Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors another student might make. Five Algebra 1 sections at a suburban mid-Atlantic public high school participated amid an early equation-solving unit. During teacher-led instruction, all five sections examined 2-3 correct worked examples. The final example varied across conditions. One section received an additional correct worked example. Two sections examined an incorrect worked example. The remaining two sections engaged in an error anticipation exercise where the teacher wrote an equation on the board and asked the students to predict errors another student might make in solving. The study measured conceptual and procedural knowledge, encoding ability, and student-generated errors. Although no meaningful significant differences were found, students in the error anticipation condition saw no difference in performance in conceptual and procedural items versus those who examined incorrect worked examples. Analysis that combined the error anticipation and incorrect worked examples conditions showed that those students trended toward outperforming those who examined correct examples only on procedural items. These results support further examination of error anticipation as a worthwhile instructional activity. / Math & Science Education

The current study assessed an error reflection intervention on Algebra I students’ conceptual and procedural knowledge and sense of belonging to mathematics. Also of interest was whether perceptions of the functionality of errors mediated the effect of condition on learning and sense of belonging to mathematics. Middle school students (N = 207) were randomly assigned within classroom to one of four conditions: 1) a Problem-Solving Control group, 2) a Correct Examples Control group, 3) a Correct Examples Error Reflection condition that promoted reflection on hypothetical errors through self-explanation prompts, or 4) an Incorrect Examples Error Reflection condition that promoted reflection on displayed errors within the example through self-explanation prompts. Conceptual and procedural knowledge, sense of belonging to mathematics and perceived functionality of errors were measured pre- and post-intervention. After controlling for unanticipated clustering effects, results suggest that reflecting on and explaining errors within a worked examples intervention is just as effective at promoting learning as traditional problem solving alone or working with traditional correct worked examples and written self-explanation prompts. Students’ sense of belonging to mathematics or perceived functionality of errors for learning were high at the start of the study and remained so throughout the intervention. Perceptions of the functionality of errors were unrelated to learning and sense of belonging to mathematics. The limited size of the minority population in the sample did not allow for exploration of differential effects of condition for underrepresented minority (URM) students. However, these students reported lower feelings of belonging to mathematics than non-URM students. Implications for theory and practice are discussed. / Educational Psychology