english Language Learners in Introductory Statistics: Lessons Learned from an Exploratory Case Study of
LAWRENCE M. LESSER
The University of Texas at El Paso
MATTHEW S. WINSOR
Despite the rapidly growing population of English language learners in U.S. colleges and schools, very little research has focused on understanding the challenges of English language learners specifically in statistics education. At a university near the United States-México border, the authors conducted an exploratory qualitative case study of issues of language in learning statistics for pre-service teachers whose first (and stronger) language is Spanish. The two strongest findings that emerged from cross-case analysis of the interviews were the importance of the role of context (the setting in which information is communicated) and the confusion among registers (subsets of language). This paper overviews and synthesizes relevant literature and offers resources and recommendations for teaching and future research.
Keywords: Statistics education research; Language; Spanish; Teacher education
Statistics Education Research Journal, 8(2), 5-32, http://www.stat.auckland.ac.nz/serj
Ó International Association for Statistical Education (IASE/ISI), November, 2009
Adams, T. L., Thangata, F., & King, C. (2005). Weigh to go: Exploring mathematical language. Mathematics Teaching in the Middle School, 10(9), 444-448.
American Statistical Association (2005). Guidelines for assessment and instruction in statistics education: GAISE college report.
Bannon, T. J. (2007). The mean means sama rata. Mathematics Teacher, 101(5), 326-327.
Barrett, B. E. (2007). Detecting bias in jury selection. American Statistician, 61(4), 296-301.
Batt, E. G. (2008). Teachers’ perceptions of ELL education: Potential solutions to overcome the greatest challenges. Multicultural Education, 5(3), 39-43.
Berry, D. A. (1996). Statistics: A Bayesian perspective. Belmont, CA: Duxbury.
Beyth-Marom, R., Fidler, F., & Cumming, G. (2008). Statistical cognition: Towards evidence-based practice in statistics and statistics education. Statistics Education Research Journal, 7(2), 20-39.
Bock, D. E., Velleman, P. F., & DeVeaux, R. D. (2007). Stats: Modeling the world (2nd ed.). Upper Saddle River, NJ: Pearson.
Bourque, A., & Jacques, S. (1995). Increasing comprehension skills through listening and asking questions. In G. Duquette (Ed.), Second language practice: Classroom strategies for developing communicative competence (pp. 14-23). Bristol, PA: Multilingual Matters Ltd.
Brown, B. A., & Ryoo, K. (2008). Teaching science as a language: A ‘content-first’ approach to science teaching. Journal of Research in Science Teaching, 45(5), 529-553.
Burrill, G. (2008, April). Addressing tough-to-teach and tough-to-learn. Paper presented at annual meeting of National Council of Supervisors of Mathematics, Salt Lake City, UT.
Carrier, K. A. (2005). Key issues for teaching English language learners in academic classrooms. Middle School Journal, 37(2), 4-9.
Chastain, K. (1988). Developing second-language skills. Theory and practice. New York: Harcourt Brace Jovanovich.
Chen, X., & Li, Y. (2008). Research in brief: Language proficiency and mathematics learning. School Science and Mathematics, 108(3), 90-93.
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801-823.
Collier, V. (1987). Age and rate of acquisition of second language for academic purposes. TESOL Quarterly, 21(4), 617-641.
Consortium for Mathematics and its Applications (2004). Mathematics as a second language: [English/Español] Mathematical glossary. Bedford, MA: Author.
Consortium for Mathematics and its Applications (2008). Mathematics as a second language: [English/Español] Terms handbook. Bedford, MA: Author.
Consortium for Mathematics and its Applications (2009). For all practical purposes: Mathematical literacy in today’s world (8th ed.). New York: Freeman.
Cummins, J. (1979). Linguistic interdependence and the educational development of bilingual children. Review of Educational Research, 49(2), 222–251.
Cummins, J. (1992). Language proficiency, bilingualism, and academic achievement. In P. A. Richard-Amato & M. A. Snow (Eds.), The multicultural classroom: Readings for content-area teachers (pp. 16-26). Reading, MA: Addison Wesley.
