Speaking, Listening and Learning in Mathematics

Progression in Speaking, Listening and Learning Mathematics Handout 2.2The following chart is based on the poster within the ‘Speaking, Listening, Learning:working with children in Key stages 1 & 2’ resource box. The poster has been adapted toreflect a mathematics focus.Year Speaking Listening Group WorkYears1/2Describe and explaintheir working giving asmuch information asneeded.Use mathematicalvocabulary appropriateto their age.Order their oral responsein some logical way.Use mathematicallanguage accurately, forexample to describe ashape.Articulate themathematics of apractical situation suchas a calculation arisingfrom a real situation.Listen with interest toquestions orexplanations makingjottings as appropriate.Listen to mathematicalinstructions and showunderstanding bycarrying them out.Ask simple questionsseeking clarification orreassurance.Listen to questions orexplanations and seekclarification or furtherdetail.Create a mental image inresponse to an idea orsituation presentedorally.Ask and answerquestions andsuggest ideas toothers.Take turns as speakerand listener whenworking in pairs orsmall groups.Consider otherpeople’s ideas,explanations ormethods.Years 3/4Describe and explain acomplete solution.Suggest and describe insome detail, analternative method.Select and useappropriate techniquessuch as gesture, visualaids or practical modelsto enhance their talk.Use mathematicallanguage appropriate totheir age with accuracyand understanding.Articulate themathematics of apractical situation or asimple abstract problem.Listen attentively toothers making follow-uppoints to extend or clarifyan idea.Listen carefully to apresentation jotting downkey information to informa response.Listen carefully to createa mental image inresponse to oral workand explain this toothers.Agree a solution withjustification ordisagree with it givingreasons.Offer possibleapproaches orstructures to amathematicalinvestigation.Take different roleswhen working ingroups of differentsizes.Keep track of themathematics beingcarried out by thegroup wheninvestigating orsolving a 2-stepproblem.1

Years 5/6Present a multi-stepsolution.Use mathematicallanguage with increasingaccuracy and use itwhen describingeveryday objects e.g.use language such assuch as pyramid andprism and semi-circle asopposed to half a circle.Show the use ofmathematical languagein a range of contextsand purposes eg use thelanguage of likelihood ifappropriate whenstructuring a convincingargument or counterargument.Reflect on the solution toa problem and structurea logical explanation topresent to others.Extract and articulate theabstract mathematicswithin or from a practicalsituation or contextListen attentively toidentify the key featuresof a mathematicalargument or counterargument.Analyse and evaluatethe key features of amathematical argument.Use the key features of amathematical argumentto solve a problem orprovide constructivefeedback.Create a mental imageand manipulate it inresponse to instructions.Offer and justify achallenge to an ideaby explaining itsconsequences.Present and justify apossible approach toa problem orinvestigation seekingfeedback from groupmembers.Contribute to therigour with which thegroup carries out itsmathematics showingincreasinglysophisticated logic,coherence andarticulation.Possible activities for developing Speaking and listening in mathematics.The Polishing Pen (linked to literacy!)Record a child’s explanation/justification/ reasoning invite the class to use the ‘polishing pen’ toredraft/extend the response. Children use mathematical vocabulary cards and working walls tostructure this process.Explain your method/reasoningExplain to a partner, group or class how you worked something out or why you believe somethingto be correct/true. Any calculation or problem solving work can provide opportunities for pupils toexplain their chosen strategy to others, allowing peers to make independent choices about themost effective strategy available to them. Listening partner has to offer reasons why s/he agreeswith the chosen strategy and/or offer an alternative strategy.Promote the vocabulary of reasoning:• It could be… because…• It can’t be……because• It won’t work, because….• If…then….• It would only work if…..The following activities require the pupils to determine which number is represented by each letterwithin the context of multiplication facts and explain how they know.2

For example: In mystery tables the digits in multiplication tables are replaced by letters. The taskis to work out which number is represented by each letter and why.In mixed up multiplication grids the multiplication tables from 1 x 1 to 9 x 9 are designed so thatrows and columns are in the wrong orders. Once again letters stand for the digits 0 – 9 and thetask is to crack the codeIn ‘Who wants to be a millionaire?’ provide a question and 4 possible answers to discuss. Theactivity can be made more fun by incorporating ‘Phone a friend’, ‘Ask the audience’ and ’50 / 50’.This game can reduce the pressure on less confident children in having to calculate an answer atspeed. However it provides opportunities for them to discuss their thinking with peers, justifyingand communicating their reasoning.In ‘Always true, sometimes true, never true’ the activity requires pupils to articulate and justifytheir reasoning. Given a statement, decide whether it is always, sometimes or never true, justifyingyour reasoning with specific examples where possible. Statements such as: multiplication by apositive number makes positive numbers larger; the total of 2 consecutive numbers is always odd,dividing a number by one half makes the answer twice as big….‘Guess my rule’ can be played as a whole class, in groups or in pairs. In each case, a pointsystem could be introduced, enabling children to win more points the fewer clues they require.Pupils can ask 10 questions, which have to be answerable with yes or no, to identify the chosennumber. With a limit of 10 questions, the children have to listen very carefully to each other andconsider the most helpful type of question, so as not to waste their chances.Pupil/team A select a one or two stage rule (function machine). Pupil/team B provides a suggestedinput number. Pupil/team A respond with the corresponding output number. Pupils then try toidentify the rule which has changed the input to the output. Pupils continue to suggest inputnumbers and receive the corresponding output number until they are able to correctly identify therule. Pupils may come to realise that the rule is easier to identify if they use a strategy eg. try low,consecutive numbers‘Just a minute’Ask children to take turns to talk for just a minute on an aspect of calculating eg How do you checkyour answers? Do you prefer addition or subtraction calculations - why?Take a standPut a statement in the middle of a group of children. Give each child their name card. Children toput their name card as close / far away from the statement depending on how confident they are insaying something about the statement.e.g the sum of any 3 consecutive numbers is divisible by 3.They could agree / disagree with this statementThey could define consecutive or divisible.They could give examples.Is very important that all children are encouraged to speak and listen, so even if they can think ofnothing original to say, they can still repeat what another child has said and agree / disagree withit.Ensure all children know the rules for speaking and listening - establish ground rules first:• no talking when someone else is talking• only speak when you are holding the 'microphone' (could be a ‘pencil’)• think about what the person is saying and ask yourself if you agree or disagree3