The Language Factor in Elementary Mathematics Assessments: Computational Skills and Applied Problem Solving in a Multidimensional IRT Framework

REFERENCES

• Abedi , J. and Hejri , F. 2004 . Accommodations for students with limited English proficiency in the National Assessment of Educational Progress . Applied Measurement in Education , 17 : 371 – 392 .
   Web of Science ®Google Scholar
• Abedi , J. and Lord , C. 2001 . The language factor in mathematics tests . Applied Measurement in Education , 14 : 219 – 234 .
   Web of Science ®Google Scholar
• Abedi , J. , Lord , C. , Hofstetter , C. and Baker , E. 2000 . Impact of accommodation strategies on English language learners' test performance . Educational Measurement: Issues and Practices , 19 ( 3 ) : 16 – 26 .
   Google Scholar
• Adams , R. J. , Wilson , M. and Wang , W. C. 1997 . The multidimensional random coefficients multinomial logit model . Applied Psychological Measurement , 21 : 1 – 23 .
   Web of Science ®Google Scholar
• Adams , R. J. and Wu , M. L. 2000 . PISA 2000 technical report , Paris : OECD .
   Google Scholar
• Albert , J. H. 1992 . A Bayesian estimation of normal ogive item response curves using Gibbs sampling . Journal of Educational Statistics , 17 : 251 – 269 .
   Google Scholar
• Anstrom , K. , DiCerbo , P. , Butler , F. , Katz , A. , Millet , J. and Rivera , C. 2010 . A review of the literature on Academic English: Implications for K–12 English Language Learners , Arlington , VA : The George Washington University Center for Equity and Excellence in Education .
   Google Scholar
• Bailey , A. L. and Butler , F. A. 2003 . An evidentiary framework for operationalizing academic language for broad application to K–12 education: A design document (CSE Tech. Rep. No. 611) , Los Angeles , CA : University of California, CRESST .
   Google Scholar
• Bailey , A. L. , Butler , F. A. and Sato , E. 2007 . Standards-to-standards linkage under Title-III: Exploring common language demands in ELD and science standards . Applied Measurement in Education , 20 : 53 – 78 .
   Web of Science ®Google Scholar
• Béguin , A. A. and Glas , C. A. W. 2001 . MCMC estimation and some model-fit analysis of multidimensional IRT models . Psychometrika , 66 : 541 – 562 .
   Web of Science ®Google Scholar
• Berends , I. E. and Van Lieshout , E. C. D. M. 2009 . The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load . Learning and Instruction , 19 : 345 – 353 .
   Web of Science ®Google Scholar
• CITO . 2005a . Leerling- en onderwijsvolgsysteem, rekenen-wiskunde groep 3 [Monitoring and evaluation system for primary pupils—Arithmetic and Mathematics, grade 1] , Arnhem , , The Netherlands : Author .
   Google Scholar
• CITO . 2005b . Leerling- en onderwijsvolgsysteem, rekenen-wiskunde groep 4 [Monitoring and evaluation system for primary pupils—Arithmetic and Mathematics, grade 2] , Arnhem , , The Netherlands : Author .
   Google Scholar
• CITO . 2006 . Leerling- en onderwijsvolgsysteem, rekenen-wiskunde groep 5 [Monitoring and evaluation system for primary pupils—Arithmetic and Mathematics, grade 3] , Arnhem , , The Netherlands : Author .
   Google Scholar
• Cumming , G. and Finch , S. 2005 . Inference by eye. confidence intervals and how to read pictures of data . American Psychologist , 60 : 170 – 180 .
   PubMed Web of Science ®Google Scholar
• Cummins , D. D. , Kintsch , W. , Reusser , K. and Weimer , R. 1988 . The role of understanding in solving word problems . Cognitive Psychology , 20 : 405 – 438 .
   Web of Science ®Google Scholar
• De Boeck , P. and Wilson , M. , eds. 2004 . Explanatory item response models: A generalized linear and nonlinear approach , New York , NY : Springer .
   Google Scholar
• De Corte , E. , Verschaffel , L. and De Win , L. 1985 . Influence of rewording verbal problems on children's problem representations and solutions . Journal of Educational Psychology , 77 : 460 – 470 .
   Web of Science ®Google Scholar
• De la Torre , J. and Patz , R. J. 2005 . Making the most of what we have: A practical application of multidimensional item response theory in test scoring . Journal of Educational and Behavioral Statistics , 30 : 295 – 311 .
   Web of Science ®Google Scholar
• Embretson , S. E. and Reise , S. P. 2000 . Item response theory for psychologists , Mahwah , NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Fuchs , L. S. , Fuchs , D. , Stuebing , K. , Fletcher , J. M. , Hamlett , C. L. and Lambert , W. 2008 . Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? . Journal of Educational Psychology , 100 : 30 – 47 .
