Developing Awareness Around Language Practices in the Elementary Bilingual Mathematics Classroom

Gladys Krause; Melissa Adams-Corral; Luz A. Maldonado Rodríguez

doi:10.21423/jume-v15i2a462

Authors

Gladys Krause William & Mary https://orcid.org/0000-0002-2001-267X
Melissa Adams-Corral California State University, Stanislaus https://orcid.org/0000-0003-4529-1203
Luz A. Maldonado Rodríguez https://orcid.org/0000-0002-9649-1144

DOI:

https://doi.org/10.21423/jume-v15i2a462

Keywords:

bilingual education, elementary, mathematics, translanguaging

Abstract

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-onone interview and of the circulating portion of a mathematics class from a secondgrade classroom. We use these examples to foreground instructional practices, for
researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal manipulation to a more academically ample discussion of perspectives that investigate critically both mathematical concepts and their modes of transmission, which involve language practices, that are crucial for educating bilingual children.

References

Adams, M. (2015). Math identities information: Latin@ students tell their math stories. [Mas-ter’s thesis, The University of Texas at Austin]. Texas ScholarWorks. http://hdl.handle.net/2152/30263

Adams, M. (2018). “I can solve all the problems”: Latinx students (re)write their math stories. In I. Goffney & R. Gutiérrez (Eds.), Annual perspectives in mathematics education 2018: Rehumanizing mathematics for Black, Indigenous, and Latinx students (pp. 121–134). Na-tional Council of Teachers of Mathematics.

Adams, M., & Busey, C. (2017). “They want to erase that past”: Examining race and Afro-Latin@ identity with bilingual third graders. Social Studies and the Young Learner, 30(1), 13–18.

Adler, J. (2002). Teaching mathematics in multilingual classrooms. Kluwer Academic Publish-ers.

Anzaldúa, G. (2012). Borderlands/La Frontera: The new Mestiza (4th ed.). Aunt Lute Books.

Ballinger, S., Lyster, R., Sterzuk, A., & Genesee, F. (2017). Context-appropriate crosslinguistic pedagogy: Considering the role of language status in immersion education. Journal of Im-mersion and Content-Based Language Education, 5(1), 30–57. https://doi.org/10.1075/jicb.5.1.02bal DOI: https://doi.org/10.1075/jicb.5.1.02bal

Barwell, R. (2009). Multilingualism in mathematics classrooms: An introductory discussion. In R. Barwell (Ed.), Multilingualism in mathematics classrooms: Global perspectives (pp. 1–13). Multilingual Matters. DOI: https://doi.org/10.21832/9781847692061-003

Bialystok, E. (2018). Bilingual education for young children: Review of the effects and conse-quences. International Journal of Bilingual Education and Bilingualism, 21(6), 666–679. https://doi.org/10.1080/13670050.2016.1203859 DOI: https://doi.org/10.1080/13670050.2016.1203859

Bossé, M. J., Bayaga, A., Fountain, C., Young, E. S., & DeMarte, A. (2019). Mathematics learning through the lens of language acquisition. International Electronic Journal of Ele-mentary Education, 12(1), 103–113. https://doi.org/10.26822/iejee.2019155342 DOI: https://doi.org/10.26822/iejee.2019155342

Byram, M. (1997). Teaching and assessing intercultural communicative competence. Multilin-gual Matters.

Campbell, P., Rowan, T., & Suarez, A. (1998). What criteria for student-invented algorithms? In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 49–55). National Council of Teachers of Mathematics.

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children’s mathematics: Cognitively guided instruction (2nd ed.). Heinemann.

Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20. https://doi.org/10.1086/461846 DOI: https://doi.org/10.1086/461846

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531. https://doi.org/10.3102%2F00028312026004499 DOI: https://doi.org/10.3102/00028312026004499

Celedón-Pattichis, S., & Turner, E. E. (2012). “Explícame tu respuesta”: Supporting the devel-opment of mathematical discourse in emergent bilingual kindergarten students. Bilingual Research Journal, 35(2), 197–216. https://doi.org/10.1080/15235882.2012.703635 DOI: https://doi.org/10.1080/15235882.2012.703635

Clarkson, P. C. (2007). Australian Vietnamese students learning mathematics: High ability bilin-guals and their use of their languages. Educational Studies in Mathematics, 64(2), 191–215. https://doi.org/10.1007/s10649-006-4696-5 DOI: https://doi.org/10.1007/s10649-006-4696-5

Cubillos, E. (1988). The Bilingual Education Act: 1988 legislation. The National Clearinghouse for Bilingual Education: Occasional Papers in Bilingual Education, 7, 1–26. https://www.ncela.ed.gov/files/rcd/BE017100/Fall88_7.pdf

DiNapoli, J., & Morales, H. (2020). Translanguaging to persevere: Supporting and recognizing the meaning-making process for Latinx bilingual students of mathematics. Teaching for Excellence and Equity in Mathematics, 11(2), 26–34.

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

Dominguez, H., & Adams, M. (2013). Más o menos: Exploring estimation in a bilingual class-room. Teaching Children Mathematics, 20(1), 36–41. DOI: https://doi.org/10.5951/teacchilmath.20.1.0036

Empson, S. B., Jacobs, V. R., Jessup, N. A., Hewitt, A., Pynes, D., & Krause, G. (2020). Unit fractions as superheroes for instruction. Mathematics Teacher: Learning and Teaching PK-12, 113(4), 278–286. https://doi.org/10.5951/MTLT.2018.0024 DOI: https://doi.org/10.5951/MTLT.2018.0024

Empson, S. B., Junk, D., Dominguez, H., & Turner, E. (2006). Fractions as the coordination of multiplicatively related quantities: A cross-sectional study of children’s thinking. Educa-tional Studies in Mathematics, 63(1), 1–28. https://doi.org/10.1007/s10649-005-9000-6 DOI: https://doi.org/10.1007/s10649-005-9000-6

Empson, S. B., & Levi, L. (2011). Extending children’s mathematics: Fractions and decimals. Heinemann.

Empson, S. B. (2014). Responsive teaching from the inside out: Teaching base ten to young children. Investigations in Mathematics Learning, 7(1), 23–53. https://doi.org/10.1080/24727466.2014.11790337 DOI: https://doi.org/10.1080/24727466.2014.11790337

Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434. https://doi.org/10.5951/jresematheduc.27.4.0403 DOI: https://doi.org/10.5951/jresematheduc.27.4.0403

Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educa-tional Research Journal, 38(3), 653–689. DOI: https://doi.org/10.3102/00028312038003653

Fránquiz, M., & Reyes, M. (1998). Creating inclusive learning communities through English language arts: From chanclas to canicas. Language Arts, 75(3), 211–220.

Gándara, P., & Orfield, G. (2010). A return to the “Mexican Room”: The segregation of Arizo-na’s English learners. The Civil Rights Project/Proyecto Derechos Civiles. https://escholarship.org/uc/item/7m67q3b9

Gándara, P., Losen, D., August, D., Uriarte, M., Gómez, M. C., & Hopkins, M. (2010). Forbid-den language: A brief history of U.S. language policy. In P. Gándara & M. Hopkins (Eds.), Forbidden language: English learners and restrictive language policies (pp. 20–33). Teachers College Press.

Gándara, P., & Escamilla, K. (2017). Bilingual education in the United States. In O. García, A. M. Y. Lin, & S. May (Eds.), Bilingual and multilingual education (3rd ed.). Springer. DOI: https://doi.org/10.1007/978-3-319-02258-1_33

García, O., & Kleifgen, J. A. (2010). Educating emergent bilinguals: Policies, programs, and practices for English language learners. Teachers College Press.

García, O. (2009). Bilingual education in the 21st century: A global perspective. Wiley-Blackwell.

García, O., Johnson, S. I., & Seltzer, K. (2016). The translanguaging classroom: Leveraging student bilingualism for learning. Caslon.

