Más o Menos: Exploring Estimation in a Bilingual Classroom

Textbooks, as well as classroom instruction, tend to present estimation as a stand-alone exercise, ignoring that "the process of estimation depends on the situation itself as well as the estimator." When taught this way, estimation is stripped of its power to help students judge the reasonableness of answers and make sense before, during, and after solving problems. Authors, Melissa Adams, a novice fourth-grade Latina bilingual teacher, and Higinio Dominguez, her bilingual Latino research partner, collaborated in a teaching unit on estimation. Early in the unit, they noticed that their students--all Latino and Latina bilinguals--were overapplying the rounding rule or not applying it at all. Noticing the difficulty that students were experiencing with the tasks, Adams commented, "I don't know why they're not getting something that seems so easy, you know?" Besides student difficulties, the authors began to notice a more fundamental problem: The teacher and students were attending to different aspects of the tasks. On the one hand, the teacher was attending to the computational aspect of estimation--learning how to estimate but not necessarily learning the purpose of estimating. Adams and Dominguez developed mathematical tasks that capitalized on the teacher and students' mutual noticing process. In the next interaction, Adams elicited from students multiple meanings related to the concept of estimation. Adams and Dominguez consistently privileged the informal words "más o menos," "casi," "about," and "almost," all common in students' everyday bilingual vocabularies--and deferred the more formal terms "aproximadamente" and "approximately" for the important point in the unit when students had had multiple opportunities to develop a strong understanding of the concept. In this teacher-researcher collaboration, the teacher learned to see estimation through her students' eyes.