CRICOS Provider No 00025B Re-visioning mathematics education at the secondary-tertiary interface:...

CRICOS Provider No 00025B

Re-visioning mathematics education at the secondary-tertiary interface:Towards creative boundary practicesMerrilyn GoosThe University of QueenslandBrisbaneAustralia


Here’s the plan:

• What’s going on?• Who cares?• How could things be different? (Let’s dream a little …)


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


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


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?


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


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.


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.


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.


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.


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.


Participants

Purposes

Guiding principles

Validation &dissemination

Where next?


CRICOS Provider No 00025B Re-visioning mathematics education at the secondary-tertiary interface:...

Documents

Transcript of CRICOS Provider No 00025B Re-visioning mathematics education at the secondary-tertiary interface:...