Getting the point: Tracing worked examples enhances learning

Embodied cognition and evolutionary educational psychology perspectives suggest pointing and tracing gestures may enhance learning. Across two experiments, we examine whether explicit instructions to trace out elements of geometry worked examples with the index finger enhance learning processes and outcomes. In Experiment 1, the tracing group solved more test questions than the non-tracing group, solved them more quickly, made fewer errors, and reported lower levels of test difficulty. Experiment 2 replicated and extended the findings of Experiment 1, providing evidence for a performance gradient across conditions, such that students who traced on the paper outperformed those who traced above the paper, who in turn outperformed those who simply studied by reading. These results are consistent with the activation of an increasing number of working memory channels (visual, kinaesthetic and tactile) for learning-related processing.     

Finding and fixing errors in worked examples: Can this foster learning outcomes?

Learning from worked examples is an effective learning method in well-structured domains. Can its effectiveness be further enhanced when errors are included? This was tested by determining whether a combination of correct and incorrect solutions in worked examples enhances learning outcomes in comparison to correct solutions only, and whether a mixture of correct and incorrect solutions is more effective when the errors are highlighted. In addition, the effectiveness of fostering self-explanations was assessed. In Experiment 1, the participants learned to solve probability problems under six conditions that constituted a 2 × 3-factorial design (Factor 1: correct and incorrect solutions with highlighting the errors vs. correct and incorrect solutions without highlighting the errors vs. correct solutions only; Factor 2: prompting written self-explanations vs. no prompts). An aptitude-treatment interaction was found: providing correct and incorrect solutions fostered far transfer performance if learners had favourable prior knowledge; if learners had poor prior knowledge correct solutions only were more favourable. Experiment 2 replicated this interaction effect. Thus, a mixture of correct and incorrect solutions in worked examples enhanced learning outcomes only for “good” learners. In addition, Experiment 2 showed that confronting learners with incorrect solutions changed the quality of their self-explanations: on the one hand, new types of effective self-explanations could be observed, but on the other hand the amount of the very important principle-based self-explanations was substantially reduced. A possible measure to prevent this negative side effect of incorrect solutions is discussed.     

Using heuristic worked examples to promote inquiry-based learning

Inquiry learning can be facilitated by having students investigate the domain through a computer simulation and express their acquired understanding in a runnable computer model. This study investigated whether heuristic worked examples can further enhance students' inquiry behaviour, the quality of the models they create, and their domain knowledge. High-school students were offered a simulation of an electrical circuit and a modelling tool. Students in the experimental condition (n = 46) could consult heuristic worked examples that explained what activities were needed and how they should be performed. Students in the control condition (n = 36) did not receive this support. Cross-condition comparisons confirmed that heuristic worked examples improved students' inquiry behaviour and enhanced the quality of their models. However, few students created a model that reflected full understanding of the electrical circuit, and the expected between-group difference in posttest scores failed to appear. Based on these findings, improvements to the design of heuristic worked examples are proposed.     

Effects of worked examples, example-problem, and problem-example pairs on novices’ learning

Research has demonstrated that instruction that relies more heavily on example study is more effective for novices’ learning than instruction consisting of problem solving. However, ‘a heavier reliance on example study’ has been implemented in different ways. For example, worked examples only (WE), example-problem pairs (WE-PS), or problem-example pairs (PS-WE) have been used. This study investigated the effectiveness of all three strategies compared to problem solving only (PS), using electrical circuits troubleshooting tasks; participants were secondary education students who were novices concerning those tasks. Based on prior research, it was hypothesized and confirmed that WE and WE-PS would lead to lower cognitive load during learning and higher learning outcomes than PS. In addition, the open questions of whether there would be any differences between WE and WE-PS, and whether there would be any differences between PS-WE and PS were explored. Results showed no differences between WE and WE-PS or between PS-WE and PS. This study can inform instructional designers on which example-based learning strategies to implement: it does not seem necessary to alternate example study and problem solving, but when doing so, example-problem pairs should be used rather than problem-example pairs.     

Case-based learning with worked examples in complex domains: Two experimental studies in undergraduate medical education

To investigate the effects of example format (erroneous examples vs. correct examples) and feedback format (elaborated feedback vs. knowledge of results feedback) on medical students' diagnostic competence in the context of a web-based learning environment containing case-based worked examples, two studies with a 2 × 2 design were conducted in the laboratory. In the first study (domain: arterial hypertension; N = 153) erroneous examples were effective in combination with elaborated feedback with respect to strategic and conditional knowledge. In the second study (domain: hyperthyroidism, N = 124), elaborated feedback supported all aspects of diagnostic competence, especially conditional knowledge.     

Effects of worked examples on step performance in solving complex problems

The instructional effect of worked examples has been investigated in many research studies. However, most of them evaluated the overall performance of the participants in solving post-intervention problems, rather than individual step performance in multi-step problems. The two experiments reported in this article investigated the relations between using worked examples and individual step performance in solving isomorphic problems. In Experiment 1, the effect of worked examples was found for overall performance for novice learners, whereas this effect was gradually reduced from Step 1 (the most difficult one) at which the effect was the strongest, to Step 3 (the easiest one) at which the effect was the weakest or even disappeared. In Experiment 2, relatively more knowledgeable participants learned the same sets of materials, and no effect of worked examples was found for either overall performance or individual step performance. Learner levels of expertise and levels of element interactivity were used to explain the results.     

