Más o Menos: Exploring Estimation in a Bilingual Classroom

• In Event: 61.086 - Roundtable Session 21
  In Roundtable Session: 61.086-19 - Democratized Knowledge: Mathematics Teachers' and Researchers' Reciprocal Learning

Abstract

Rationale:
Mathematical estimation “depends on the situation itself as well as the estimator” (Markovits & Herschkowitz, 1997, p. 30). Unless instruction reflects this emphasis, estimation is stripped of its power to help students judge the reasonableness of answers (NCTM, 2000;CCSSI, 2010). The collaborating researcher and a fourth-grade Latina bilingual teacher noticed early in an estimation unit that the Latino/a bilingual students were “misapplying” the estimation rules. They suspected something occupying students’ minds was more transcendental than the ability to follow estimation rules.
Theoretical Framework:
“Teachers may interpret situations thinking only of their own perspective, not considering the perspectives of their students for whom the same point may appear significantly different (Wagner & Herbel-Eisenmann, 2009, p. 9). The teacher and researcher in this study wondered: Do bilinguals notice different things in their two languages as they solve problems? The teacher viewed Spanish as the language of inclusion in her classroom; her research partner viewed bilingualism and everyday experiences as cognitive resources for learning mathematics (Dominguez, 2011).
Methods and Data Sources
The teacher and researcher realized that reviewing students’ solutions to estimation tasks was only half of what they needed to attend to. The other half had to come directly from the students’ perspectives. Therefore they interviewed students about how they had solved the tasks. Using these interview results, the researcher and teacher revised the tasks in ways that reflected the teacher and students’ mutual noticing processes. Quantities, words more familiar to students, and more relevant contexts became central in these task revisions. In the first lesson that included these revisions, the teacher noticed how students were making sense of the tasks and solving them successfully. Rules for estimating—previously considered as key indicators of learning—lost their appeal as the teacher and students engaged in more meaningful conversations regarding the usefulness of estimation as a sense making tool.
At the unit conclusion, the teacher reflected on
the incredible role that language plays in students’ understanding of mathematics. Often for teacher, it can be difficult to know what language [previous] teachers used to introduce mathematical concepts and whether students were able to make sense in that language or used their own terms. This makes noticing on the part of the teacher particularly crucial. To activate students’ prior knowledge and engage them in estimation tasks, we must teach them to recognize that their math experiences from the past are still relevant and important in the present tasks. Later, once they have developed richer understandings of the mathematics, students are more readily able to notice and adapt to the teacher’s academic language.
Questions:
In this Working Group Roundtable, I would like to explore the question: How does a professional development project—with its intention to create transformations in teachers’ practices—transform our work as mathematics education researchers? I feel that the teacher in my study has helped me transform my own work in many ways. This question fits with explorations of the democratization of knowledge.

Author

• Higinio Dominguez, Michigan State University