Computer-assisted learning for mathematical problem solving

Previous computer-assisted problem-solving systems have incorporated all the problem-solving steps within a single stage, making it difficult to diagnose stages at which errors occurred when a student encounters difficulties, and imposing a too-high cognitive load on students in their problem solving. This study proposes a computer-assisted system named MathCAL, whose design is based on four problem-solving stages: (1) understanding the problem, (2) making a plan, (3) executing the plan and (4) reviewing the solution. A sample of one hundred and thirty fifth-grade students (aged 11 years old) completed a range of elementary school mathematical problems and empirically demonstrated. The results showed MathCAL to be effective in improving the performance of students with lower problem solving ability. This evaluation allowed us to address the problem of whether the assistances in various stages help students with their problem solving. These assistances improve students’ problem-solving skills in each stage.     

Integrating modified WebQuest activities for programming learning

The study designed WebQuest activities and explored the learning performance of learners to understand the suitability of using WebQuest in a college programming course. The study modified the processes of WebQuest based on social constructivism and scaffolding learning, and included programming tasks such as debugging practice to encourage learners to develop their problem-solving abilities. The WebQuest learning sheets include the following four parts, introduction, task, resources and evaluation, and the learners had to complete the tasks without the detailed processes. After they had tried to solve the problem for approximately two weeks, the detailed WebQuest processes were provided. A total of 109 learners (third year of college) participated in the study and were separated into two groups. The experimental group underwent WebQuest teaching, while the control group received the traditional IT-integrated teaching. The study duration was 18 weeks (3 hr/week). The results indicated that the modified WebQuest activity gave learners scaffolding to do try-and-revise practice, and the processes of using provided possible information to test and debug the resulting codes encouraged them to associate and analyze learning information before programming and then to generalize the programming steps on their own instead of following the instructor's step-by-step instructions. The learners thus have a deep understanding of the programming concept rather than surface learning. The findings revealed that the modified WebQuest activity is a helpful form of scaffolding for promoting learners' positive learning experiences regarding organizing information and problem solving and reasoning skills. Besides, integrating debugging practice in the WebQuest activity could promote learners' intermediate and advance level programming ability. Subsequent research could further explore the effects of adding after-practice WebQuest activities to assist and trigger learners' self-reflection for refining their problem-solving processes after the in-class WebQuest activities.     

Powering up flipped learning: An online learning environment with a concept map-guided problem-posing strategy

Scholars have suggested that flipped learning can be enhanced by designing effective in-class learning activities to improve students' higher order thinking skills. Problem posing has been recognized as such a learning strategy that has great potential for improving students' higher order thinking skills. However, it has been reported as a challenging task for most students. Research evidence has indicated the potential of engaging students in group learning with step-by-step hints when conducting problem-posing activities. Therefore, this study proposed a multilevel concept mapping-based problem-posing strategy to assist students in completing the problem-posing tasks in flipped learning. To understand the effectiveness of the proposed strategy, a flipped learning system was developed and adopted in the science class of an elementary school. Seventy-five fifth graders from three classes were divided into experimental group A, experimental Group B and a control group. Students in Group A used the concept map-guided problem-posing strategy for flipped learning (CMPP-FL), students in Group B used the problem-posing strategy-based flipped learning, while students in the control group used the conventional flipped learning strategy. The results showed that the CMPP-FL was effective in terms of improving students' learning performance, especially for students with higher levels of critical thinking tendency.     

