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Connections

PurposeThe purpose of this section is:To identify the importance for Teaching &Learning of making connectionsTo consider the types of connections it isbeneficial to makeTo alert us as a community of educators tothe importance of connecting with theschool literacy and numeracy policy.

What should students learn in Maths at schoolHow todo/useMathsThatMaths isusefulbybybyTo see theMaths ineverydaythingsMakingConnections“It is essential to make connections in mathematics ifone intends to develop mathematical understanding.”Hiebert and Carpenter (1992)

Mathematical understanding involves knowing-that (stating) knowing-how (doing) knowing-why (explaining) knowing-when (applying)Among the objectives of Junior Certificate Mathematics are todevelop procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, andappropriately adaptive reasoning—capacity for logical thought, reflection, explanation, justificationand communication strategic competence—ability to formulate, represent, and solve mathematical problemsin both familiar and unfamiliar contextsJunior Certificate Mathematics Syllabus

To Make Connections inMathematicsWhat does this mean for you?

Connections in WorldFutureAcrossStrands

Connections in MathematicsPastMaking connections is an important human activity.“Seeking patterns and connections is the naturalactivity of the brain.”Caine &Caine 1990Isolated pieces of information require more time toassimilate than learning experiences that areconnected with a person’s prior knowledge.

Connections in MathematicsPastMaking the connection to this prior knowledge isvaluable because it:assists students in relating new information (or skills)to what they already know and can docreates a scaffold for new learningallows for the surfacing of misconceptions that mayimpede learningidentifies gaps in knowledge or skills that may exist

Connections in MathematicsPastThe History of Mathematics“No subject loses more when divorced from its history thanmathematics”Bell E.T

Connections in MathematicsThe History of MathematicsHumanises MathematicsPastStudents’ problems have been present in historyCultural linksFoundation for better understandingHighlights interaction between mathematics &society

Connections in MathematicsFutureWithout an explicit focus on connections, studentsmay view their learning of mathematics as theaccumulation of unrelated and discrete ideas.“Mathematical learning is cumulative with work ateach level building on and deepening what studentshave learned at the previous level to foster the overalldevelopment of understanding.”Junior Certificate Mathematics Syllabus

Connections in MathematicsWithinStrandsConnections that draw together key ideas and topicswithin a strand help students develop a more coherentunderstanding of the concept or process they arelearning.

Connections in MathematicsDecimalsUsed inFractionsRational NumbersExpress as partsCompared to powers of tenWithinStrandsMeasurementPercent

Connections in MathematicsquadrilateralWith one pairof sides allelParallelogramRhombusRectangleSquare

Connections in MathematicsAcrossStrands“To students, the typical curriculum presents anendless array of facts and skills that are unconnected,fragmented, and disjointed ”Beane, 1991

Connections in tionsThe strand structure of the syllabusshould not be taken to imply that Geometry&topics are to Juniorbe studiedinisolation.Trigonometry&Leaving connectionsWhere appropriate,Certificateshould be madewithin and acrossSyllabusthe strands andwith other areas oflearning.”Junior & Leaving Certificate MathematicsSyllabusAlgebraNumber

Connections in etry&TrigonometryFunctionsRatio /ProportionAlgebraNumber

Connections in MathematicsRatio /Proportion

Connections in MathematicsTrigonometryAll trig functions are ratiosProbabilityDivisionScaleThe ratio of 2 to 3 canbe written as divisionrelationshipsThe scale of a map is 2cmper 1km. We write thisas the ratio 1:50 000All probabilities can beexpressed as ratiosSlopeComparisonsThe ratio of sunny days torainy days is greater inDublin than in DingleUnit Price125g/ 19.95. that is 39.90 for 250g or 159.60 per kgRatio /ProportionThe ratio of the rise tothe run is ⅕GeometryBusinessThe ratio of the circumference of acircle to its diameter is always πProfit and loss are figuredas ratios of income to totalcostAny two similar figures havecorresponding measurements that areproportional (in the same ratio)

Connections in MathematicsAcrossStrandsConnections to, and translations between, differentrepresentations of a concept are important cognitiveprocesses which lead to a more robust understandingof concepts.

Connections in MathematicsAcrossStrandsStory

Connections in MathematicsAcrossStrands

Connections in MathematicsCurriculumSubjectsMathematics is not learned in isolation. It has significantconnections with other curriculum subjects.Junior Certificate SyllabusScience learners are expected to be able to work with data,produce graphs, and interpret patterns and trends.In Technical Graphics, drawings are used in the analysis andsolution of 2D and 3D problems through the rigorous applicationof geometric principles.

Connections in MathematicsCurriculumSubjectsMathematics is not learned in isolation. It has significantconnections with other curriculum subjects.Junior Certificate SyllabusIn Geography, learners use ratio to determine scale; graphsand statistics to analyse dataIn Home Economics learners use mathematics whenbudgeting and making value for money judgements

Connections in MathematicsCurriculumSubjectsMathematics is not learned in isolation. It has significantconnections with other curriculum subjects.Junior Certificate SyllabusIn Business Studies learners see how mathematics can be usedby business organisations in budgeting, consumer education,financial services, enterprise, and reporting on accounts.In Music the graph of the sound wave of a tuning fork playing anote looks like a perfect sine wave.

Connections in MathematicsCurriculumSubjectsMathematics is not learned in isolation. It has significantconnections with other curriculum subjects.Junior Certificate SyllabusIn Art techniques like tiling, tessellation, perspective, pattern,ratio and symmetry are commonly used.

