Cross-Cultural Comparability of SAM-math results Irina Brun Elena Kardanova National Research University Higher School of Economics, Institute of Education, Moscow, Russia Higher School of Economics, Moscow, th Annual AEA-Europe Conference 6-8 November 2014 Tallinn, Estonia 1

Higher School of Economics, Moscow, 2014 The Instrument SAM Student Achievement Monitoring Assessment of students at the end of primary school (10 years old). SAM tool: Russian language, Mathematics. SAM was created for use in Russia, initially not developed as cross- cultural assessment tool. Framework: Vygotsky’s sociocultural theory of development. Cognitive growth can be described as a process of internalizing culturally transmitted knowledge, which involves acquisition of generalized schemas of thinking and symbolic systems. 2 Nezhnov, Kardanova, Vasilyeva, Ludlow, 2014

Higher School of Economics, Moscow, 2014 The Instrument: SAM 3 Level of Math Knowledge Short description ProceduralChild knows specific algorithms and standard procedures that have been directly taught. In problem solving child is mostly oriented towards external (descriptive) features of the problem, which allow him to relate problem to specific category and identify algorithm for this category. ConceptualChild understands how to solve a whole range of problems related to the same concept, regardless of whether they are formulated in a standard or novel way. The student needs to analyze the meaning of the problem, which may require transforming its description in order to understand how to approach its solution. FunctionalChild develops the depth of understanding and conceptual flexibility that will allow him to see a full range of possible mental “moves” within the problem space and identify the sequence of moves that leads to a solution. the child compares multiple ways of approaching the problem and chooses best strategy to achieve the results.

Test Structure 4 It is hard to establish reliability only on 15 items

Higher School of Economics, Moscow, 2014 SAM measurement design Subtitle text text text 5 SAM was constructed in an Item Response Theory (IRT) framework. One-parameter Rasch model was selected as a model for test data modeling and students scaling. SAM-Math test can be considered as essentially unidimensional. All items demonstrate satisfactory psychometric characteristics and model fit. SAM-math was translated into Tajik and Kazakh languages. Functional level items Conceptual level items Procedural level items

Higher School of Economics, Moscow, 2014 Estimation of examinees 6

Higher School of Economics, Moscow, 2014 The problem 7 Why do Tajik results differ from other countries’ so much? Does the instrument measure the same construct in the same way? Proficiency levels All countries have a common soviet past. Educational systems are similar even nowadays. We focus on comparing Russian results with Tajik results.

Higher School of Economics, Moscow, 2014 Methodology One can only compare test results from different countries after establishing the equivalence between results from these countries. To establish equivalence means to prove that there is no bias in the results. Modern psychometric research identifies 3 types of bias: 8 Vijver, Hambleton, 1996; Vijver, Tanzer, 2004; Ercikan, Gierl, McCreith, Puhan & Koh, AERA, APA & NCME, 1999; ITC 2010; Hambleton, de Jon, Type of biasdescriptionMethods for identifying Construct Different versions of the test measure different constructs Exploratory factor analysis, Confirmatory factor analysis Construct maps Method Occurs when administration process varies significantly across countries. This also includes familiarity with the stimuli, testing format and sample bias Randomized-block design, regression analysis, monotrait- multimethod study, collateral information study Item Items behave differently in different countries DIF-analysis Has to be planned for in advance

Higher School of Economics, Moscow, 2014 Methodology 2 What we did: 1.Created subsample for Russian data, established its properties. 2.Analyzed psychometric properties of the test (both Russian and Tajik versions). 3.Detected 3 types of bias: 1)Compared construct maps, performed “reverse” operationalization. 2)Analyzed Tajik translations, visual stimuli, and adaptation study results. 3)Performed DIF-analysis (Mantel-Haenzsel, Logistic regression, standardization and t-statistic). 4)Identified common items for a single scale construction. 4. Constructed a single scale for two countries (simultaneous calibration). 9 Vijver, Hambleton, 1996; Vijver, Tanzer, 2004; Ercikan, Gierl, McCreith, Puhan & Koh, Sample Russian Federation. Novgorod region, general population th graders. Tajikistan. Representative sample towards Tajikistan (cluster method) th graders.

Higher School of Economics, Moscow, 2014 Analysis 10 Difficulty (CCT) of items Functional level Russia Tajikistan 3 rd level items excluded from further analysis. Items remaining for scale construction: 30. Construct maps 2 items in the Tajik version measure a different part of the construct “math competence” compared to the Russian version Random subsample of Russian data N= items left for common scale construction Content areas Relations and Functions Numbers and Operations Measurement Geometry Patterns

Higher School of Economics, Moscow, Analysis 3.3 DIF analysis on 28 remaining items 14 items showed DIF. What is the source of bias? 1.Item wording 2.Item visual representation Russian versionTajik version 2 lines Review 3.2, 5 more items were excluded Only partial equivalence can be established. Common scale construction might be done on these 9 items. 3.2 Verifying translation. Significant changes in wording: 4 items Changes in representation:15 items Still 28 items left 14 items left 3.4 Conclusion: 9 items

Higher School of Economics, Moscow, 2014 Analysis. Common scale construction Method: simultaneous calibration. 408 students Tajikistan Russia 19 unique items 9 common items 19 unique items We analyzed the psychometric properties of these 47 items. The items fit the Rasch model and there is no second dimension in the data. Then we scaled the results on a 1000-point scale and set thresholds Items that showed DIF by country or had changes in wording/ representation

Higher School of Economics, Moscow, 2014 Analysis. Common scale construction 13 Common scale After constructing a common scale the number of Tajik students, who reached the 2 nd level (conceptual), increased slightly Item/person map for combined data

Higher School of Economics, Moscow, 2014 The results 14 We showed how equivalence can be tested for assessment tools, which were not created as tools for cross-cultural comparison. Construct bias: EFA & CFA, maps of construct Item bias: verifying translation and item representation, DIF analysis. Partial equivalence was established. 3 rd level of math proficiency is not present in Tajikistan. DIF can occur not only because of changes in wording, but also because of visual representation of the item (scale of pictures, arrangement of response options, additional numbering).

Higher School of Economics, Moscow, 2014 Discussion 15 The math curriculum in Tajikistan is almost the same as in Russia. Content areas were checked during the adaptation process. Does the curriculum represent what is actually taught in classrooms? GDP, 2012 (per person): World bank Russian Federation23549 Tajikistan2247 Kazakhstan

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Items. Example of levels 17 Nezhnov, Kardanova, Vasilyeva, Ludlow, 2014