Using Worked Examples to Support Secondary Mathematics Students in an Urban Setting

• In Event: Using Examples to Help Students Learn Mathematics: How, When, and With Whom to Use Worked Examples

Abstract

Purpose
College readiness involves a range of knowledge, attitudes, and skills to ensure success in credit bearing courses without the need for remediation (Conley, 2011). Remediation requires time and can reduce the likelihood that a student graduates with a degree. Students from low-income families are particularly at risk for needing remediation. This paper explores the use of comparison and worked examples to support urban high school students’ placement into credit-bearing mathematics courses.

Perspectives
Side-by-side worked examples have been effectively used in algebra classrooms to increase procedural knowledge and flexible strategy use (Rittle-Johnson & Star, 2007; Star, Caronongan, et al, 2015; Star, Pollack, et al., 2015). When worked examples are presented side-by-side, students can compare problems and strategies in order to notice important features, to understand why a particular strategy works, or to address a common error (if one example is incorrect). However, research involving comparison in more advanced courses is lacking. Moreover, there is a need to understand how this tool can be used to support learning and college readiness for students in urban settings.

Methods
Participants were 11th and 12th graders in a large, urban high school. According to the district website, 100% of the students were economically disadvantaged, 4% were proficient in mathematics, and 27% enrolled in college after graduation. Across six observations, attendance during the targeted courses ranged from 48-67%.

The teacher and student teacher incorporated Worked Example Pairs (WEPs) into the regular instruction about once per week, throughout the year. The WEPs targeted algebra topics such as linear equations, polynomials, and rational expressions. Based on end of year data, in Year 2 we created WEPs that targeted remedial topics (e.g., fractions, integers), encouraged more consistent use of WEPs, and included WEPs targeting functions and trigonometry.

Data
Students took a 50-item pretest and posttest based on a university mathematics placement exam, consisting of three sections: (1) remedial mathematics, (2) algebra, and (3) precalculus topics. No calculator was allowed.

Findings
In Year 1, there were no significant change from pretest to posttest for subtests 1 or 3. For subtest 2, there was a main effect for grade (12th graders scored higher) and a significant interaction (see Figure 1). Whereas 12th graders remained stable, 11th graders increased significantly on the algebra subtest, with a large effect size (p = .007, partial eta squared = .208). An analysis by topic revealed that the greatest improvements were in factoring, distributing, and properties of exponents.
In Year 2, the pattern was similar across grades. That is, there was a significant increase from pretest to posttest on the algebra subtest (F = 15.61, p = .001, partial eta squared = .394). Again, factoring, distributing, and properties of exponents showed the greatest gains. The increases for subtest 1 (p=.08, partial eta squared = .262) and subtest 3 (p=.068, partial eta squared = .295) approached significance for 12th graders, with large effect sizes.

Significance
Low levels of college attendance and high remediation needs for low-income students requires targeted attention. The use of WEPs with urban, high school students holds some promise.

Authors

• Kristie Jones Newton, Temple University

• Sue Kelley, Temple University

• Xiaojuan Ke, Temple University