The effect of manipulatives on mathematics achievement across different learning styles

The current study investigates the influence of manipulatives used in combination with traditional approaches to mathematics education and how varying amounts of time spent on manipulative use influence student achievement across different learning styles. Three learning environments were created that incorporated varying proportions of traditional teaching approaches and manipulative methods. In one of the learning environments, the teacher used strictly lecture- and exercise-based teaching activities, which are more conducive to abstract learning. Abstract learners showed higher academic performance compared with concrete learners in the environment where only traditional methods were used. For the other two environments, which utilised varying combinations of manipulative tools and traditional methods, the differences in the mathematics achievement levels among students of varying learning styles were not statistically significant. The study also showed that concrete learners demonstrated higher performance in mathematics when manipulatives were used than did their counterparts in the environment where only abstract activities were used; however, in the third learning environment, increasing the amount of manipulative use did not provide an extra benefit to concrete learners.     

The effects of teacher discourse on students’ discourse,problem-solving and reasoning during cooperative learning

The study sought to determine if teachers who are taught specific communication skills designed to challenge students’ cognitive and metacognitive thinking during cooperative learning use more challenging and scaffolding behaviours to mediate students’ learning than teachers who implement cooperative learning or small-group work who have not been taught these skills. The study involved 51 teachers in three conditions (cooperative + communication conditions; cooperative condition, group-work condition) and two groups of students from each of the above teachers’ classes. The results show that the teachers in the cooperative + communication condition used significantly more challenging and scaffolding behaviours than teachers in the group-work condition but not more than the teachers in the cooperative condition. The study also showed that the children in the cooperative + communication condition provided significantly more elaborative and help-giving behaviours to group members than peers in the other two conditions and they obtained higher scores on the follow-up reasoning and problem-solving activities than their peers in the group-work condition.     

美国教育技术专业校际合作的演化与发展——学习科学的崛起与学媒关系及教育技术领域的未来

“教学设计与技术教授会”（PIDT）及其前身“大学教学开发与技术协作组”（UCIDT）在40余年的发展历史中,以其独特的方式开启了教育技术专业校际合作的先河,见证了教育技术专业校际合作主题的时代转换,并推动了教育技术培训的范式变更,促进了教育技术专业建设的历史进程,为教育技术领域的健康发展作出了重要贡献。     

Differential effects of problem-solving demands on individual and collaborative learning outcomes

The effectiveness and efficiency of individual versus collaborative learning was investigated as a function of instructional format among 140 high school students in the domain of biology. The instructional format either emphasized worked examples, which needed to be studied or the equivalent problems, which needed to be solved. Because problem solving imposes a higher cognitive load for novices than does studying worked examples it was hypothesized that learning by solving problems would lead to better learning outcomes (effectiveness) and be more efficient for collaborative learners, whereas learning by studying worked examples would lead to better learning outcomes and be more efficient for individual learners. The results supported these crossover interaction hypothesis. Consequences of the findings for the design of individual and collaborative learning environments are discussed.     

The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency

A regression design was used to test the unique and interactive effects of self-efficacy beliefs and metacognitive prompting on solving mental multiplication problems while controlling for mathematical background knowledge and problem complexity. Problem-solving accuracy, response time, and efficiency (i.e. the ratio of problems solved correctly to time) were measured. Students completed a mathematical background inventory and then assessed their self-efficacy for mental multiplication accuracy. Before solving a series of multiplication problems, participants were randomly assigned to either a prompting or control group. We tested the motivational efficiency hypothesis, which predicted that motivational beliefs, such as self-efficacy and attributions to metacognitive strategy use are related to more efficient problem solving. Findings suggested that self-efficacy and metacognitive prompting increased problem-solving performance and efficiency separately through activation of reflection and strategy knowledge. Educational implications and future research are suggested.     

The influence of self-efficacy and working memory capacity on problem-solving efficiency

We investigated the influence of self-efficacy beliefs and working memory capacity on mathematical problem-solving performance, response time, and efficiency (i.e., the ratio of problems solved correctly to time). Students completed a letter-recoding task (Experiment 1) or an operation span task (Experiment 2), rated their self-efficacy for solving mental multiplication problems, and then solved similar problems of varying complexity. We tested the motivational efficiency hypothesis, which predicted that motivational beliefs, such as self-efficacy, increase problem-solving efficiency through focused effort and strategy use. Experiments 1 and 2 reported a significant effect for self-efficacy on problem-solving performance and efficiency, but limited effects for time. A self-efficacy by working memory interaction occurred in Experiment 1, suggesting self-efficacy is beneficial as demands on working memory increase. These findings suggested that self-efficacy increased problem-solving efficiency through strategic performance rather than faster solution times, and were consistent with the motivational efficiency hypothesis.     

Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks

This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layers – general strategies, which adopted Pólya’s four-stage problem-solving model, and specific strategies, which consisted of 17 different problem-solving heuristics such as ‘acting it out,’ ‘looking for a pattern,’ ‘working backwards,’ etc. Both similarities and differences in the representation of problem-solving procedures in the textbooks across the three countries were revealed and compared. The possible reasons for the similarities and especially for the differences were explored. Suggestions about how to improve the representation of problem-solving in mathematics textbooks were provided at the end of the study.