   PubMed Web of Science ®Google Scholar
• Greer , B. 1997 . Modelling reality in mathematics classrooms: The case of word problems . Learning and Instruction , 7 : 293 – 307 .
   Web of Science ®Google Scholar
• Hartig , J. and Höhler , J. 2008 . Representation of competencies in multidimensional IRT models with within-item and between-item multidimensionality . Zeitschrift für Psychologie/Journal of Psychology , 216 : 89 – 101 .
   Web of Science ®Google Scholar
• Hickendorff , M. and Janssen , J. 2009 . De invloed van contexten in rekenopgaven op de prestaties van basisschoolleerlingen [The effect of contexts in mathematics items on primary-school pupils' performance] . Reken-wiskundeonderwijs: onderzoek, ontwikkeling, praktijk , 28 ( 4 ) : 3 – 11 .
   Google Scholar
• Janssen , J. , Van der Schoot , F. and Hemker , B. 2005 . Balans van het reken-wiskundeonderwijs aan het einde van de basisschool 4 [Fourth assessment of mathematics education at the end of primary school] , Arnhem , , The Netherlands : CITO .
   Google Scholar
• Kilpatrick , J. , Swafford , J. and Findell , B. 2001 . Adding it up. Helping children learn mathematics , Washington , DC : National Academy Press .
   Google Scholar
• Koedinger , K. R. , Alibali , M. W. and Nathan , M. J. 2008 . Trade-offs between grounded and abstract representations: Evidence from algebra problem solving . Cognitive Science , 32 : 366 – 397 .
   PubMed Web of Science ®Google Scholar
• Kraemer , J.-M. , Janssen , J. , Van der Schoot , F. and Hemker , B. 2005 . Balans van het reken-wiskundeonderwijs halvewege de basisschool 4 [Fourth assessment of mathematics education halfway primary school] , Arnhem , , The Netherlands : CITO .
   Google Scholar
• Leighton , J. P. and Gierl , M. J. , eds. 2007 . Cognitive diagnostic assessment for education: Theory and application , New York , NY : Cambridge University Press .
   Google Scholar
• Lesaffre , E. and Spiessens , B. 2001 . On the effect of the number of quadrature points in a logistic random-effects model: An example . Journal of the Royal Statistical Society Series C—Applied Statistics , 50 : 325 – 335 .
   Web of Science ®Google Scholar
• Molenberghs , G. and Verbeke , G. 2004 . “ An introduction to (generalized (non)linear mixed models ” . In Explanatory item response models: A generalized linear and nonlinear approach , Edited by: De Boeck , P. and Wilson , M. 111 – 153 . New York , NY : Springer .
   Google Scholar
• Mullis , I. V. S. , Martin , M. O. and Foy , P. 2008 . TIMSS 2007 international mathematics report. Findings from IEA's Trends in International Mathematics and Science Study at the fourth and eighth grades , Boston , MA : Boston College, TIMSS & PIRLS International Study Center .
   Google Scholar
• National Council of Teachers of Mathematics . 1989 . Curriculum and evaluation standards for school mathematics , Reston , VA : NCTM .
   Google Scholar
• National Council of Teachers of Mathematics . 2000 . Principles and standards for school mathematics , Reston , VA : NCTM .
   Google Scholar
• OECD . 2004 . Learning for tomorrow's world. First results from PISA 2003 , Paris : Author .
   Google Scholar
• OECD . 2009 . PISA 2006 technical report , Paris : Author .
   Google Scholar
• Penfield , R. D. and Lee , O. 2010 . Test-based accountability: Potential benefits and pitfalls of science assessment with student diversity . Journal of Research in Science Teaching , 47 : 6 – 24 .
   Web of Science ®Google Scholar
• Prenger , J. 2005 . Taal telt! Een onderzoek naar de rol van taalvaardigheid en tekstbegrip in het realistische rekenonderwijs. [Language counts! A study into the role of linguistic skill and text comprehension in realistic mathematics education] , PhD thesis, University of Groningen, The Netherlands .
   Google Scholar
• Raykov , T. 2012 . Evaluation of latent construct correlations in the presence of missing data: A note on a latent variable modelling approach . British Journal of Mathematical and Statistical Psychology , 65 : 19 – 31 .
   PubMed Web of Science ®Google Scholar
• R. Development Core Team. (2009). R: A language and environment for statistical computing. [Computer software manual]. Vienna, Austria. http://www.R-project.org (http://www.R-project.org)
   Google Scholar
• Reckase , M. D. 2009 . Multidimensional item response theory , New York , NY : Springer .
