Mathematic Lesson Design for English Learners Versus Non-English Learners From Perspectives of Equity and Intersection



culturally responsive mathematics teaching, English learners, equity of mathematics education, mathematical discourse, mathematical instructions for English learners


Calls for “mathematics for all” or “mathematics for social justice” bring light to the importance of equity issues within and through mathematics education. Employing the theoretical perspectives of equity and social justice for mathematics education, and the intersection of language, culture, and mathematics, this study examined how a group of in-service teachers working in inner-city settings designed mathematics tasks and strategies for English Learners (EL) in comparison with non-ELs. The data, 23 sets of lesson design responding to two learner profiles, was analyzed using inductive content analysis. Findings suggest that meaningful opportunities to learn the same mathematics concept were presented less often to ELs, who also were more likely to experience a lack of active participation and engagement than non-ELs. From the intersectional perspective, teachers heavily relied on ELs’ native language support rather than exploring the complexity of mathematical discourse. The lack of cultural integration in their lesson designs was also notable. These findings imply that the attention of mathematics education for ELs needs to be redirected from language support per se to the interplay between language, culture, and mathematical concepts in order to create a level playing field.


Abedi, J., & Herman, J. (2010). Assessing English language learners’ opportunity to learn math-ematics: Issues and limitations. Teachers College Record, 112(3), 723–746.

Aguirre, J. M., & del Rosario Zavala, M. (2013). Making culturally responsive mathematics teaching explicit: A lesson analysis tool. Pedagogies: An International Journal, 8(2), 163–190.

Amador, J. M. (2018). Teachers’ gender considerations during elementary mathematics lesson design. School Science & Mathematics, 118(7), 290–299.

Banse, H. W., Palacios, N. A., Merritt, E. G., & Rimm-Kaufman, S. E. (2017). Scaffolding English language learners’ mathematical talk in the context of Calendar Math. The Journal of Educational Research, 110(2), 199–2018.

Barajas-López, F. (2014). Mexican immigrant students’ schooling experiences and the construc-tion of disengagement in mathematics learning contexts. Journal of Latinos and Educa-tion, 13(1), 14–32.

Bartell, T. G. (2013). Learning to teach mathematics for social justice: Negotiating social justice and mathematical goals. Journal for Research in Mathematical Education, 44(1), 129–163.

Biza, I., Nardi, E., & Zachariades, T. (2007). Using tasks to explore teacher knowledge in situa-tion-specific contexts. Journal of Mathematics Teacher Education, 10(4–6), 301–309.

Cenoz, J. (2015). Content-based instruction and content and language integrated learning: The same or different? Language, Culture and Curriculum, 28(1), 8–24.

Cho, J. Y., & Lee, E.-H. (2014). Reducing confusion about grounded theory and qualitative con-tent analysis: Similarities and differences. The Qualitative Report, 19(32), Article 2.

Chval, K. B., & Pinnow, R. J. (2018). A path to discourse-rich communities. Teaching Children Mathematics, 25(2), 104–113.

Civil, M. (2014). Why should mathematics educators learn from and about Latina/o students’ in-school and out-of-school experiences? Journal of Urban Mathematics Education, 7(2), 9–20.

Civil, M. (2018). Intersections of culture, language, and mathematics education: Looking back and

looking ahead. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited lectures from the 13th International Congress on Mathematical Education (pp. 31-47). Springer.

Clark, L. M., DePiper, J. N., Frank, T. J., Nishio, M., Campbell, P. F., Smith, T. M., Griffin, M. J., Rust, A. H., Conant, D. L., & Choi, Y. (2014). Teacher characteristics associated with mathematics teachers’ beliefs and awareness of their students’ mathematical disposi-tions. Journal for Research in Mathematics Education, 45(2), 246–284.

Creswell, J. W. (2013). Qualitative inquiry and research design: Choosing among five ap-proaches (3rd ed.). SAGE.

Creswell, J. W. (2015). 30 essential skills for the qualitative researcher. SAGE.

de Araujo, Z., Roberts, S. A., Willy, C., & Zahner, W. (2018). English learners in K–12 math-ematics education: A review of the literature. Review of Educational Research, 88(6), 879–919.

