Effect of worked examples and Cognitive Tutor training on constructing equations

Algebra students studied either static-table, static-graphics, or interactive-graphics instructional worked examples that alternated with Algebra Cognitive Tutor practice problems. A control group did not study worked examples but solved both the instructional and practice problems on the Cognitive Tutor (CT). Students in the control group requested fewer hints and made fewer errors on the CT practice problems but required more learning time on the instructional examples. There was no difference among the four groups in constructing equations on a paper-and-pencil posttest or on a delayed test that included training and transfer problems. However, students who studied worked examples with a table were best at identifying the meaning of the equation components. The concept of transfer-appropriate processing (the overlap between instructional task and assessment task) aided our interpretation of the findings. Although the CT had a short-term effect on reducing errors and hint requests on CT practice problems, the worked examples were as effective on delayed paper-and-pencil tests. The subsequent construction of a new module for the Animation Tutor (Reed and Hoffman, Animation Tutor: Mixtures. Instructional software, 2011) used both the interactive-graphics and static-table worked examples to take advantage of the complementary strengths of different representations (Ainsworth, Learn Instr 16:183–198, 2006).     

Tracing worked examples: effects on learning in geometry

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to isolate the variable of drawing attention. Students employing the tracing method obtained higher transfer test scores compared to those employing the cueing and non-tracing methods, rating the far transfer test as easier. The tracing effect was verified to have a greater impact on learning than solely focusing learners’ attention. Experiment 2 compared the learning effects among three methods – tracing with the index finger, tracing with a computer mouse, and observing others tracing. Students who merely observed tracing obtained lower far transfer scores than those who traced either with their finger or with the mouse, rating the tests as more difficult. There was no significant difference between the other two groups. Tracing promotes learning more than merely observing tracing. The learning benefits of tracing partly stem from the fact that it is action-based and can be generalized to mouse tracing.     

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.     

Redirecting learners' attention during training: effects on cognitive load,transfer test performance and training efficiency

Cognitive load theory provides guidelines for improving the training of complex cognitive skills and their transfer to new situations. One guideline states that extraneous cognitive load that is irrelevant to the construction of cognitive schemata should be minimised. Experiment 1 (N=26) compares completion problems, conventional problems, and a learner-controlled condition in which learners may choose between problem formats. Completion problems decrease cognitive load during training and have a zero or positive effect on transfer performance. A second guideline states that germane cognitive load that is directly relevant to schema construction should be optimised. In Experiment 2 (N=69) practice schedules of either high or low contextual interference are compared (HCI and LCI). HCI increases cognitive load during training and shows a trend towards higher transfer performance. Experiment 3 (N=87) combines both guidelines in a factorial experiment with the factors problem format (completion vs. conventional) and contextual interference (HCI vs. LCI). It is hypothesised that redirecting attention from extraneous to germane processes will improve training efficiency, i.e. positively affect the balance between cognitive load during training and transfer test performance. In support of this hypothesis, it is found that the completion-HCI group shows highest training efficiency. But transfer test performance for this group is disappointing. The results are discussed in relation to the operationalisation of HCI in combination with completion problems.     

Cognitive load theory and the effects of transient information on the modality effect

Based on cognitive load theory and the transient information effect, this paper investigated the modality effect while interpreting a contour map. The length and complexity of auditory and visual text instructions were manipulated. Experiment 1 indicated that longer audio text information within a presentation was inferior to the equivalent longer visual text information demonstrating a reversal of the modality effect due to transient information imposing a heavy working memory load. However, the expected modality effect was not obtained from the equivalent shorter auditory text presentation compared to shorter visual text information. It was hypothesised that the shorter text still contained too much auditory information for working memory to readily process. Experiment 2 further decreased the shorter auditory text information which then resulted in a traditional modality effect including a modality by text length interaction in which shorter, audio-visual information was better than visual only information but longer, audio-visual information was worse than visual only information.     

Cognitive load theory and music instruction

In two experiments, the principles of cognitive load theory were applied to the design of alternatives to conventional music instruction hypothesised to facilitate learning. Experiment 1 demonstrated that spatial integration of visual text and musical notation, and dual‐modal delivery of auditory text and musical notation, were superior to the spatially separated placement of the same visual materials, demonstrating the split‐attention and modality effects respectively. In Experiment 2 there were four conditions differentiated by the presence or absence of musical notation and the simultaneous or successive presentation of auditory music, written explanations, and musical notation. Results indicated that the presence of music notation had no effects, but that the simultaneous presentation of either two or three information sources was superior to successive presentation. These results provide further empirical support for the need to consider cognitive load theory when designing instruction in any domain.     

Cognitive load theory and educational technology

Educational technology research and development - Cognitive load theory provides instructional recommendations based on our knowledge of human cognition. Evolutionary psychology is used to assume...     

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.     

Effects of process-oriented worked examples on troubleshooting transfer performance

In the domain of electrical circuits troubleshooting, a full factorial experiment investigated the hypotheses that (a) studying worked examples would lead to better transfer performance than solving conventional problems, with less investment of time and mental effort during training and test, and (b) adding process information to worked examples would increase investment of effort during training and enhance transfer performance; whereas adding it to conventional problems would increase investment of effort, but would not positively affect transfer performance. The first hypothesis was largely confirmed by the data; the second was not: adding process information indeed resulted in increased investment of effort during training, but not in higher transfer performance in combination with worked examples.     

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.     

Cognitive efficiency: Toward a revised theory of media

Within and beyond the field of educational technology, Richard Clark's writings are widely believed to have shown that any number of media are equally capable of delivering any instruction, so that media choices are about cost and efficiency but not about cognition and learning (Clark, 1983; 1994b). However, if it is accepted that one type of efficiency is cognitive efficiency, then it follows that media choices are often about cognition and learning and can profit from an understanding of cognitive processes. Media and learning can then be reconnected in limited ways that do not compromise any of Clark's main points, and doing this will bring media work into line with current research into the role of surface information codes.     

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.     

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,the transient information effect and e-learning

When using modern educational technology, some forms of instruction are inherently transient in that previous information usually disappears to be replaced by current information. Instructional animations and spoken text provide examples. The effects of transience due to the use of animation-based instructions (Experiment 1) and spoken information under audio-visual conditions (Experiment 2) were explored in a cognitive load theory framework. It was hypothesized that for transient information presented in short sections, animations would be superior to static graphics, due to our innate ability to learn by observing. For transient information in long sections, animations should lose their superiority over static graphics, due to working memory overload associated with large amounts of transient information. Similarly, the modality effect under which audio-visual information is superior to visual only information should be obtainable using short segments but disappear or reverse using longer segments due to the working memory consequences of long, transient, auditory information. Results supported the hypotheses. The use of educational technology that results in the transformation of permanent into transitory information needs to be carefully assessed.     

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.     

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.     

The expertise reversal effect and worked examples in tutored problem solving

Prior research has shown that tutored problem solving with intelligent software tutors is an effective instructional method, and that worked examples are an effective complement to this kind of tutored problem solving. The work on the expertise reversal effect suggests that it is desirable to tailor the fading of worked examples to individual students’ growing expertise levels. One lab and one classroom experiment were conducted to investigate whether adaptively fading worked examples in a tutored problem-solving environment can lead to higher learning gains. Both studies compared a standard Cognitive Tutor with two example-enhanced versions, in which the fading of worked examples occurred either in a fixed manner or in a manner adaptive to individual students’ understanding of the examples. Both experiments provide evidence of improved learning results from adaptive fading over fixed fading over problem solving. We discuss how to further optimize the fading procedure matching each individual student’s changing knowledge level.     

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.