Dale, T. C., & Cuevas, G. J. (1992). Integrating mathematics and language learning. In P. A. Richard-Amato & M. A. Snow (Eds.), The multicultural classroom: Readings for content-area teachers (pp. 330-348). Reading, MA: Addison Wesley.
DeAvila, E. A. (1988). Bilingualism, cognitive function, and language minority group membership. In R. R. Cocking & J. P. Mestre (Eds.), Linguistic and cultural influences on learning mathematics (pp. 101-121). Mahwah, NJ: Lawrence Erlbaum Associates.
Dragt, J. (Ed.) (2009). ISI Multilingual Glossary of Statistical Terms. International Statistical Institute.
Ernest, P. (2008). Towards a semiotics of mathematical text. For the Learning of Mathematics, 28(3), 42-49.
Esch, C. E., Chang-Ross, C. M., Guha, R., Humphrey, D. C., Shields, P. M., Tiffany- Morales, J. D., et al. (2005). The status of the teaching profession. Santa Cruz, CA: Center for the Future of Teaching and Learning.
Fang, Z., & Schleppegrell, M. J. (2008). Reading in secondary content areas: A language-based pedagogy. Ann Arbor, MI: University of Michigan Press.
Fischer, J., & Perez, R. (2008). Understanding English through mathematics: A research-based ELL approach to teaching all students. Research Monograph of TODOS, 1, 43-58.
Flick, U. (1998). An introduction to qualitative research. Thousand Oaks, CA: Sage.
Flores, A. (1997). Sí se puede, ‘it can be done’: Quality mathematics in more than one language. In J. Trentacosta & M. J. Kenney (Eds.), Multicultural and gender equity in the mathematics classroom: The gift of diversity (pp. 81-91). Reston, VA: National Council of Teachers of Mathematics.
Garaway, G. B. (1994). Language, culture, and attitude in mathematics and science learning: A review of literature. Journal of Research and Development in Education, 27(2), 102-9.
Garrison, L., & Mora, J. K. (2003). Adapting mathematics instruction for English language learners: The language-concept connection. In W. G. Secada, L. Ortiz-Franco, N. G. Hernandez, & Y. De La Cruz (Eds.), Changing the faces of mathematics: Perspectives on Latinos (pp. 35-48). Reston, VA: National Council of Teachers of Mathematics.
Gay, A. S. (2008). Helping teachers connect vocabulary and conceptual understanding. Mathematics Teacher, 102(3), 218-223.
Gephart, Jr., R. P. (1988). Ethnostatistics: Qualitative foundations for quantitative research. Newbury Park, CA: Sage Publications.
Gibbons, P. (1998). Classroom talk and the learning of new registers in a second language. Language and Education, 12(2), 99-118.
Goldenberg, C. (2008). Teaching English language learners: What the research does - and does not - say. American Educator, 33(2), 8-19, 22-23, 42-44.
Green, D. R. (1984). Talking of probability… Bulletin of the Institute of Mathematics and Its Applications, 20(9/10), 145-149.
Groth, R. E. (2008). Assessing teachers’ discourse about the Pre-K-12 guidelines for assessment and instruction in statistics education (GAISE). Statistics Education Research Journal, 7(1), 16-39.
Hale, P. (2007). They know the math, but the words get in the way. Focus on Learning Problems in Mathematics, 29(1), 28-47.
Halliday, M. A. K. (1975). Some aspects of sociolinguistics. In E. Jacobson (Ed.), Interactions between linguistics and mathematics education (pp. 64–73). Final report of the symposium sponsored by UNESCO, CEDO, and ICMI. Nairobi, Kenya, September 1–11, 1974. (UNESCO Report No. ED-74/CONE 808. Paris: UNESCO).
Hubbard, R. (1991). Teaching statistics to students who
are learning in a foreign language. In D. Vere-Jones (Ed.), Proceedings of
the Third International Conference on Teaching Statistics, Volume 1 (pp.