Connections in MathematicsCurriculumSubjectsMathematics is not learned in isolation. It has significantconnections with other curriculum subjects.Junior Certificate Syllabus

CurriculumSubjectsConnections in MathematicsAccounting 2013 HLProvide for depreciation on plant and machinery at the annual rate of 10% ofcost from the date of purchase to the date of sale.A provision for bad debts to be created equal to 4% of debtors.The purchase price was discharged by granting the seller 380,000 shares at 1each in Cooper Ltd at a premium of 20c per share.On the same day goods were sold on credit to Galvin for 450. This was amark-up on cost of 25%.Kelly borrowed 72,000 on 1/7/2012, part of which was used to purchase anadjoining warehouse costing 60,000. It was agreed that the sum borrowedwould be repaid in 12 equal instalments over a six year period commencing onthe 1 January 2013. Interest was to be charged at the rate of 10% per annumand paid monthly.

CurriculumSubjectsConnections in MathematicsAccounting 2013 HLProvide for depreciation on plant and machinery at the annual rate of 10% ofcost from the date of purchase to the date of sale.A provision for bad debts to be created equal to 4% of debtors.The purchase price was discharged by granting the seller 380,000 shares at 1each in Cooper Ltd at a premium of 20c per share.On the same day goods were sold on credit to Galvin for 450. This was amark-up on cost of 25%.Kelly borrowed 72,000 on 1/7/2012, part of which was used to purchase anadjoining warehouse costing 60,000. It was agreed that the sum borrowedwould be repaid in 12 equal instalments over a six year period commencing onthe 1 January 2013. Interest was to be charged at the rate of 10% per annumand paid monthly.

CurriculumSubjectsConnections in MathematicsAccounting 2013 OL LC

CurriculumSubjectsConnections in MathematicsAccounting 2013 OL LC

CurriculumSubjectsConnections in MathematicsAgricultural Economics 2013 HL LCUsing the above tableconstruct a total productcurve, placing the amount offertilizer used on thehorizontal x-axis and the cropyield on the vertical y-axis.

CurriculumSubjectsConnections in MathematicsAgricultural Economics 2013 HL LCUsing the above tableconstruct a total productcurve, placing the amount offertilizer used on thehorizontal x-axis and the cropyield on the vertical y-axis.

CurriculumSubjectsTechnical Graphics 2013 JC OL

CurriculumSubjectsTechnical Graphics 2013 JC HL

CurriculumSubjectsBusiness 2013 LC HL

CurriculumSubjectsConnections in MathematicsChemistry 2012 HL

Connections in MathematicsDesign & Communication Graphics 2013 HLIt is planned to package the cube, without the stand, ina plastic sphere. Determine the diameter of thesmallest possible sphere that will contain the cube anddraw that sphere in the end view.2012 HL

CurriculumSubjectsConnections in MathematicsEconomics 2012 HL

CurriculumSubjectsConnections in MathematicsMathematics2011 2013paperLC2 OLLCHL Q7Geography

Connections in MathematicsGeography

CurriculumSubjectsConnections in MathematicsGeography 2012 LC HL

Connections in MathematicsGeography 2012 LC HL

Connections in MathematicsHome Economics Scientific & Social 2012 HL

Connections in MathematicsPhysics 2012 HLExplain the shape of your graph.

CurriculumSubjectsConnections in MathematicsPhysics 2012 OL

CurriculumSubjectsConnections in MathematicsTechnology 2012 HL

CurriculumSubjectsConnections in MathematicsTechnology 2013 HL

CurriculumSubjectsConnections in MathematicsChemistry 2013 LC HL

Connections in MathematicsCurriculumSubjectsNumeracy encompasses the ability to use mathematicalunderstanding and skills to solve problems and meet the demands ofday-to-day living in complex social settings. To have this ability, ayoung person needs to be able to think and communicatequantitatively, to make sense of data, to have a spatial awareness, tounderstand patterns and sequences, and to recognise situationswhere mathematical reasoning can be applied to solve problems.Literacy includes the capacity to read, understand and criticallyappreciate various forms of communication including spokenlanguage, printed text, broadcast media, and digital media.LITERACY AND NUMERACY FOR LEARNING AND LIFE The National Strategy to Improve Literacyand Numeracy among Children and Young People 2011-2020

Connections in MathematicsCurriculumSubjectsNumeracy encompasses the ability to use mathematicalunderstanding and skills to solve problems and meet the demands ofday-to-day living in complex social settings. To have this ability, ayoung person needs to be able to think and communicatequantitatively, to make sense of data, to have a spatial awareness, tounderstand patterns and sequences, and to recognise situationswhere mathematical reasoning can be applied to solve problems.Literacy includes the capacity to read, understand and criticallyappreciate various forms of communication including spokenlanguage, printed text, broadcast media, and digital media.LITERACY AND NUMERACY FOR LEARNING AND LIFE The National Strategy to Improve Literacyand Numeracy among Children and Young People 2011-2020

Connections in MathematicsCurriculumSubjectsVocabulary DifficultiesAre you a mean teacher if you do not tell your students what themean means?I am right when I say, in your right hand you are holding a rightangleOn foot of measuring the man’s foot I know that it is a foot long.

Connections in MathematicsCurriculumSubjectsVocabulary DifficultiesAre you a mean teacher if you do not tell your students what themean means?I am right when I say, in your right hand you are holding a rightangleOn foot of measuring the man’s foot I know that it is a foot long.IT SAID PUT IT IN THEOVEN AT 130 DEGREES