Simultaneous Development of Language and Mathematical Ideas Among Students Bureaucratically Designated as English Learners

• In Event: Ecological/Sociocultural Approaches to Educative Curriculum Design and Assessment

Abstract

Objectives
This empirical study focused on students’ participation in a full field trial of three-week summer bridge course designed to introduce English Learners to cross-cutting concepts that undergird and connect the topics of high school mathematics. As described below, the course integrates students’ oral interactions with one another and the teacher with activity that develops deep conceptual understanding of mathematical ideas alongside increasingly sophisticated engagement in mathematical practices, in contrast with more typical delivery-oriented or remediation-focused approaches (Choppin et al., 2020; De Araujo & Smith, 2021). The purpose of this study is to identify the conditions that seemed to support students’ development in accelerated and generative ways.

Framework
The curriculum was designed from a sociocultural/ecological approach to learning for English Learners in secondary mathematics and a design-based research approach to iterative development (Bronfenbrenner & Morris, 2006; Anderson & Shattuck, 2012). For students, this design means that learning is centered on ideas that are generative and powerful through opportunities that are both deliberately and contingently scaffolded at multiple instructional scales. Further, focus on language is on form—the role of language in meeting broader disciplinary purposes, rather than grammatical forms that are taught in isolation (Walqui & Bunch, 2019).

Methods/Modes of inquiry
This study draws upon data collected from three weeks of classroom activity as the full intervention was field tested. Part of the broader iterative development design was to engage in cycles of rapid inquiry, focused on descriptive questions about student work with the materials as well as improvement questions that were more focused on the effectiveness of the materials and activities as designed.

Data
Primary data collection for this study included classroom observations, developer field notes, and teacher focus groups and reflections. Two students were shadowed for more than 30 hours of the intervention, and their work artifacts were collected. The study team analyzed these data iteratively to describe the participation, understanding, and practices of focal students. Analytic memos identified themes and were refined into emerging portraits of student learning trajectories.

Results/Arguments
We present results in three ways. We consider how overall the discourse observed from students was characterized by more sustained talk and somewhat more reciprocal interactions. For each of the focal students, we illustrate their growth over time with vignettes of both their discussion in small groups as well as samples of their writing. The focal students’ growth was not very well aligned across their written reflections and their participation in class discussions—meaning that looking for both kinds of evidence was critical to fully understanding their growth. We consider the roles of mathematical topic and practices as a moderating variable in students’ language development, as well as the role of co-construction activities in supporting their development.

Significance
The empirical growth of these two students illustrate the complex, dynamic nature of development, which is not linear. Within the context of the broader iterative development project, we consider how these students’ growth patterns informed the refinement and revision of activities to more directly support their development of autonomy and agency.

Authors

• Andrew Haiwen Chu, WestEd
  Presenting Author

• Leslie Hamburger, WestEd
  Non-Presenting Author