Building virtual cities,inspiring intelligent citizens: Digital games for developing students’ problem solving and learning motivation

This study investigates the effectiveness digital game-based learning (DGBL) on students’ problem solving, learning motivation, and academic achievement. In order to provide substantive empirical evidence, a quasi-experimental design was implemented over the course of a full semester (23 weeks). Two ninth-grade Civics and Society classes, with a total of 44 students (15–16 years old), were randomly assigned to one of two conditions: an experimental group (incorporating DGBL) and a comparison group (taught using traditional instruction). Two-way mixed ANOVA was employed to evaluate changes in problem solving ability and compare the effectiveness the two strategies, while ANCOVA was used to analyze the effects on learning motivation and academic achievement. The results of this study are summarized as follows: (1) The DGBL strategy was clearly effective in promoting students’ problem solving skills, while the control group showed no improvement. Additionally, data from the mid-test and post-test demonstrate that, as a higher order thinking skill, problem-solving requires a full semester to develop. (2). DGBL resulted in better learning motivation for students in the experimental group as compared to learners receiving TI. (3) Contrary to some suggestions that digital games could inhibit academic achievement, no statistically significant difference was found between the two groups. Most importantly, the quantitative improvement in problem-solving and learning motivation suggest that DGBL can be exploited as a useful and productive tool to support students in effective learning while enhancing the classroom atmosphere. Future research in DGBL should emphasize the evaluation of other higher order elements of the cognitive domain in terms of academic achievement outcomes and skills, such as critical and creative thinking.     

A creative thinking approach to enhancing the web-based problem solving performance of university students

Along with the advancement of information and communication technology, researchers have pointed out the necessity and challenges of developing effective instructional strategies to enhance students' web-based problem-solving performance, which refers to the ability of investigating a series of related problems via searching for, abstracting and summarizing information on the web. In this study, a creative thinking strategy is proposed to cope with this problem. Moreover, an experiment was conducted on 80 freshmen from two classes of a university to evaluate the effectiveness of the proposed approach. The experimental results show that the proposed approach improved the students' web-based problem solving performance in comparison with the conventional approach in terms of “problem finding” and “idea finding.” Moreover, it was found that the proposed approach could improve the “fact finding” performance of the students with intuitive-type cognitive style. Accordingly, some implications and suggestions are given for educators who attempt to conduct web-based problem-solving activity.     

A hybrid approach to promoting students’ web-based problem-solving competence and learning attitude

Fostering problem-solving abilities has long been recognized as an important issue in education; however, past studies have shown that it is difficult and challenging to find effective learning strategies or tools for improving students’ problem-solving abilities. To cope with this problem, in this study, a hybrid approach that integrates the cognitive apprenticeship model with the collaborative learning strategy is proposed for conducting web-based problem-solving activities. Students’ problem-solving performance is examined in such a hybrid learning context. Furthermore, past studies indicate that cognitive load could affect learners’ performance; thus, the influence of cognitive load on students’ problem-solving effectiveness with this new approach is investigated in depth. The experimental results show that middle- and low-achievement students in the experimental group gained significant benefits from the hybrid approach in comparison with those who learned with the traditional approach. Accordingly, a discussion of how to accommodate the needs of different learning ability groups is provided.     

A computational model for distributed knowledge systems with learning mechanisms

This paper addresses the issues of machine learning in distributed knowledge systems, which will consist of distributed software agents with problem solving, communication and learning functions. To develop such systems, we must analyze the roles of problem-solving and communication capabilities among knowledge systems. To facilitate the analyses, we propose a computational model: LPC. The model consists of a set of agents with (a) a knowledge base for learned concepts, (b) a knowledge base for problem solving, (c) prolog-based inference mechanisms and (d) a set of beliefs on the reliability of the other agents. Each agent can improve its own problem-solving capabilities by deductive learning from the given problems, by memory-based learning from communications between the agents and by reinforcement learning from the reliability of communications between the other agents. An experimental system of the model has been implemented in Prolog language on a Window-based personal computer. Intensive experiments have been carried out to examine the feasibility of the machine learning mechanisms of agents for problem-solving and communication capabilities. The experimental results have shown that the multiagent system improves the performance of the whole system in problem solving, when each agent has a higher learning ability or when an agent with a very high ability for problem solving joins the organization to cooperate with the other agents in problem solving. These results suggest that the proposed model is useful in analyzing the learning mechanisms applicable to distributed knowledge systems.     

