通过对比进行学习:多重样例变异性与先前知识的作用

基于解一元一次方程两个关键特征(问题类型和解法)的单独变异和同时变异设计4种变异类型的多重样例。251名初一年级学生对比类型和解法的单独变异再对比两者的同时变异、对比解法或类型的单独变异再对比两者的同时变异、或者对比类型和解法的单独变异但没有对比两者的同时变异。结果显示变异类型与先前知识具有显著的交互作用:对于在前测中没有使用简便方法的学生,类型和解法先单独变异再同时变异的方法最能提高他们的变通性知识和概念性知识。相反对于在前测中有使用简便方法的学生,这种方法的学习效果最差。先前知识不同的学生学习时感知到不同的关键特征,多重样例的对比要基于学生学习的关键特征。     

多重样例变异性与先前知识对样例学习效果的影响述评

样例学习研究表明多重样例的学习效果好于单个样例。然而研究者关于如何有效设计多重样例得出了不同的发现。通过综述已有关于多重样例学习的实证研究,总结出两个尚未得到解决的问题：（1）多重样例之间的相似或相异程度应该如何;（2）学生的先前知识在多重样例学习中的作用如何。针对已有研究的局限性,本文指出,具有不同先前知识的学生学习时感受到不同的关键属性,多重样例应该基于学生学习时的关键属性设计特定的变易范式以帮助学生学习。     

先前知识和样例设计对学习分数乘法规则的影响

研究通过3个实验,以6年级学生为被试,考察了先前知识在分数乘法规则单、双内容样例学习中的作用以及“标记法”、“标记+注释法”样例设计方法对低先前知识学生学习双内容样例的促进效果。结果发现：（1）高先前知识学生学习两种样例的迁移成绩无显著差异,且均好于低先前知识学生的成绩;（2）低先前知识学生学习单内容样例的迁移成绩明显优于双内容样例;（3）与学习普通样例相比,低先前知识学生学习“标记法”双内容样例的后测成绩无显著差异,但学习“标记+注释法”设计的样例的成绩明显更好。结果表明,学生单、双内容样例的学习效果受其先前知识水平的影响;低先前知识学生未能从“标记法”设计的双内容样例中获益,但学习“标记+注释法”设计的样例效果更佳。     

材料的呈现方式如何影响学习的效果和过程

１引言传统教学和示例学习是两种不同的教学模式,它们的主要差别是学习材料的呈现方式不同。在传统的教学中,学习材料主要是以文字陈述的方式呈现的,并需要老师作细致的讲解．学生通过听讲获取知识,而在示例学习中,学习材料主要以例题或问题的形式呈现,学生通过考察例题和解决问题获取知识。在示例学习中,例题的呈现也可以有不同的方式。例如,可以采用“图文分离”的方式呈现,也可以采用“图文整合”的方式呈现。本文以“一元二次不等式解法”的学习为实验任务,用教师讲解、图文分离的样例、图文整合的样例等三种不同的方式呈现学…     

算术应用题二重变异样例学习的迁移效果

设计并运用了三种表面特征变异的二重样例和三种结构特征变异的二重样例,对二年级小学生解决算术应用题的迁移效果进行了实验研究。结果表明：一个原样例的学习就能明显促进了二年级小学生解决与原样例表面特征不同而结构特征相同的近迁移问题;学习三种表面特征变异的二重样例后没有产生明显的远迁移效果;而学习了三种结构特征变异的二重样例后产生了不同程度的远迁移效果,其中,规则平行组合二重样例学习的远迁移效果最好,其次是规则变异二重样例学习的远迁移效果,规则镶嵌组合变异二重样例学习的远迁移效果最差     

认知方和学习方式对运算性程序知识学习迁移的影响

探讨认知广度和学习方式两个因素对运算性程序知识学习迁移的影响。结果表明：（1）场独立性的学习在样例学习和试干学习中的运算性程序知识的迁移成绩均明显优于场依存性的学习;（2）样例学习比试干学习有着更高的迁移效应;（3）样例学习和试干学习在运算性程序知识的迁移中有着不同的特点和作用。     

