Mathematics - Curriculum

1 MathematicsTeacher GuidelinesPrimary SchoolCurriculumDUBLINPUBLISHED BY THE STATIONERY OFFICETo be purchased directly from theGOVERNMENT PUBLICATIONS SALE OFFICESUN ALLIANCE HOUSEMOLESWORTH STREETDUBLIN 2or by mail order fromGOVERNMENT PUBLICATIONSPOSTAL TRADE SECTION4-5 HARCOURT ROADDUBLIN 2(Tel: 01-6476834-5; Fax: 01-4752760)or through any booksellerDesign Consultancy:Bradley McGurk PartnershipDesigned by:The Identity BusinessPhotography:Christy McNamaraTypesetting:Spectrum Print ManagementPrinted by:Mozzon Giuntina - Florence andOfficine Grafiche De Agostini - Novara 1999 Government of IrelandMathematicsTeacher GuidelinesContentsMathematics in the primary curriculumIntroduction 2 Mathematics in a child-centred curriculum3 The content of the Mathematics curriculumStructure of the curriculum8 strand content9 School planning for mathematicsCurriculum planning18 Organisational planning20 Classroom planning for mathematicsClassroom organisation24 Section 1 Section 3 Section 4 Section 2 Mathematics Teacher GuidelinesApproaches and methodologiesTeaching approaches30 Mathematical language30 Estimation strategies for number32 Problem-solving35 Some activities with odd and even numbers37 Paper-folding and fractions38 Early mathematical activities40 Place value notation boards42 Integration.

2 Linkage and cross- strand planning46 Mathematical trails47An example of cross- strand planning59 Using technology60 Looking at children s work64 AppendixOverview of skills development68 Overview of symbols, numerals, fractions and terminology70 Suggested list of mathematical equipment72 Source references for the Curriculum and guidelines74 Glossary76 Membership of the Curriculum Committee for Mathematics78 Membership of the Primary Co-ordinating Committee79 Acknowledgements80 Section 5 Section 6 Children learn fromthe people andmaterials around themMathematicsin the primarycurriculumSection 1 IntroductionMathematics is recognised as one of the sciences and has been describedand defined in many different ways. It is a creative activity and is one of themost useful, fascinating and stimulatingdivisions of human knowledge. It is aprocess of managing and communicatinginformation and has the power to predictand provide solutions to practicalproblems as well as enabling theindividual to create new imaginativeworlds to explore.

3 We use mathematicsin everyday life, in science, in industry,in business and in our free education is concernedwith the acquisition, understanding and application of skills. Mathematicalliteracy is of central importance inproviding the child with the necessaryskills to live a full life as a child andlater as an adult. Society needs peoplewho can think and communicatequantitatively and who can recognisesituations where Mathematics can beapplied to solve problems. It is necessaryto make sense of data encountered inthe media, to be competent in terms ofvocational mathematical literacy and touse appropriate technology to supportsuch applications. This Curriculum willbe a key factor in preparing children tomeet the demands of the applications are requiredin many subjects. The ability to interpretand handle data is of particular relevancein history and geography. Measures andShape and spacerelate to the visual arts,physical education and gives the child a reason and motivation to develop mathematicalskillsand concepts that can be used inall subjects.

4 Numeracy and estimation are particular to Mathematics , whileevaluating findings, reporting back,predicting and reasoning are used both in Mathematics and throughoutthe Curriculum . Section 1 Mathematics in the primary curriculumMathematics in the primarycurriculum2 Mathematics in a child-centred curriculumThe child learns from the people and materials around him/her. It isexperience of the social and physicalworld that is the source of concepts,ideas, facts and skills. Integration ofthese experiences is the vital the child is given the chance tomanipulate, touch and see objects thathelp him/her to acquire an understand-ing of concepts, he/she will understandmore effectively than if words andsymbols are the only learning discovery learning alone will notbe enough. The child needs guidance in formulating theories about what it is he/she is discovering. The child alsoneeds help in developing the languagefor describing accurately what it is he/she is doing.

