Previous studies have shown that socioeconomic status (SES) and ‘opportunity to learn’ (OTL), which can be typified as ‘curriculum content covered’, are significant predictors of students’ mathematics achievement. Seeing OTL as curriculum variable, this paper explores multilevel models (students in classrooms in countries) and appropriate classroom (teacher) level variables to examine SES and OTL in relation to mathematics achievement in the 2011 Trends in International Mathematics and Science Study (TIMSS 2011). Results suggest that the combination of SES and OTL explains a considerable amount of variance at the classroom and country level, but that this is not caused by country level OTL.
Assumptions variables not to include: Gender: no reason to believe there are differences in gender
ICME 2016 presentation
OPPORTUNITY TO LEARN
A CURRICULUM APPROACH
WITH TIMSS 2011 DATA
Dr. Christian Bokhove
Southampton Education School
• enGasia project, studying geometry education in
• Differences in curriculum
• Existing international comparisons like TIMSS and PISA
• Recently published paper ‘Opportunity to Learn’ (Schmidt,
Burroughs, Zoido, & Houang, 2015)
• Also plays large role in recent OECD report on maths:
“Equations and Inequalities - Making Mathematics
Accessible to All”
Opportunity to Learn
• ‘Content covered’
• Relationship Socioeconomic status and achievement (e.g.
Sirin, 2005; Chudgar & Luschei, 2009)
• One factor: role of curriculum, exposure to curriculum
• Opportunity to learn (OTL; Carroll, 1963), content coverage
Schmidt, Burroughs, Zoido & Houang (2015)
• Role of schooling in perpetuating
• PISA 2012 data
• Opportunity to Learn
• “instructional content as a
mediator for socioeconomic
• Student level indicators?
• Key question what is involved in
OTL? Surely the
teacher/classroom level is
• Educational outcomes are influenced by
variables at the student level, the
classroom level, the school level and
national/regional level. Dynamic model
(Creemers & Kyriakides, 2008).
• ‘Management of time’ at
teacher/classroom level one of the most
significant factors of effectiveness.
• OTL specifically:
– national/regional level
(e.g. national curriculum),
– classroom (content
covered by teacher)
– and to a lesser extent
So a curriculum approach
• Do students know best what contents is covered?
• And if they do, then isn’t that more a proxy for achievement?
• With content covered, teachers perhaps know best?
• TIMSS more curriculum oriented than PISA (Rindermann &
• TIMSS samples classrooms
“TIMSS 2011 is the fifth in IEA’s series of international
assessments of student achievement dedicated to
improving teaching and learning in mathematics and
science. First conducted in 1995, TIMSS reports every
four years on the achievement of fourth and eighth grade
• TIMSS’ curriculum model (Mullis, Martin, Ruddock,
O’Sullivan, & Preuschoff, 2009)
– intended curriculum (the educational system's aims and
– implemented curriculum (the actual strategies,
practices, and activities found in classrooms)
– attained curriculum (student learning)
Multilevel: students in classrooms in countriesMultilevel: students in classrooms in countries
Methodology: analytical approach
• Secondary data analysis of TIMSS 2011 data
• Use multilevel models
• Take into account complex sampling design of TIMSS 2011
– Different probabilities of units being selected
(classrooms, students) → sampling weights
– Rotated-booklet design → Plausible Values combined by
Rubin’s rules (Rubin, 1987).
– No jackknife for correct SE measurement → multilevel
approach should cater for this
Methodology: analytical approach
• IDB analyser used to create datasets for three levels
• HLM 6.08 used to build four models
– A null model
– A model with SES variables
– A model with OTL variables
– A model with both SES and OTL variables
• Further assumptions
– Group-centered variables at student and classroom levels
– Grand mean centered at country level
– Full Maximum Likelihood
– Missing data imputed with EM algorithm 11
• TIMSS 2011 grade 8 data
• Data at three levels
– achievement and background data of students,
– classroom level data from the teacher questionnaire,
– curriculum data at the country level.
• After data preparation: 287395 students in 11688
classrooms in 50 countries.
• Choice of variables
• Five plausible values for maths achievement, BSMMAT01
Independent variables: student level
• ‘Home Economic Resources’
– Proxy for SES (and related to prior knowledge)
– Numbers of books at home, highest level education of
either parent, number of home study support
– One scale through IRT scaling (Rasch partial credit
• No OTL measure at student level for reasons explained
Independent variables: class level
• Mean SES in a class → Classroom SES
• Two newly created OTL measures → Classroom OTL
– classOTL1: Percentage of the content domain covered
– classOTL2: Percentage+ Maths
instruction time, expressed in
variable between 0
and 2 of content
Independent variables: country level
• Mean SES in a country → Country SES
• 3 newly created OTL measures → Country OTL
– countryOTL1: combination of
• Is there a national curriculum?
• Does curriculum prescribe goals and objectives?
• Curriculum coverage (content domains: number,
algebra, geometry and data and chance)
• Variable between 0 and 3 content coverage
– countryOTL2: mean of all classOTL1
– countryOTL3: only curriculum coverage
• SES variables reduce classroom and country variance, OTL
variables too, but less
• SES variables significant positive predictors
• OTL significant positive predictors at classroom level, at
country level depends on operationalisation of OTL
• But after controlling for SES all models classroom OTL
significantly positive predictor, country OTL not.
• Content domains: number, algebra, geometry and data and
• Sampling classrooms
• Different correlations between the different
operationalisations of OTL, for example:
• More information:
Carroll, J.B. (1963). A model of school learning. Teachers College Record, 64(8), 723-733.
Chudgar, A. & Luschei, T.F. (2009). National income, income inequality, and the importance of schools: A hierarchical cross-
national comparison. American Educational Research Journal, 46(3), 626-658.
Creemers, B.P.M. & Kyriakides, L. (2008). The dynamics of educational effectiveness: a contribution to policy, practice and
theory in contemporary schools. London: Routledge.
Mullis, I.V.S., Martin, M.O., Ruddock, G.J., O’Sullivan, C.Y., & Preuschoff, C. (2009). TIMSS 2011 Assessment frameworks.
Lynch School of Education, Boston College.
Mullis, I.V.S., Martin, M.O., Foy, P., & Arora, A. (2012). TIMSS 2011 International results in mathematics. Lynch School of
Education, Boston College.
Rindermannm H, & Baumeister, A.E.E. (2015). Validating the interpretations of PISA and TIMSS tasks: A rating study.
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Schmidt, W.H., Zoido, P., & Cogan, L.S. (2013). Schooling matters: Opportunity to learn in PISA 2012 (OECD Education
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Schmidt, W.H., Burroughs, N.A., Zoido, P., & Houang, R.T. (2015). Educational Researcher, 44(7), 371-386.
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Educational Research, 75(3), 417–453. 22