Transcript elizabeth_oldham.pps

THE PISA
MATHEMATICS RESULTS
IN CONTEXT
Elizabeth Oldham
Trinity College, Dublin
Second National PISA Symposium
6 April 2005
Outline
• Historical background
– Realistic Mathematics Education v. “modern
mathematics”
• Current relevant issues in Ireland
• The PISA 2003 Irish mathematics results
– Overall results
– Performance on subscales and individual items
• Implications and possibilities
Historical Background
• Origins of Realistic Mathematics Education
– A (Freudenthal’s!) reaction to “modern mathematics”
• The “modern mathematics” movement
– Mathematics of the “Bourbaki group” (from France)
• Abstract (sets & structures) – very “pure,” no contexts
• Rigorous, logical, with precise terminology
• Vertical, not horizontal, mathematisation emphasised
– School mathematics was dated – mismatched to this
• Hence, a “top down” and “mathematical” influence…
• … not a pedagogical one
• Influence in Ireland
– The 1960s second level syllabuses “bought into”
modern mathematics
• … and continued to do so in the early 1970s revision
– The 1971 Primary curriculum was less affected
• Developments
– The legacy at second level persists, albeit diluted
• … with some indications of change in exams.;
• No chance since the 1960s for a basic critique!!!
– There is more focus on horizontal mathematising
in the revised Primary Curriculum
• … which emphasises problem-solving
Current Relevant Issues in Ireland
• Dissatisfaction with achievement; e.g. see
– Reactions to Ordinary LC performance, 2001 on
– Dropout/difficulty at third level
• Culture of maths. teaching and learning
– Not a mathematising culture
• … especially for lower achievers?
– Focus on teaching towards predictable
examinations (Elwood & Carlisle, 2003)
• … and associated didactical contract: “This technique
will be used in Paper II, Question 6, part (b) (iii)”
• In fact
– “Three-part” questions in the exams. were intended
to include applied / problem-solving “part (c)”s
• … ensuring but restricting the “problem” aspects
• However, teachers and students maybe try to cover all
possibilities as isolated example types…
• … increasing the “content” and not achieving the
“process”
– The JC Guidelines (pp. 91, 96-100) emphasise the
importance of the other objectives
• … and lay the groundwork for their eventual assessment?
• [Many other factors
– “outside the scope”]
The PISA 2003 Irish Maths. Results
• The reports contain
– Descriptive data on achievement
• Ranking of countries by mean score
• Country means and standard deviations
• Scores at key percentiles
• Percentage of students at “proficiency levels”
• Subscale scores
– Further analyses
• Achievement differences between schools
• Associations with background variables
… etc., etc., etc.
Note
Ranks tell one
almost nothing
until one knows
the context …
… and will find
more
… but in this
case we have
been given some
context …
Overall results
“The story
as before”
(i.e. in 2000)
Ranks and means
• Note
– OECD mean is 500, SD is 100
• Ranks
– 2000: Ireland was 15th out of 27
– 2003: Ireland is 17th out of 29 / 20th out of 40
• Means
– 2000: Ireland’s was 502.9
– 2003: Ireland’s is 502.8
• … effectively on the OECD mean
• … both times
“Could do
better?”
• Country comparisons in 2003
– Countries scoring significantly higher than Ireland
include
• Pacific Rim (as always!)
• The Netherlands (they should, shouldn’t they?)
• Finland (the success story of PISA 2003...)
– Countries scoring at the same level include
• France
• Germany
– Countries scoring significantly lower include
• Hungary (“success” in earlier TIMSS study)
• USA
Distribution
• Standard deviations
– 2000: Ireland’s was 83.6
– 2003: Ireland’s is 85.3
• … in each case, one of the lowest
• Scores at key percentiles
Rather
homogeneous
system
– Not a great “tail”
• … i.e. comparatively few low scorers…
– … but not a great “head” either
• “Proficiency levels” (see handout)
• Empirically determined, but can be associated with skills
– Again, Irish scores “bunch” (see graph below)
Subscale scores
• Recall the four subscales
– Uncertainty
Some items
“released” for
inspection
• Mainly statistics and probability
– Change & Relationships
• Algebra and functions, but other areas also
– Quantity
• Number, applied arithmetic and measure
– Space & Shape
• Not so much formal geometry as measure etc.
• Also recall the competency clusters
– Reproduction, Connections, Reflection
Probability aspect missing from
many syllabuses
• Uncertainty
– Mean score (517) significantly above the OECD
mean (502)
• Released items (see handout – more on web)
– “Robberies” (Connections, level 6 for full credit)
• Statistics, close to the syllabus, but hard; better than
OECD mean with regard to partial credit
– “Earthquakes” (Reflection, level 4)
• Probability; outside the syllabus but above OECD mean
• In our culture?
No learned
helplessness
Chancers
?
• Change & Relationships
– Above the OECD mean (506 versus 499)
• Released items
– “Internet relay chat” qus. 1 (Connections, level 3)
& 2 (Reflection, level 5)
• Qu. 2 tests what?
• … we scored well above the OECD mean
– “Walking” (Reproduction, level 5)
• Algebra; on at least the Higher syllabus, but not an
emphasised “routine” – below-average score
• Quantity
– 502 in Ireland; OECD mean 501
• Released items
– “Exchange rate” qus. 1 & 2 (Reproduction, levels
1 & 2) & 3 (Reflection, level 4)
• Applied arithmetic; illustrates Irish scores “bunching”
– “Skateboard” qus. 1 (Reproduction, level 3 for
full credit) & 2 (Reproduction, level 4)
• Qu. 2 is on the LC syllabus…
• … hence, not reproduction for us, and relatively hard
Archetypal PISA: picture, context
knowledge probably helpful...
• Space & Shape
– 476 compared to OECD 496; significantly lower
• Released items include
– “Carpenter” (Connections, level 6)
• Measure / geometry; hard, especially for us!
– “Number cubes” (Connections, level 3)
• Outside the syllabus; below OECD mean score
Curricular clash!
Implications and Possibilities
• We do not know all “raw” scores / item facilities
– We are talking relative performance
• Overall picture: strengths and weaknesses
– The low scorers do get off the ground (relative to such
in other countries)….
• … we do present most students with more than (say) social
arithmetic sums?
• … on unfamiliar items, they had not learned to be helpless?
• … we have fewer “minorities”?
– Our higher scorers “could do better”
• … the culture of mathematics teaching and learning?!!!
Possibilities for change
• Difficult, but….
• The French connection
A vignette based
on visiting
student-teachers
Curricular mismatch with
PISA is not an excuse...
… but neither is it
an automatic recipe
for change
A challenge!
Where do we want to go?
PISA / RME: horizontal
and vertical components
Ireland / Bourbaki:
vertical component