Skip to main content
Log in

Examining English language learners’ learning needs through the lens of algebra curriculum materials

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Curriculum materials have a substantial influence on mathematics instruction and, consequently, students’ learning opportunities. Many curriculum programs provide instructional notes for teachers and tasks for students as a means of accommodating particular student groups, such as those identified for English language learners. The presence of such materials communicates a narrative about the students they seek to accommodate. In particular, this narrative entails what English language learners need to learn mathematics. We examined the curriculum materials in four commercially available curriculum programs to understand the learning opportunities they provide for the target group and their assumed needs inferred from analyzing those opportunities. We found the curriculum materials implied a homogenous view of English language learners as a group who requires mathematical remediation and additional vocabulary practice. The curriculum materials provided a narrow set of learning opportunities, in terms of both mathematics and language, and may reinforce teachers’ existing deficit perspectives.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Data availability

Not applicable

Code availability

Not applicable

Notes

  1. We use the term English language learner (ELL) in this article because this is the term used within the textbooks we analyzed. We recognize this term privileges English and highlights what students lack (i.e., English) as opposed to what they possess.

  2. In the USA, ELLs are defined as individuals of ages 3–21, enrolled in K-12 schools, whose native language is other than English, and whose difficulties in English impedes their academic success and full participation in society (US Department of Education, 2016). Once they acquired English sufficiently, students are then re-classified as former ELLs. The English proficiency threshold is captured by language tests and varies by state or even district.

References

  • Abedi, J., Lord, C., Hofstetter, C., & Baker, E. (2000). Impact of accommodation strategies on English language learners’ test performance. Educational Measurement: Issues and Practice, 19(3), 16–26. https://doi.org/10.1111/j.1745-3992.2000.tb00034.x

    Article  Google Scholar 

  • Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching. African Journal of Research in Mathematics, Science and Technology Education, 19(3), 237–254.

    Article  Google Scholar 

  • Association for Supervision and Curriculum Development. (2016). Digital content goes to school: Trends in K-12 classroom learning. Retrieved from http://www.ascd.org/ASCD/pdf/siteASCD/misc/DigitalContentTrendsReport.pdf

  • Association for Supervision and Curriculum Development. (2019). The 2019 K-12 digital content report. Retrieved from https://information.ascd.org/hubfs/Whitepaper/2019_Overdrive_K-12_Digital_Content.pdf

  • Ballantyne, K. G., Sanderman, A. R., & Levy, J. (2008). Educating English language learners: Building teacher capacity. Washington Retrieved from http://www.ncela.gwu.edu/practice/mainstream_teachers.htm

  • Banilower, E. R., Smith, P. S., Weiss, I. R., Malzahn, K. A., Campbell, K. M., & Weis, A. M. (2013). Report of the 2012 national survey of science and mathematics education. Horizon Research.

  • Banilower, E. R., Smith, P. S., Malzahn, K. A., Plumley, C. L., Gordon, E. M., & Hayes, M. L. (2018). Report of the 2018 NSSME+. Horizon Research, Inc..

  • Barwell, R. (2005). Working on arithmetic word problems when English is an additional language. British Educational Research Journal, 31(3), 329–348. https://doi.org/10.1080/01411920500082177

    Article  Google Scholar 

  • Barwell, R. (2018). From language as a resource to sources of meaning in multilingual mathematics classrooms. The Journal of Mathematical Behavior, 50, 155–168.

    Article  Google Scholar 

  • Ben-Peretz, M. (1990). The Teacher-curriculum encounter: Freeing teachers from the tyranny of texts. State University of New York Press.

  • Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.-S. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039

    Article  Google Scholar 

  • Brenner, M. E. (1998). Development of mathematical communication in problem solving groups by language minority students. Bilingual Research Journal, 22(2–4), 149–174.

    Article  Google Scholar 

  • Brown, M. W. (2009). The teacher–tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17–36). Routledge.

  • Bryant, B. R., Bryant, D. P., Kethley, C., Kim, S. A., Pool, C., & Seo, Y. J. (2008). Preventing mathematics difficulties in the primary grades: The critical features of instruction in textbooks as part of the equation. Learning Disability Quarterly, 31(1), 21–35.