Using computer supported collaborative learning strategies for helping students acquire self-regulated problem-solving skills in mathematics

The main objective of this paper is to investigate the effectiveness of a proposed computer-based instructional method in Primary Education for self-regulated problem solving. The proposed instructional method is based on Sternberg’s model of problem solving within an authentic context. It consists of three main phases: observation, collaboration and semi-structured guidance. The ultimate learning objective is to augment the autonomous problem-solving skills of primary school children. In our study the Synergo tool was used, which is a synchronous computer supported collaborative learning tool, as well as the Moodle learning management system. The context which frames the method is authentic, very close to a students’ realistic learning situation. The findings of this study advocate that students can increase their problem-solving skills in a relatively short period of time. At the same time, they can improve their approach to the solution of a given mathematical problem, performing significant signs of autonomy.     

Transfer of problem-solving strategy using Covlan

Psychological evidence suggests that humans use visual knowledge and reasoning in solving complex problems. We present Covlan, a visual knowledge representation language for representing visual knowledge and supporting visual reasoning. We describe Galatea, a computer program that uses Covlan for analogical transfer of problem-solving procedures from known analogs to new problems. We present the use of Galatea to model analogical visual problem solving by four human experimental participants, and describe one of the four cases in detail. The Galatea model of human problem solving suggests that problem-solving procedures can be effectively represented with Covlan.     

Assessing problem solving in expert systems using human benchmarking

The human benchmarking approach attempts to assess problem solving in expert systems by measuring their performance against a range of human problem-solving performances. We established a correspondence between functions of the expert system GATES and human problem-solving skills required to perform a scheduling task. We then developed process and outcome measures and gave them to people of different assumed problem-solving ability. The problem-solving ability or “intelligence” of this expert system is extremely high in the narrow domain of scheduling planes to airport gates as indicated by its superior performance compared to that of undergraduates, graduate students and expert human schedulers (i.e. air traffic controllers). In general, the study supports the feasibility of using human benchmarking methodology to evaluate the problem-solving ability of a specific expert system.     

Scaffolding online argumentation during problem solving

Abstract  In this study, constraint-based argumentation scaffolding was proposed to facilitate online argumentation performance and ill-structured problem solving during online discussions. In addition, epistemological beliefs were presumed to play a role in solving ill-structured diagnosis–solution problems. Constraint-based discussion boards were implemented to scaffold pre-service teachers' online discussions about behaviour management (diagnosis–solution) problems. The scaffolded discussion group generated more evidence notes and also generated more hypothesis messages and hypothesis testing messages as well as problem space construction messages. There was a relationship between epistemological beliefs and ill-structured problem solving. Simple knowledge, omniscient authority, and fixed ability significantly predicted problem-solving performance. A significant negative relationship between simple knowledge and individual problem-solving performance was found. This implies that individuals who believe in simple knowledge may be less inclined to explore more solution alternatives. However, contrary to prediction, omniscient authority and fixed ability beliefs were positively associated with problem-solving processes.     

Virtual reality in problem-based learning contexts: Effects on the problem-solving performance,vocabulary acquisition and motivation of English language learners

Learning a foreign language requires interaction with language input while involved in a task. Given that problem-based learning (PBL) offers hands-on application in realistic contexts, and that virtual reality (VR) enables learners to interact with multiple modalities of information, this study examines how the integration of VR technology into PBL contexts affects students' motivation for, problem-solving during, and vocabulary acquisition in learning English as a foreign language (EFL). A total of 84 engineering majors who enrolled in a course of English for specific purposes were randomly assigned to either an experimental group or a control group. Students in the experimental group participated in a VR-assisted PBL context, in which they were to view a PBL scenario using VR technology and then to create VR videos about solving the given problems. Those in the control group participated in a PBL context without the use of VR technology for viewing and solving the identical scenario. After the intervention, all the students wrote a problem-solving analysis, took a vocabulary knowledge test, completed a learning motivation questionnaire, and participated in individual interviews. The results showed that the students in the experimental group significantly outperformed those in the control group in terms of vocabulary acquisition, and were more motivated to learn English related to their future careers, whereas there was no significant difference in the problem-solving performance of the two groups. Implications of these findings highlight the value of engaging EFL learners in immersive environments for contextualized learning through the integrated use of VR and PBL.     