Improving problem solving with subgoal labels in expository text and worked examples

In highly procedural problem solving, procedures are typically taught with context-independent expository text that conceptually describes a procedure and context-dependent worked examples that concretely demonstrate a procedure. Subgoal labels have been used in worked examples to improve problem solving performance. The effect of subgoal labels in expository text, however, has not been explored. The present study examined the efficacy of subgoal labeled expository text and worked examples for programming education. The results show that learners who received subgoal labels in both the text and example are able to solve novel problems better than those who did not. In addition, subgoal labels in the text appear to have a different, rather than an additive, effect on learners compared to subgoal labels in the example. Specifically, subgoal labels in the text appear to help the learner articulate the procedure, and subgoal labels in the example appear to help the learner apply the procedure.     

Example-based learning: The benefits of prompting organization before providing examples

Example-based learning often follows a design in which learners first receive instructional explanations that communicate new principles and concepts and second examples thereof. In this setting, using the knowledge components of the instructional explanations to explain the examples (i.e., generating principle-based self-explanations) is considered to be a highly important learning process. However, a potential suboptimality of this learning process is that it scarcely requires learners to organize the content of the instructional explanations into coherent mental representations. Thus, in two experiments we investigated whether prompting learners to organize the content of the instructional explanations before providing them with the examples (and self-explanation prompts) enhances the effectiveness of example-based learning. We consistently found that organization prompts fostered learning regardless of whether the learners also received self-explanation prompts. Hence, in example-based learning, learners should be prompted to not only generate principle-based self-explanations but also to organize the content of the instructional explanations.     

Effects of different sequences of examples and problems on motivation and learning

Recent research has shown that example study only (EE) and example-problem pairs (EP) were more effective (i.e., higher test performance) and efficient (i.e., attained with less effort invested in learning and/or test tasks) than problem-example pairs (PE) and problem solving only (PP). We conducted two experiments to investigate how different example and problem-solving sequences would affect motivational (i.e., self-efficacy, perceived competence, and topic interest) and cognitive (i.e., effectiveness and efficiency) aspects of learning. In Experiment 1, 124 technical students learned a mathematical task with the help of EEEE, EPEP, PEPE, or PPPP and then completed a posttest. Students in the EEEE Condition showed higher posttest performance, self-efficacy, and perceived competence, attained with less effort investment, than students in the EPEP and PPPP Condition. Surprisingly, there were no differences between the EPEP and PEPE Condition on any of the outcome measures. We hypothesized that, because the tasks were relevant for technical students, starting with a problem might not have negatively affected their motivation. Therefore, we replicated the experiment with a different sample of 81 teacher training students. Experiment 2 showed an efficiency benefit of EEEE over EPEP, PEPE, and PPPP. However, only EEEE resulted in greater posttest performance, self-efficacy, and perceived competence than PPPP. We again did not find any differences between the EPEP and PEPE Condition. These results suggest that, at least when short training phases are used, studying examples (only) is more preferable than problem solving only for learning. Moreover, this study showed that example study (only) also enhances motivational aspects of learning whereas problem solving only does not positively affect students’ motivation at all.     

Example-based learning: Effects of different types of examples on student performance,cognitive load and self-efficacy in a statistical learning task

Previous research has indicated the disconnect between example-based research focusing on worked examples (WEs) and that focusing on modeling examples. The purpose of this study was to examine and compare the effect of four different types of examples from the two separate lines of research, including standard WEs, erroneous WEs, expert (masterly) modeling examples, and peer (coping) modeling examples, on student performance (knowledge retention, near transfer, and far transfer), cognitive load, and self-efficacy. One hundred and sixteen students participated in the study by undergoing computer-based instruction in one of the four versions differing in how examples were provided. The results showed that, overall, expert modeling examples were most effective in promoting knowledge retention, near transfer, and far transfer, while peer modeling examples were shown to be superior in fostering self-efficacy among the four different types of examples.     

The effects of worked examples in computer-based instruction: focus on the presentation format of worked examples and prior knowledge of learners

The aim of this study is to investigate the effects of presentation formats of worked examples and the interaction effects between the presentation formats of worked examples and the prior knowledge of learners. An investigation with 97 middle school students working in four conditions (CPWE, CWE, PWE, and the control group) was conducted. The results indicate that CPWE was the most effective condition in retention and transfer. In addition, a partial expertise reversal effect was revealed in the element transfer test. High prior knowledge learners in both CPWE and PWE were superior to those who were in CWE and the control group, while low prior knowledge learners in CPWE were superior to those who were in other conditions.     