García, O., & Wei, L. (2014). Translanguaging: Language, bilingualism and education. Pal-grave Macmillan. DOI: https://doi.org/10.1057/9781137385765_4

Ginsburg, H. (1997). Entering the child’s mind: The clinical interview in psychological research and practice. Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511527777

Grosjean, F. (2010). Bilingual: Life and reality. Harvard University Press. DOI: https://doi.org/10.4159/9780674056459

Gutiérrez, K. D., & Rogoff, B. (2003). Cultural ways of learning: Individual traits or repertoires of practice. Educational Researcher, 32(5), 19–25. https://doi.org/10.3102%2F0013189X032005019 DOI: https://doi.org/10.3102/0013189X032005019

Hackenberg, A., & Lee, M. Y. (2015). Relationships between students’ fractional knowledge and equation writing. Journal for Research in Mathematics Education, 46(2), 196–243. https://doi.org/10.5951/jresematheduc.46.2.0196 DOI: https://doi.org/10.5951/jresematheduc.46.2.0196

Hakuta, K. (1987). Mirror of language: The debate on bilingualism. Basic Books.

Hamman-Ortiz, L. (2019). Troubling the “two” in two-way bilingual education. Bilingual Re-search Journal, 42(4), 387–407. https://doi.org/10.1080/15235882.2019.1686441 DOI: https://doi.org/10.1080/15235882.2019.1686441

Henry, D., Nistor, N., & Baltes, B. (2014). Examining the relationship between math scores and English language proficiency. Journal of Educational Research and Practice, 4(1), 11–29.

Hickey, P. (2016). “They always keep us in line”: Neoliberalism and elementary emergent bilin-guals. Journal for Critical Education Policy Studies, 14(2), 14–40.

Jacobs, J. K., & Morita, E. (2002). Japanese and American teachers’ evaluations of videotaped mathematics lessons. Journal for Research in Mathematics Education, 33(3), 154–175. DOI: https://doi.org/10.2307/749723

Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM, 48(1–2), 185–197. https://doi.org/10.1007/s11858-015-0717-0 DOI: https://doi.org/10.1007/s11858-015-0717-0

Jacobs, V. R., Empson, S. B., Pynes, D., Hewitt, A., Jessup, N., & Krause, G. (2019). The Re-sponsive Teaching in Elementary Mathematics Project. In P. Sztajn & P. H. Wilson (Eds.), Learning trajectories for teachers: Designing effective professional development for math instruction (pp. 73–103). Teachers College Press; National Council of Teachers of Mathematics.

Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching Chil-dren Mathematics, 15(5), 260–266. DOI: https://doi.org/10.5951/TCM.15.5.0260

Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional de-velopment focused on children’s algebraic reasoning in elementary school. Journal for Re-search in Mathematics Education, 38(3), 258–288.

Khisty, L. (1995). Making inequality: Issues of language and meanings in mathematics teaching with Hispanic students. In W. G. Secada, E. Fennema, & L. B. Adajian (Eds.), New direc-tions for equity in mathematics education (pp. 279–297). Cambridge University Press.

Kohli, R. (2014). Unpacking internalized racism: Teachers of color striving for racially just class-rooms. Race Ethnicity and Education, 17(3), 367–387. https://doi.org/10.1080/13613324.2013.832935 DOI: https://doi.org/10.1080/13613324.2013.832935

Krause, G., & Colegrove, K. S.-S. (2020). Preparing bilingual pre-service teachers to foster equi-table and open communication with Latinx immigrant parents en la enseñanza de matemát-icas. Teaching for Excellence and Equity in Mathematics, 11(3), 41–49.

Kroll, J. F., & Dussias, P. E. (2017). The benefits of multilingualism to the personal and profes-sional development of residents of the US. Foreign Language Annals, 50(2), 248–259. https://doi.org/10.1111/flan.12271 DOI: https://doi.org/10.1111/flan.12271

Lager, C. (2010). Conserving the mathematics construct: Improving mathematics item accessibil-ity for English-Language Learners. TODOS Research Monograph, 2, 19–38.

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 DOI: https://doi.org/10.1080/02702710600642475

MacDonald, V.-M. (2004). Latino education in the United States: A narrated history from 1513–2000. Palgrave Macmillan. DOI: https://doi.org/10.1057/9781403982803

Maldonado Rodríguez, L. A., Krause, G., & Adams-Corral, M. (2020). Flowing with the translanguaging corriente: Juntos engaging with and making sense of mathematics. Teach-ing for Excellence and Equity in Mathematics, 11(2), 17–25.

