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The role of ‘opportunity to learn’ in the geometry currriculum

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The role of ‘opportunity to learn’ in the geometry currriculum

  1. 1. THE ROLE OF ‘OPPORTUNITY TO LEARN’ IN THE GEOMETRY CURRRICULUM A multilevel comparison of six countries Birkbeck, 6 June 2019 Christian Bokhove University of Southampton United Kingdom
  2. 2. Who am I ? • Christian Bokhove • From 1998-2012 teacher maths and computer science, secondary school Netherlands • PhD from Utrecht University • Associate Professor at University of Southampton • Maths education • Technology use • Research methods • Large-scale assessment
  3. 3. enGasia project • England – Geometry - Asia • British Academy • 3 years International Partnership • England, Japan, Hong Kong
  4. 4. enGasia project 1. Compare geometry education in England, Japan and Hong Kong. 2. Two digital resources (electronic books) will be designed. They are then implemented in classrooms in those countries. 3. The methodology will include a more qualitative approach based on lesson observations and a quasi-experimental element.
  5. 5. Background • International largescale assessments like PISA and TIMSS for secondary mathematics • English government looks to Asia • Focus on ‘geometry’ or ‘space and shapes’ as at face value there seem to be a lot of curriculum differences. Even larger gap. UK/ENG JAP HK KOR SGP USA PISA 2012 475 (494) 558 (536) 567 (561) 573 (554) 580 (573) 463 (481) TIMSS 2015 514 (518) 598 (586) 602 (594) 612 (606) 617 (621) 500 (518) TIMSS 2011 498 (507) 586 (570) 597 (586) 612 (613) 609 (611) 485 (509) TIMSS 2007 513 (513) 584 (570) 580 (572) 600 (597) 590 (593) 480 (508)
  6. 6. Curriculum changes For example Key Stage 3 (11-13 yr olds) “understand, from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not” (DfEE, 1999, p. 38) “use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles” (DfE, 2013, p.8)
  7. 7. Describe different parts project 1. Curriculum effects 2. Item analysis 3. Design of digital books 4. Effects of the books
  8. 8. Describe different parts project 1. Curriculum effects 2. Item analysis 3. Design of digital books 4. Effects of the books Mainly about this
  9. 9. 1. Curriculum effects Understand the role of curricular elements in mathematics and science achievement, with a particular emphasis on geometry education, at lower secondary level within and across selected countries in the East and West. 1. Align different frameworks into one framework 2. Use largescale assessment data to explore its application
  10. 10. Dynamic model • Dynamic model of educational effectiveness, as developed by Creemers and Kyriakides (2008) The first implication for our theoretical lens is that we will adopt a multilevel approach in our study.
  11. 11. Opportunity to Learn • Carroll (1963) • Schmidt and others: greater OTL in mathematics was related to higher student achievement in mathematics. • But many definitions (e.g. see Scheerens et al., 2017). • Interaction with SES We propose that we focus on variables regarding ‘opportunity to learn’ (OTL) in our study. In doing so we should include controls for SES and proxies for quality of instruction.
  12. 12. TIMSS curriculum framework • Intended • Implemented • Attained • Contrary to PISA has a curriculum focus. We use TIMSS 2011 data in this study because of its curriculum focus.
  13. 13. DOC framework Dynamic model Opportunity to learn Curriculum - TIMSS National OTL School and classroom OTL Student OTL
  14. 14. DOC framework Dynamic model Opportunity to learn Curriculum - TIMSS National level Curriculum content coverage Intended curriculum Classroom (teacher) and school • Instructional hours in the classroom • Curriculum content coverage • Curriculum content preparation • Degree and experience teacher Implemented curriculum Student Time spent on mathematics Socio-Economic Status Attained curriculum
  15. 15. Using the model: research questions I. How much of the variance in student achievement is explained by student- and classroom-level OTL curriculum factors within and across the six countries? II. How much are these OTL curriculum factors related to geometry achievement at grade eight in England, Japan, Hong Kong SAR, Korea, Singapore and the USA?
  16. 16. Secondary data analysis • TIMSS 2011 • Complex sampling design (Rutkowski et al, 2010) • Weights • Plausible Values • Multilevel models • Multilevel models in HLM 6.08.