5 The teacher and the child speers have a vital role to play in his/hereducational experience. Yet ultimately it is the child who creates the balancebetween his/her knowledge and theknowledge of those around Constructivist approaches are central to this Mathematics Curriculum . To learnmathematics children must constructtheir own internal structures. As inreading and writing, children inventtheir own procedures. We accept thatchildren must go through the inventedspelling stage before they begin todevelop a concept of the structures ofspelling. The same is true of children attempt to count ororder things in the environment andthey develop rules for themselves to doso. They should be encouraged to tryout these personal strategies, to refinethem by discussion and to engage in awide variety of tasks. It is in the interpersonal domain thatchildren can test the ideas they haveconstructed and modify them as a resultof this interaction.

6 When working in a constructivist way children usuallyoperate in pairs or small groups to solveproblems co-operatively. Tasks that arewritten on one sheet can be given togroups of two or more children. Thismakes consultation, discussion and co-operation essential. Children work attheir own pace but are encouraged tocomplete the task as fully as possiblewithin the set time. They are expectedto respect one another s solutions, notto discredit partners reasoning, and to discuss the train of thought used inthe constructivist approachOne procedure would be asfollows: children discuss the problem try a possible approach further discussion modify arising from theinteraction construct concepts fromdeductions arrive at a solution orsolutions discuss results recordMathematics in a child-centred curriculum3 Mathematics Teacher GuidelinesThis sociocultural theory sees cognitivedevelopment as a product of socialinteraction between partners who solveproblems together.

7 It acknowledges theimportance of the home and family inthe child s learning and focuses on groupinteraction. It is a process approachrather than a step-like, incremental one. One form of instruction used isscaffolding. Here the teacher modifiesthe amount of support according to theneeds of the child by modelling thebehaviour, for example possible methodsof approaching a problem. The teacherbreaks down the task and makes thetask manageable for the individual child,thus supporting the development of thechild s own problem-solving discussion the child becomesaware of the characteristics of a must be encouraged to use thecorrect vocabulary needed for a particulartask. Young children are egocentric, andit is through social interaction that theycan begin to appreciate the points ofview of other people. Sequences ofinstruction involve discussion, hands-onexperience and practical adults we expect objects to behave in a stable and predictable have to learn to recognisethese attributes.

8 They need to handleand use a variety of objects in order to form their own rules and structuresfor dealing with the world. This is ofparticular importance in need to work out when to use a particular plan, what they want to achieve and the actual procedureneeded to complete the task. Throughexperiencing many different types ofproblems they become more wider the range of problems theyencounter the more likely they are togeneralise the rules and use them innew direct instruction is very importantin Mathematics , children also need todevelop their own learning need to teach children to look at howthey arrived at a result ratherthan justconcentrating on the answer as an endin itself. Children need training in the skills of collaboration and co-operation, inlistening to, accepting and evaluatingthe views of others. These skills areapplicable throughout the on open-ended problems, wherethe emphasis is placed on using skillsand discussion rather than seeking aunique solution, is recommended.

9 Many methods may be used in solving a mathematical 1 Mathematics in the primary curriculum4 Mathematics in a child-centred curriculum5 Mathematics Teacher GuidelinesExploring the propertiesof 3-D shapesThe contentof themathematicscurriculumSection 2 Structure of thecurriculumThe areas of content in thismathematics Curriculum are referred toas strands. The strands form a networkof related and interdependent are further developed as strandunits. Each strand unit contains thecontent and some exemplars for thatunit. Measures, Shape and space, Dataand Algebraform a greater part of thecurriculum than Number but number is an integral component of all of thestrands. No strand stands alone and this should be reflected in timetabling. How the content is presented content is presented in two-yearblocks, for example first class on theleft and second class on the right ofeach page. The treatment of contentis common to both classes.

10 Thispresentation helps the teacher inplanning and in revision the strand unit is in coloured type tothe left of the page the content statement is indicatedby a bullet the content of the exemplars is initalic type. These are limitedsuggestions for implementing thestrand unit. It is envisaged thatteachers will develop and extendthese suggestions as they workthrough the programme vocabulary relevant to the strandunit is shown in bold type, forexample long/longer,short/shorter, positive/negative the sequence of presentation of thestrands in the content document is:Number, Algebra, Shape and space,Measures and Data. This does notimply a hierarchy. Strands can betaught in parallel rather than oneafter the other and this facilitatesthe use of aspects of numberthroughout the mathematicscurriculum. This is called linkage; forexample, in teaching fractions it ispossible to link with the strandShape and space integration opportunities areindicated in some strand units but these are merely suggestions.