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Helping Teachers to Use and Students To Learn From Contrasting Examples


 This 5-year project begins with the adaptation of existing materials for use in a yearlong algebra course and a one-week professional development program. A pilot study is planned for Year 2, where a small cohort of teachers will complete the professional development program and then implement the contrasting examples instructional approach. In Years 3, 4, and 5, a randomized controlled trial of the intervention will be conducted. Using a time-series design, a volunteer sample of Algebra I teachers will be randomly assigned to receive the professional development in Year 3 or in Year 4. Teacher implementation will be assessed by validated teacher logs and by direct observation of teachers' practice. Student outcome variables will include standardized test scores and a researcher-designed assessment.
The project will provide critical experimental evidence of the efficacy of a promising instructional approach closer to scale. In addition, designing contrasting examples for a full-year course will also reveal a variety of comparisons that could be useful to student learning, which will provide avenues for future experimental research to better understand how different types of comparison facilitate learning.
The broader impact of the project emerges from its combined emphases on discovery (the intellectual merit of a closer-to-scale evaluation of a promising instructional approach), teacher training, and student learning. With respect to teacher training, the project design can lead to broad dissemination of the contrasting examples instructional approach and of "best practices" in mathematics teaching to a diverse group of students and teachers. In terms of student learning, the target course, Algebra I, is a particularly critical juncture, as success in algebra has become a de facto requirement for many educational and workplace opportunities.