Project Activities
First, the research team will run a small-scale study to validate their fidelity of implementation measure and provide an opportunity for the research team to receive training on how to deliver the intervention professional development (PD). Subsequently, the research team will conduct an RCT to test the efficacy of ICUE. Finally, the research team will analyze the data and disseminate the results.
Structured Abstract
Setting
Participating elementary schools will be located in three large suburban school districts in California.
Sample
The study sample will include about 130 second grade teachers and approximately 2600 second grade students each year, for a total of about 5200 students over two years. The sample reflects a diverse population, and includes English language learners and a large proportion of students qualifying for free and reduced priced meals.
ICUE is a fully-developed intervention that supplements teachers' existing mathematics instruction and helps students develop a robust understanding of mathematical equivalence. Students participate in two 15-to-20-minute sessions per week for sixteen weeks, for approximately 8-10 total hours of instruction. ICUE includes teacher manuals, student workbooks, manipulatives, assessment items, and a two hour PD workshop to provide teachers with information about how to implement the intervention. Lessons feature four components shown to promote student learning: 1) non-traditional arithmetic practice, 2) exposure to the equal sign outside of arithmetic contexts, 3) fading from concrete to abstract representations, and 4) explanation prompts for problem solving strategies and procedures.
Research design and methods
Initially, the research team will conduct a small-scale study to validate measures of fidelity of implementation and to provide an opportunity for research staff to be trained to deliver the intervention PD to teachers. Subsequently, the research team will conduct a cluster-randomized trial to test the efficacy of ICUE. Because ICUE is delivered at the classroom level, random assignment to the intervention or control condition will occur at the teacher level. First, teachers and students will complete baseline measures and teachers will receive PD for their condition. Teachers will implement the intervention for two years (with different groups of students each year). At the end of each year, students will complete post-tests. Researchers will collect fidelity measures and teacher logs and will conduct interviews to look for any evidence of contamination given that teachers at the same school will be participating in different conditions.
Control condition
The control condition will receive an intervention consisting of nontraditional arithmetic practice alone, which has been shown to have positive student outcomes in prior research. This control will equate time on task and minimize attrition, as teachers in both conditions will receive materials and implementation support.
Key measures
Student outcome measures include researcher-developed measures of mathematical equivalence understanding and performance tasks and standardized tests, including the Mathematics Assessment Resource Service performance tasks, the Iowa Test of Basic Skills on Math Concepts, and the Smarter Balanced Assessment in mathematics. Fidelity of implementation will be measured through teacher logs, teacher surveys, and student workbooks. Researchers will also collect background information from teachers and student demographic variables.
Data analytic strategy
To determine the intervention's impact on our proximal and distal learning measures, the research team will fit a two-level hierarchical linear model for each type of data. Researchers will test for moderation by extending the model and representing moderator effects as interactions between the treatment and the moderator variable of interest.
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
The products of this project will be evidence of the efficacy of the ICUE intervention for second grade students and peer-reviewed publications.
Publications:
Davenport, J. L., Kao, Y. S., Johannes, K. N., Hornburg, C. B., & McNeil, N. M. (2023). Improving children’s understanding of mathematical equivalence: An efficacy study. Journal of Research on Educational Effectiveness, 16(4), 615-642.
Johannes, K., & Davenport, J. (2019). Targeted Mathematical Equivalence Training Lessens the Effects of EarlyMisconceptions on Equation Encoding and Solving. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 41).
Johannes, K., Davenport, J., Kao, Y., Hornburg, C. B., & McNeil, N. M. (2017). Promoting children’s relational understanding of equivalence. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 39).
Johannes, K., McNeil, N. M., Kao, Y., & Davenport, J. (2021). Predicting learning and knowledge transfer in two early mathematical equivalence interventions. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 43, No. 43).
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