charting ways ahead: a personal perspective
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Charting Ways Ahead: A Personal Perspective. Kaye Stacey University 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 - PowerPoint PPT PresentationTRANSCRIPT
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Charting Ways Ahead: A Personal Perspective
Kaye StaceyUniversity of Melbourne
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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
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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”
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Good maths teaching attends to:
conceptual understanding
reasoning & explanation
productive dispositions
applications & real world links
procedural fluency
strategic competence
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What does good maths look like in school?
Have we got it yet?
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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
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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.
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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
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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
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Mathematical Links between Problems in a Lesson
0%10%20%30%40%50%60%70%80%90%
100%
AU CZ HK JP
MathRelThemRelRepeatUnrel
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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
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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
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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
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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
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Uni Melb “Science Methods” enrolment trends (* approx numbers e.g. from class lists)
020406080
100120140160180200
1999 2000 2001 2002
ITMathsPhysChemBioTotal*
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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?
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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
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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%
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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)
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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
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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
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Maths from Images and Videos
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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
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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
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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!)
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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.
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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