    Article  Google Scholar 

  • Burger, E. B., Chard, D. J., Kennedy, P. A., Leinwand, S. J., Renfro, F. L., Roby, T. W., & Waits, B. K. (2012). Holt McDougal Algebra 1. Houghton Mifflin Harcourt.

  • Carter, J. A., Cuevas, G. J., Day, R., & Malloy, C. (2012). Glencoe Algebra 1. McGraw Hill.

  • Charles, R. I., Hall, B., Kennedy, D., Bellman, A., Bragg, S. C., Handlin, S. C., … Wiggins, G. (2015). Algebra 1: Common core. Pearson.

  • Chval, K.B., Smith, E., Trigos-Carrillo, L. & Pinnow, R. (2021). Teaching math to multilingual students positioning English learners for success: Grades K–8. Corwin.

  • Cirillo, M., Bruna, K. R., & Herbel-Eisenmann, B. (2010). Acquisition of mathematical language: Suggestions and activities for English language learners. Multicultural Perspectives12(1), 34–41.

  • Clarkson, P. C. (2007). Australian Vietnamese students learning mathematics: High ability bilinguals and their use of their languages. Educational Studies in Mathematics, 64, 191–215. https://doi.org/10.1007/s10649-006-4696-5

    Article  Google Scholar 

  • de Araujo, Z. (2012a). Transferring demand: Secondary teachers’ selection and enactment of mathematics tasks for English language learners. Doctoral dissertation University of Georgia, Athens.

  • de Araujo, Z. (2012b). An examination of non-mathematical activities in the mathematics classroom. In L. R. Van Zoest, J. Lo, & J. L. Kratky (Eds.), Proceedings of the 34th annual meeting for the North American Chapter for the Psychology of Mathematics Education (pp. 339–342). Western Michigan University.

  • de Araujo, Z. (2017). Connections between secondary mathematics teachers’ beliefs and their selection of tasks for English language learners. Curriculum Inquiry, 47, 363–389. https://doi.org/10.1080/03626784.2017.1368351

    Article  Google Scholar 

  • de Araujo, Z., Smith, E., & Sakow, M. (2016). Reflecting on the dialogue regarding the mathematics education of English Learners. Journal of Urban Mathematics Education, 9(2), 33–48.

    Google Scholar 

  • de Araujo, Z., Roberts, S. A., Willey, C., & Zahner, W. (2018). English learners in k–12 mathematics education: A review of the literature. Review of Educational Research, 8, 879–919. https://doi.org/10.3102/0034654318798093

    Article  Google Scholar 

  • De Jong, E. J., & Harper, C. A. (2005). Preparing mainstream teachers for English-language learners: Is being a good teacher good enough? Teacher Education Quarterly, 32(2), 101–124.

    Google Scholar 

  • Dominguez, H. (2011). Using what matters to students in bilingual mathematics problems. Educational Studies in Mathematics, 76(3), 305–328. https://doi.org/10.1007/s10649-010-9284-z

    Article  Google Scholar 

  • Erath, K. (2018). Creating space and supporting vulnerable learners: Teachers’ options for facilitating participation in oral explanations and the corresponding epistemic processes. In R. Hunter, M. Civil, B. Herbel-Eisenmann, N. Planas, & D. Wagner (Eds.), Mathematical discourse that breaks barriers and creates space for marginalized learners (pp. 39–59). Sense.

  • Erath, K., & Prediger, S. (2018). What characterizes quality of mathematics classroom interaction for supporting language learners? Disentangling a complex phenomenon. In N. Planas & M. Schütte (Eds.), Proceedings of the fourth ERME topic conference 'classroom-based research on mathematics and language' (pp. 49-56). Dresden: Germany: Technical University of Dresden/ERME.

  • Erath, K., Ingram, J., Moschkovich, J., & Prediger, S. (2021). Designing and enacting instruction that enhances language for mathematics learning: A review of the state of development and research. ZDM-Mathematics Education, forthcoming.

