Learning Algebra from Worked Examples
Mathematics Teacher Volume 107, Number 7, ISSN 0025-5769
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the "activity of generating explanations to oneself" (Chi 2000, p. 164), especially "in attempt to make sense of new information" (p. 163) as one reads or studies. A "worked example problem," to be differentiated from "working an example problem," shows students an already completed problem and directs their attention to certain steps of the task as the focus of questioning. Self-explanation, then, specifically encourages students to identify the reasoning behind the steps that they see carried out and to explain why these steps were completed. This strategy of providing worked example problems coupled with prompts for self-explanation has recently been shown to influence students' learning positively in both traditional (Booth, Koedinger, and Paré-Blagoev 2011) and computer-based classrooms (Booth et al. 2013). A unique and powerful aspect of using worked examples in the classroom occurs with the inclusion of examples of both correct and incorrect solutions (subsequently referred to as correct and incorrect examples). Using incorrect examples forces students to think about the steps that have been carried out and the reasons why these actions are wrong and then to confront their own possible underlying misconceptions. The desired result is a deeper understanding of mathematics for all students, regardless of prior skill level. By using probing questions that require students to explain a previously worked example, teachers can ensure that students are making sense of what solving equations really entails. Students also engage in reasoning while constructing explanations and strengthen critical thinking skills while critiquing the correct or incorrect solutions. These tasks, carried out in conjunction with the Common Core State Standards, serve to promote deeper understanding of solving equations, which will help students of all ability levels prepare for higher-level mathematics. This article explores using examples in a computer-based activity, using examples in a traditional classroom, the student experience, and targeting student misconceptions.
Lange, K.E., Booth, J.L. & Newton, K.J. (2014). Learning Algebra from Worked Examples. Mathematics Teacher, 107(7), 534-540.