样例多样性和流畅性信念对类别学习判断的影响

目的:通过三个实验考查样例特征、流畅性和信念对类别学习及其元认知判断的影响。方法:实验1采用2(样例特征)×2(测试类型)的组内设计以检验样例特征的作用; 实验2采用2(样例特征)×2(测试类型)×2(流畅性)的组内设计以检验流畅性的作用; 实验3采用2(样例特征)×2(测试类型)×2(流畅性信念)的混合设计以检验信念对类别学习判断的作用。结果表明:样例特征影响学习成绩、类别学习判断和流畅感; 流畅性不会影响类别学习判断; 原理解释能够有效建立“关于流畅性的信念”,且“关于流畅性的信念”对类别学习判断起作用。即样例多样性和流畅性信念对类别学习判断起作用,支持信念假说。     

表面概貌对原理运用的影响的实验研究

探讨样例与作业问题的表面概貌相似性对原理运用的影响作用。实验１扩大了Ｒｏｓｓ的研究材料中样例与测题表面概貌方面的差异程度,探讨两者的表面概貌相似性对原理运用的影响。实验２探讨样例与测题在表面概貌的事件类型方面发生改变的条件下,两者的表面概貌相似性对原理运用的影响。实验３探讨在样例与测题表面概貌有两个级别差异的条件下,两者的表面概貌相似性对原理运用的影响。３个实验均采用被试内设计,要求被试学习原理及样例后完成与样例的表面概貌有不同相似关系的测题。结果表明：（１）样例与问题的表面概貌对原理运用有影响,当两者表面概貌发生较大的变化尤其是在表面概貌的事件类型方面发生变化时,其表面概貌相似性对原理运用的影响就会明显地表现出来;（２）样例与问题的表面概貌对原理运用的影响作用,受到两者对象对应性质的制约,当对象对应相似时,其表面概貌相似就会促进解答测题时运用原理,而当两者的对象对应相反时,其表面概貌相似就会对原理运用产生干扰作用。据此可以认为,样例与作业问题表面概貌的相似性,不仅会影响原理的通达,而且也会影响原理的运用。Ｒｏｓｓ关于表面概貌相似与否不影响原理运用的结论应该予以修正。     

类别学习中的认知学习机制

采用归类任务,比较不同知识条件、不同特征呈现方式下,对非定义特征维度的掌握,验证类别学习的认知学习机制。结果发现对非定义特征维度的掌握,在样例特征固定位置呈现条件下较多,而在样例特征随机呈现条件下较少;在知识定义特征维度条件下较多,而在机械定义特征维度条件下较少。研究结果支持了类别学习的认知学习机制。     

类比比较样例对物理综合题学习迁移效果的影响

研究通过三个实验,比较了普通样例和类比比较样例在学习物理综合题中的效果,并在此基础上,进一步分析两种不同类型的类比比较样例对物理综合题学习的迁移效果以及“提示”这一样例设计方法的促进作用。结果发现:(1)通过类比比较样例学习物理综合题的效果优于普通样例;(2)相比于单综概念类比比较样例,综合概念类比比较样例能更好地提高物理综合题学习的近迁移成绩,但未提高其远迁移成绩;(3)提示能明显促进类比比较样例在物理综合题学习中的作用,但不同提示类型的影响无显著差异。该结果表明:类比比较样例是学习物理综合题的有效样例形式,而其中综合概念类比比较样例效果最佳;开放式提示和支架式提示均能较好地促进类比比较样例的学习。     

Learning about the equal sign: Does comparing with inequality symbols help?

This study investigated whether instruction that involves comparing the equal sign with other relational symbols is more effective at imparting a relational interpretation of the equal sign than instruction about the equal sign alone. Third- and fourth-grade students in a comparing symbols group learned about the greater than, less than, and equal signs and had the opportunity to compare the inequality symbols with the equal sign. Students in an equal sign group learned about the equal sign only. A third group of students served as a control group. Three aspects of students’ knowledge were assessed before and after the lesson: (a) conceptual understanding of the equal sign, (b) equation encoding, and (c) problem solving. Students in the comparing symbols group showed greater gains in conceptual understanding from pretest to posttest than students in the other two groups, and students in the comparing symbols group also scored higher on a posttest that assessed knowledge about inequality symbols and inequality problem solving. Thus, they learned about three symbols in the same amount of time as other students learned about the equal sign alone or not at all. Therefore, an instructional approach involving comparison can be an effective tool for learning about concepts in mathematics.     

