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.     

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.     

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.     

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.     

解析几何问题中简化运算的有效途径

解析几何是用代数的方法研究几何问题的一门数学学科,因此在解析几何题的运算中,代数运算不可避免;若使用方法不当,往往会使解题过程繁琐冗长,以至很难解答出问题结果;因此如何选取合理解题途径与方法简化运算,就显得尤为重要．本文就该问题谈一谈自己在解题中的几点体会,仅供读者参考．     

向量法解立体几何求角问题

为适应高中数学教材改革的新情况,需要研究用向量方法求解立体几何的各种问题.本文以近几年的高考题为例,来讨论如何用向量方法解决立几求角的问题.立体几何中的求角问题,大致有三种类型,即:求二异面直线的夹角;求两个平面的夹角--二面角的平面角;以及求直线与平面的夹角.现分别举例说明如下.     

运用法向量巧解立几题

向量作为一种数学工具引入新教材,为立几教学注入了新的活力．原来对空间想象能力要求较高的作二面角的平面角和作异面直线的公垂线等问题,现在已弱化为法向量与其它向量之间简单的代数运算,从而大大提高了学生学习立几的兴趣和效果．本文就如何用法向量求空间角和距离问题作一归纳,供读者参考．     

空间几何问题解决过程中工作记忆资源分配策略的个体差异

中学生工作记忆资源分配策略的研究结果表明:(1)随着问题难度的增加,首次内部思考时间也在增加.在解决简单问题时,学优生与学困生的首次内部思考时间没有显著差异,但是在解决中等题和难题时,学优生与学困生的首次内部思考时间存在显著差异.(2)学优生使用外部策略的总频数呈现随着数学问题难度的增大而增加的趋势,而学困生使用外部策略的频数呈下降的趋势.这说明,较学困生而言,学优生能够较合理地利用工作记忆资源.     

Preparatory effects of problem solving versus studying examples prior to instruction

Instructional Science - The Productive Failure (PF) approach prompts students to attempt to solve a problem prior to instruction – at which point they typically fail. Yet, research on PF...     

场认知风格与图式水平对初中生几何问题表征的影响

考察中学生的场认知风格、图式水平对其几何问题解决成绩、问题表征方面存在的影响,结果表明：高图式水平组的学生比低图式水平组的学生更偏爱使用图式表征的方式来表征问题;在表征平面几何问题时,学生最经常出现的是偏离性表征错误;低图式水平组的学生比高图式水平组的学生更容易出现表征错误;场依存者比场独立者更容易受到无关信息的干扰。     

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.     

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.     

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).     

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.     

法律课教学中案例的使用及选择

法律基础知识课程的教学不能没有案例,缺少案例的法律教学将是枯燥乏味、苍白无力的.而案例的使用能否达到预期的目的,取得理想的效果,又取决于使用案例的方法是否得当及选用的案例是否恰当.下面,笔者就法律基础知识课程教学中案例的使用及选择谈点粗浅的体会.……     

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.     

从“应用题”到“解决问题”——小学数学解决问题的教育价值与教学研究

从应用题到解决问题,这绝不仅是名称上的变化.弄清楚这其中变化的实质,有助于我们更好地继承应用题教学宝贵的、成功的经验,也有助于我们更好地开展解决问题的教学.该文立足于应用题和解决问题的内涵,探讨解决问题的教育价值,并结合当今小学数学教学实际,提出了解决问题的教学建议.