Activity theory as a framework for designing constructivist learning environments

The epistemic assumptions of constructive learning are different from those of traditional instruction, so classical methods of needs and task analysis are inappropriate for designing constructivist learning environments (CLEs). This paper argues that activity theory provides an appropriate framework for analyzing needs, tasks, and outcomes for designing CLEs. Activity theory is a socio-cultural, socio-historical lens through which designers can analyze human activity systems. It focuses on the interaction of human activity and consciousness within its relevant environmental context. Since conscious learning emerges from activity (performance), not as a precursor to it, CLEs should attempt to replicate the activity structures, tools and sign systems, socio-cultural rules, and community expectations that performers must accommodate while acting on some object of learning. After explicating assumptions of activity theory and briefly describing the components of CLEs, this paper describes a process for using activity theory as a framework for describing the components of an activity system that can be modeled in CLEs.His current research focuses on designing constructivist learning environments, cognitive tools for learning, knowledge representation methods, problem solving, computer-supported collaborative argumentation, cognitive task analysis, and individual differences and learning.His current research focuses on designing constructivist learning environments, cognitive tools for learning, knowledge representation methods, problem solving, computer-supported collaborative argumentation, cognitive task analysis, and individual differences and learning.Her research interests include activity theory and structural knowledge.     

问题解决情境下认知工具的设计研究——以数学应用题为例

运用有效认知工具支持学生的问题解决过程逐渐成为当前研究的热点和趋势。针对目前问题解决过程中缺乏有效认知工具支持的现状,文章首先梳理了国内外对认知工具的相关研究,然后以数学应用题为例,总结了影响解题的一般因素,并针对影响因素提出可以辅助教师教学设计和学生学习的认知工具,旨在提高学生的问题解决能力。在此基础上,从问题解决的角度提出了相应认知工具的设计原则和系统模型。     

Concept Development in Relation to the Particulate Theory of Matter in the Middle School

The paper explores the concept of cognitive style as a feature of individuality and its importance as a component of problem‐solving. Also considered are the nature of the problem and the interpretation of the situation by the person encountering the problem as vital influences. A review of work in this area is provided before supporting empirical evidence is presented. Findings from a controlled investigation of the problem‐solving abilities of 142 students studying physics at advanced secondary school level in the UK are given. A comparison of their solving activities with Field Articulation, Category Width and Impulsivity Reflectivity scores suggests that while further work must be carried out, caution must be exercised in making any extravagant claims for the importance of cognitive style in overall problem‐solving ability.     

Development of a Framework for Analysing Mathematical Problem Solving Behaviours

The taxonomy described in this paper was developed to investigate the process of mathematical problem solving in terms of definable behaviours. It was also used as an instrument to classify and encode behaviours in their sequence of observed occurrence during the process of mathematical problem solving. It is a behavioural analysis framework formulated to examine the “thinking-aloud” protocols of individuals for comprehensive information about the problem solving process itself, the individual differences in the behaviours of subjects and the strategies applied by each in dealing with non-routine mathematical problems.     

Practitioner Perceptions of the A3 Method for Process Improvement in Health Care

The focus of this article is to present students' perceptions of the recently developed A3 method, a structured problem-solving approach based on lean concepts and tools that have been adapted to the health care environment. The students were all employees of a large health care provider and were enrolled in a customized health care executive MBA Program. Each student was required to complete an individual A3 Project in order to improve a process at the department for which they worked. At the end of the semester the students presented their A3 projects to their peers who voted on the best projects. A survey measuring perceptions of the A3 method for problem solving in health care was administered and from it we present propositions for A3 implementation. These propositions are applicable both to health care practitioners and to academic researchers.     

Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving

In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning mathematics via problem solving. Two novice MTEs worked with an experienced MTE and reflected on the process of learning to teach via problem solving and supporting PTs in developing deep understandings of foundational mathematical ideas. Taking a position of inquiry as stance, we examined our experiences teaching mathematics content courses for PTs via problem solving. We found that all of the MTEs used and developed some MKTT through (a) understanding and deciding on the mathematical goals of both the individual lessons and the two-course sequence as a whole, (b) choosing and facilitating tasks, and (c) using questions to scaffold PTs learning and engage them in mathematical processes such as making conjectures, justifying their reasoning, and proving or disproving conjectures.     

