Co-Principal Investigators: McGinn, Kelly M., Schneider, W. Joel; Barbieri, Christina A.; Donovan, Suzanne

Purpose: In this project, researchers will iteratively develop and test GeometryByExample, an intervention that incorporates explanation of correct and incorrect examples of varied geometric content, to improve student learning of high school Geometry. GeometryByExample 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.

Project Activities: The project team will develop GeometryByExample assignments, assessments, and teacher resources.The researchers will investigate the moderating effects of 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 that will facilitate learning of varied geometric content for a diverse population of high school students.

Products: The team will produce peer-reviewed publications and present at local, regional, and national researcher and practitioner conferences and meetings. The research team will also develop a project website where resources for teachers will be freely available.

Structured Abstract

Setting: The study will take place in urban high schools in California and Maryland, and rural high schools in Iowa.

Sample: The sample of urban high schools from California and Maryland have a majority (approximately 90%) ethnic minority student population and over 70% of the students qualifying for free or reduced-price lunch. The sample of high schools from rural Iowa has a student population that it is 17% ethnic minority and 30% qualifying for free or reduced-price lunch.

Intervention: For the intervention, researchers will address five main content topics covered in high school Geometry courses: 1) Geometry Basics and Reasoning, 2) Parallel and Perpendicular Lines, 3) Triangles, 4) Quadrilaterals, Polygons, and Similarity, and 5) Circles. 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 materials developed for each geometry content unit will include some assignments based on computation skills and others based on proof skills. The researchers will separately examine the usability and feasibility of worked examples assignments on each type of skill (computation vs. proof skills).

Research Design and Methods: The research team will draft initial assignments, which will be reviewed and improved with feedback from teacher co-developers. For each assignment block, the researchers will develop a brief individual assessment of student knowledge and performance. Each assessment will consist of approximately 8-12 items, 2 per assignment within the block. Each item will directly target one or more of the key concepts or procedures in the associated assignment. It is anticipated that each assessment will contain some computation items and some proof items.

The team will carry out experimental classroom studies to determine the usability and feasibility of the materials as well as the appropriate dosage of worked example activities for computation versus proof-based problems throughout the geometry curriculum. The researchers will also examine whether and how the impact of these materials varies based on individual differences in student characteristics such as prior content knowledge and spatial visualization skills. Each of the five assignment blocks will be tested with 4 classes (~ 2 teachers). A total of 20 classrooms (~ 10 teachers) and approximately 500 students will be involved in data collection.

The researchers will use an underpowered efficacy study design for the pilot study. A year-long experiment will be conducted with 15 geometry teachers to test whether using the entire set of GeometryByExample assignments in classrooms significantly improves student learning. For each teacher, individual classes will be randomly assigned such that each teacher has at least one experimental class and one control class participating in the pilot study (total of at least 30 classrooms and approximately 750 students).

Control Condition: For the pilot study, students in the control classrooms will receive business-as-usual instruction and assignments.

Key Measures: As part of the development process, the researchers will collect and review student assignments, classroom observations, and student and teacher surveys. To assess student learning outcomes as part of the pilot study, the researchers will use released items from the standardized tests used by the participating school districts. In addition, researcher-designed assessments of student geometry knowledge will be developed and tested. To examine factors which may moderate the impact of the intervention, the researchers will also collect data on a variety of student characteristics including spatial visualization using the mental rotation, paper folding, and paper folding and cutting tasks; working memory (Letter-Number Sequencing subtest and the Visual Span subtest from the Wechsler Intelligence Scale for Children–Fifth Edition); and logical reasoning (International Cognitive Ability Resource battery).

Data Analytic Strategy: The team will use descriptive statistics to analyze usability and feasibility data collected from the experimental classroom studies. They will conduct multiple regression analyses to determine the effect of each type of assignment on posttest scores for each of the five units. For the pilot study, the researchers will analyze the classroom, or cluster-level, effects of the experimental GeometryByExample assignments using a series of multilevel models.

Cost Analysis: Using the ingredients approach, the researchers will detail the resources required for schools to implement GeometrybyExample (for example, materials, time commitments). The researchers will determine whether the time identifying, planning, and grading the intervention is about the same, greater, or less than time spent implementing similar math worksheets. The research team will collect the data as part of the teacher survey so that relative time and material costs can be examined.

Related IES Projects: Transforming Algebra Assignments (R305A100150); MathByExample: Dislodging Misconceptions Before They Take Root (R305A150456)