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Re-visioning mathematics education at the secondary-tertiary interface:Towards creative boundary practicesMerrilyn GoosThe University of QueenslandBrisbaneAustralia
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Here’s the plan:
• What’s going on?• Who cares?• How could things be different? (Let’s dream a little …)
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What’s going on … in secondary and university mathematics education in Australia?
Low participation and too few graduates in
university mathematics
Too few mathematically qualified secondary
school teachers
School students don’t experience an engaging & challenging
mathematics education
Negative student perceptions of mathematics + poor
mathematics achievement
Students opt out of advanced mathematics in senior secondary school
School teachers
University mathematicians
Mathematics education researchers & teacher educators
CRICOS Provider No 00025B
What’s going on … in secondary and university mathematics education in Australia?
Low participation and too few graduates in
university mathematics
Too few mathematically qualified secondary
school teachers
School students don’t experience an engaging & challenging
mathematics education
Negative student perceptions of mathematics + poor
mathematics achievement
Students opt out of advanced mathematics in senior secondary school
CRICOS Provider No 00025B
What’s going on … in secondary and university mathematics education in Australia?
Low participation and too few graduates in
university mathematics
Too few mathematically qualified secondary
school teachers
School students don’t experience an engaging & challenging
mathematics education
Negative student perceptions of mathematics + poor
mathematics achievement
Students opt out of advanced mathematics in senior secondary school
CRICOS Provider No 00025B
What’s going on … in secondary and university mathematics education in Australia?
Low participation and too few graduates in
university mathematics
Too few mathematically qualified secondary
school teachers
School students don’t experience an engaging & challenging
mathematics education
Negative student perceptions of mathematics + poor
mathematics achievement
Students opt out of advanced mathematics in senior secondary school
CRICOS Provider No 00025B
Who cares?
• School teachers• University mathematicians• Mathematics education researchers & teacher educators
Policy makers
Communitymembers (parents,employers etc)
Ways of interacting with other stakeholder groups
1. Ignore: stay on the “outside” by pursuing one’s own teaching or research agenda, communicating only with fellow teachers or researchers.
2. Oppose: stay on the “outside” but criticise so as to undermine the opposing agenda.
3. Yield: work on the “inside” but in ways dictated by the other stakeholder group, thus losing one’s autonomy and credibility as a teacher or researcher.
4. Engage: work on the “inside” by trying to understand stakeholders’ goals, strategies and agendas, making connections with one’s own teaching and research agendas in ways consistent with one’s interests and values, while retaining the right to criticise constructively as an autonomous professional.
How could things be different?
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Boundary practices
Refers to the range of outreach, entry and transition factors at the interface between school and university that affect students’ participation in senior secondary and university mathematics.
Standard approaches and possibilities:•Career advisers in schools need to provide students with accurate and useful information on mathematics-focused careers
•Universities need to provide accurate information on prerequisites for mathematics-based courses•Universities need to develop good quality programs to support the mathematical transition from secondary school to university
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Transition issues
Institutional perspectives: different didactic contracts
(unwritten “rules” of the classroom) CRICOS Provider No 00025B
Cognitive perspectives: different modes of thinking and ways of organising knowledge
Sociocultural perspectives: different social practices in the
university mathematics community (language, reasoning)
Creative boundary practices?
Increase collaboration between school mathematics teachers and university mathematicians to …
•foster awareness of the cognitive, sociocultural and institutional differences between learning mathematics in school and university;•build mutual understanding of each other’s educational roles;•draw on complementary areas of expertise (mathematical, pedagogical)
… for the benefit of students in transition from school to university mathematics.
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From humble beginnings …
As a mathematics teacher educator my goal was to produce graduates with a licence to thrill … who could make a real difference to the students they would teach and to the teaching profession.
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One way I tried to do this was by connecting university teacher education students with the professional community of mathematics teachers in schools.
Using technology in mathematical modelling
Predicting the transit of Venus
Plus 400 yearsAlignment
(days past node) Years Year Ht above ecliptic
56756.82 31-Oct 1759 -89340.18 -244.8 1759 3.56443257340.75 6-Jun 1761 -88756.25 -243.2 1761 0.19153957924.67 11-Jan 1762 -88172.33 -241.6 1762 -3.87622559676.44 29-Oct 1767 -86420.56 -236.8 1767 3.78441460260.36 4-Jun 1769 -85836.64 -235.2 1769 -0.07702360844.28 9-Jan 1770 -85252.72 -233.6 1770 -3.65903398215.34 5-May 1873 -47881.66 -131.2 1873 -3.38699698799.26 10-Dec 1874 -47297.74 -129.6 1874 -0.40254999383.18 16-Jul 1876 -46713.82 -128.0 1876 4.042279
101134.95 2-May 1881 -44962.05 -123.2 1881 -3.611938101718.87 7-Dec 1882 -44378.13 -121.6 1882 -0.134212102302.80 13-Jul 1884 -43794.20 -120.0 1884 3.830413145513.08 3-Nov 2002 -583.92 -1.6 2002 3.659155146097.00 9-Jun 2004 0.00 0.0 2004 0.076875146680.92 13-Jan 2006 583.92 1.6 2006 -3.784294147264.85 20-Aug 2007 1167.85 3.2 2007 6.083329147848.77 26-Mar 2009 1751.77 4.8 2009 -6.118357148432.69 31-Oct 2010 2335.69 6.4 2010 3.876343149016.61 6-Jun 2012 2919.61 8.0 2012 -0.191687
From humble beginnings …
As Director of a university Teaching and Learning Institute my goal is to enhance the professionalism, visibility and status of teaching across the university.
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One way I try to do this is by connecting university mathematicians with the professional community of mathematics teachers in schools.
A day in the life …
Yr 1 Yr 3 Yr 5 Yr 7 Yr 9 Yr 10 Yr 11 Yr 12
Place value to 100sRepresent simple fractions5-7 am
Simple equivalent fractionsDecimal fractions to hundredthsSymmetryTransformations9-11 am
IntegersAddition of fractionswith same denominatorConversion betweenfractions, decimals, %Order of operationsTables of valuesCongruence1-3 pm
Rational numbersIndex notationVariablesManipulation of algebraicexpressionsSolution & graphing of linear equationsSimilaritySimple deductive geometry5-7 pm
Solution ofquadratic andsimultaneous equations7-9 pm
Families of functionsTrig functionsExponential & log functions9-10 pm
Rates of changeDerivatives of trig, exponential, log fns10-11 pm
OptimisationIntro to integrationApplied statistical analysis11pm – 12 am
Notional time allocations for topics in Mathematics B (over 2 years)
Topic Notional Time Allocation
Introduction to functions 35 hrs
Rates of change 35 hrs
Periodic functions & applications 30 hrs
Exponential and logarithmic functions & applications
35 hrs
Introduction to integration 25 hrs
Applied statistical analysis 25 hrs
Optimisation 30 hrs
TOTAL 215 hrs
Equivalent to 28 minutesin a “day in the life” of amathematics student, some time after 11pm!
… to something more ambitious
As a mathematics educator who now has experience in working in the school and higher education sectors, my goal is to improve student participation in post-compulsory (senior secondary and undergraduate university) mathematics.
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Part of my strategy is to develop and test new types of boundary practices that promote collaboration between school and university mathematics teachers, and mathematics education researchers/teacher educators.
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Participants
Purposes
Guiding principles
Validation &dissemination
Where next?
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