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THE PISA MATHEMATICS RESULTS IN CONTEXT

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

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THE PISA MATHEMATICS RESULTS IN CONTEXT

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  1. THE PISAMATHEMATICS RESULTSIN CONTEXT Elizabeth Oldham Trinity College, Dublin Second National PISA Symposium 6 April 2005

  2. 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

  3. 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

  4. 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

  5. Current Relevant Issuesin 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)”

  6. 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”]

  7. 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.

  8. Note • Ranks tell one almost nothing until one knows the context … … but in this case we have been given some context … … and will find more

  9. Overall results “The story as before” (i.e. in 2000)

  10. 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?”

  11. 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

  12. Distribution Rather homogeneous system • 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 • 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)

  13. Some items “released” for inspection Subscale scores • Recall the four subscales • Uncertainty • 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

  14. 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?

  15. 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

  16. 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...

  17. 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!

  18. 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?!!!

  19. Possibilities for change • Difficult, but…. • The French connection A vignette based on visiting student-teachers

  20. Curricular mismatch with PISA is not an excuse... … but neither is it an automatic recipe for change A challenge!

  21. Where do we want to go? PISA / RME: horizontal and vertical components Ireland / Bourbaki: vertical component

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