514-517). Voorburg, The
Huberty, C. J. (2000). Judgment in quantitative research. The Mathematics Educator, 10(1), 5-10.
Johnson, A. (2010). Teaching mathematics to culturally and linguistically diverse learners. Boston: Pearson.
Kaplan, J. J., Fisher, D. G., & Rogness, N. T. (2009). Lexical ambiguity in statistics: What do students know about the words association, average, confidence, random and spread? Journal of Statistics Education, 17(3).
Kazima, M. (2007). Malawian students’ meanings for probability vocabulary. Educational Studies in Mathematics, 64(2), 169-189.
Khisty, L. L. (1997). Making mathematics accessible to Latino students: Rethinking instructional practice. In J. Trentacosta & M. J. Kenney (Eds.), Multicultural and gender equity in the mathematics classroom: The gift of diversity (pp. 92-101). Reston, VA: National Council of Teachers of Mathematics.
Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259-289.
Kotsopoulos, D. (2007). Mathematics discourse: It’s like hearing a foreign language. Mathematics Teacher, 101(4), 301-305.
Lacelle-Peterson, M. W., & Rivera, C. (1994). Is it real for all kids? A framework for equitable assessment policies for English language learners. Harvard Educational Review, 64(1), 55-75.
Lavy, I., & Mashiach-Eizenberg, M. (2009). The interplay between spoken language and informal definitions of statistical concepts. Journal of Statistics Education, 17(1).
Lee, O., & Luykx, A. (2006). Science education and student diversity: Synthesis and research agenda. New York: Cambridge University Press.
Lesser, L. (2001). Representations of reversal: An exploration of Simpson’s paradox. In A. Cuoco & F. Curcio (Eds.), The roles of representation in school mathematics (pp. 129-145). Reston, VA: National Council of Teachers of Mathematics.
Lesser, L. (in press). Simple datasets for distinct basic summary statistics. Teaching Statistics.
Marín, G., & Marín, B. V. O. (1991). Research with Hispanic populations [Applied social research methods series]. Newbury Park, CA: Sage Publications.
Martin, M. A. (2003). ‘It’s like … you know’: The use of analogies and heuristics in teaching introductory statistical methods. Journal of Statistics Education, 11(2). [Online: http://www.amstat.org/publications/jse/v11n2/martin.html]
Martynenko, G. (2003). Semiotics of statistics. Journal of Quantitative Linguistics, 10(2), 105-115.
McCoy, L. P., Buckner, S., & Munley, J. (2007). Probability games from diverse cultures. Mathematics Teaching in the Middle School, 12(7), 394-402.
Meaney, T. (2002). Symbiosis or cultural clash? Indigenous students learning mathematics. Journal of Intercultural Studies, 23(2), 167-187.
Mestre, J. (1986). Teaching problem solving strategies to bilingual students: What do research results tell us? International Journal of Mathematical Education in Science and Technology, 17(4), 393-401.
Mestre, J. P. (1988). The role of language comprehension in mathematics and problem solving. In R. R. Cocking & J. P. Mestre (Eds.), Linguistic and cultural influences on learning mathematics (pp. 201-218). New Jersey: Lawrence Erlbaum Associates.
Mestre, J., Gerace, W. J., & Lochhead, J. (1982). The interdependence of language and translational math skills among bilingual Hispanic engineering students. Journal of Research in Science Teaching, 19(5), 399-410.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage.
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A new framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.
Moll, L. C. (1992). Bilingual classroom studies and community analysis: Some recent trends. Educational Researcher, 21(2), 20-24.
Moore, D. S. (1988). Should mathematicians teach statistics? The College Mathematics Journal, 19(1), 3-7.
Moschkovich, J. N. (2000). Learning mathematics in two languages: Moving from obstacles to resources. In W. Secada (Ed.), Changing faces of mathematics: Perspectives on multiculturalism and gender equity (pp. 85-93). Reston, VA: National Council of Teachers of Mathematics.
Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2/3), 189-212.
