stacey by huangyuarong

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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
  –   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

        procedural         strategic
        fluency            competence

                          applications &
       reasoning &        real world links
       explanation

                 productive
                 dispositions
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 reasoning
At 7-country “worst” on these measures
 Mathematical Links between
 Problems in a Lesson
100%
 90%
 80%
 70%
                               MathRel
 60%
                               ThemRel
 50%
                               Repeat
 40%
                               Unrel
 30%
 20%
 10%
  0%
       AU    CZ    HK     JP
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
100%
 90%
 80%                          Making
 70%                          Connections
 60%                          Stating Concepts
 50%
                              Using Procedures
 40%
 30%                          Giving Results Only
 20%
 10%
  0%
       AU   CZ   HK   JP
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)
200
180
160
                                                    IT
140
                                                    Maths
120
                                                    Phys
100
                                                    Chem
 80
                                                    Bio
 60
                                                    Total*
 40
 20
  0
        1999       2000       2001       2002
Most common reasons for
choosing teaching
1. Enjoy teaching / always wanted to
2. Need a job
3. Want secure job with opportunities for
   advancement
4. Want satisfying work with positive
   social contribution
Very 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      25%            50%
-under 30      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         Engineers,    Research,
careers          IT            environment

2+ quals         65%           25% (plus
before DipEd                   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
                                       Enabled by IT
Real world problems used
more substantially




     Stronger                   Lessons with more
     engagement                 cognitive demand



 Better outcomes and more complete understanding of maths
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 world
Additionally 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.
         conceptual
         understanding

 procedural            strategic
 fluency               competence
                                        0   -0.08   0.00
                     applications &  1.38    0.62   0.75
reasoning &          real world links
                                     2.77
                                     4.31
                                             1.31
                                                2
                                                    1.47
                                                    2.21
explanation                          5.77    2.62   2.86
                                     7.23    3.23   3.46
                                     8.77    3.77   4.05
          productive                10.38
                                    12.08
                                             4.38
                                             4.77
                                                    4.61
                                                    5.13
          dispositions                 14    5.38   5.64
                                       16    5.92   6.09
                                    18.23    6.46   6.49
                                    20.38    6.92   6.76
              Kaye Stacey           22.31    7.15   6.92
                                    24.08    7.31   6.99
     University of Melbourne

								
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