Driver, M. K., & Powell, S. R., (2017). Culturally and linguistically responsive schema interven-tion: Improving word problem solving for English language learners with mathematics dif-ficulty. Learning Disability Quarterly, 40(1), 41–53.

Elliott, V. (2018). Thinking about the coding process in qualitative data analysis. The Qualitative Report, 23(11), 2850–2861.

Erickson, A., Herbst, P., Ko, I., & Dimmel, J. (2021). When what routinely happens conflicts with what ought to be done: A scenario-based assessment of secondary mathematics teach-ers’ decisions. Research in Mathematics Education, 23(2) 188–207.

Ewing, J., Gresham, G. J., & Dickey, B. (2019). Pre-service teachers learning to engage all stu-dents, including English language learners, in productive struggle. Issues in the Under-graduate Mathematics Preparation of School Teachers, 2, 1–11.

Felton-Koestler, M. D. (2020). Teaching sociopolitical issues in mathematics teacher preparation: What do mathematics teacher educators need to know? The Mathematics Enthusiast, 17(2/3), 435–468.

Gay, G. (2010). Acting on beliefs in teacher education for cultural diversity. Journal of Teacher Education, 61(1–2), 143–152. https://doi:10.1177/0022487109347320

Gee, J. P. (1989). Literacy, discourse, and linguistics: Introduction. Journal of Education, 171(1), 5–17.

Gonzalez, L. (2009). Teaching mathematics for social justice: Reflections on a community of practice for urban high school mathematics teachers. Journal of Urban Mathematics Educa-tion, 2(1), 22–51.

González, N., Moll, L. C., & Amanti, C. (Eds.). (2005). Funds of knowledge: Theorizing prac-tices in households, communities, and classrooms. Erlbaum

Gower, B. S. (2015). Teaching mathematics for social justice. Mathematics Teaching, 245, 6–9.

Hansen-Thomas, H. (2009). Reform-oriented mathematics in three 6th grade classes: How teachers draw in ELLs to academic discourse. Journal of Language, Identity & Education, 8(2–3), 88–106.

Hur, J., & Suh, S. (2012). Making learning active with interactive whiteboards, podcasts, and digital storytelling in ELL classrooms. Computers in the Schools, 29(4), 320–338.

Jeffries, C., & Maeder, D. W. (2011). Comparing vignette instruction and assessment tasks to classroom observations and reflections. The Teacher Educator, 46 (2), 161–175.

Kennedy, M. M. (1999). Approximations to indicators of student outcomes. Educational Evalua-tion and Policy Analysis, 21(4), 345–363.

Kersaint, G., Thompson, D. R., & Petkova, M. (2013). Teaching mathematics to English lan-guage learners (2nd ed.). Routledge.

Kurz, T., Gómez, C., & Jimenez-Silva, M. (2017). Guiding preservice teachers to adapt mathe-matics word problems through interactions with ELLs. Journal of Urban Mathematics Ed-ucation, 10(1), 32–51.

Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educa-tional Research Journal, 32(3), 465–491.

Ladson-Billings, G. (2014). Culturally relevant pedagogy 2.0: a.k.a the remix. Harvard Educa-tional Review, 84(1), 74–84.

Larnell, G. V., Bullock, E. C., & Jett, C. C. (2016). Rethinking teaching and learning mathemat-ics for social justice from a critical race perspective. Journal of Education, 196(1), 19–29.

Leonard, J., Napp, C., & Adeleke, S. (2009). The complexities of culturally relevant pedagogy: A case study of two secondary mathematics teachers and their ESOL students. The High School Journal, 93(1), 3–22.

McLeman, L., Fernandes, A., & McNulty, M. (2012). Regarding the mathematics education of English learners: Clustering the conceptions of preservice teachers. Journal of Urban Math-ematics Education, 5(2), 112–132.

Moore, P., & Lorenzo, F. (2015). Task-based learning and content and language integrated learn-ing materials design: Process and product. The Language Learning Journal, 43(3), 334–357.

Morin, R., Parker, K., Stepler, R., & Mercer, A. (2017). Behind the badge. Pew Research Center.

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

Moschkovich, J. N. (2015). Academic literacy in mathematics for English learners. The Journal of Mathematical Behavior, 40, 43–62.