Moschkovich, J. N. (2003). Understanding the needs of Latino students in reform-oriented mathematics classrooms. In W. G. Secada, L. Ortiz-Franco, & N. G. Hernandez (Eds.), Changing the faces of mathematics: Perspectives on Latinos (pp. 5-12). Reston, VA: National Council of Teachers of Mathematics.
Moschkovich, J. N. (2007). Using two languages when learning mathematics. Educational Studies in Mathematics, 64(2), 121-144.
Murrey, D. L. (2008). Differentiating instruction in mathematics for the English language learner. Mathematics Teaching in the Middle School, 14(3), 146-153.
National Council of Teachers of Mathematics (2000). Principles and standards of school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (2008). NCTM position statement: Teaching mathematics to English language learners. NCTM News Bulletin, 45(5), 4.
Nolan, V. (2002). Influence of attitude towards statistics, English language ability and mathematical ability in the subject quantitative techniques at the Vaal Triangle Technikon, South Africa. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
Ortiz, J. J., Cañizares, M. J., Batanero, C., & Serrano, L. (2002). An experimental study of probabilistic language in secondary school textbooks. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
Pappamihiel, N. E., & Mihai, F. (2006). Assessing English language learners’ content knowledge in middle school classrooms. Middle School Journal, 39(1), 34-43.
Phillip, L., & Wright, G. (1977). Cultural differences in viewing uncertainty and assessing probabilities. In H. Jungermann & G. De Zeeuw (Eds.), Decision making and change in human affairs (pp. 507-519). Dordrecht: Reidel.
Pilar, R. (2003). Spanish-English language issues in the mathematics classroom. In W. G. Secada, L. Ortiz-Franco, & N. G. Hernandez (Eds.), Changing the faces of mathematics: Perspectives on Latinos (pp. 23-34). Reston, VA: National Council of Teachers of Mathematics.
Rangecroft, M. (2002). The language of statistics. Teaching Statistics, 24(2), 34-37.
Rollnick, M. (1998). The influence of language on the second language teaching and learning of science. In W. W. Cobern (Ed.), Socio-cultural perspectives in science education (pp. 121-137). Dordrecht, Netherlands: Kluwer.
Rumsey, D. J. (2009). Teaching bits: Random thoughts on teaching. Journal of Statistics Education, 17(1).
Santa Cruz, R. M. (2009). Giving voice to English language learners in mathematics. NCTM News Bulletin, 45(6), 4.
Santa Cruz, R. M., & Sanchez-Gutiérrez, I. (2009). Supporting writing skills in English language learners. NCTM News Bulletin, 45(7), 4.
Schleppegrell, M. J. (2004). The language of schooling: A functional linguistics perspective. Mahwah, NJ: Lawrence Erlbaum Associates.
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465-494). New York: Macmillan.
Shuy, R. W. (1981). Conditions affecting language learning and maintenance among Hispanics in the United States. NABE Journal, 6, 1–18.
Siegel, M. A., Wissehr, C., & Halverson, K. (2008). Sounds like success: A framework for equitable assessment – how to revise written assessments for English language learners. The Science Teacher, 75(3), 43-46.
Solano-Flores, G., & Nelson-Barber, S. (2001). On the cultural validity of science assessments. Journal of Research in Science Teaching, 38(5), 553-573.
Sullivan, M. (2010). Statistics: Informed decisions using data. Upper Saddle River, NJ: Pearson.
Utts, J. M. (2005). Seeing through statistics (3rd ed.). Belmont, CA: Thomson Brooks/Cole.
Valverde, L. A. (1984). Underachievement and underrepresentation of Hispanics in mathematics and mathematics-related classes. Journal for Research in Mathematics Education, 15(2), 123-133.
Vogt, W. P. (2007). Quantitative research methods for professionals. Boston: Pearson.
Weisstein, E. W. (2009). Disjoint sets. From MathWorld - A Wolfram Resource.
Winsor, M. S. (2007). Bridging the language barrier in mathematics. Mathematics Teacher, 101(5), 372-378.
LAWRENCE M. LESSER
Department of Mathematical Sciences
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