  • Gibbons, P. (1992). Supporting bilingual students for success. Australian Journal of Language and Literacy, 15(3), 225–236.

    Google Scholar 

  • Hemmi, K., Bråting, K., & Lepik, M. (2020). Curricular approaches to algebra in Estonia. Finland and Sweden – A comparative study. Mathematical Thinking and Learning, 23, 1–23. https://doi.org/10.1080/10986065.2020.1740857

    Article  Google Scholar 

  • Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 65–97). National Council of Teachers of Mathematics.

  • Huntley, M. A., & Terrell, M. S. (2014). One-step and multi-step linear equations: A content analysis of five textbook series. ZDM-Mathematics Education, 46(5), 751–766. https://doi.org/10.1007/s11858-014-0627-6

    Article  Google Scholar 

  • Jackson, K., Gibbons, L., & Sharpe, C. J. (2017). Teachers’ views of students’ mathematical capabilities: Challenges and possibilities for ambitious reform. Teachers College Record, 119(7), 1–43.

    Article  Google Scholar 

  • Kanold, T. D., Burger, E. B., Dixon, J. K., Larson, M. R., & Leinwand, S. J. (2015). Algebra 1. Houghton Mifflin Harcourt.

  • Kaput, J. J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. In S. Fennel (Ed.), The nature and role of algebra in the K-14 curriculum: Proceedings of a National symposium (pp. 25–26). National Research Council, National Academy Press.

  • Kieran, C. (2007). Learning and teaching of algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Information Age Publishing.

  • Kloosterman, P., & Walcott, C. (2010). What we teach is what students learn: Evidence from national assessment. In B. Reys & R. E. Reys (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 89–102). National Council of Teachers of Mathematics.

  • Lager, C. A. (2004). Unlocking the language of mathematics to ensure our English learners acquire algebra. No. PB-006-1004. University of California.

  • Lager, C. A. (2006). Types of mathematics-language reading interactions that unnecessarily hinder algebra learning and assessment. Reading Psychology, 27(2–3), 165–204. https://doi.org/10.1080/02702710600642475

    Article  Google Scholar 

  • Lambert, R., & Tan, P. (2020). Does disability matter in mathematics educational research? A critical comparison of research on students with and without disabilities. Mathematics Education Research Journal, 32, 5–35. https://doi.org/10.1007/s13394-019-00299-6

    Article  Google Scholar 

  • Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234–241. https://doi.org/10.2307/749754

    Article  Google Scholar 

  • Martin, D. B. (2003). Hidden assumptions and unaddressed questions in mathematics for all rhetoric. The Mathematics Educator, 13(2), 7–21.

    Google Scholar 

  • Means, B., & Knapp, M. S. (1991). Cognitive approaches to teaching advanced skills to educationally disadvantaged students. Phi Delta Kappan International, 73(4), 282–289.

    Google Scholar 

  • Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2–3), 189–212. https://doi.org/10.1207/S15327833MTL04023_5

    Article  Google Scholar 

  • Moschkovich, J. N. (Ed.). (2010). Language and mathematics education: Multiple perspectives and directions for research. IAP.

  • Moschkovich, J. (2013). Principles and guidelines for equitable mathematics teaching practices and materials for English language learners. Journal of Urban Mathematics Education, 6(1), 45–57.

    Google Scholar 

  • Moschkovich, J. N. (2015a). Academic literacy in mathematics for English Learners. The Journal of Mathematical Behavior, 40, 43–62. https://doi.org/10.1016/j.jmathb.2015.01.005

    Article  Google Scholar 

  • Moschkovich, J. N. (2015b). Scaffolding student participation in mathematical practices. ZDM-Mathematics Education, 47(7), 1067–1078. https://doi.org/10.1007/s11858-015-0730-3

    Article  Google Scholar 

  • Moschkovich, J. N. (2019). Codeswitching and mathematics learners: How hybrid language practices provide resources for student participation in mathematical practices. In J. MacSwan & C. Faltis (Eds.), Codeswitching in the classroom: Critical perspectives on teaching, learning, policy, and Ideology (pp. 88–113). Routledge.