Scaffolding game-based learning: Impact on learning achievements,perceived learning,and game experiences

One of the central challenges of integrating game-based learning in school settings is helping learners make the connections between the knowledge learned in the game and the knowledge learned at school, while maintaining a high level of engagement with game narrative and gameplay. The current study evaluated the effect of supplementing a business simulation game with an external conceptual scaffold, which introduces formal knowledge representations, on learners' ability to solve financial-mathematical word problems following the game, and on learners' perceptions regarding learning, flow, and enjoyment in the game. Participants (M_age = 10.10 years) were randomly assigned to three experimental conditions: a “study and play” condition that presented the scaffold first and then the game, a “play and study” condition, and a “play only” condition. Although no significant gains in problem-solving were found following the intervention, learners who studied with the external scaffold before the game performed significantly better in the post-game problem-solving assessment. Adding the external scaffold before the game reduced learners' perceived learning. However, the scaffold did not have a negative impact on reported flow and enjoyment. Flow was found to significantly predict perceived learning and enjoyment. Yet, perceived learning and enjoyment did not predict problem-solving and flow directly predicted problem solving only in the “play and study” condition. We suggest that presenting the scaffold may have “problematized” learners' understandings of the game by connecting them to disciplinary knowledge. Implications for the design of scaffolds for game-based learning are discussed.     

Learning to Improve Coordinated Actions in Cooperative Distributed Problem-Solving Environments

Coordination is an essential technique in cooperative, distributed multiagent systems. However, sophisticated coordination strategies are not always cost-effective in all problem-solving situations. This paper presents a learning method to identify what information will improve coordination in specific problem-solving situations. Learning is accomplished by recording and analyzing traces of inferences after problem solving. The analysis identifies situations where inappropriate coordination strategies caused redundant activities, or the lack of timely execution of important activities, thus degrading system performance. To remedy this problem, situation-specific control rules are created which acquire additional nonlocal information about activities in the agent networks and then select another plan or another scheduling strategy. Examples from a real distributed problem-solving application involving diagnosis of a local area network are described.     

Effects of mental process integrated nursing training using mobile device on students’ cognitive load,learning attitudes,acceptance, and achievements

Clinical nursing training is important to nursing educators and student nurses in nursing education since safe and competent care depends on good clinical problem solving skills. Therefore, developing better cognitive problem-solving strategies or tools are essential for clinical nursing practices. Moreover, learning diagnosis is also a critical determinant in the acquisition, processing, and application of clinical skills in nursing practices. Bearing this in mind, this study aims to develop a mobile interactive learning and diagnosis (MILD) system to support problem-based learning (PBL) in a clinical nursing course based on the testing-based approach. Using mobile devices as a learning tool to integrate both real-world and digital-world resources for students and adopting PBL as a learning strategy to facilitate the development of the clinical problem solving skills. To show the effectiveness of the proposed approach, an experiment was conducted in a foundations of nursing course at a nursing college in Taiwan. The experimental results show that the proposed approach is helpful to students in improving learning performance and reducing cognitive loads. Moreover, it was also found that most students showed positive perceptions toward the usage of the proposed system.     

The effect of simulation games on the learning of computational problem solving

Simulation games are now increasingly applied to many subject domains as they allow students to engage in discovery processes, and may facilitate a flow learning experience. However, the relationship between learning experiences and problem solving strategies in simulation games still remains unclear in the literature. This study, thus, analyzed the feedback and problem solving behaviors of 117 students in a simulation game, designed to assist them to learn computational problem solving. It was found that students when learning computational problem solving with the game were more likely to perceive a flow learning experience than in traditional lectures. The students’ intrinsic motivation was also enhanced when they learned with the simulation game. In particular, the results of the study found a close association between the students’ learning experience states and their problem solving strategies. The students who perceived a flow experience state frequently applied trial-and-error, learning-by-example, and analytical reasoning strategies to learn the computational problem solving skills. However, a certain portion of students who experienced states of boredom and anxiety did not demonstrate in-depth problem solving strategies. For instance, the students who felt anxious in the simulation game did not apply the learning-by-example strategy as frequently as those in the flow state. In addition, the students who felt bored in the simulation game only learned to solve the problem at a superficial level.     

