When and How Do Worked Examples Work? Use of Worked Examples in Textbook Homework Assignments

• In Event: 66.026 - Scaling Up Cognitive Learning Principles to Redesign a Mathematics Curriculum for Improved Learning

Abstract

Worked examples (WEs) provide powerful learning opportunities, but these opportunities are not always realized. Using the revised CMP2-R materials (6th and 8th grade content), we examined students’ thought processes when studying WEs, and compared the results to a theoretical model of desired learning with WEs (see Figure 1). To assess immediate learning from WEs, we developed matched sequences of a pretest item, WE, and posttest item. Ten middle school students completed a total of 24 such sequences while thinking aloud. Though encouraging that six of eight students reported in a post interview the WEs helped them learn, a quantitative pre-post comparison was less clear. Of 17 sequences where the pre-item was incorrect (the other 7 were correct on both pre and post), 4 ended with a correct post-item (clear evidence of learning), 13 involved an incorrect strategy on the post-item that was different from the strategy used on the pre-item (possible learning not revealed in simple correctness), and 4 repeated the same incorrect strategy on both the pre- and post-items (evidence of no learning). Our main goal of the analysis was to identify limitations in the meta-cognitive learning strategies students employ.

Students deviated from the desired model in several ways. During example study, some students only read part of the WE and gave no sign of any reflective processing, missing steps 4-9 in the model (Figure 1a). In one case, there was no verbal indication the student even noticed the WE (missed step 2). Furthermore, we found no explicit evidence of students extracting problem-solving strategies while studying the WEs (step 9) other than their attempts to answer the self-explanation questions in the WE text (step 7 also includes spontaneous explanation).

Students may demonstrate learning from a solution example (either a WE or a self-created solution from a prior problem) when solving a subsequent problem. As Figure 1b shows, students may refer back to prior examples either to induce relevant patterns/features (step 3) or to check their solution (step 7). One student finding the area of an irregular shape on a post-item verbalized “I’ll divide it like he did,” referring to the WE strategy (Figure 2). This example illustrates a student extracting a deep feature from a WE and adapting to the current problem.

Students also acquire shallow features from solution examples. A pre-item asked “Draw two different shapes with an area of 16 square units. What is the perimeter of each shape?” One student, started with a 4x4 square. The student chose a 2x8 rectangle for the second shape, and indicated that it too had a perimeter of 16 (suggesting use of a shallow strategy of copying the perimeter from the first shape).

Many studies demonstrating benefits of WEs have used older students, with better metacognitive skills (as illustrated in Figure 1). Although middle school students have experience with WEs, they may require more and repeated support to develop the necessary metacognitive skills to make the best use of them.

Authors

• Eliane Stampfer Wiese, Carnegie Mellon University

• Elizabeth McLaughlin

• Julie L. Booth, Temple University

• Kenneth R. Koedinger, Carnegie Mellon University