Using PROC GLIMMIX to Analyze the Animal Watch, a Web-Based Tutoring System for Algebra Readiness

In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch project, a computer-based initiative designed to improve the mathematical skills of children from grades 5-8 in the Southwest. A sample of 86 students (26 ELs and 60 EPs), clustered in four different classes, was used for this project. A Generalized Linear Mixed Model (GLMM) approach with the GLIMMIX procedure in SAS 9.3 showed that students from the classes that had a higher percentage of EL students performed better than those in the classes where the EL concentration was lower. Classes with more EL males were better at learning mathematics than classes with more EP females. The results also indicated: (a) a positive correlation between the students’ ability to solve algebra word problems on their first attempt and their success ratio in solving all problems, and (b) a negative correlation between the percentage of problems solved correctly and those considered too hard from the very beginning. I conclude my dissertation by making specific recommendations for further research.

[1]  Seth Leon,et al.  An Investigation of the Language Demands in Content Assessments for English Language Learners , 2009 .

[2]  Frank K. Lester,et al.  Results and Interpretations of the 1990 through 2000 Mathematics Assessment of the National Assessment of Educational Progress. , 2004 .

[3]  D. Joanes,et al.  Comparing measures of sample skewness and kurtosis , 1998 .

[4]  J. Janzen,et al.  Teaching English Language Learners in the Content Areas , 2008 .

[5]  B. Tabachnick,et al.  Using Multivariate Statistics , 1983 .

[6]  J. Neter,et al.  Applied Linear Regression Models , 1983 .

[7]  Deborah J. Short,et al.  School Reform and Standards-Based Education: A Model for English-Language Learners , 2006 .

[8]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[10]  Marilyn E. Strutchens,et al.  A Closer Look at Gender in NAEP Mathematics Achievement and Affect Data: Intersections with Achievement, Race/Ethnicity, and Socioeconomic Status. , 2006 .

[11]  W. Lambert.  Culture and Language as Factors in Learning and Education. , 1973 .

[12]  Michel Lejeune,et al.  A Simple Predictive Density Function , 1982 .

[13]  M. Swain,et al.  A longitudinal study of bilingual and cognitive development(1) , 1976 .

[14]  Peter Galbraith,et al.  Bilingualism and Mathematics Learning: Another Perspective. , 1992 .

[15]  R. Guglielmi,et al.  Native Language Proficiency, English Literacy, Academic Achievement, and Occupational Attainment in Limited-English-Proficient Students: A Latent Growth Modeling Perspective. , 2008 .

[16]  Walter G. Secada.  Urban Students Acquiring English and Learning Mathematics in the Context of Reform , 1996 .

[17]  S. Lubienski,et al.  Who's counting? A survey of mathematics education research 1982-1998 , 2000 .

[18]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[19]  R. Schall.  Estimation in generalized linear models with random effects , 1991 .

[20]  Xiaoxia Ai,et al.  Gender Differences in Growth in Mathematics Achievement: Three-Level Longitudinal and Multilevel Analyses of Individual, Home, and School Influences , 2002 .

[21]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[22]  L. Dawe.  Bilingualism and mathematical reasoning in English as a second language , 1983 .

[23]  Judit N. Moschkovich,et al.  A Situated and Sociocultural Perspective on Bilingual Mathematics Learners , 2002 .

[24]  Barbara Freeman,et al.  Creating a Middle School Mathematics Curriculum for English-Language Learners , 2008 .

[25]  D. J. Saer,et al.  THE EFFECT OF BILINGUALISM ON INTELLIGENCE , 1923 .

[26]  Seymour Geisser,et al.  Estimative influence measures for the multivariate general linear model , 1985 .

[27]  J. Cummins,et al.  Linguistic Interdependence and the Educational Development of Bilingual Children , 1979 .

[28]  Noel Enyedy,et al.  Revoicing in a Multilingual Classroom , 2008 .

[29]  Elizabeth Peal,et al.  The relation of bilingualism to intelligence. , 1962 .

[30]  Judith D. Singer,et al.  Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models , 1998 .

[31]  P. Clarkson,et al.  Language and mathematics: A comparison of bilingual and monolingual students of mathematics , 1992 .

[32]  Lynn M. Osen.  Women in mathematics , 1974 .

[33]  Carolyn Kessler,et al.  Language Minority Children's Linguistic and Cognitive Creativity. , 1987 .

[34]  Guillermo Solano-Flores,et al.  Who Is Given Tests in What Language by Whom, When, and Where? The Need for Probabilistic Views of Language in the Testing of English Language Learners , 2008 .

[35]  E. Fennema,et al.  Gender differences in mathematics performance: a meta-analysis. , 1990, Psychological bulletin.

[36]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[37]  Lisa C. Pray.  How Well Do Commonly Used Language Instruments Measure English Oral-Language Proficiency? , 2005 .

[38]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[39]  John O’Donoghue,et al.  The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish , 2009 .

[40]  Diane Rodriguez,et al.  Meeting the Needs of English Language Learners With Disabilities in Urban Settings , 2009 .

[41]  James Cummins.  The Influence of Bilingualism on Cognitive Growth: A Synthesis of Research Findings and Explanatory Hypotheses. Working Papers on Bilingualism, No. 9. , 1976 .

[42]  Judit N. Moschkovich,et al.  Using Two Languages When Learning Mathematics , 2006 .

[43]  Peter E. Rossi,et al.  Bayesian analysis of dichotomous quantal response models , 1984 .

[44]  Deborah J. Stipek,et al.  Gender differences in children's achievement-related beliefs and emotional responses to success and failure in mathematics. , 1991 .

[45]  E. Fennema.  Gender Equity for Mathematics and Science. , 2000 .

[46]  Roel Bosker,et al.  Sustainability of teacher expectation bias effects on long-term student performance. , 2010 .

[47]  M. Bulmer,et al.  Principles of Statistics , 1968 .

[48]  James Cummins.  Bilingualism and the Development of Metalinguistic Awareness , 1978 .

[49]  Paul R. Cohen,et al.  Reading Proficiency and Mathematics Problem Solving by High School English Language Learners , 2010 .

[50]  E. Gutstein,et al.  Culturally Relevant Mathematics Teaching in a Mexican American Context , 1997 .

[51]  M. Boekaerts,et al.  Gender-Related Differences in Self-Referenced Cognitions in Relation to Mathematics. , 1996 .

[52]  David J. Francis,et al.  Accommodations for English Language Learners Taking Large-Scale Assessments: A Meta-Analysis on Effectiveness and Validity , 2009 .

[53]  L. Hedges,et al.  Intraclass Correlation Values for Planning Group-Randomized Trials in Education , 2007 .

[54]  Maria Martiniello,et al.  Language and the Performance of English-Language Learners in Math Word Problems. , 2008 .

[55]  Stephen G. Sireci,et al.  An Analysis of the Psychometric Properties of Dual Language Test Forms. , 2002 .

[56]  Dean J. Champion,et al.  Basic Statistics for Social Research , 1970 .

[57]  Jere Brophy,et al.  Teachers' communication of differential expectations for children's classroom performance: Some beha , 1970 .