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THE PISA MATHEMATICS RESULTS IN CONTEXT

This presentation by Elizabeth Oldham from Trinity College, Dublin, delves into the historical background of Mathematics Education in Ireland, contrasting "modern mathematics" with Realistic Mathematics Education. It discusses the Irish mathematics results from the PISA 2003 assessment, highlighting overall performance, subscale scores, and individual item analysis. The implications and possibilities arising from these results are explored, shedding light on relevant issues in the Irish education system. The presentation emphasizes the need for a shift towards problem-solving and application-based learning to improve mathematics achievement.

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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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