Re-Examining Curricula as a Means to Improve Access for

Latina/o Mathematics Learners

Abstract:  New approaches are needed to translate what we know about effective mathematics curriculum and instruction for bilingual Latina/o learners, into concrete actions in the classroom.  This symposium reports on a study investigating curricular features that support teachers and students as they navigate the world of language-rich mathematics curriculum and pedagogy.

Education or Scientific Importance:  The demographic reality for schools today is that over 40% of U.S. teachers have language minority students – of whom Latinos/as are the majority – in their classrooms, but only 12.5 % of the teachers have had more than eight hours of training to prepare them to teach these students  ADDIN EN.CITE <EndNote><Cite><Author>NCTM</Author><Year>2004</Year><RecNum>339</RecNum><record><rec-number>339</rec-number><foreign-keys><key app="EN" db-id="e2w5vxevwt0wpbe5tx7pffx4500xt2fxfrf9">339</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>NCTM,,</author></authors></contributors><titles><title>NCTM Research Catalyst Conference</title></titles><dates><year>2004</year></dates><pub-location>Reston, VA</pub-location><publisher>National Council of Teachers of Mathematics</publisher><urls></urls></record></Cite></EndNote>(NCTM, 2004). Additionally, for the past two decades, school reform efforts have largely focused on developing teachers who are "highly qualified" in subject matter (i.e. mathematics) rather than in approaches for teaching diverse populations (Echevarria, Short & Powers, 2006). Moreover, there has been little attention devoted to investigating ways to fundamentally make mathematics curricula that are more accessible and engaging for emerging bilingual learners and that support teachers' pedagogy.  In short, if curriculum and pedagogy are going to serve as tools to advance mathematical understanding amongst Latina/o students, we need to closely examine the nexus of curriculum, critical pedagogy, and student interactions – precisely the focus of this symposium.

Although research would suggest that current U.S. mathematics reform curricula support most students in improving achievement, there is evidence that Latino/a students have not benefited equally from these curricula  ADDIN EN.CITE <EndNote><Cite><Author>Sconiers</Author><Year>2003</Year><RecNum>523</RecNum><record><rec-number>523</rec-number><foreign-keys><key app="EN" db-id="e2w5vxevwt0wpbe5tx7pffx4500xt2fxfrf9">523</key></foreign-keys><ref-type name="Report">27</ref-type><contributors><authors><author>Sconiers, Sheila</author><author>Isaacs, Andy C.</author><author>Higgins, T.</author><author>McBride, Jim</author><author>Kelso, Catherine Randall</author></authors></contributors><titles><title>The ARC Center tri-state student achievement study</title></titles><keywords><keyword>EM</keyword><keyword>Student Achievement</keyword></keywords><dates><year>2003</year></dates><pub-location>Lexington, MA</pub-location><publisher>The Consortium for Mathematics and Its Applications</publisher><urls></urls></record></Cite></EndNote>(Sconiers, Isaacs, Higgins, McBride, & Kelso, 2003). Given this reality and the increasing representation of Latinas/os (and other English language learners) in U.S. K-12 schools, there is a need to better understand how to support teachers in their mathematics instruction of Latinos/as in a way that bridges recognized, positive factors in effective instruction of language minority students with existing curricula.

The objective of this study was to synthesize analyses of the design of Finding Out/ Descubrimiento (FO/D) – elementary-level mathematics/science materials from the 1980's that proved successful for Latina/o ELLs – and theories about improving instruction for bilingual learners, with the goal of outlining recommendations for redesigning existing curricula  ADDIN EN.CITE <EndNote><Cite><Author>Cohen</Author><Year>1997</Year><RecNum>836</RecNum><record><rec-number>836</rec-number><foreign-keys><key app="EN" db-id="e2w5vxevwt0wpbe5tx7pffx4500xt2fxfrf9">836</key></foreign-keys><ref-type name="Book Section">5</ref-type><contributors><authors><author>Cohen, Elizabeth G.</author><author>Bianchini, Julie A.</author><author>Cossey, Ruth</author><author>Holthus, Nicole C.</author><author>Morphew, Christopher C.</author><author>Whitcomb, Jennifer A.</author></authors><secondary-authors><author>Cohen, Elizabeth G.</author><author>Lotan, Rachel A.</author></secondary-authors></contributors><titles><title>What did students learn?: 1982-1994</title><secondary-title>Working for equity in heterogeneous classrooms</secondary-title></titles><pages>137-165</pages><dates><year>1997</year></dates><pub-location>New York</pub-location><publisher>Teachers College Press</publisher><urls></urls></record></Cite><Cite><Author>Cohen</Author><Year>1989</Year><RecNum>793</RecNum><record><rec-number>793</rec-number><foreign-keys><key app="EN" db-id="e2w5vxevwt0wpbe5tx7pffx4500xt2fxfrf9">793</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Cohen, Elizabeth G.</author><author>Lotan, Rachel A.</author><author>Leechor, Chaub</author></authors></contributors><titles><title>Can classrooms learn?</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>75-94</pages><volume>62</volume><number>2</number><dates><year>1989</year></dates><publisher>American Sociological Association</publisher><isbn>00380407</isbn><urls><related-urls><url>http://www.jstor.org/stable/2112841</url></related-urls></urls></record></Cite></EndNote>(Cohen et al., 1997; Cohen, Lotan, & Leechor, 1989).