   Google Scholar
• Rijmen , F. , Tuerlinckx , F. , De Boeck , P. and Kuppens , P. 2003 . A nonlinear mixed model framework for item response theory . Psychological Methods , 8 : 185 – 205 .
   PubMed Web of Science ®Google Scholar
• Rizopoulos , D. 2006 . ltm: An R package for latent variable modeling and item response theory analyses . Journal of Statistical Software , 17 ( 5 ) : 1 – 25 .
   Web of Science ®Google Scholar
• Royal Netherlands Academy of Arts and Sciences . 2009 . Rekenonderwijs op de basisschool. Analyse en sleutels tot verbetering [Mathematics education in primary school. Analysis and recommendations for improvement] , Amsterdam , , The Netherlands : KNAW .
   Google Scholar
• SAS Institute . 2002 . SAS online doc (version 9) , Cary , NC : SAS Institute Inc .
   Google Scholar
• Scarcella , R. 2003 . Accelerating Academic English: A focus on the English Learner , Irvine , CA : University of California .
   Google Scholar
• Sheu , C.-F. , Chen , C.-T. , Su , Y.-H. and Wang , W.-C. 2005 . Using SAS PROC NLMIXED to fit item response theory models . Behavior Research Methods , 37 : 202 – 218 .
   PubMed Web of Science ®Google Scholar
• Sinharay , S. , Puhan , G. and Haberman , S. J. 2010 . Reporting diagnostic scores in educational testing: Temptations, pitfalls, and some solutions . Multivariate Behavioral Research , 45 : 553 – 573 .
   PubMed Web of Science ®Google Scholar
• Solano-Flores , G. and Trumbull , E. 2003 . Examining language in context: The need for new research and practice paradigms in the testing of English-language learners . Educational Researcher , 32 ( 2 ) : 3 – 13 .
   Google Scholar
• Staphorsius , G. 1994 . Leesbaarheid en leesvaardigheid. de ontwikkeling van een domeingericht meetinstrument , Arnhem , , The Netherlands : CITO .
   Google Scholar
• Stone , C. A. , Ye , F. , Zhu , X. and Lane , S. 2010 . Providing subscale scores for diagnostic information: A case study when the test is essentially unidimensional . Applied Measurement in Education , 23 : 63 – 86 .
   Web of Science ®Google Scholar
• Van den Boer , C. 2003 . Als je begrijpt wat ik bedoel. Een zoektocht naar verklaringen van achterblijvende prestaties van allochtone leerlingen in het wiskundeonderwijs [If you get what I mean. A search for explanations of lagging achievement of non-native students in mathematics education] , Utrecht , , The Netherlands : CD-β press .
   Google Scholar
• Van Schilt-Mol , T. M. M. L. 2007 . Differential item functioning en itembias in de Cito-Eindtoets Basisonderwijs [Differential item functioning and item bias in CITO's End of Primary School Test] , PhD thesis, Tilburg University, The Netherlands .
   Google Scholar
• Verhelst , N. D. and Glas , C. A. W. 1995 . “ The one-parameter logistic model ” . In Rasch models. Foundations, recent developments and applications , Edited by: Fischer , G. H. and Molenaar , I. 215 – 237 . New York , NY : Springer .
   Google Scholar
• Verhelst , N. D. and Verstralen , H. H. F. M. 2002 . Structural analysis of a univariate latent variable (SAUL) (computer program and manual) , Arnhem , , The Netherlands : CITO .
   Google Scholar
• Verschaffel , L. , Greer , B. and De Corte , E. 2000 . Making sense of word problems , Lisse , , The Netherlands : Swets and Zeitlinger .
   Google Scholar
• Vicente , S. , Orrantia , J. and Verschaffel , L. 2007 . Influence of situational and conceptual rewording on word problem solving . British Journal of Educational Psychology , 77 : 829 – 848 .
   PubMed Web of Science ®Google Scholar
• Von Davier , M. and Sinharay , S. 2009 . Stochastic approximation methods for latent regression item response models (ETS-RR-09-09) , Princeton , NJ : Educational Testing Service .
   Google Scholar
• Wilson , M. and De Boeck , P. 2004 . “ Descriptive and explanatory item response models ” . In Explanatory item response models: A generalized linear and nonlinear approach , Edited by: De Boeck , P. and Wilson , M. 43 – 74 . New York , NY : Springer .
   Google Scholar
• Wu , M. and Adams , R. 2006 . Modelling mathematics problem solving item responses using a multidimensional IRT model . Mathematics Education Research Journal , 18 : 93 – 113 .
   Google Scholar
• Zou , G. J. 2007 . Toward using confidence intervals to compare correlations . Psychological Methods , 12 : 399 – 413 .
   PubMed Web of Science ®Google Scholar