Presentation on theme: "The what, when, how, and why of the secondary school mathematics curriculum Merrilyn Goos."— Presentation transcript:
1The what, when, how, and why of the secondary school mathematics curriculum Merrilyn Goos
2Here’s the plan … What mathematics gets taught in Queensland schools? When are the main topics introduced and how much time is allocated to them?Who makes the big curriculum decisions (about what gets taught to whom and why)?How has the school mathematics curriculum changed over time and what might happen next?
3Years 1-10 Mathematics Content: Number (numeration, operations) Algebra (patterns, functions, equations)Measurement (length, mass, area, volume)Space (shape, location and direction)Chance and DataProcesses (Working Mathematically):RepresentationEstimationProblem solvingApplicationsReasoningJustificationCommunicationReflection
4Minimum time allocations for Years 1-10 Mathematics Years 1-3: 200 hours/year (5 hours/week)Years 4-7: 160 hours/year (4 hours/week)Years 8-10: 80 hours/year (2 hours/week)In practice, more time is allocated, especially in Years 8-10 (about 3 hours/week).
5Years 11 and 12 MathematicsThree subjects: Mathematics A (financial mathematics, applied geometry, statistics & probability + electives) Mathematics B (algebra, functions, calculus, statistics; no electives) Mathematics C (group theory, complex numbers, matrices, vectors, advanced calculus, structures & patterns + options)General objectives (and assessment criteria):Knowledge and proceduresModelling and problem solvingCommunication and justificationMinimum time allocation:110 hours/yearIn practice, timetabled for 3.5 hours/week.
6Choosing senior mathematics subjects Mathematics A: precursor to training in technical trades, administrative and managerial employment, some tertiary studies with moderate mathematical demand.Mathematics B: precursor to tertiary studies with high mathematical demand (science, medicine, engineering, info tech, mathematics, finance, business, economics).Mathematics C: recommended companion subject to Mathematics B; provides additional preparation for tertiary studies with high mathematical demand.
7A day in the life … Families of functions Trig functions Exponential & log functions9-10 pmOptimisationIntro to integrationApplied statistical analysis11pm – 12 amRates of changeDerivatives of trig, exponential, log fns10-11 pmYr 1Yr 3Yr 5Yr 7Yr 9Yr 10Yr 11Yr 12Rational numbersIndex notationVariablesManipulation of algebraic expressionsSolution & graphing of linear equationsSimilaritySimple deductive geometry5-7 pmSolution of quadratic and simultaneous equations7-9 pmPlace value to 100sRepresent simple fractions5-7 amSimple equivalent fractionsDecimal fractions to hundredthsSymmetryTransformations9-11 amIntegersAddition of fractions with same denominatorConversion between fractions, decimals, %Order of operationsTables of valuesCongruence1-3 pm
8Notional time allocations for topics in Mathematics B (over 2 years) Introduction to functions35 hrsRates of changePeriodic functions & applications30 hrsExponential and logarithmic functions & applicationsIntroduction to integration25 hrsApplied statistical analysisOptimisationTOTAL215 hrsEquivalent to 28 minutesin a “day in the life” of a mathematics student, some time after 11pm!
9Who makes curriculum decisions? Potential stakeholders:Ministers for EducationOfficers of state education departments, Catholic Education, independent schoolsState curriculum and assessment authoritiesTeachers and teacher unionsTeacher professional associationsPrincipalsParent organisationsStudentsEmployers and business organisationsUniversity academicsTextbook writers and publishersMediaEducational consultants and lobby groupsCurriculumMathematicsSocietyLearnerSources of influence on curriculum content
10How does mathematics syllabus development work in Queensland? Queensland Studies Authority is responsible for developing, revising, maintaining syllabuses via subject based Syllabus Advisory Committees (SACs).SAC membership includes teachers (all levels of schooling, all sectors), university education academics; representatives of teacher unions, professional associations, parent organisations, business organisations. Each SAC is supported by a subject based professional officer of the QSA.Senior syllabus revisions occur on a 7 year cycle. Consultation takes place with teachers (state wide survey), university academics (subject specialists), business organisations leading to preparation of a design brief for syllabus revision. SAC sub-committees made up of experienced teachers are established to undertake the revision, with support from QSA officers and oversight from the SAC.The revised syllabus must be approved by the QSA Curriculum Committee.Major syllabus revisions have a trial/pilot stage and state wide professional development, provided by the QSA, before full implementation.
11How have school mathematics curricula changed over time? 1800Influence of English curriculum models and newly established universities (Sydney, Melbourne). Curriculum was narrowly focused in preparing students for university entrance examinations.19001960“New Maths” – Cold War influence – emphasis on abstraction and mathematical structures.19701980Social and economic changes led to new emphasis on problem solving and real life applications.1990First attempt at a national curriculum – 8 Key Learning Areas and outcomes focus.20002010Second attempt at a national curriculum – making explicit what teachers must teach, what students should learn, and to what standard.
12What will the national mathematics curriculum look like? Three content strands:Number and algebraMeasurement and geometryStatistics and probabilityFour proficiency strands:Understanding (conceptual)Fluency (procedural)Problem solving (strategic competence)Reasoning (adaptive)
13Proposed national curriculum structure All students to experience the full mathematics curriculum to the end of Year 9, with mathematics remaining compulsory in Year 10.Differentiation of subjects in Years 11 and 12 (schools must preserve for all students the possibility of studying mathematics in Year 11).Probably three levels of mathematics in Years 11 and 12: “elementary” (cf Maths A), “intermediate” (cf Maths B), “advanced” (cf Maths C).
14Challenges for the national mathematics curriculum Engage more students, especially in the middle years, and increase the proportion of students taking advanced subjects in the senior secondary years.Cater for the great spread of achievement amongst students, but …Impose no barriers to progression in mathematics before the senior secondary years.Identify and emphasise the “big ideas” or core topics in mathematics (thin out the crowded curriculum).