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The what, when, how, and why of the secondary school mathematics curriculum Merrilyn Goos

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Here’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?

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Years 1-10 Mathematics Content: Number (numeration, operations) Algebra (patterns, functions, equations) Measurement (length, mass, area, volume) Space (shape, location and direction) Chance and Data Processes (Working Mathematically): Representation Estimation Problem solving Applications Reasoning Justification Communication Reflection

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Minimum 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).

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Years 11 and 12 Mathematics Three 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 procedures Modelling and problem solving Communication and justification Minimum time allocation: 110 hours/year In practice, timetabled for 3.5 hours/week.

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Choosing 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.

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A day in the life … Yr 1Yr 3Yr 5Yr 7Yr 9Yr 10Yr 11Yr 12 Place value to 100s Represent simple fractions 5-7 am Simple equivalent fractions Decimal fractions to hundredths Symmetry Transformations 9-11 am Integers Addition of fractions with same denominator Conversion between fractions, decimals, % Order of operations Tables of values Congruence 1-3 pm Rational numbers Index notation Variables Manipulation of algebraic expressions Solution & graphing of linear equations Similarity Simple deductive geometry 5-7 pm Solution of quadratic and simultaneous equations 7-9 pm Families of functions Trig functions Exponential & log functions 9-10 pm Rates of change Derivatives of trig, exponential, log fns 10-11 pm Optimisation Intro to integration Applied statistical analysis 11pm – 12 am

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Notional time allocations for topics in Mathematics B (over 2 years) TopicNotional Time Allocation Introduction to functions35 hrs Rates of change35 hrs Periodic functions & applications30 hrs Exponential and logarithmic functions & applications 35 hrs Introduction to integration25 hrs Applied statistical analysis25 hrs Optimisation30 hrs TOTAL215 hrs Equivalent to 28 minutes in a “day in the life” of a mathematics student, some time after 11pm!

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Who makes curriculum decisions? Potential stakeholders: Ministers for Education Officers of state education departments, Catholic Education, independent schools State curriculum and assessment authorities Teachers and teacher unions Teacher professional associations Principals Parent organisations Students Employers and business organisations University academics Textbook writers and publishers Media Educational consultants and lobby groups Curriculum Mathematics SocietyLearner Sources of influence on curriculum content

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How 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.

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How have school mathematics curricula changed over time? 1800 1900 1960 1970 1980 1990 2000 2010 Influence of English curriculum models and newly established universities (Sydney, Melbourne). Curriculum was narrowly focused in preparing students for university entrance examinations. “New Maths” – Cold War influence – emphasis on abstraction and mathematical structures. Social and economic changes led to new emphasis on problem solving and real life applications. First attempt at a national curriculum – 8 Key Learning Areas and outcomes focus. Second attempt at a national curriculum – making explicit what teachers must teach, what students should learn, and to what standard.

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What will the national mathematics curriculum look like? Three content strands: Number and algebra Measurement and geometry Statistics and probability Four proficiency strands: Understanding (conceptual) Fluency (procedural) Problem solving (strategic competence) Reasoning (adaptive)

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Proposed 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).

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Challenges 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).

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