English learners (ELs) face the challenge of learning English, both conversational and academic, as well as subject matter, including mathematics (Abedi & Herman, 2010). This is clearly a difficult task for ELs, with most states facing huge gaps in mathematics achievement and opportunities between those who are ELs and those who are not (Abedi & Herman, 2010). It is not only ELs who face this challenge but also their teachers, very few of whom have had any training to support ELs in content courses(Echevarria, Short, & Powers, 2006). This study examines how a teacher varied her instruction between two sixth grade classes: one a class composed of only ELs and the other an advanced class.

This study’s goal is to try to isolate and identify some of the strategies that this teacher uses specifically to support ELs in her classroom. This study uses ideas about Mathematics Knowledge for Teaching (MKT), a way of understanding of mathematics that extends beyond the knowledge teachers learned in college (Ball & Bass, 2003), to understand the decisions this teacher makes related to supporting ELs in mathematics classrooms. The information gathered in this study attempts to add to the sparse literature base about how teachers can best support ELs in secondary mathematics classrooms.

Methods

The key research question in this study is:

• What specifically does a teacher of ELs do to support her students in an all-EL sixth grade mathematics classroom, and how does this support compare to her work with an advanced sixth grade class?

This study used intentional sampling to a teacher who was identified as consistently supporting ELs in mathematics classrooms, seeking out new strategies to support ELs, and working with other teachers to help them support their ELs. While this is a limited sample size, an examination of an individual teacher allows for discerning the nuances between these classes.

Data analysis included writing analytic memos and using ethnographic microanalysis of interaction (Erickson, 1992). This analysis involved creating content logs, identifying events in which there were consistencies or inconsistencies between the two classes, and coding these events. For example, a code called, “using visual to solve problem” allowed for analyzing comparable events to establish patterns between and across the two classes.

Data

This study draws on two different lessons for both an advanced and all-EL course. The goal was to videotape the same content, multiplying and dividing fractions, being taught in two different courses. The study used two cameras – one focused on the teacher and the other focused on a small group of students working. The second source of data for this study is interviews with the teacher of these classes conducted prior to collecting the videotape data and at the conclusion of the data collection.

Results
The teacher taught multiplication and division of fractions using Bits and Pieces II (Lappan, Fey, Fitzgerald, Friel, & Philips, 2009) with both classes. The teacher felt that both classes were able to understand the content by moving from using visuals (area models) to seeing a pattern in these visuals to moving to using a standard algorithm.

While both classes used the same text, there were two key differences in instruction. The first was that the all EL class discussed the problem context in more detail (i.e blocks of cheese and brownies) to support students in understanding the context to get to the mathematics. A second key difference was that the teacher re-typed the investigation for her EL students so that the problem was partitioned with: a space for the numerical answer, the visual answer, and a sentence explaining the solution. The teacher had students complete an iterative visual that repeated prior steps to help them see connections between the language they were using, the mathematics they were doing, and the algorithm that was evident through this work.

There were two key differences in the overall flow of the classroom instruction between the two classes. The first was the use of “skip counting” (counting by multiples of a number) with the all EL class at the beginning of each lesson. The teacher felt this helped students with multiplication skills, place value, and estimation. The second difference was using less vocabulary with EL students. The teacher said that she carefully chose words to focus upon (e.g. product) and was clear about what students should learn by hearing and using them.

Educational Importance

This teacher made decisions about how to support the ELs in her class, particularly in the use of a reform-based text that included more context and language. Chunking the text and focusing on vocabulary are not particularly related to mathematics instruction. However, the use of an iterative visual might be considered as such. Future research and professional development might focus on working with teachers to think through how one might use particular visuals with particular mathematics problems. This research aims to identify some tools that such teachers might consider. Additionally, this study aims to make a link between supporting ELs and MKT – to identify what teachers of ELs might think about as they prepare and enact instruction and curriculum.

References

Abedi, J. & Herman, J. (2010). Assessing English language learners’ opportunity to learn mathematics: Issues and limitations. Teachers College Record, 112(3), 723-736.

Ball, D.L. & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3-14). Edmonton, AB: CMESG/GCEDM.

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

Erickson, F. (1992). Ethnographic microanalysis of interaction. In M.D. LeCompte, W.L. Millory, and J. Preissle (Eds.), The handbook of qualitative research in education (pp. 201-225). New York: Academic Press.Freeman & Crawford, 2008;

Lappan,G., Fey, J.T., Fitzgerald, W.M, Friel, S.N., & Philips, E. (2009). Bits and pieces II : Using fraction operations. Boston: Pearson Prentice Hall.