数学问题解决系统案例分析及启示

近年来,学生的"数学问题解决"能力越来越受到重视,我国已将学生的数学问题解决能力作为数学的教学目标之一。在信息技术迅猛发展的今天,如何借助信息技术和人工智能更好地帮助学生提高问题解决能力成为我国研究者亟待解决的一个问题。文章介绍了在美国取得较好反响的两个问题解决系统——贾斯珀系列和IMMEX系统,并分析了这两套系统各自的特点,最后为建设更加完善的数学问题解决系统提出了自己的建议。     

Color research and its application to the design of instructional materials

This paper is divided into three major sections: Color as Seen—Physiological; Color as Seen—Psychological; and Color and Learning. The first section deals with color adaptations and the effects of color on acuity and relates these to the design of instructional materials. The second section covers color meanings and preferences, as well as color harmony and the relationships of these factors to the design of instructional materials. The third section provides an overview of research on color and learning. It includes the effects of color on attention, search tasks, other objective and non-objective measures of learning, and the use of color for cathode ray tube (CRT) displays. Although the measurable effects of color may be slight, colored materials are preferred and they are used almost universally. Therefore, designers of instructional materials need to use color wisely by paying attention to the physiological and psychological effects of color and the effect of color on learning.     

The CLIA-model: A framework for designing powerful learning environments for thinking and problem solving

A major challenge for education and educational research is to build on our present understanding of learning for designing environments for education that are conducive to fostering in students self-regulatory and cooperative learning skills, transferable knowledge, and a disposition toward competent thinking and problem solving. Taking into account inquiry-based knowledge on learning and recent instructional research, this article presents the CLIA-model (Competence, Learning, Intervention, Assessment) as a framework for the design of learning environments aimed to be powerful in eliciting in students learning processes that facilitate the acquisition of productive knowledge and competent learning and thinking skills. Next, two intervention studies are described that embody major components of this framework, one focussing on mathematical problem solving in primary school, and a second one relating to self-regulatory skills in university freshmen. Both studies were carried out in parallel with the development of the framework, and were instrumental in identifying and specifying the different components of the model. They yielded both promising initial support for the model by showing that CLIA-based learning environments are indeed powerful in facilitating in students the acquisition of high-literacy learning results, especially the acquisition and transfer of self-regulation skills for learning and problem solving.     

生成性理念指导下的探究式教学活动设计

针对探究式教学过程形式化、生成性价值鲜有体现等问题,借助智慧课堂在动态数据采集、分析、反馈方面的优势,以探究流程为主要脉络,在探究活动设计中引入生成性教学理念。从学情诊断、目标设定、情境创设、活动开展、评价实施、拓展迁移6个方面提取要素,并结合智慧课堂课前、课中、课后3个阶段对探究式教学活动进行重构,以期增强探究活动的生成性和动态性,为探究式教学活动开展提供参考。     

Practicality Studies: How to Move From What Works in Principle to What Works in Practice

In his article “Principled Practical Knowledge: Not a Bridge but a Ladder,” Carl Bereiter (2014) argues that theoretical knowledge is too shallow to support the generation of innovative learning activities. He makes a case for principled practical knowledge (PPK)—“principled know-how and know-why”—to fulfill this practical generative role. We argue and illustrate in this commentary that PPK as portrayed by Bereiter does not offer much practical guidance for 2 potential users: professional designers and teachers. For professional designers PPK should be further specified in order to fulfill its generative role. But even this enriched form of PPK still does not suffice to address the challenging issues of practicality teachers face. We explain the magnitude and dimensions that underlie practicality in the everyday work of teachers and suggest how recent work on fast and frugal heuristics can contribute to helping teachers to make instructional innovations practical.     

Is Peer Interaction Necessary for Optimal Active Learning?

Meta-analyses of active-learning research consistently show that active-learning techniques result in greater student performance than traditional lecture-based courses. However, some individual studies show no effect of active-learning interventions. This may be due to inexperienced implementation of active learning. To minimize the effect of inexperience, we should try to provide more explicit implementation recommendations based on research into the key components of effective active learning. We investigated the optimal implementation of active-learning exercises within a “lecture” course. Two sections of nonmajors biology were taught by the same instructor, in the same semester, using the same instructional materials and assessments. Students in one section completed in-class active-learning exercises in cooperative groups, while students in the other section completed the same activities individually. Performance on low-level, multiple-choice assessments was not significantly different between sections. However, students who worked in cooperative groups on the in-class activities significantly outperformed students who completed the activities individually on the higher-level, extended-response questions. Our results provide additional evidence that group processing of activities should be the recommended mode of implementation for in-class active-learning exercises.     

