1. CRICOS Provider No 00025B Re-visioning mathematics education at the secondary-tertiary interface: Towards creative boundary practices Merrilyn Goos The University of Queensland Brisbane Australia

2. CRICOS Provider No 00025B Here’s the plan: What’s going on? Who cares? How could things be different? (Let’s dream a little …)

3. 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 School teachers University mathematicians Mathematics education researchers & teacher educators

4. 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

5. 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

6. 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

7. CRICOS Provider No 00025B Who cares? School teachers University mathematicians Mathematics education researchers & teacher educators Policy makers Community members (parents, employers etc)

8. 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.

9. How could things be different? CRICOS Provider No 00025B

10. 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 CRICOS Provider No 00025B

11. 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)

12. 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. CRICOS Provider No 00025B

13. 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. CRICOS Provider No 00025B One way I tried to do this was by connecting university teacher education students with the professional community of mathematics teachers in schools.

14. Using technology in mathematical modelling Predicting the transit of Venus

15. 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. CRICOS Provider No 00025B One way I try to do this is by connecting university mathematicians with the professional community of mathematics teachers in schools.

16. 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

17. 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!

18. … 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. CRICOS Provider No 00025B 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.

19. CRICOS Provider No 00025B Maths Exchange Events Develop authentic real world tasks Set up continuing school- university collaborations Trial tasks with students; Reference Group & conferences; Sponsorship Collaboration cannot be mandated but can be encouraged. Ideas are traded on equal terms. School teachers & students; university teachers & students Participants Purposes Guiding principles Validation & dissemination

20. Where next? CRICOS Provider No 00025B