  • Moschkovich, J. N., & Zahner, W. (2018). Using the academic literacy in mathematics framework to uncover multiple aspects of activity during peer mathematical discussions. ZDM-Mathematics Education, 50(6), 999–1011. https://doi.org/10.1007/s11858-018-0982-9

    Article  Google Scholar 

  • Moses, R. P., & Cobb, C. E. (2001). Radical equations: Math literacy and civil rights. Beacon.

  • National Academies of Sciences, Engineering, and Medicine. (2018). English learners in STEM subjects: Transforming classrooms, schools, and lives (p. 10.17226/25182). The National Academies Press.

  • National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core standards for mathematics. Author.

  • Ní Ríordáin, M., & O’Donoghue, J. (2009). The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish. Educational Studies in Mathematics, 71, 43–64. https://doi.org/10.1007/s10649-008-9158-9

    Article  Google Scholar 

  • Pepin, B., Gueudet, G., & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: Two contrasted case studies in France and Norway. ZDM-Mathematics Education, 45(5), 685–698. https://doi.org/10.1007/s11858-013-0526-2

    Article  Google Scholar 

  • Pettit, S. K. (2011). Teachers’ beliefs About English language learners in the mainstream classroom: A review of the literature. International Multilingual Research Journal, 5(2), 123–147. https://doi.org/10.1080/19313152.2011.594357

    Article  Google Scholar 

  • Planas, N. (2018). Language as resource: A key notion for understanding the complexity of mathematics learning. Educational Studies in Mathematics, 98, 215–229. https://doi.org/10.1007/s10649-018-9810-y

    Article  Google Scholar 

  • Planas, N. (2021). How specific can language as resource become for the teaching of algebraic concepts? ZDM-Mathematics Education, online first., 53, 277–288. https://doi.org/10.1007/s11858-020-01190-6

    Article  Google Scholar 

  • Planas, N., & Setati-Phakeng, M. (2014). On the process of gaining language as a resource in mathematics education. ZDM-Mathematics Education, 46(6), 883–893. https://doi.org/10.1007/s11858-014-0610-2

    Article  Google Scholar 

  • Prediger, S., & Wessel, L. (2013). Fostering German-language learners’ constructions of meanings for fractions—design and effects of a language- and mathematics-integrated intervention. Mathematics Education Research Journal, 25, 435–456. https://doi.org/10.1007/s13394-013-0079-2

    Article  Google Scholar 

  • Razfar, A. (2012). Discoursing mathematically: Using discourse analysis to develop a sociocritical perspective of mathematics education. Mathematics Educator, 22(1), 39–62.

    Google Scholar 

  • Razfar, A. (2013). Multilingual mathematics: Learning through contested spaces of meaning making. International Multilingual Research Journal, 7(3), 175–196.

    Article  Google Scholar 

  • Remillard, J. (2009). Considering what we know about the relationship between teachers and curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 85–92). Routledge.

  • Remillard, J. T., Herbel-Eisenmann, B. A., & Lloyd, G. M. (2009). Mathematics teachers at work: Connecting curriculum materials and classroom instruction. Routledge.

  • Schmidt, W. H., Burroughs, N. A., Zoido, P., & Houang, R. T. (2015). The role of schooling in perpetuating educational inequality: An international perspective. Educational Researcher, 44(7), 371–386.

    Article  Google Scholar 

  • Schreier, M. (2014). Qualitative content analysis. In W. Flick (Ed.), SAGE handbook of qualitative data analysis (pp. 170–183). Sage.