论“先学后导—问题评价”有效教学模式——兼论一种具有操作性的新课程“FFS”教学模式

"先学后导-问题评价"教学模式是以问题发现生成解决为主线、以问题评价为手段、以任务驱动为问题解决途径的有效教学模式。旨在教师指导下使学生和教师以问题发现为主线进行评价性的自主合作学习,对生成问题进行互导性的合作探究学习,并在此基础上进行以任务驱动为载体的问题探究学习。此模式运行要求课型、教师角色、学生角色相应地发生变化:一是课型创新为"问题发现课"、"问题生成课"、"问题解决课"和"综合解决课"等;二是教师角色转型为问题发现者、学习活动设计者、学生有效学习的服务者等;三是学生学习方式变化为自主合作探究学习,学生角色转变为课前主动学习者、课中体验学习者、课后回归学习者。     

问题式学习:一条集中体现建构主义思想的教学改革思路

国外当前教育改革的浪潮中 ,问题式学习是一种与建构主义学习理论及其教学原则非常吻合的教学模式 ,目前正越来越多地被许多教育和培训领域所采用和重视。这种模式以问题为核心 ,让学生围绕问题展开知识建构过程 ,藉此过程促进学生掌握灵活的知识基础和发展高层次的思维技能、解决问题能力及自主学习能力。其学习过程包括组织小组、启动问题、循环反复解决问题、成果展示以及最后的反思和评价等环节。这种教学模式与我国当前教育改革的趋势比较一致 ,对国内教学改革思路很有启迪意义。     

The use of schema theory in the design of instructional materials: A physics example

What are the implications of cognitive science for the design of instructional materials given its central concern with meaningful learning? This question was addressed during an attempt to improve the quality of learning in an introductory non-calculus college physics course where a major intellectual problem that many students face is the development of a coherent view of the information provided to them. The absence of a conceptual framework may contribute to the rapid loss of information often observed among many students shortly after their taking a test. Lack of a conceptual framework also may account for the frequent use of trial-and-error approaches to using formulae. This report cites the use of schema theory for the development of a generative schema or a set of schemas that could be used by students to integrate all of the physics content, and for the design of a means for representing and teaching the schema(s) in a set of instructional materials.     

Effects of Instruction on Verbal Interactions During Collaborative Problem Solving

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving.     

How do students’ achievement goals relate to learning from well-designed instructional videos and subsequent exam performance?

Well-designed instructional videos are powerful tools for helping students learn and prompting students to use generative strategies while learning from videos further bolsters their effectiveness. However, little is known about how individual differences in motivational factors, such as achievement goals, relate to how students learn within multimedia environments that include instructional videos and generative strategies. Therefore, in this study, we explored how achievement goals predicted undergraduate students’ behaviors when learning with instructional videos that required students to answer practice questions between videos, as well as how those activities predicted subsequent unit exam performance one week later. Additionally, we tested the best measurement models for modeling achievement goals between traditional confirmatory factor analysis and bifactor confirmatory factor analysis. The bifactor model fit our data best and was used for all subsequent analyses. Results indicated that stronger mastery goal endorsement predicted performance on the practice questions in the multimedia learning environment, which in turn positively predicted unit exam performance. In addition, students’ time spent watching videos positively predicted practice question performance. Taken together, this research emphasizes the availing role of adaptive motivations, like mastery goals, in learning from instructional videos that prompt the use of generative learning strategies.     

Viewing or visualising—which concept map strategy works best on problem‐solving performance?

The purpose of this study was to investigate the effects of two types of maps (generative vs. completed) and the amount of prior knowledge (high vs. low) on well‐structured and ill‐structured problem‐solving performance. Forty‐four undergraduates who were registered in an introductory instructional technology course participated in the study. Participants were randomly assigned to two treatments that used generative and completed concept maps. Within those treatment groups, participants were differentiated by prior domain knowledge, high or low. Although the high knowledge‐generative group outperformed the other three groups on well‐structured problem‐solving performance, it did not have an effect on ill‐structured problem‐solving performance.     

Instructional design for advanced learners: Establishing connections between the theoretical frameworks of cognitive load and deliberate practice

Cognitive load theory (CLT) has been successful in identifying instructional formats that are more effective and efficient than conventional problem solving in the initial, novice phase of skill acquisition. However, recent findings regarding the “expertise reversal effect” have begun to stimulate cognitive load theorists to broaden their horizon to the question of how instructional design should be altered as a learner's knowledge increases. To answer this question, it is important to understand how expertise is acquired and what fosters its development. Expert performance research, and, in particular, the theoretical framework of deliberate practice have given us a better understanding of the principles and activities that are essential in order to excel in a domain. This article explores how these activities and principles can be used to design instructional formats based on CLT for higher levels of skills mastery. The value of these formats for e-learning environments in which learning tasks can be adaptively selected on the basis of online assessments of the learner's level of expertise is discussed. In their preparation of this article, the first and last authors were supported by an Internationalization grant from the Netherlands Organization for Scientific Research (NWO, The Hague, project number 411-01-010).     

Cooperative learning and computer-based instruction

Much published research focuses on the benefits of learning in small groups. However, little research has differentiated small-group learning methods or considered the implications of related research for designing instructional software. In this article, the origins of small-group learning are traced, and one method, cooperative learning, is distinguished from other small-group learning methods. The instructional and social benefits of cooperative learning are examined and theoretical explanations for the effects of grouping are presented. Finally, issues relevant to designing instructional software for cooperative learning are examined and suggestions for future research are made.Thanks are extended to Jim Klein for his review of an earlier version of this paper.     

Customizing Instruction to Maximize Functional Outcomes for Students With Profound Multiple Disabilities

This article describes a process for customizing instruction for students with profound multiple disabilities that has been used to design instructional programs and maximize the attainment of functional outcomes for students. The process focuses on collaborative teamwork and problem solving to design and implement instructional programs by ensuring that the 5 components of the process are included. Team members determine (a) prepositioning handling procedures; (b) overall body positioning for instruction; (c) hand, arm, and head positioning; (d) instructional adaptations and materials; and (e) handling procedures to combine with systematic instructional strategies.