Individual differences in the preference for worked examples: Lessons from an application of dispositional learning analytics

Worked-examples have been established as an effective instructional format in problem-solving practices. However, less is known about variations in the use of worked examples across individuals at different stages in their learning process in student-centred learning contexts. This study investigates different profiles of students' learning behaviours based on clustering learning dispositions, prior knowledge, and the choice of feedback strategies in a naturalistic setting. The study was conducted on 1,072 students over an 8-week long introductory mathematics course in a blended instructional format. While practising exercises in a digital learning environment, students can opt for tutored problem solving, untutored problem solving, or call worked examples. The results indicated six distinct profiles of learners regarding their feedback preferences in different learning phases. Finally, we investigated antecedents and consequences of these profiles and investigated the adequacy of used feedback strategies concerning ‘help-abuse’. This research indicates that the use of instructional scaffolds as worked-examples or hints and the efficiency of that use differs from student to student, making the attempt to find patterns at an overall level a hazardous endeavour.     

Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge

Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on algebraic feature knowledge and solving quadratic equations. Middle school algebra students (N = 206) were randomly assigned to four conditions. Two errorful conditions either displayed errors and asked students to explain or displayed correct solutions and primed students to reflect on potential errors by problem type. A correct example condition and problem-solving control group were also included. Studying and explaining common errors displayed in incorrect examples improved equation-solving ability. An aptitude-by-treatment interaction revealed that learners with limited understandings of algebraic features demonstrated greater benefits. Theoretical implications about using examples to promote learning from errors are considered in addition to suggestions for educational practice.     

It pays to compare: An experimental study on computational estimation

Comparing and contrasting examples is a core cognitive process that supports learning in children and adults across a variety of topics. In this experimental study, we evaluated the benefits of supporting comparison in a classroom context for children learning about computational estimation. Fifth- and sixth-grade students (N = 157) learned about estimation either by comparing alternative solution strategies or by reflecting on the strategies one at a time. At posttest and retention test, students who compared were more flexible problem solvers on a variety of measures. Comparison also supported greater conceptual knowledge, but only for students who already knew some estimation strategies. These findings indicate that comparison is an effective learning and instructional practice in a domain with multiple acceptable answers.     

Developing procedural flexibility: Are novices prepared to learn from comparing procedures?

Background. A key learning outcome in problem‐solving domains is the development of procedural flexibility, where learners know multiple procedures and use them appropriately to solve a range of problems (e.g., Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009 ). However, students often fail to become flexible problem solvers in mathematics. To support flexibility, teaching standards in many countries recommend that students be exposed to multiple procedures early in instruction and be encouraged to compare them. Aims. We experimentally evaluated this recommended instructional practice for supporting procedural flexibility during a classroom lesson, relative to two alternative conditions. The alternatives reflected the common instructional practice of delayed exposure to multiple procedures, either with or without comparison of procedures. Sample. Grade 8 students from two public schools (N= 198) were randomly assigned to condition. Students had not received prior instruction on multi‐step equation solving, which was the topic of our lessons. Method. Students learned about multi‐step equation solving under one of three conditions in math class for about 3 hr. They also completed a pre‐test, post‐test, and 1‐month‐retention test on their procedural knowledge, procedural flexibility, and conceptual knowledge of equation solving. Results. Novices who compared procedures immediately were more flexible problem solvers than those who did not, even on a 1‐month retention test. Although condition had limited direct impact on conceptual and procedural knowledge, greater flexibility was associated with greater knowledge of both types. Conclusions. Comparing procedures can support flexibility in novices and early introduction to multiple procedures may be one important reason.     