  17. 17. Variables Dependent variables: • 5 Plausible Values for Geometry achievement Student level variables: • Home Economic Resources as proxy for SES • Weekly time for homework Classroom (teacher) level variables: • Classroom SES and Homework time • OTL measures: percentage geometry content coverage and mathematics instructional hours per week • Teacher: edulevel, years experience, teachers prepared to teach geometry
  18. 18. Results
  19. 19. Some interesting things to note • SES England, Japan, USA comparable. Singapore, Hong Kong slightly lower. Korea much higher. • English, Japanese, Korean students less time homework. • Japan lowest number of mathematics instruction hours, USA highest. • Geometry taught highest in Japan and Korea, lowest England and Singapore. • English teachers feel most prepared to teach geometry, Japanese teachers least. And more…
  20. 20. Multilevel tables (highlighted)
  21. 21. Some interesting things to note • Japan and Korea very little variance at classroom level: homogeneous. • At student level SES positive predictor in Japan, Korea, England, USA. But not Singapore and Hong Kong, likely more homogeneity. • OTL predictors mixed picture. For example: • Homework differential effect student and class level • Geometry content coverage not predictor • Most teacher quality variables not predictor • Instructional hours in Japan
  22. 22. Conclusions 1 I. How much of the variance in student achievement is explained by student- and classroom-level OTL curriculum factors within and across the six countries? Differs between countries, might reveal heterogeneity.
  23. 23. Conclusions 2 II. How much are these OTL curriculum factors related to geometry achievement at grade eight in England, Japan, Hong Kong SAR, Korea, Singapore and the USA? Geometry content coverage and teacher preparedness no predictors. Teacher variables only here and there. Instructional hours important for Japan. Weekly time spent on homework differential effects but not always intuitive. In short: it’s complex
  24. 24. Describe different parts project 1. Curriculum effects 2. Item analysis 3. Design of digital books 4. Effects of the books
  25. 25. Which of these is the reason that triangle PQR is a right angle triangle? A. 32 + 42 = 52 B. 5 < 3 + 4 C. 3 + 4 = 12 – 5 D. 3 > 5 – 4
  26. 26. Describe different parts project 1. Curriculum effects 2. Item analysis 3. Design of digital books 4. Effects of the books
  27. 27. 3. Design of digital books • Based on design principles • ‘Widgets’ (needs to cater for diversity of features) • Interaction (includes feedback, like Intelligent Tutoring Systems) • Interoperability (different parts of the book should work together eg graph element and formula element) • Storing results (teachers should be able to see how students used the books) • Standards (needs to work on any device) • Authorability (should be able to modify content)
  28. 28. This time we took a real textbook
  29. 29. And we made two sections with geometry into digital textbooks
  30. 30. Demo
  31. 31. Digitalbooks
  32. 32. With feedback and answer checking 34
  33. 33. 35
  34. 34. https://youtu.be/0KxOqT7iB38
  35. 35. Parts of the project 1. Curriculum effects 2. Item analysis 3. Design of digital books 4. Effects of the books Still looking at this One challenge here was that the local conditions in the three countries couldn’t really be the same and this caused methodological issues. It’s a set of mixed data from different parts of the books. For example in England we focused Mental Rotation Skills.
  36. 36. Discussion • Interplay SES and OTL (curriculum time) …what can we address? • Definitions of OTL • Academic Learning Time? • Quality of instruction?) • Role shadow education • Not the final word: these analyses need to be complemented with more detailed, qualitative data about the curriculum. For example low scores Japan on the task to the right; they only did Pythagoras one year later. Which of these is the reason that triangle PQR is a right angle triangle? A. 32 + 42 = 52 B. 5 < 3 + 4 C. 3 + 4 = 12 – 5 D. 3 > 5 – 4
  37. 37. Other projects https://bokhove.net/aera-2019/ https://www.slideshare.net/cbokhove/mental-rotation-skills-90673428
  38. 38. Thank you • C.Bokhove@soton.ac.uk • University of Southampton • Twitter: @cbokhove • Website: www.bokhove.net • British Academy IPM-2014 PM130271 project

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