to a new year group. For our lowest attainers to develop connections between different areas of the maths curriculum linking thinking and for our highest attainers to develop depth in mathematics rather than just fast recall, Reasoning must be a part of every maths lesson. Moreover, all children deserve the opportunity to practise and learn from each other s Reasoning .

3 Yet Reasoning is not a naturally occurring element in maths lessons. For Reasoning to be required, logic should be needed to solve a puzzle, there might be a range of strategies or starting points, there might be missing information, or different solutions might be possible. Teachers must see these as essential ingredients to be planned for and probed in calculation lessons. It s essential that we ask questions that are sometimes unfair , as explained by Tim Oates, Group Director of Assessment at Cambridge Assessment and Chair of the expert panel that informed the New Curriculum (see link below). These questions must move children beyond procedure to adventure in their zone of proximal development!*We wanted our question stems to develop:- Linking thinking between concrete-visual-abstract representations- Logical thought- Fluidity with the inverse- Awareness that there s more than one way to skin a cat!

4 - Articulate mathematicians - Teachers who can capitalise on conversations and press children to explain their Classrooms full of probing, unfair designed our question stems to help teachers develop well-articulated justifications in maths lessons,with children becoming used to the expectation of speaking in full sentences to explain their ideas.*The zone of proximal development, often abbreviated to ZPD, is what psychologist Lev Vygotsky termed the difference between what a learner can do without help and what he or she can do with help. As teachers, we should pitch our teaching and questioning at a child s ZPD; if our lesson is too easy, it falls into the child s comfort zone and if it s too hard, it falls into the child s zone of confusion!What are question stems?We collaborated on a way to place Reasoning at the heart calculation lessons, developing easily adapted types of questions and activities that would require children to explore their understanding as well as recall facts.

5 We called these the question stems , from which Reasoning can grow!The seeds of our question stems came from research and advice from NRICH and the National Centre For Excellence In Teaching Mathematics (NCETM). We learnt much from Jennie Pennant, NRICH s Primary Professional Development Lead, and Debbie Morgan, Director for Primary at the NCETM. The NCETM has published progression documents laying out the New Curriculum objectives in strands so that teachers can see how expectations progress across year groups. We matched each calculation objective with several question stems and examples that can bring Reasoning to the fore so it doesn t stay inside our heads!Natalie from Elea nor Palmer on The e mpty box! There is nothing better than that magic moment in a maths lesson when a child can explain how they worked something out. Whenever you put empty boxes or missing information in a calculation, children start talking about what the answer couldn t or could be.

6 You get wonderful answers using language like, well I know this must be .. Empty boxes elicit that delicious logical thinking which pushes the highest attaining mathematicians to have uncomfortable moments (that we call learning!) and then to articulate their thinking. Empty boxes also stop by rote mathematicians in their tracks. If there s anything better than one empty box, it s two! This opens up children to multiple possibilities so that there s not just one right answer. Children adore puzzles to crack and the empty box looks like a code or mystery in fact it s the start of one form of algebraic thinking. Using empty boxes in calculation lessons sends a message to our children that we like fun puzzles in maths and that we value reasoned, logical thought. 12 x = 60 What s in the empty box? x x 6 = 726 r 3 = - 4 Give children 2 clouds of numbers and get them to fill the empty boxes: - = 3 r 133257162822321987321075K ate from Holy Trinity NW3 on Give me a n exa mple I find that children can be afraid to get the wrong answer and no matter how much you talk about good mistakes , there are always children who are afraid to give their ideas.

7 That is why I love Give me an example All of a sudden, a plethora of could be right answers present themselves. It encourages the higher attaining mathematicians to exhaust all the possibilities, and then use different operations or units of measurement in their thinking to extend themselves even further. It then also allows the less confident mathematicians to experience success. Once another child has given an example of 1x12 for two numbers which multiply to make 12, and another has given 2x6, they can follow the pattern (using a different maths skill) to offer 3x4. It then encourages them to work logically to find all the possibilities. Using Give me an example of in calculation lessons tells the children that, while there might be errors, there is more than one way to skin a cat. Monica from Brecknock on Ca n you ma ke up a story?..Teaching pure maths can be beneficial when securing strategies and methods.

8 However, to ensure rich mathematical thinking along with confident and successful application, Can you make up a story? allows both the child and teacher to explore maths in context, enhancing a child s experience of how maths is used all around us. Contextualising maths allows children to understand the importance and relevance of maths in their daily lives along with the significance maths has in the world. Using their own imagination to create a story to describe a mathematical concept, develops their confidence in mathematical thinking and Reasoning as well as the opportunity to explore how creative maths can be! Give me an example of .. and another!A common factor of 66 and 24A multiple of 3 over 200 (using the rule that multiples of 3 have digits that add to 3, 6 or 9)A multiple of 6 over 1000 (using the rule that multiples of 6 must be even multiples of 3)Can you make up/draw a story/real situation for this equation.

9 ?Create stories for a division where you round up/down after you find the filling boxes, or booking coaches!136 - 3 = 45 r1 so when would the answer be 45 and when 46?Ti m Oates explains assessment after levels: stems to help you plan for Reasoning .. What is the same / different about ..Which of these numbers/calculations are trickier? Why?Do you agree or disagree that .. Is it always/sometimes/never true that ..Give me an example of .. and another ..Spot the mistake .. explain the mistakeWhat couldn t it be? What could it be?Give me a silly suggestion for ..Convince me that ..Prove by drawing/using dienes/using algebra that ..What comes next .. What came before?The answer is .., what s the question?What s in the empty box?If we know .. what else do we know?Spot the pattern, explain the an equivalent for ..Can I change the order I do this in?Can you make up a story/real situation for this maths?

10 What I can t doWhat I can do with helpZPDWhat I can doZone of Proximal development ReasoningNeW CuRRiCulumProblem Solving FluencyDeveloping ReasoningThe key to teaching calculation effectivelyA summary of the findings of a Joint Practice Development Group of the Camden Primary Partnership Teaching School Alliance 2014. Camden Primary Partnership Teaching School Alliance. Design and production: L C Creative Design 07958 002 is one page from our Question Stems document. For a full copy of our Question Stems document, if you re interested in being part of a new JPD group, or to join the Alliance, contact the project lead: Natalie Stevenson, deputy headteacher at Eleanor Palmer via Thanks to these teachers who took part from our Alliance member schools:Lucy Foster Eleanor Palmer, Monica Gallagher Brecknock, Tom Gibson Eleanor Palmer, Callum Moore Brecknock, Rhian Mulji Fleet, Kate Roscoe Holy Trinity NW3, Claire Trewhella Torriano JuniorsAnd to Debbie Morgan, NCETM, and Gorden Pope, Institute of Education, for their support and s the same?