Implementation of training programs in self-regulated learning strategies in Moodle format: results of a experience in higher education

This paper tests the efficacy of an intervention program in virtual format intended to train studying and self-regulation strategies in university students. The aim of this intervention is to promote a series of strategies which allow students to manage their learning processes in a more proficient and autonomous way. The program has been developed in Moodle format and hosted by the Virtual Campus of the University of Oviedo. The present study had a semi-experimental design, included an experimental group (n=167) and a control one (n=206), and used pretest and posttest measures (self-regulated learning strategies' declarative knowledge, self-regulated learning macro-strategy planning-execution-assessment, self-regulated learning strategies on text, surface and deep learning approaches, and academic achievement). Data suggest that the students enrolled in the training program, comparing with students in the control group, showed a significant improvement in their declarative knowledge, general and on text use of learning strategies, increased their deep approach to learning, decreased their use of a surface approach and, in what concerns to academic achievement, statistically significant differences have been found in favour of the experimental group.     

Self-Explanations: How Students Study and Use Examples in Learning to Solve Problems

The present paper analyzes the self-generated explanations (from talk-aloud protocols) that “Good” and “Poor” students produce while studying worked-out examples of mechanics problems, and their subsequent reliance on examples during problem solving. We find that “Good” students learn with understanding: They generate many explanations which refine and expand the conditions for the action parts of the example solutions, and relate these actions to principles in the text. These self-explanations are guided by accurate monitoring of their own understanding and misunderstanding. Such learning results in example-independent knowledge and in a better understanding of the principles presented in the text. “Poor” students do not generate sufficient self-explanations, monitor their learning inaccurately, and subsequently rely heavily on examples. We then discuss the role of self-explanations in facilitating problem solving, as well as the adequacy of current AI models of explanation-based learning to account for these psychological findings.     

Kooperatives Lernen auf der Grundlage komplementären Vorwissens: ein Experiment und eine Simulationsstudie

Summary. Knowledge acquisition in collaborative problem solving is mainly realized by two activities: (1) when participants mutually impart their knowledge and (2) when they elaborate their knowledge together. Both activities are favoured by differences in the participants' prior knowledge. To support this thesis, an experimental study and a cognitive simulation are described. In the study, pairs of students were systematically taught complementary knowledge about qualitative resp. quantitative aspects of classical mechanics. During the subsequent collaborative problem solving the students successfully exchanged information about their complementary knowledge. Students who had been taught knowledge about qualitative aspects of physics gained more from their partners than students who had been taught knowledge about quantitative aspects. A cognitive model simulates problem solving and learning under the conditions set up in the study. In a simulation study based on the cognitive model it was possible to reconstruct the main results of the experimental study. Finally, the role of dialogue analysis and external representations are discussed and conclusions for the design of computer systems supporting collaborative problem solving are drawn. Zusammenfassung. Wissenserwerb bei der Kooperation vollzieht sich vor allem durch zwei Aktivitäten: (1) gegenseitige Wissensvermittlung und (2) gemeinsame Elaboration des Wissens. Für beides ist unterschiedliches Vorwissen der Beteiligten eine günstige Voraussetzung. Um diese These zu unterstützen, wird im vorliegenden Artikel eine experimentelle Studie dargestellt, in der Paaren von Schülerinnen systematisch komplementäres Vorwissen über qualitative bzw. quantitative Aspekte der klassischen Mechanik vermittelt wurde. Beim anschließenden kooperativen Problemlösen vermittelten die Schülerinnen sich gegenseitig erfolgreich Teile ihres Wissens. Schülerinnen, die zuvor Wissen über qualitative Aspekte der Physik erworben hatten, lernten dabei mehr von ihren Partnerinnen als Schülerinnen, die zuvor Wissen über quantitative Aspekte erworben hatten. Ein nachfolgend implementiertes kognitives Modell simuliert kooperatives Lernen und Problemlösen unter den Bedingungen der Studie und ist in der Lage, die zentralen Befunde der Studie zu rekonstruieren. In der Diskussion wird auf die Rolle des Dialogverhaltens und der Nutzung externer Repräsentationen für das kooperative Lernen und Problemlösen eingegangen. Abschließend werden Schlußfolgerungen für die Gestaltung von Computersystemen zur Unterstützung kooperativen Lernens und Problemlösens gezogen.