Martin–Beltrán, M. (2010). The two‐way language bridge: Co‐constructing bilingual language learning opportunities. The Modern Language Journal, 94(2), 254–277. https://doi.org/10.1111/j.1540-4781.2010.01020.x DOI: https://doi.org/10.1111/j.1540-4781.2010.01020.x

Martínez-Álvarez. (2017). Language multiplicity and dynamism: Emergent bilinguals taking own-ership of language use in a hybrid curricular space. International Multilingual Research Journal, 11(4), 255–276. https://doi.org/10.1080/19313152.2017.1317506 DOI: https://doi.org/10.1080/19313152.2017.1317506

Martínez, R. A., Hikida, M., & Durán, L. (2015). Unpacking ideologies of linguistic purism: How dual language teachers make sense of everyday translanguaging. International Multi-lingual Research Journal, 9(1), 26–42. https://doi.org/10.1080/19313152.2014.977712 DOI: https://doi.org/10.1080/19313152.2014.977712

Martínez, R., & Martínez, D. C. (2019). Chicanx and Latinx students’ linguistic repertoires. Moving beyond essentialist and prescriptivist perspectives. In J. MacSwan & C. J. Faltis (Eds.), Codeswitching in the Classroom. Critical perspectives on teaching, learning, poli-cy, and ideology (pp. 225¬–246). Routledge. DOI: https://doi.org/10.4324/9781315401102-10

Martiniello, M. (2010). Linguistic complexity in mathematics assessments and the performance of English-Language Learners. TODOS Research Monograph, 2, 1–17.

Masakhane. (n.d.). A grassroots NLP community for Africa, by Africans. Retrieved August 22, 2021, from https://www.masakhane.io/home

Moschkovich, J. (1999). Supporting the participation of English Language Learners in mathemat-ical discussions. For the Learning of Mathematics, 19(1), 11–19.

Moschkovich, J. (2007). Using two languages when learning mathematics. Educational Studies in Mathematics, 64(2), 121–144. https://doi.org/10.1007/s10649-005-9005-1 DOI: https://doi.org/10.1007/s10649-005-9005-1

Moschkovich, J. (2012). Mathematics, the Common Core, and language: Recommendations for mathematics instruction for ELs aligned with the Common Core. In K. Hakuta & M. San-tos (Eds.), Understanding language: Commissioned papers on language and literacy is-sues in the Common Core State Standards and Next Generation Science Standards (pp. 17–31). Stanford University.

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

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. https://doi.org/10.21423/jume-v3i1a47 DOI: https://doi.org/10.21423/jume-v3i1a47

National Center for Education Statistics. (2018). Digest of education statistics 2018 (NCES 2020-009). U.S. Department of Education, Institute of Education Sciences. https://nces.ed.gov/pubs2020/2020009.pdf

No Child Left Behind Act of 2001, Pub. L. No. 107-110, § 101, Stat. 1425 (2002).

Omi, M., & Winant, H. (2014). Racial formation in the United States (3rd ed.). Routledge. DOI: https://doi.org/10.4324/9780203076804

Otheguy, R., García, O., & Reid, W. (2015). Clarifying translanguaging and deconstructing named languages: A perspective from linguistics. Applied Linguistics Review, 6(3), 281–307. https://doi.org/10.1515/applirev-2015-0014 DOI: https://doi.org/10.1515/applirev-2015-0014

Palmer, D., & Martínez, R. A. (2013). Teacher agency in bilingual spaces: A fresh look at prepar-ing teachers to educate Latina/o bilingual children. Review of Research in Education, 37(1), 269–297. https://doi.org/10.3102%2F0091732X12463556 DOI: https://doi.org/10.3102/0091732X12463556

Paris, D. (2012). Culturally sustaining pedagogy: A needed change in stance, terminology, and practice. Educational Researcher, 41(3), 93–97. https://doi.org/10.3102%2F0013189X12441244 DOI: https://doi.org/10.3102/0013189X12441244

Patel, L. (2016). Decolonizing educational research: From ownership to answerability. Routledge. DOI: https://doi.org/10.4324/9781315658551

Rosa, J. D. (2016). Standardization, racialization, languagelessness: Raciolinguistic ideologies across communicative contexts. Journal of Linguistic Anthropology, 26(2), 162–183. DOI: https://doi.org/10.1111/jola.12116

Ryan, C. (2013). Language use in the United States: 2011 (ACS-22). U.S. Census Bureau. https://www2.census.gov/library/publications/2013/acs/acs-22/acs-22.pdf

Saldaña, J. (2015). The coding manual for qualitative researchers (3rd ed.). SAGE.