  • Setati, M. (2005). Teaching mathematics in a primary multilingual classroom. Journal for Research in Mathematics Education, 36(5), 447–466. https://doi.org/10.2307/30034945

    Article  Google Scholar 

  • Shein, P. P. (2012). Seeing with two eyes: A teacher’s use of gestures in questioning and revoicing to engage English language learners in the repair of mathematical errors. Journal for Research in Mathematics Education, 43(2), 182–222. https://doi.org/10.5951/jresematheduc.43.2.0182

    Article  Google Scholar 

  • Sherman, M. F., Walkington, C., & Howell, E. (2016). A comparison of symbol-precedence view in investigative and conventional textbooks used in Algebra courses. Journal for Research in Mathematics Education, 47(2), 134–146. https://doi.org/10.5951/jresematheduc.47.2.0134

    Article  Google Scholar 

  • Sood, S., & Jitendra, A. K. (2007). A comparative analysis of number sense instruction in reform-based and traditional mathematics textbooks. The Journal of Special Education, 41(3), 145–157.

    Article  Google Scholar 

  • Spanos, G., & Crandall, J. (1990). Language and problem solving: Some examples from math and science. In A. M. Padilla, H. H. Fairchild, & C. M. Valadez (Eds.), Bilingual Education: Issues and Strategies (pp. 157–170). Sage.

  • Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 2014-4333). National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website: http://whatworks.ed.gov

  • Stein, M. K., & Kim, G. (2009). The role of mathematics curriculum materials in large-scale urban reform: An analysis of demands and opportunities for teacher learning. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 37–55). Routledge.

  • Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3, 268–275.

    Article  Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455–488.

    Article  Google Scholar 

  • The New Teacher Project (TNTP). (2018). The opportunity myth: What students can show us about how school is letting them down—and how to fix it. https://tntp.org/assets/documents/TNTP_The-Opportunity-Myth_Web.pdf

  • United States Department of Education. (2016). Non-regulatory guidance: English learners and title III of the elementary and secondary education act (ESEA), as amended by the Every Student Succeeds Act (ESSA). Retrieved from https://www2.ed.gov/policy/elsec/leg/essa/essatitleiiiguidenglishlearners92016.pdf

  • Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Kluwer Academic Publishers.

  • van Garderen, D., Scheuermann, A., & Jackson, C. (2012). Developing representational ability in mathematics for students with learning disabilities: A content analysis of grades 6 and 7 textbooks. Learning Disability Quarterly, 35(1), 24–38.

    Article  Google Scholar 

  • Wilhelm, A. G., Munter, C., & Jackson, K. (2017). Examining relations between teachers’ explanations of sources of students’ difficulty in mathematics and students’ opportunities to learn. The Elementary School Journal, 117(3), 345–370.

    Article  Google Scholar 

  • Yerushalmy, M., & Chazan, D. (2002). Flux in school algebra: Curricular change, graphing technology, and research on student learning and teacher knowledge. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 725–755). Lawrence Erlbaum.

  • Yoon, B. (2008). Uninvited guests: The influence of teachers’ roles and pedagogies on the positioning of English language learners in the regular classroom. American Educational Research Journal, 45(2), 495–522. https://doi.org/10.3102/0002831208316200

    Article  Google Scholar 

  • Zahner, W. (2015). The rise and run of a computational understanding of slope in a conceptually focused bilingual algebra class. Educational Studies in Mathematics, 88(1), 19–41.

    Article  Google Scholar 

  • Zahner, W., Velazquez, G., Moschkovich, J., Vahey, P., & Lara-Meloy, T. (2012). Mathematics teaching practices with technology that support conceptual understanding for Latino/a students. The Journal of Mathematical Behavior, 31(4), 431–446 https://doi.org/10.1016/j.jmathb.2012.06.002

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge Amy Dwiggins for her help with earlier iterations of the analysis of this data set. We also wish to thank the reviewers and the editor for their helpful feedback throughout the review process.

Funding

The University of Missouri’s Cambio Center provided financial support for this study.

Author information

Authors and Affiliations

Authors

Contributions

The authors are listed in alphabetical order and each contributed 50%.

Corresponding author

Correspondence to Zandra de Araujo.

Ethics declarations

Conflict of interest

Erin Smith serves as a consultant for Illustrative Mathematics.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Araujo, Z., Smith, E. Examining English language learners’ learning needs through the lens of algebra curriculum materials. Educ Stud Math 109, 65–87 (2022). https://doi.org/10.1007/s10649-021-10081-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-021-10081-w

Keywords

Navigation