Comparing the Effects of Varied Worked Example Types for Teaching Fraction Equivalence

• In Event: Poster Session 04
  In Poster Session: PS 04 Topic - Education, Schooling

Abstract

Worked examples, or worked out problem solutions, improve learning in STEM, and some work suggests particular benefits of incorrect worked examples (Adams et al., 2014, Durkin & Rittle-Johnson, 2012), especially for students with low prior knowledge (Barbieri & Booth, 2016). However, results are inconclusive and the mechanism underlying these benefits remains unclear. The present study aims to compare the effectiveness of using incorrect examples versus and in combination with correct examples for teaching fraction equivalence to students with low prior knowledge, and to explore how student thinking evoked by the varied examples differs.
Based on an incorrect response to a screening question, 120 students (4th to 12th grade; 56 male, 46 female, 18 failed to respond) were entered into the study through the Assistments computerized tutoring system. Students were randomly assigned to one of five conditions: (1) Correct examples only, (2) Incorrect examples only, (3) Correct and incorrect examples presented sequentially, (4) Comparison of correct and incorrect examples, or (5) Problem-solving control (See Figure 1). After completing a pretest on fraction equivalence concepts, students in the four worked examples conditions saw a set of eight worked examples from their condition, and were asked to explain in their own words why the work in the example was correct or incorrect before solving a paired practice problem with feedback. Students in the control group simply solved practice problems with feedback. All students then completed a posttest.
Preliminary results suggest that example conditions that exposed students to both correct and incorrect examples helped student learning more than the conditions where there was only one type of example. An ANCOVA on posttest, controlling for pretest, revealed significant differences in performance between students who received both correct and incorrect examples (i.e., sequential and comparison conditions), either correct or incorrect examples (i.e., correct and incorrect conditions), and the problem solving control (F (2,105) = 6.591, p = .002). Both the control group and the group receiving both types of examples outperformed those receiving only one type. Additional analyses, to be completed by the time of the conference, will further explore the mechanism behind these differences, by examining whether there were differences in the correctness of student explanations evoked by the varied example types, and whether correctness of student explanations partially accounts for the effect of condition on posttest scores. Student responses have already been coded based on the coding scheme in Table 1. The hypothesis that correctness of student responses acts as a mediator of the effect of condition on posttest scores will be tested. Results point to the inclusion of both correct and incorrect worked examples when teaching students with low prior knowledge. Results of the pre-registered analysis will also contribute to our theoretical understanding on the mechanisms behind the benefits of incorrect worked examples when teaching mathematics.

Authors

• Brianna Devlin, University of Oregon
  Presenting Author

• Christina Areizaga Barbieri, University of Delaware
  Non-Presenting Author