Co-Principal Investigator: Mary Avalos (University of Miami)

Purpose: In 2009, 43 percent of English language learners (ELLs) in 4th grade scored below basic proficiency on the NAEP mathematics test, and this percentage increased to 72 percent among 8th graders and 80 percent among 12th graders. Many schools lack wide-spread expertise in how to address the instructional and language learning needs of ELLs. In particular, little attention has been devoted to understanding how ELLs learn the conventions and expectations for language use in mathematics in order to master the linguistic complexity of mathematical discourse. To address this need, the researchers will develop an intervention called Language in Math (LiM) that is intended to increase upper elementary and middle-school ELLs' knowledge of academic language used in math (M-AL). An additional goal of this intervention is to enhance elementary teachers' ability to teach mathematics to ELLs.

Project Activities: A student intervention and accompanying professional development program intended to increase math academic language will be developed, using an iterative design process. The intervention will target Florida's new standards in mathematics for grades 4-8. Assessments of student and teacher knowledge of academic language for math will be developed and revised in order to provide measures for use in refining and implementing the intervention. Ten teachers will participate throughout the project in the development and revision of the intervention materials and will pilot test the final version of the intervention and assessments in the spring of 2013.

Products: The products of this study will be an intervention intended to increase English Language Learners (ELLs) knowledge of academic language for math, as well as assessments of teacher and student knowledge of academic language for math. Published reports describing the intervention, assessments, and preliminary evidence of the promise of the intervention will be prepared.

Structured Abstract

Setting: The study will take place in a large school district in south Florida, located in an urban area serving high numbers of Hispanic ELLs.

Population: Ten teachers from the participating schools will work with the research team in developing and refining instructional materials. Approximately 300 4th through 8th grade students enrolled in the math classes of these teachers will participate in the iterative development and pilot-testing phases.

Intervention: The intervention will be developed based on linguistic frameworks that characterize mathematical language and general academic language in terms of (a) syntax and semantics typical of academic writing and (b) syntax, semantics, morphology and phonology appropriate for discussions. The intervention will focus student attention on the mathematical problem to be solved, the relevant textual information, procedural and conceptual aspects of the problem, and justification of the solution. In addition, the proposed intervention requires that teachers have adequate knowledge of academic language in math. Therefore, professional development will be developed that emphasizes teachers' understanding of language and language teaching to develop pedagogical practices to support students' math-literacy development. The assessment of student math-academic language will include both audio recording of math conversations by ELLs and written responses. Rubrics will be developed that describe expectations for proficiency on each scale (such as "Talking and Thinking Like Math Experts") through analysis of field notes, focus group sessions with teachers, transcribed academic conversations, and classroom observations.

Research Design and Methods: In Year 1, the research team will select 10 teachers (two each in grades 4 to 8) to assist in developing and refining instructional materials throughout the three years of the study. The intervention will focus on helping students identify the math problem to be solved, what relevant information is provided in the text, what mathematical concepts are relevant to the problem, and how to justify a solution. Forty-five students will be followed throughout the year for in-depth data collection, including audio-recordings of academic conversations between pairs of students and analysis of math journal entries. Researchers will also create professional development materials that focus on bridging theory and practice, understanding of the lexical, grammatical, and organizational features of the discourse in math, and planning curriculum to support student acquisition of academic language in math. Both student and teacher assessments of academic language in math will be developed in Year 1 and 2. The student assessment will consist of rating scales that describe level of proficiency in such topics as talking and thinking like a math expert, focusing on the problem to be solved, and supporting ideas through well-reasoned explanation. The teacher assessment will include both a questionnaire to elicit teacher's self-rating of pedagogy and knowledge in teaching academic language in math and an observation protocol. In the spring of Year 3, the final version of the intervention will be piloted and tested in the classrooms of the 10 teachers. The performance of students on standardized math tests, performance assessments, and researcher-designed measures of academic language in math will be compared for students who received the intervention for 3 years versus those who received the intervention for only one or two years.

