Project Activities
The project team developed GeometryByExample assignments, assessments, and teacher resources. The researchers considered individual differences in student characteristics such as prior content knowledge, spatial visualization skills, formal/logical reasoning, and executive functioning, to develop an optimal combination of materials to facilitate learning of varied geometric content for a diverse population of high school students.
Structured Abstract
Setting
The study took place in high schools in Pennsylvania and Wisconsin.
Sample
Participating in this study were 384 high school geometry students in 17 classrooms across 4 schools in the United States. 10 of the classrooms were randomly assigned to the experimental condition (N = 227 students), and 7 classrooms served as the control condition (N = 157 students). The demographic breakdown of the sample was as follows: 52% female; 50.7% White, 9.5% Black, 28.9% Hispanic, 4.8% Asian, 5.8% Biracial, 0.3% Other; 37% of the students were classified as coming from families with low socioeconomic status.
The GeometryByExample intervention provides strategically designed, worked-example based assignments for students to complete in class in place of more typical practice assignments. Instead of solving all the practice problems themselves, students study correct or incorrect examples of solutions to half of the problems and respond to prompts asking them to write explanations of why those procedures are correct or incorrect. The full set of over 100 GeometryByExample assignments covers content for high school geometry as well as for foundational geometry knowledge typically taught in upper elementary and middle school.
Research design and methods
The research team drafted initial assignments, which were reviewed and improved with feedback from teacher co-developers. Due to COVID-related disruptions during the formative school years of this grant, the researchers developed a system to organize and collect ongoing feedback from teachers in various districts across the country, rather than limiting feedback to a couple partner districts as was originally planned. Collaborating teachers reviewed study materials independently to provide feedback about the scope and sequence of the worksheets, as well as any common misconceptions or errors that were not adequately reflected in the study materials. Teachers were also asked to pilot assignments in class with their students to gain informal usability and fidelity data, in addition to reviewing and commenting on the assignments. Revisions to the worksheets were made based on all of this feedback prior to the start of the pilot study.
During the 2022-2023 school year, the researchers utilized an underpowered efficacy study design for the pilot study. A year-long experiment was conducted with 17 geometry classrooms to test whether having access to the entire set of GeometryByExample assignments in classrooms significantly improved student learning. Individual classes (within teacher) were randomly assigned to condition and each teacher had at least one experimental class and one control class participating in the pilot study.
Control condition
For the pilot study, students in the control classrooms received business-as-usual instruction and assignments.
Key measures
To assess student learning outcomes in the pilot study, the researchers used released items from standardized tests related to prerequisite algebraic content, basic geometry content (e.g., that typically taught in grades 3-8), and high school geometry content. The researchers also collected data on a variety of student characteristics including spatial visualization, working memory, logical reasoning, student perceptions of belonging to the mathematics classroom, and student mathematics identity.
Data analytic strategy
The researchers analyzed the classroom, or cluster-level, effects of the experimental GeometryByExample assignments using a series of multilevel models.
Cost analysis strategy
The GeometryByExample materials are openly accessible as free downloads to distribute and photocopy under a Creative Commons license. Based on the cost-analysis conducted using the ingredients method, the workbook, available to purchase from a print-on- demand printer for convenience, costs $19.95 per student, which is the highest potential cost associated with using the intervention. Printing select individual assignments or the set of assignments at schools could have lower associated costs. Alternatively, teachers may choose to direct students to use PDF annotation software licensed by district learning managment systems (LMS), which would reduce the marginal cost to zero. Regarding time to adopt and implement the intervention, by design there is no associated training for the intervention. Further, teachers noted no differences in planning to use GeometryByExample assignments when compared to other mathematics assignments. Therefore, there are no new human capital costs. Further analyses may be conducted on cost-impact ratios once impacts are published in peer-reviewed journals.
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