Mosqueda, E. (2010). Compounding inequalities: English proficiency and tracking and their rela-tion to mathematics performance among Latina/o secondary school youth. Journal of Ur-ban Mathematics Education, 3(1), 57–81.

National Council of Teachers of Mathematics. (2014). Teaching mathematics to English language learners: A position of the National Council of Teachers of Mathematics.

Nebesniak, A. L., & Heaton, R. M. (2010). Student confidence & student involvement. Mathe-matics Teaching in the Middle School, 16(2), 96–103.

New York State Education Department. (2019). New York State multilingual learner/English lan-guage learner (MLL/ELL) data report: NYS MLLs/ELLs demographics & performance 2018–19.

Nutta, J. W., Mokhtari, K., & Strebel, C. (2012). Preparing every teacher to reach English learners: A practical guide for teacher educators. Harvard Education Press.

O’Halloran, K. L. (2015). The language of learning mathematics: A multimodal perspective. The Journal of Mathematical Behavior, 40, 63–74.

Peng, P., Lin, X., Ünal, Z. E., Lee, K., Namkung, J., Chow, J., & Sales, A. (2020). Examining the mutual relations between language and mathematics: A meta-analysis. Psychological Bulletin, 146(7), 595–634.

Richards, L. (2015). Handling qualitative data: A practical guide (3rd ed.). SAGE.

Rios-Aguilar, C., Kiyama, J. M., Gravitt, M., & Moll, L., C. (2011). Funds of knowledge for the poor and forms of capital for the rich? A capital approach to examining funds of knowledge. Theory and Research in Education, 9(2), 163–184.

Schreier, M. (2012). Qualitative content analysis in practice. SAGE.

Simpson, A., & Cole, M. W. (2015). More than words: A literature review of language of math-ematics research. Educational Review, 67(3), 369–384.

Son, J.-W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multipli-cation and division of fractions. Educational Studies in Mathematics, 74(2), 117–142.

Song, K. H., & Coppersmith, S. A. (2020). Working toward linguistically and culturally respon-sive math teaching through a yearlong urban teacher training program for English learners. Journal of Urban Mathematics Education, 13(2), 60–86.

Sorto, A. M., & Mejía Colindres, C. A., & Wilson, A. T. (2014). Informing practice: Uncover-ing and eliciting perceptions in linguistically diverse classrooms. Mathematics Teaching in the Middle School, 20(2), 72–77.

Takeuchi, M. A. (2016). Friendships and group work in linguistically diverse mathematics class-rooms: Opportunities to learn for English language learners. Journal of Learning Sciences, 25(3), 411–437.

Teachers of English to Speakers of Other Languages. (2006). TESOL pre-K–12 English language proficiency standards framework.

Thomas, D. R. (2006). A general inductive approach for analyzing qualitative evaluation data. American Journal of Evaluation, 27(2), 237–246.

Turkan, S., & de Jong, E. J. (2018). An exploration of preservice teachers’ reasoning about teach-ing mathematics to English language learners. Teacher Education Quarterly, 45(2), 37–60.

Turner, E. E., Drake, C., Roth McDuffie, A., Aguirre, J. M., Bartell, T. G., & Foote, M. Q. (2012). Promoting equity in mathematics teacher preparation: A framework for advancing teacher learning of children’s multiple mathematics knowledge bases. Journal of Mathemat-ics Teacher Education, 15(1), 67–82.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.

Wagner, A. A. (2012). Incorporating out-of-school mathematics: From cultural context to embed-ded practice. Journal of Mathematics Teacher Education, 15(1), 9–23.

Welner, K. G., & Carter, P. L. (2013). Achievement gaps arise from opportunity gaps. In P. L. Carter & K. G. Welner (Eds.), Closing the opportunity gap: What America must to give every child an even chance (pp.1–10). Oxford University Press.

Yang, D.-C., & Huang, K.-L. (2014). An intervention study on mental computation for second graders in Taiwan. The Journal of Educational Research, 107(1), 3–15.

Zahner, W., Milbourne, H., & Wynn, L. (2018). Developing and refining a framework for math-ematical and linguistic complexity in tasks related to rates of change. The Journal of Math-ematical Behavior, 52, 21–36.