Simulations with Elaborated Worked Example Modeling: Beneficial Effects on Schema Acquisition

Worked examples have been effective in enhancing learning outcomes, especially with novice learners. Most of this research has been conducted in laboratory settings. This study examined the impact of embedding elaborated worked example modeling in a computer simulation practice activity on learning achievement among 39 undergraduate students within a classroom environment. The students from one introductory forensic science course were randomly assigned to one of two groups that worked through computer-based simulations containing worked example modeling conditions presented in varied order. The computer software administered the modeled simulations, prior knowledge test, pretest, posttests, and a second domain test. Findings from this study suggest that embedded worked example modeling within practice simulations can be an effective method for transfer of learning with novice learners. This article describes the dissertation study completed by Debra K. Meier under the guidance of David W. Brooks at the University of Nebraska, Lincoln.     

Relations between the worked example and generation effects on immediate and delayed tests

The contradiction between the worked example effect that occurs when learners presented with more instructional guidance learn more than learners presented with less guidance and the generation effect that occurs when the reverse result is obtained can be resolved by the suggestion that the worked example effect is obtained using materials high in element interactivity, whereas simpler, low element interactivity materials result in the generation effect. A 2 (guidance: low vs. high) × 2 (element interactivity: low vs. high) × 2 (expertise: low vs. high) experiment investigated this hypothesis with high school trigonometry learners. On an immediate test, high guidance reflecting a worked example effect was found for novices, but a generation effect was obtained for more knowledgeable learners. In contrast, on a delayed test, a three-way interaction between guidance, element interactivity and expertise was found. This interaction was caused by a worked example effect for material high in element interactivity and a generation effect for material low in element interactivity for novices while for more knowledgeable learners, a generation effect was obtained for both low and high element interactivity materials. These results suggest firstly, that both the worked example and generation effects may be more likely on delayed than immediate tests and secondly, that the worked example effect relies on high element interactivity material while the generation effect relies on low element interactivity material.     

The effect of worked examples on student learning and error anticipation in algebra

Instructional Science - The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students...     

Cognitive load theory and aging: effects of worked examples on training efficiency

Cognitive load theory (CLT) is aimed at developing training material that efficiently makes use of the available cognitive processing capacity and stimulates the learner's ability to use acquired knowledge and skills in new situations. It is claimed that CLT-based training formats meet the cognitive abilities of elderly learners particularly well. That is, cognitive aging brings about several declines of working memory, which impede the acquisition of complex cognitive skills. By making an optimal use of the ‘remaining’ cognitive resources, learning can be enhanced. For that purpose, CLT provides a promising range of training formats that have proven their effectiveness relative to conventional formats in young adults. This article presents an experimental study (N=54) aimed at the efficiency of worked examples as a substitute for conventional practice problems in training both elderly and young adults. According to CLT, studying worked examples is a more efficient means of training complex skills than solving conventional problems. As predicted, the results show that — with respect to the elderly — the efficiency of studying worked examples is higher than the efficiency of solving conventional problems in that less training time and cognitive load leads to a comparable level of performance.     

Problem Solving in Geometry: Comparing the effects of non-goal specific instruction and conventional worked examples

This study examines the extended effects of an instructional program designed to enhance schema development by using non-goal specific problems, in the teaching of geometry to high school students in need of remedial tuition. A multiple baseline across-subjects experimental design was used to compare the effects of this program with another method of teaching this subject--that is, using worked examples. This methodology provides detailed information on the shifts and changes associated with learning processes for particular individuals during the actual process of schema acquisition. Dependent measures included test performance, error analysis, time analysis, directionality and generalisation. Results indicate that participants in the non-goal specific group showed greater improvements, solving problems faster, more efficiently, more accurately and with fewer errors and greater consistency. These findings are discussed in terms of their implications for the design of mathematics instructional material.     

Teaching and learning floating and sinking: A meta-analysis

Floating and sinking (FS) is a key topic in science education, both at primary and secondary levels. The interpretation of FS phenomena, however, is challenging due to the difficulty of the scientific concepts and explanatory models involved (e.g., density, buoyancy), along with students' everyday experiences, which conflict with scientific explanations. Consequently, many studies over the last few decades have investigated how FS could be taught effectively to students of different ages while utilizing multiple teaching approaches. This meta-analysis summarizes findings from 69 intervention studies on teaching FS conducted between 1977 and 2021. Over all studies, we estimated a mean effect size of g = 0.85 (95% CI = 0.71, 0.99). This large effect size demonstrates that, although FS is a challenging concept, teaching FS is effective even in elementary school. Moreover, in a moderator analysis, we investigate the effect of intervention characteristics, students' age, as well as study design, and assessment features on the mean study effect size. To analyze the effect of these moderator variables, we use a three-level hierarchical meta-regression model for dealing with multiple effect sizes from single studies. We found two intervention characteristics that explain variance in study effect sizes: longer lasting interventions result in larger effect sizes and interventions where hands-on experiments are applied are more effective than those utilizing virtual experiments. Furthermore, studies with a treatment-control group comparison have significantly smaller effect sizes than studies with a pre-post design. We discuss the implications of our findings regarding the moderator variables for effective teaching of FS and further research on FS.