Shannon, S., & Milian, M. (2002). Parents choose dual language programs in Colorado: A sur-vey. Bilingual Research Journal, 26(3), 681–696. https://doi.org/10.1080/15235882.2002.10162584 DOI: https://doi.org/10.1080/15235882.2002.10162584

Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. https://doi.org/10.1080/10986060802229675 DOI: https://doi.org/10.1080/10986060802229675

Stillwell, J. (2010). Mathematics and its history (3rd ed.). Springer. DOI: https://doi.org/10.1007/978-1-4419-6053-5

Swaby, A. (2017, February 21). Texas school districts struggle to recruit bilingual certified teachers. The Texas Tribune. https://www.texastribune.org/2017/02/21/texas-school-districts-struggle-bilingual-certified-teachers/

Texas Education Agency. (2017). Bilingual and English as a second language education pro-grams. https://statutes.capitol.texas.gov/Docs/ED/htm/ED.29.htm#B

Turner, E. E., Dominguez, H., Empson, S., & Maldonaldo, L. A. (2013). Latino/a bilinguals and their teachers developing a shared communicative space. Educational Studies in Mathemat-ics, 84(3), 349–370. DOI: https://doi.org/10.1007/s10649-013-9486-2

Turner, E. E., & Celedón-Pattichis, S. (2011). Mathematical problem solving among Latina/o kindergartners: An analysis of opportunities to learn. Journal of Latinos and Education, 10(2), 146–169. DOI: https://doi.org/10.1080/15348431.2011.556524

U.S. Census Bureau. (2019). Language spoken at home (S1601) [Data set]. https://data.census.gov/cedsci/table?q=speaking%20spanish&tid=ACSST1Y2019.S1601

Valdés, G. (2017). Entry visa denied: The construction of symbolic language borders in educa-tional settings. In O. García, N. Flores, & M. Spotti (Eds.), The Oxford handbook of lan-guage and society (321–348). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190212896.013.24 DOI: https://doi.org/10.1093/oxfordhb/9780190212896.013.24

Valencia Mazzanti, C., & Allexsaht-Snider, M. (2018). ¿Es lo mismo? Bilingual children count-ing and making sense of numbers. In I. Goffney & R. Gutiérrez (Eds.), Annual perspectives in mathematics education 2018: Rehumanizing mathematics for Black, Indigenous, and Latinx students (pp. 135–145). National Council of Teachers of Mathematics.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Pearson.

VERBI Software. (2020). MAXQDA 2020 [computer software]. https://www.maxqda.com

Villaseñor, A., & Kepner, H. (1993). Arithmetic from a problem-solving perspective: An urban implementation. Journal for Research in Mathematics Education, 24(1), 62–69. DOI: https://doi.org/10.5951/jresematheduc.24.1.0062

Wei, L., & Ho, W. (2018). Language learning sans frontiers: A translanguaging view. Annual Review of Applied Linguistics, 38, 33–59. https://doi.org/10.1017/S0267190518000053 DOI: https://doi.org/10.1017/S0267190518000053

Welch, I. (2015). Building interactional space in an ESL classroom to foster bilingual identity and linguistic repertoires. Journal of Language, Identity & Education, 14(2), 80–95. https://doi.org/10.1080/15348458.2015.1019784 DOI: https://doi.org/10.1080/15348458.2015.1019784

Wild, S. (2021, August 18). African languages to get more bespoke scientific terms. Nature, 596, 469–470. https://doi.org/10.1038/d41586-021-02218-x DOI: https://doi.org/10.1038/d41586-021-02218-x