基于专题学习网站的课堂教学设计实例及解析

文章是在信息技术与课程整合的理念下,在对《大瀑布的葬礼》做教学设计、制作《大瀑布的葬礼》专题学习网站和具体的教学实践的前提下,将相关教学理论与教学实践结合起来分析了整个教学设计的思路及其理论依据,并在此基础上对整个教学设计与教学实践进行了反思。     

问题解决研究的一个世纪:回顾与前瞻

本文首先分析了问题解决的含义以及研究的重要性 ,然后重点梳理了过去一个世纪 ,特别是最近五十年里认知心理学关于问题解决研究的历史脉络 ,最后展望了今后的研究方向。笔者认为问题解决研究应该建立在信息加工与建构主义思想整合的基础上 ,坚持主客体相互作用观 ,把问题解决既看作信息加工过程 ,又视为知识建构过程 ,继续深入研究。     

Quality of geometry instruction and its short-term impact on students' understanding of the Pythagorean Theorem

This article presents findings from a German–Swiss video-based classroom study. The research examines how three basic dimensions of instructional quality impact the development of students' understanding of the Pythagorean Theorem. The study sample comprised 19 German and 19 Swiss mathematics classes. A three-lesson introductory unit on the Pythagorean Theorem was videotaped in all classes. Multilevel analyses revealed both classroom management and cognitive activation to have positive effects on mathematics achievement. The results also provide empirical evidence that cognitive activation and a supportive climate moderate the relationship between mathematics-related interest and mathematics achievement.     

Individual differences in the effect of relevant concreteness on learning and transfer of a mathematical concept

The concreteness of training materials influences learning and—perhaps more importantly—transfer. Building on prior research finding abstract representations best facilitated transfer to a game task, we conducted a similar study using training figures varying in concreteness but directly assessed transfer to modular arithmetic problems. Training figures: (a) were purely abstract, (b) were abstract but with features relevant to the transfer task, or (c) included additional concrete-relevant features. We hypothesized that concreteness—or number of relevant features—would be positively correlated with learning and transfer—especially among younger and/or lower-ability students. Although there was no overall difference in initial learning, the concrete-relevant and abstract-relevant features independently facilitated near-transfer, where concrete-relevant features supported lower-reasoning students. For far-transfer, eighth-graders benefited from the abstract-relevant features, whereas sixth-graders required additional concrete-relevant features. These findings suggest that concreteness interacts with learner and task characteristics to produce learning and transfer outcomes.     

教学设计的内涵及其应用

教学设计的内涵随着社会的发展得到不断的深化,对此不但可以从狭义和广义两方面来理解,还可以从绩效技术的发展、教学设计的科学性和艺术性等角度来认识。通过对教学设计的应用层面、应用模式等基本要素的简要分析,阐述了教学设计应用的两个现实问题。     

The popularization of China’s higher education and its influence on university mathematics education

This paper introduces the current situation of the popular Chinese university education, points out the impact of popularized Chinese higher education on its university mathematics education, and presents the actualities and existing problems of university mathematics education research in China.     

教学设计的概念及其对学科教学的影响

本文探讨了教学设计的发展、概念、特点以及对学科教学工作的影响,其成果有利于学科教学工作人员将教学设计理论运用到具体的课程中,提高课堂的教学效果。     

高等院校物理专业教育技术应用的现状与对策研究

在对高等院校物理专业教育技术应用现状进行调查研究的基础上，指出目前高等院校物理专业教育技术存在资料陈旧，缺乏层次，应用中目的性差，软、硬件设施落后等问题，有针对性地对高校物理专业教育技术的应用和提高提出对策和建议。     

基于任务驱动的中职《图形图像处理》课程教学设计

针对当前中职计算机课程教学中的＂重知识传授轻能力培养＂的问题,将＂任务驱动教学法＂引入中职计算机课程中,以《图形图像处理》课程为例,从教学设计、实施、评价等方面总结了任务驱动教学法的具体应用,并就应用进行了反思,希望能为相关的教学研究和实施带来启示.     

The effects of informational complexity and working memory on problem-solving efficiency

This study investigated the influence of informational complexity and working memory capacity on problem-solving efficiency. We examined two predictions of thesituational efficiency hypothesis, which states that the efficiency of problem solving varies as a function of situational constraints. One prediction is that informational complexity affects problem-solving efficiency. A second prediction is that working memory capacity affects problem-solving efficiency. Students completed a working memory task and solved abstract and concrete syllogisms. Participants solved abstract syllogisms more accurately than concrete syllogisms and spent more time solving abstract syllogisms. Thus participants demonstrated greater problem-solving efficiency when solving concrete syllogisms. Results indicate that there is a trade-off between problem-solving accuracy and problem-solving time when information differs with respect to informational complexity, a phenomenon we refer to as theefficiency paradox. Working memory capacity did not affect accuracy or efficiency. The results support the conclusion that problem-solving efficiency is situational and a function of the complexity of information. Educational implications and directions for future research are suggested.     

改革《中学数学教材教法》的实践与认识

论述了高师院校《中学数学教材教法》课程改革的必要性;介绍了天津师范大学数学教材教法课程在教学内容、教学方法及考核方式等方面的做法;简析了天津师范大学教材教法课程改革理论上的初步认识．