Control Condition: There is no control condition during Years 1 and 2. Matched comparison group of teachers will be used in the pilot study in Year 3.

Key Measures: Measures include the Florida Comprehensive Assessment Test in math and writing, Florida Writes! (Florida's writing assessment for grades 4 and 8), district benchmark tests, Comprehensive English Language Learning Assessment (CELLA), ONPAR assessment for ELLs (developed by the Center for Applied Linguistics and the World-Class Instructional Design and Assessment Consortium), math performance assessments, researcher-developed measures of academic Language in math, and classroom observation measures.

Data Analytic Strategy: During iterative development, the team will use qualitative methods to analyze information obtained from teacher focus groups, interviews and classroom observations. Student understanding of math concepts will be assessed by comparing pre- and post-measures on performance assessments in math during the intervention development phase. The pilot study will compare the pre- and post-performance of students in the LiM intervention with those who do not experience the intervention on standardized achievement measures of academic language and FCAT scores. The assessment of academic language in math will be evaluated for inter-rater reliability of scoring, and content and criterion-related evidence of validity. The validity of the teacher knowledge of academic language in math measure will be established by comparing questionnaire responses to classroom observations and performance on the Language Development Test, a research instrument that assesses teacher knowledge of academic language in math through written responses to hypothetical classroom teaching and learning situations. The growth and achievement rates in mathematics for ELLs' who have LiM for one year or all three years will be examined using repeated measures MANOVA. Paired-sample t-tests will compare English Proficiency Assessment scores (as measured by the CELLA) to explore the effects of LiM on "everyday" language proficiency and English acquisition.

Products and Publications

Book chapter

Avalos, M.A., Bengochea, A., and Secada, W.G. (2015). Reading Mathematics: More Than Words and Clauses; More Than Numbers and Symbols on a Page. In K. Santi, and D. Reed (Eds.), Improving Reading Comprehension of Middle and High School Students (pp. 49–74). Switzerland: Springer International Publishing.

Avalos, M.A., Medina, E., and Secada, W.G. (2015). Planning for Instruction: Increasing Multilingual Learners' Access to Algebraic Word Problems and Visual Graphics. In A. Bright, H. Hansen–Thomas, and L. de Oliveira (Eds.), Common Core State Standards in Math, High School (pp. 5–23). Alexandria, VA: TESOL Press.

Avalos, M.A., Zisselsberger, M., Langer–Osuna, J., and Secada, W.G. (2015). Building Teacher Knowledge of Academic Literacy and Language Acquisition: A Framework for Cross–Disciplinary Professional Development. In D. Molle, T. Boals, E. Sato, and C.A. Hedgspeth (Eds.), Sociocultural Context of Academic Literacy Development for Adolescent English Language Learners. New York: Routledge Publishers.

Journal article, monograph, or newsletter

Langer–Osuna, J. M. (2016). The Social Construction of Authority Among Peers and its Implications for Collaborative Mathematics Problem Solving. Mathematical Thinking and Learning: An International Journal, 18(2), 107–124.

Langer–Osuna, J., and Avalos, M.A. (2016). "I'm 'Trying' to Figure This Out. Why Don't 'You' Come up Here?": Heterogeneous Talk and Dialogic Space in a Mathematics Discussion. ZDM Mathematics Education, 47(7): 1313–1322.

Proceeding

Langer–Osuna, J. (2012). The Authority of Ideas: How Students Become Influential in Linguistically Heterogeneous Small Group Discussions. In Proceedings of the 10th International Conference of the Learning Sciences (ICLS 2012), Vol 2 (pp. 547–5489). Sydney, Australia: International Society of the Learning Sciences.

Secada, W.G., Zisselsberger, M., Langer–Osuna, J., and Avalos, M.A. (2011). Developing Teachers' Repertoires for Language in the Mathematics Classroom. In Proceedings of the ICMI Study 21 Mathematics and Language Diversity. Sao Paulo, Brazil: International Commission on Mathematical Instruction.