Charting Ways Ahead: A Personal Perspective

1. Charting Ways Ahead: A Personal Perspective Kaye Stacey University of Melbourne

2. Maths, Science and Environmental Sciences are mutually supportive but separate disciplines Differences in • Role in education of a citizen • Values which they impart • Links to natural and/or social worlds • Time scale of change in subject matter • Role of a central core of fundamental knowledge • Nature of reasoning and evidence • Degree of abstraction • Ways in which they can be best learned

3. Good pedagogy for maths does not just copy other subjects • Maths can be important in cross-discipline studies, but usually as “servant” (recent examples from ASMS Adelaide, Singapore ) • Maths can’t be adequately taught just as another “literacy”

4. Good maths teaching attends to: conceptual understanding strategic competence procedural fluency applications & real world links reasoning & explanation productive dispositions

5. What does good maths look like in school? Have we got it yet?

6. TIMSS Video Study “Teaching Mathematics in Seven Countries” • Australia, Czech Republic, Hong Kong, Japan, Netherlands, Switzerland, United States • Data collection 1999/2000 in YEAR 8 • One randomly selected lesson in each of 87 randomly selected schools in Australia • Extremely detailed and careful categorisation of lesson features and procedures • Backdrop: Australia doing reasonably well in international comparisons of achievement

7. TIMSS 1999 video study International Report Hiebert, J., Gallimore, R., Garnier, H., Givvin, K.B., Hollingsworth, H., Jacobs, J., Chui, A.M.-Y., Wearne, D., Smith, M., Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P., & Stigler, J. (2003). Teaching Mathematics in Seven Countries: Results from the TIMSS 1999 Video Study (NCES 2003-013). U.S. Department of Education. Washington DC: National Center for Education Statistics. Australian report Hollingsworth, H., Lokan, J., & McCrae, B. (2003). Teaching Mathematics in Australia: Results from the TIMSS 1999 Video Study. Melbourne: Australian Council for Educational Research. Commentary Stacey, K. & McCrae, B. (2003) The shallow teaching syndrome. Proceedings of Annual Conference of Mathematical Association of Victoria. http://nces.ed.gov/timsshttp://www.lessonlab.com/timss1999.

8. Overall findings • Australian schools have good relationships and classroom environment • Countries have reasonably distinctive styles of lessons – Japan is different • Some expectations not upheld e.g. Australia only average in use of real world contexts in maths

9. Shallow Teaching Syndrome: Procedures without Reasons • Excessive Repetition • 76% of problems exact repeats • 65% of time repeating demonstrated procedures • Low complexity of problems • 77% of problems low complexity • Absence of mathematical reasoning At 7-country “worst” on these measures

10. Mathematical Links between Problems in a Lesson

11. Absence of mathematical reasoning • No Australian lessons showed deductive reasoning (loosely defined) • 15% of problems in “making connections” category • 2% of public problem solutions in “making connections” category

12. Nature of Public Reasoning

13. Conclusion We have a long way to go Question Can we get there? Advantages Current group of new teachers External climate conducive to working on teaching

14. Tomorrow’s teachers in “science methods” • University of Melbourne DipEd and BTeach • Enrolment trends – not official numbers • Survey of 90 students in 2002 (repeated 2003) about background and aspirations

15. Uni Melb “Science Methods” enrolment trends (* approx numbers e.g. from class lists)

16. Most common reasons for choosing teaching • Enjoy teaching / always wanted to • Need a job • Want secure job with opportunities for advancement • Want satisfying work with positive social contribution Very good for education but what does it say about science?

17. Tomorrow’s teachers

19. Consequences • Substantial experience of life, work and research • Challenge to schools to keep them! • Science teachers trained as scientists; maths teachers NOT trained as mathematicians (consequences for some aspects of curriculum)

20. RITEMaths Project • Universities of Melbourne & Ballarat • Kaye Stacey, Gloria Stillman, Robyn Pierce and colleagues • Funded by Australian Research Council, six secondary schools and Texas Instruments Real world problems and ITEnhancing Mathematics

21. RITEMaths Project Enabled by IT Real world problems used more substantially Lessons with more cognitive demand Stronger engagement Better outcomes and more complete understanding of maths

22. Maths from Images and Videos

23. Image Analysis Software • GridPic • created for Luther College, Melbourne • especially for Years 9 – 11 • part of work of RITEMaths Project • Start GridPic here • DigitiseImage • By Jeff Waldock, SHU Maths, OK • Start DigitiseImage here

24. Vision Increasing engagement in lessons by using real world situations (and IT) Harnessing teachers’ and schools’ desire to increase IT use IT naturally mathematises the world Additionally work on

25. Why use IT? • IT naturally mathematises the world • Students like it • Teachers and schools want to use it • Opportunities to extend what we can do • (And don’t forget the negatives!)

26. Why use real world problems • Aim to capture students’ interests • Important that students learn about how maths is used • Research exploring use of situations to ground concept development (e.g. in algebra) • Research on how to use real world situations deeply to promote reasoning etc.

27. conceptual understanding strategic competence procedural fluency applications & real world links reasoning & explanation productive dispositions Kaye Stacey University of Melbourne