Study #4

Iterative Development of Educative Math Curriculum Materials

Co-Principal Investigator: Haiwen Chu  |  Co-Investigator: Leslie Hamburger

This study is part of the Center’s second line of inquiry: to develop and test new approaches that may enable English Learners to realize their full potential in college, career, and life. The Reimagining and Accelerating Mathematics Participation, Understanding, and Practices (RAMP-UP) project will develop and test curricula aimed at strengthening classroom learning opportunities for English Learners in mathematics.

The study will develop educative instructional materials that challenge English Learners, while simultaneously modeling for teachers how they can support students to develop agency and efficacy in learning mathematics. Using an iterative development process, study staff will develop and test a three-week summer bridge program for 8th graders to prepare them for success in 9th grade Algebra I or other integrated mathematics courses. The purpose of this course is not to pre-teach content, but to offer students a framework consisting of cross-cutting concepts to organize new core ideas they will explore in high school mathematics.

The course will introduce some of the central ideas in algebra (e.g., functions and rate of change) and will emphasize cross-cutting concepts, such as equivalence/transformation as applied across multiple domains. For example, in geometry, two shapes are congruent if there is a rigid motion that transforms one into the other; in algebra, two equations are equivalent if operations transform them into each other. The curriculum will also include support for English Learners as they engage in key mathematical practices including:

  • Make sense of problems and persevere in solving them,

  • Construct viable arguments and critique the reasoning of others, and

  • Look for and make use of structure.


Algebra is an important intervention area for English Learners, as it is a prerequisite for other math courses, yet English Learners are under-enrolled in Algebra I, with less than 3 percent of 8th grade English Learners enrolled in this course (US DOE, 2018). Furthermore, English Learners are more likely to repeat Algebra I (e.g., Jaquet & Fong, 2017), with “long-term” English Learners (68%) being the most likely subgroup to repeat the course. Because mathematics as a school discipline has long been taught sequentially (e.g., Stodolsky & Grossman, 1995), it is critical for English Learners to experience success in Algebra I to have access to higher-level courses (c.f. Gwynne et al., 2012).

Iterative Design and Development Process

We will employ Design-Based Research to iteratively create, refine, and test the curriculum materials with students and teachers. We will address:

  • the usability of the materials,

  • the feasibility of their use in authentic educational settings, and

  • the fidelity of their implementation at scale.


For each component, we will engage in cycles of inquiry:

  • enacting in practical trials,

  • studying implementation to describe how the component works and identify what may be improved, and

  • refining the component through focused revisions to be validated by additional field testing.


The educative curriculum materials developed for the summer course will consist of five components:

  • Disciplinary Practice Bookmark. The disciplinary practice bookmark is a metacognitive/metalinguistic discussion tool to support English Learners as they engage in a disciplinary practice with peers (Walqui, 2006).

  • Rich, Engineered Text. Text engineering is a text-modification practice designed to increase text accessibility for English Learners (Bunch et al., 2014; Walqui & van Lier, 2010). Coupled with teachers’ guidance, engineered texts direct students to focus on central ideas and to distinguish them from ideas that are more peripheral or secondary.

  • Writing Extension Activities. Writing extension activities are tasks that integrate students’ reading, writing, and interaction.

  • Teacher Manual. A teacher manual for each module will provide guidance to enable teachers to implement the units independently. Drawing on research on teacher learning, the teacher manual serves as representation of practice to guide teachers’ classroom work (Ball et al., 2014).

  • Curriculum Workshop. For the three modules, we will create a nine-hour workshop to introduce teachers to the materials. This workshop complements and makes use of the teacher manual to orient teachers on how to implement the curriculum.


Pilot Study

The mathematics curriculum materials pilot study is a delayed-intervention randomized controlled trial with individual random assignment. Participants will be enrolled in a lottery to determine whether they will attend in the first or second of two staggered summer school cohorts. A total of 600 students will participate either in the first or second session of a three-week summer intervention course using the educative materials developed for the project. We will oversample for English Learners so that a total of 300 English Learners will be randomly assigned to either intervention or comparison.

The research question for the pilot study is: Does participation in the summer bridge program improve English Learners’ math scores compared to English Learners who have not yet taken the course?

The outcome for this study is a widely used math test used for diagnostic purposes. We will administer the test before and after the summer bridge course, with impact measured as a difference in differences: the difference between the groups’ standardized difference in scores.