GENETICA: A computer language that supports general formal expression with evolving data structures

This paper presents a general problem-solving method combining the principles of artificial intelligence and evolutionary computation. The problem-solving method is based on the computer language GENETICA, which stands for "Genetic Evolution of Novel Entities Through the Interpretation of Composite Abstractions." GENETICAs programming environment includes a computational system that evolves data abstractions, viewed as genotypes of data generation scenarios for a GENETICA program, with respect to either confirmation or optimization goals. A problem can be formulated as a GENETICA program, while the solution is represented as a data structure resulting from an evolved data generation scenario. This approach to problem solving offers: 1) generality, since it concerns virtually any problem stated in formal logic; 2) effectiveness, since formally expressed problem-solving knowledge can be incorporated in the problem statement; and 3) creativity, since unpredictable solutions can be obtained by evolved data structures. It is shown that domain specific languages, including genetic programming ones, that inherit GENETICAs features can be developed in GENETICA. The language G-CAD, specialized to problem solving in the domain of architectural design, is presented as a case study followed by experimental results.     

Developing an effective support system for inquiry learning in a Web-based environment

Abstract Sixty-five teams of basic and secondary school students solved problem-solving tasks during a virtual hike in a Web-based inquiry-learning simulation 'Hiking Across Estonia'. This environment provided learners with all necessary background information for problem-solving and tools for carrying out experiments. There were 25 tasks in certain order about ecological and environmental issues. The teams were clustered according to the data about participants, the results of the pre- and post-test, and their achievement in problem-solving tasks of the virtual hike. Only two out of five clusters were regarded as effective in solving problems and analysing tables, graphs, figures, and photos. The others had difficulties in forming contextual or task and process awareness. A support system for increasing the effectiveness of inquiry learning and enhancing their development of analytical skills was developed on the basis of the strategies that the members of five clusters had used in solving the problems, their achievement in solving the tasks during the virtual hike and in the pre- and post-test, and the personal data about the teams. The support system contained different notes before solving the problems and changed sequence of the tasks on the virtual hike for some clusters. The usage of this system was evaluated in a second study with 60 teams. The comparison of two studies demonstrated significant effectiveness of the support system to both general problem-solving ability and analytical skills. The characteristics of each cluster and the influence of the support system are discussed in this paper.     

Effects of system display format on performance in a fault location task

It has been suggested that complexity in fault diagnosis tasks is largely a function of problem complexity and little to do with the perceptual complexity of the format in which the system representation is displayed. An experimental study is reported which shows that a left-to-right diagonal display format improves the speed and diagnostic efficiency with which faults are located. The differences in display format which appear to be most beneficial do not affect problem-solving complexity in any obvious way. Differences in display format which could affect problem-solving complexity, such as constraints on direction of signal flow, do not apparently affect fault diagnosis performance. The improvements in performance apparently stem from an increased ability to perceive components of the system relevant to the observed symptoms.     

Measuring problem solving in computer environments: current and future states

The first part of this article will review the status of technology and educational reform; the second will treat traditional approaches to problem-solving measurement common today in technological settings; and the third will propose how problem-solving assessment may change and, in particular, the role that authoring strategies may play in measuring problem-solving performance successfully in computer environments. We will suggest four areas that must be considered in which computers would increase the fidelity and validity of measures of complex problem solving: (1) the intentions and skills of assessment designers; (2) the range of performance that counts as problem solving; (3) the ways in which validity evidence can be sought; and (4) the degree to which the measurement produces results that generalize across tasks and contexts.