# Investigating the Benefits of Using Worked Examples to Improve Mathematical Explanations for Students Who Struggle

**Effective Years:** 2020-2024

When students explain their solution approaches in mathematics, they are able to make linkages with prior knowledge, build new insights, and deepen their understanding of the mathematics they are learning. Students with mathematics difficulties (those performing below the 25th percentile) struggle to articulate their understanding of mathematical principles as they explain their solution approaches. Learning and understanding fractions in upper elementary school is especially challenging for students and often impedes learning for students as they advance in middle and high school mathematics. The purpose of the project is to improve mathematical explanations for students who struggle in mathematics, specifically with fractions. To accomplish this, the project will investigate the benefits of worked examples (i.e., already worked-out problems) as a mechanism to improve explanations for students who struggle. The project will develop worked example materials focused on fractions concepts for use with students with mathematics difficulties in Grade 5 and examine whether this approach to instruction enhances studentsâ€™ mathematical explanations during intervention.

The proposed project consists of three phases: development work, two short-duration randomized controlled trials (RCTs), and a feasibility pilot study followed by a multi-site RCT. First, the team will develop various types of worked examples (correct vs. incorrect solutions; one vs. two solutions) that address critical fractions concepts and operations in Grade 5 standards. Researchers will then conduct two short-duration RCTs to determine which worked example types are most promising for developing explanations for students with mathematics difficulties. Finally, worked example materials will be further developed and embedded as an instructional component into a previously validated fractions intervention. Intervention lessons will be examined in a feasibility pilot, which will be followed by a multi-site RCT. Eighty eligible students will be randomly assigned to receive small-group fractions intervention with worked examples or business-as-usual control. Student data will include measures of fractions concepts and procedures and assessments of written and verbal explanations. Assessments of working memory and attention will also be included. Implementation data will be collected using fidelity of treatment instruments and the CLASS observation system. Data analysis procedures involve a two-level hierarchical model and will explicitly account for the nesting of students in small instructional groups in the treatment condition but not in the control condition. A moderator analysis will be conducted by adding the interaction of condition with prior fractions knowledge, working memory, and attention. This project is supported by the EHR Core Research Program (ECR) which supports fundamental research on STEM teaching and learning.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.