Theory of Interlocutory Logic and Sequential Analysis of Interactive Problem-Solving Situations: A Powerful Method

According to Vygotsky's theory of development and its instructional applications, a good way to increase students' knowledge and cognitive abilities is to organise at school co-operative and co-elaborative learning situations. Under some conditions, when students interact, the process of sharing problem-solving procedures results in reorganising and developing their own cognition. But, given that such co-resolution interactive settings can lead to students' individual cognitive progress, we need to explain how. The main aim of this article is to present a theoretical and methodological system to analyse the socio-cognitive processes within an interaction. A pragmatic interlocutory theory, founded on the theory of speech acts, is used and tested with a small group of students involved in solving a mathematical problem at school. Hypotheses about mechanisms of progress invoke the role of semiotic mediations, via speech acts, as a vehicle as well as a tool for sharing the meaning of linguistic signs (construction of intersubjectivity). Thanks to the double function of language signs (communicative and representative) and to the individual internalisation of shared processes, students become able to (re-) organise their thoughts and to increase not only knowledge, but also cognitive and metacognitive tools. This revised version was published online in July 2006 with corrections to the Cover Date.     

Performance on Middle School Geometry Problems With Geometry Clues Matched to Three Different Cognitive Styles

ABSTRACT— This study investigated the relationship between 3 ability‐based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems provided clues compatible with their cognitive style. Students were identified as having a particular cognitive style when they scored equal to or above the median on the measure assessing this ability. A geometry test was developed in which each problem could be solved on the basis of verbal reasoning clues (matching verbal deductive cognitive style), mental rotation clues (matching spatial imagery cognitive style), or shape memory clues (matching object imagery cognitive style). Straightforward cognitive style–clue‐compatibility relationships were not supported. Instead, for the geometry problems with either mental rotation or shape memory clues, students with a combination of both verbal and spatial cognitive styles tended to do the best. For the problems with verbal reasoning clues, students with either a verbal or a spatial cognitive style did well, with each cognitive style contributing separately to success. Thus, both spatial imagery and verbal deductive cognitive styles were important for solving geometry problems, whereas object imagery was not. For girls, a spatial imagery cognitive style was advantageous for geometry problem solving, regardless of type of clues provided.     

Varying effects of subgoal labeled expository text in programming,chemistry, and statistics

Originally intended as a replication study, this study discusses differences in problem solving performance among different domains caused by the same instructional intervention. The learning sciences acknowledges similarities in the learners’ cognitive architecture that allow interventions to apply across domains, but it also argues that each domain has characteristics that might affect how interventions impact learning. The present study uses an instructional design technique that had previously improved learners’ problem solving performance in programming: subgoal labeled expository text and subgoal labeled worked examples. It intended to replicate this effect for solving problems in statistics and chemistry. However, each of the experiments in the three domains had a different pattern of results for problem solving performance. While the subgoal labeled worked example consistently improved performance, the subgoal labeled expository text, which interacted with subgoal labeled worked examples in programming, had an additive effect with subgoal labeled worked examples in chemistry and no effect in statistics. Differences in patterns of results are believed to be due to complexity of the content to be learned, especially in terms of mapping problem solving procedures to solving problems, and the familiarity of tools used to solve problems in the domain. Subgoal labeled expository text was effective only when students learned more complex content and used unfamiliar problem solving tools.     

Developing Design through a Creative Problem‐Solving Process: A Group Community Art Project

For the past few years, creativity has gradually become an important element in the national cultivation of talent in Taiwan. Although traditionally art education is closely linked with creativity, the academic research on general art education is very insufficient. Therefore, the goal of this research is to investigate how creativity could be cultivated in curriculum planning for general art education at technology universities as well as what students’ learning process was when they participated in a course's creative activity. The research applied the theory and steps of creative problem‐solving (CPS) on a general art course to design a group practical activity combining with the local community. This involved converting the steps of creative problem‐solving into different stages of group design activities with the goal of constructing a design process equivalent to the process of problem‐solving. The main research results revealed that students could experience the problem‐solving process through group design activities and develop their divergent and convergent thinking at the same time. Moreover, the cooperative learning model is the most appropriate teaching strategy for students from non‐art‐related departments when cultivating their creativity.     

基于数学问题解决的模式识别研究述评

数学问题解决中的模式识别的研究视角,可以分为基于数学解题认知过程与解题策略角度、基于"归类"的视角、基于数学问题解决中模式识别与其他因素的关系的视角等,具体研究领域涉及几何解题中的视觉模式识别、几何问题解决中的模式识别、解代数应用题的认知模式、数学建模中的模式识别等.由于在知觉领域与问题解决领域"模式识别"的表述存在一定的混乱性,将基于数学问题解决的模式识别界定为:当主体接触到数学问题后,与自己认知结构中的某数学问题图式相匹配的思维与认知过程.并进一步通过其与"归类"的区别与联系、与"化归"的区别与联系使"基于数学问题解决的模式识别"的概念得以澄清.在范围上,把问题解决中的模式识别界定为一种思维过程的阶段或者思维策略,认为它是解题的重要组成部分,但并不是解题的全部.对于未来的展望,期望系统的理论研究、期望对学生问题解决中模式识别的认知过程与机理的实质性的研究以及对学生问题解决中模式识别的教学实验研究.     

