Charting Ways Ahead: A Personal Perspective

Kaye StaceyUniversity of Melbourne

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

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”

Good maths teaching attends to:

conceptual understanding

reasoning & explanation

productive dispositions

applications & real world links

procedural fluency

strategic competence

What does good maths look like in school?

Have we got it yet?

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

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/timss http://www.lessonlab.com/timss1999.

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

Shallow Teaching Syndrome: Procedures without Reasons

1. Excessive Repetition• 76% of problems exact repeats• 65% of time repeating demonstrated

procedures

2. Low complexity of problems• 77% of problems low complexity

3. Absence of mathematical reasoningAt 7-country “worst” on these

measures

Mathematical Links between Problems in a Lesson

0%10%20%30%40%50%60%70%80%90%

100%

AU CZ HK JP

MathRelThemRelRepeatUnrel

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

Nature of Public Reasoning

0%10%20%30%40%50%60%70%80%90%

100%

AU CZ HK JP

MakingConnectionsStating Concepts

Using Procedures

Giving Results Only

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

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

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

020406080

100120140160180200

1999 2000 2001 2002

ITMathsPhysChemBioTotal*

Most common reasons for choosing teaching

1. Enjoy teaching / always wanted to2. Need a job 3. Want secure job with

opportunities for advancement4. Want satisfying work with positive

social contributionVery good for education but what

does it say about science?

Tomorrow’s teachers

N=90 Maths-Phys-IT

Bio-Chem-Sci

Average age 34 27

Age profile-under 25-under 30

25%50%

50%75%

Men : Women

60:40 30:70

Men 8 yrs older than women in both groups

N=90 Maths-Phys-IT

Bio-Chem-Sci

First degree Engineering Science

First career ? 3% 55%

Previous careers

Engineers,IT

Research, environment

2+ quals before DipEd

65% 25% (plus many hons)

From overseas

45% 11%

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)

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 IT Enhancing Mathematics

RITEMaths Project

Better outcomes and more complete understanding of maths

Stronger engagement

Lessons with more cognitive demand

Real world problems used more substantially

Enabled by IT

Maths from Images and Videos

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

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 worldAdditionally work on

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!)

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.

0 -0.08 0.001.38 0.62 0.752.77 1.31 1.474.31 2 2.215.77 2.62 2.867.23 3.23 3.468.77 3.77 4.0510.38 4.38 4.6112.08 4.77 5.1314 5.38 5.6416 5.92 6.09

18.23 6.46 6.4920.38 6.92 6.7622.31 7.15 6.9224.08 7.31 6.99

0 -0.08 0.001.38 0.62 0.752.77 1.31 1.474.31 2 2.215.77 2.62 2.867.23 3.23 3.468.77 3.77 4.0510.38 4.38 4.6112.08 4.77 5.1314 5.38 5.6416 5.92 6.09

18.23 6.46 6.4920.38 6.92 6.7622.31 7.15 6.9224.08 7.31 6.99

conceptual understanding

reasoning & explanation

productive dispositions

applications & real world links

procedural fluency

strategic competence

Kaye Stacey

University of Melbourne