Pedagogical Decision-Making in Implementing Secondary Mathematics Curriculum With English Learners

• In Event: Reconceptualizing and Improving the Education of Adolescent English Learners: An Ecological Approach

Abstract

Objectives
This empirical study focused on teachers’ pedagogical reasoning as they implemented and tested selections from a three-week summer bridge course designed to introduce English Learners to key ideas of high school mathematics. The curriculum materials include features that are meant to be educative for teachers (Davis et al., 2017) while generally enhancing their usability and feasibility in authentic educational settings.

Framework
Our design approach draws upon current frameworks in mathematics education that distinguish curriculum as “delivery mechanism” from materials that serve as a “thinking tool” to foster educator reasoning (Choppin et al., 2020). The “thinking tool” orientation of curriculum materials is better aligned with an ecological/sociocultural approach to pedagogical reasoning, as it positions teachers not as individuals who “follow” a curriculum, but as participants in complex, multilayered systems in which they collaborate with colleagues as they make sense of instructional practice (van Lier, 2004). The educative design of our curriculum materials is further informed by design principles that we refine iteratively based upon empirical tests (Moore et al., 2018).

Methods/Modes of inquiry
This study consisted of iterative design cycles, each of which were guided by descriptive and improvement questions. Developers framed each cycle within a problem of practice, identified questions to describe how well activities worked, and questions focused on how activities could be incrementally improved. The design team then collected and analyzed relevant implementation data, as detailed below, and composed analytic memos for each cycle, focused on description and improvement.

Data
Primary data collection for this study included classroom observations, developer field notes, teacher focus groups and reflections, and teacher implementation logs. The study team analyzed these data iteratively to directly inform the refinement of curriculum materials. Analytic memos guided both the refinement of specific materials and instructions as well as the overarching design principles.

Results/Arguments
Through our cross-case analysis of five improvement cycles, we identified three patterns in pedagogical decision-making (Yin, 2014). First, teachers used guidance offered in materials to adjust the intensity of scaffolding through formats, participation structures, and language offered to students to maintain the cognitive demand of activities. Second, teachers used guidance offered to decide which optional activities to omit or abridge during implementation. Finally, teachers supplemented existing materials and activities with additional practice they thought would help students through application of procedures to a variety of problem contexts. These patterns indicate that while the materials were overall successful in guiding teachers, the belief that repetitive practice is necessary remains deeply entrenched.

Significance
Given persistent differences in the mathematics achievement of English Learners compared to students who have access to the full curriculum, teachers need more tools with which to challenge and support English Learners in ambitious mathematical learning. The educative curriculum materials offer explicit guidance and structured pedagogical decision-making for educators, while developing cross-cutting concepts that span the subdomains of secondary mathematics. Results can guide further curriculum development and professional learning efforts. Teachers’ interactions with each other in the focus group also provide a venue for further exploring curriculum within a sociocultural/ecological approach.

Authors

• Andrew Haiwen Chu, WestEd

• Leslie Hamburger, WestEd