高职“药物检测技术”项目课程的开发与实践

基于工作过程系统化的职教理论,坚持学科本位向学生能力本位转化的教改思路,应用文献查阅、企业访谈、实践总结的研究方法。就项目课程开发的步骤、项目课程在教学实践中实施的过程、项目课程的教学评价体系、项目课程教学资源开发等问题,对高职“药物检测技术”课程进行项目课程开发。实践证明,项目教学课程模式的应用可以改变学生学习“药物检测技术”兴趣不足的现状,可以加强培养学生分析问题和解决问题能力的培养,是目前课改思路中较为有效的一种途径。     

Facilitating Students’ Problem Solving in a Technological Context: Prospective Teachers’ Learning Trajectory

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working with two different groups of students. Case study methods were used to identify and analyze critical events that occurred throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies; (3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent with the nature of their interactions and perceived role with students. The implications inform the development of an expanded learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics in technology-rich environments.     

A working memory model applied to mathematical word problem solving

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.     

An examination of middle school students’ representation practices in mathematical problem solving through the lens of expert work: towards an organizing scheme

Representation is viewed as central to mathematical problem solving. Yet, it is becoming obvious that students are having difficulty negotiating the various forms and functions of representations. This article examines the functions that representation has in students’ mathematical problem solving and how that compares to its function in the problem solving of experts and broadly in mathematics. Overall, this work highlights the close connections between the work of experts and students, showing how students use representations in ways that are inherently similar to those of experts. Both experts and students use representations as tools towards the understanding, exploration, recording, and monitoring of problem solving. In social contexts, experts and students use representations for the presentation of their work but also the negotiation and co-construction of shared understandings. However, this research also highlights where students’ work departs from experts’ representational practices, hence, providing some directions for pedagogy and further work.     

Appropriating geometric series as a cultural tool: a study of student collaborative learning

The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure, four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of five excerpts focused on the students’ social processes of knowledge objectification and the corresponding semiotic means, i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating the cultural tool of geometric series. From the excerpts, it is evident that the students’ participation changes throughout their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming and by establishing shared meanings for the concept and its theoretical components.     

Investigating the role of computer‐supported annotation in problem‐solving‐based teaching: An empirical study of a Scratch programming pedagogy

For more than 2 years, Scratch programming has been taught in Taiwanese elementary schools. However, past studies have shown that it is difficult to find appropriate learning methods or tools to boost students’ Scratch programming performance. This inability to readily identify tutoring tools has become one of the primary challenges addressed in Scratch programming studies. To cope with this problem, we propose an innovative approach, which combines an Annotation‐based Scratch Programming (ASP) tool with the problem‐solving‐based teaching approach in Scratch programming pedagogy. The ASP tool was developed to enable students to create, review and share Scratch programming and homework annotations. In a quasi‐experimental study, we have evaluated Scratch programming pedagogy at a North Taiwanese elementary school to investigate the effects of instructional‐tools‐supported programming instructional modes on Scratch programming performance. The experimental results show that students who received ASP tool support in conjunction with a problem‐solving‐based teaching approach performed significantly better than the other groups. Based on our findings, the innovative approach was believed to play an important role in improving the learning patterns of younger pupils. Therefore, we suggest that teachers consider incorporating the innovative method into their teaching environments in order to boost students’ learning achievements in the area of Scratch programming and the subsequent learning process.     

Worked example effects in individual and group work settings

This study compared the effects of worked example and problem‐solving approaches in individual or group work settings on learning to solve geometry problems. One hundred and one seventh graders from Indonesia were randomly allocated to four experimental groups using a 2 (problem‐solving vs. worked examples) × 2 (individual vs. group study) design. Performance measures on numeric and reasoning abilities using both similar and transfer tasks were collected. The results indicated a significant superiority of the worked example approach in both the individual and group work settings. Supporting data revealed that students could understand the material more easily using worked examples than when solving problems. The experiment provided evidence that the advantage of using worked examples over solving problems extends to a group work context.     

Strategies, competence and style—Problem solving in engineering design

In a series of laboratory studies, mechanical engineers and engineering students with different levels of experience and knowledge designed a device. As a starting point, the numerous ways of solving the problem were classified. Secondly, a model was tested which explained differences in designing as an interaction of domain-specific and heuristic competence. Thirdly, individual characteristics, marking not only the ways of proceeding in design, but also in other complex situations, are considered as a designer's personal style. The article closes with some hypotheses about the development of differences in the use of strategies, competence and style.