Perspectives or Theoretical Framework for the Research:
This project incorporated sociocultural views of learning in and through interactions, as well as the perspective that student learning is visible as meaningful participation in a classroom community.  A major assumption of this perspective is that human development is fundamentally social in nature, rooted in concrete communicative activity or participation in local practices.  Importantly, meaning resides in activity, its actions, and the language attached to them.  This set of assumptions served as our basis as we iteratively refined existing mathematics lessons to engage bilingual learners in different ways; access to powerful mathematical ideas comes through activities that help students construct what it means to be mathematical and opportunities to develop proficiency in communicating mathematically.

Methods, Techniques, or Modes of Inquiry for the Research:
We began with a list of design principles generated during a previous analysis of FO/D and refined these to better reflect current research on bilingual learners. We then selected a U.S. reform elementary school curriculum structured to encourage and support significant student interactions and group work. We identified design principles from the list that were relevant to features of the lessons in the reform curriculum—design principles that might provide a foundation for making recommendations. Next, we selected lessons in the reform curriculum that specified both group work and partner work since these contexts provide opportunities for student interaction and exploration. We randomly chose one lesson to use as a model for generating recommendations based on the design principles. We engaged in a cycle of 1) redesigning sections of the lesson according to the design principles; 2) evaluating the changes to the lesson according to how they would engage students in opportunities to learn and in what ways the redesigned lesson might support student engagement; and 3) developing and refining general recommendations for how to redesign lessons. At the conclusion, we had a specific and concise list of recommendations tied to research on instruction for Latina/o ELLs.

Data Sources or Evidence for the Research:  This is not a study in which we collected new data; rather, we examined a multitude of historical documents (including FO/D) and literature (both empirical and theoretical) and converted this knowledge base into a set of guiding principles – the Bilingual Mathematics Framework. We used these principles to anchor and focus our work on curriculum modification.  We asked ourselves the following key questions: 1) What does mathematic learning look like for bilingual learners?  2) Which contextual, curricular, and pedagogical arrangements need to be emphasized to maximize opportunities to learn?

Additional data sources include our modified lessons and first-hand accounts of what happened when this lesson was piloted with teachers and teacher candidates.

Results and Conclusions:  In this presentation, we will briefly describe the critical first steps of this unique study, present and contrast the original lesson with the revised lesson, and share the recommendations that we developed. We will also showcase a method in which we operationalized mathematics and bilingual education theory; we will specifically outline the process we went through to convert our knowledge of learning mathematics in a second language into curricular features that promise to increase access and engagement of the students while also providing teachers with a model for promoting mathematical discourse development. We believe this work can serve as a foundation for building a bridge between research and practice. The recommendations for revising elementary school mathematics curriculum to better support Latina/o ELLs goes beyond questions of "just good teaching" to explicitly outline critical and crucial pedagogy for bilingual learners.

References

 ADDIN EN.REFLIST Cohen, E. G., Bianchini, J. A., Cossey, R., Holthus, N. C., Morphew, C. C., & Whitcomb, J. A. (1997). What did students learn?: 1982-1994. In E. G. Cohen & R. A. Lotan (Eds.), Working for equity in heterogeneous classrooms (pp. 137-165). New York: Teachers College Press.

Cohen, E. G., Lotan, R. A., & Leechor, C. (1989). Can classrooms learn? Sociology of Education, 62(2), 75-94.

Echevarria, J., Short, D., & Powers, K. 2006. School reform and standards-based education: A model for English language learners. Journal of Educational Research, 99(4): 195–210.

National Council of Teachers of Mathematics (NCTM). (2004). NCTM Research Catalyst Conference. Reston, VA: National Council of Teachers of Mathematics.

Sconiers, S., Isaacs, A. C., Higgins, T., McBride, J., & Kelso, C. R. (2003). The ARC Center tri-state student achievement study. Lexington, MA: The Consortium for Mathematics and Its Applications.