Examining the Ways in Which Teachers Attend to Precision in Mathematics Instruction for English Learners

• In Event: Understanding the Implications of the Common Core Mathematical Practice Standards for English Learners: An Interactive Symposium

Abstract

Objectives
This paper examines how two ninth grade algebra teachers accommodated their linguistically diverse students, focusing on their orientation to the practice standard “attend to precision.” The CCSSM states, “mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning” (2010, p. 7). These cases investigate characteristics of precise communication and the use of clear definitions for students learning English, and the ways in which teachers support English Learners in meeting this standard.

Theoretical Framework
Drawing on Moschkovich’s (2002) sociocultural approach to studying mathematics learning in bilingual settings, learning mathematics is examined as both learning facts and procedures as well as learning to engage in Discourse practices (Gee, 1996) unique to mathematics. These Discourse practices include such practices as defining, conjecturing, and imagining alternatives (Moschkovich, 2007). Moschkovich’s framework fits well here because the mathematical Discourse practices described by Moschkovich (2007) parallel the CCSSM Mathematical Practice standards.

Methods & Data Sources
The primary data are six weeks of video-recorded classroom instruction in two ninth grade algebra classes at Campo High, corresponding with a curricular unit on linear functions. Additional data include daily field notes, records of informal conversations with each teacher, and a formal debriefing interview.
Ninety five percent the students were Latino/a, over 75% were bilingual, and 35% were classified as English Learners. One focal teacher, Ms. V., was experienced and she tailored her algebra class for English Learners. Ms. W. was a new teacher and new to teaching English Learners. Both teachers used the same curriculum (Fendell et al., 1996).
Similar to the method in Zahner et al. (2012), the analysis focuses on two key episodes where both teachers taught the same key problems.

Results & Significance
Ms. V. systematically anticipated and highlighted language demands in the mathematics, while Ms. W.’s was less systematic. For example, in teaching one problem about combinations, Ms. V. used the fact that a+b=b+a to highlight “commutative.” Ms. W. also used commutative when teaching the same problem, but then told her students “The words aren't as important as understanding the concept.”

Ms. V. also made strategic decisions to approximate—i.e. be less precise—at times. For example, when teaching the meaning of slope she rounded a slope of 3.33… to 3 in order to emphasize that the slope of 3 indicated a rate of 3 y per x. There was less of a clear-cut pattern in how Ms. W. oriented to precision, both numerically and in terms of language use. Altogether this shows that Ms. V. was using a subtle understanding of precision as she taught her class full of bilingual students and English Learners.

The contrasting cases show that teaching with/for precision is not a simple proposition when teaching ELs. For mathematics educators, this leads to the significant conclusion that when and how teachers choose to use precise language and precise numbers may be a key hallmark of expertise teaching mathematics to ELs.

Author

• William Carl Zahner, Boston University