Schoenfeld’s problem solving theory in a student controlled learning environment

This paper evaluates the effectiveness of a student controlled computer program for high school mathematics based on instruction principles derived from Schoenfeld’s theory of problem solving. The computer program allows students to choose problems and to make use of hints during different episodes of solving problems. Crucial episodes are: analyzing the problem, selecting appropriate mathematical knowledge, making a plan, carrying it out, and checking the answer against the question asked.     

How can self‐regulated learning be supported in mathematical E‐learning environments?

Abstract This study compares two E-learning environments: E-learning supported with IMPROVE self-metacognitive questioning (EL+IMP), and E-learning without explicit support of self-regulation (EL). The effects were compared between mathematical problem-solving and self-regulated learning (SRL). Participants were 65 ninth-grade students who studied linear function in Israeli junior high schools. Results showed that EL+IMP students significantly outperformed the EL students in problem-solving procedural and transfer tasks regarding mathematical explanations. We also found that the EL+IMP students outperformed their counterparts in using self-monitoring strategies during problem solving. This study discusses both the practical and theoretical implications of supporting SRL in mathematical E-learning environments.     

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.     

How indirect supportive digital help during and after solving physics problems can improve problem-solving abilities

This study investigates the effectiveness of computer-delivered hints in relation to problem-solving abilities in two alternative indirect instruction schemes. In one instruction scheme, hints are available to students immediately after they are given a new problem to solve as well as after they have completed the problem. In the other scheme, hints are only available as worked out problems after students have finished their solution. The instruction schemes are supplied by means of a web-based program, Physhint, which supports the development of strategic knowledge [Pol, H. J., Harskamp, E. G., & Suhre, C. J. M. (2008). The effect of the timing of instructional support in a computer-supported problem-solving program for students in secondary physics education. Computers in Human Behavior, 24, 1156–1178]. This program supports novice problem solvers while undertaking physics problems concerned with forces by providing hints structured in accordance with Schoenfeld’s episodes [Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching (pp. 224–270). New York: McMillan Publishing].     

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.     

The effect of the timing of instructional support in a computer-supported problem-solving program for students in secondary physics education

Many students experience difficulties in solving applied physics problems. Researchers claim that the development of strategic knowledge (analyze, explore, plan, implement, verify) is just as necessary for solving problems as the development of content knowledge. In order to improve these problem-solving skills, it might be profitable to know at what time during problem solving is the use of instructional support most effective: before, during or after problem solving.     

Embedding game-based problem-solving phase into problem-posing system for mathematics learning

A problem-posing system is developed with four phases including posing problem, planning, solving problem, and looking back, in which the “solving problem” phase is implemented by game-scenarios. The system supports elementary students in the process of problem-posing, allowing them to fully engage in mathematical activities. In total, 92 fifth graders from four different classes were recruited. The experimental group used the problem-posing system, whereas the control group followed the traditional paper-based approach. The study investigates the effects of the problem-posing system on students’ problem-posing ability, problem-solving ability, and flow experiences. The results revealed more flow experiences, and higher problem-solving and problem-posing abilities in the experimental group.     

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.     

Promoting college students’ knowledge acquisition and ill-structured problem solving: Web-based integration and procedure prompts

This study examined how web-based integration and procedure question prompts differentially affected students’ knowledge acquisition and ill-structured problem solving skills, particularly in representing problem(s), developing solutions, and monitoring and evaluating a plan of action within the social science context. Eighty-four undergraduate pre-service teachers were recruited and randomly assigned to one of the four conditions: (1) an IP condition that required students to complete integration prompts, (2) a PP condition that required students to complete procedure prompts, (3) an IPP condition that required students to complete both integration and procedure prompts, or (4) a control condition that did not provide access to any prompts. The findings show that students who received integration prompts outperformed those who did not receive any in knowledge acquisition and problem representation for solving an ill-structured problem. Integration prompts also helped the development and integration of cognitive schema, whereas procedure prompts helped direct students’ attention to specific features of the problem in order to arrive at the solution(s). In fact, the presence of an integration prompt alone is not sufficient to support successful ill-structured problem solving unless a procedure prompt is provided. Based on these findings, this study offers implications for designing Web-based learning environments, engineered to promote integrative knowledge and ill-structured problem solving skills.     

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.     

Examining the effects of field dependence–independence on learners' problem-solving performance and interaction with a computer modeling tool: Implications for the design of joint cognitive systems

An investigation was carried out to examine the effects of cognitive style on learners' performance and interaction during complex problem solving with a computer modeling tool. One hundred and nineteen undergraduates volunteered to participate in the study. Participants were first administered a test, and based on their test scores they were classified into three groups, namely field-dependent, field-mixed, and field-independent learners. Participants then received the same set of integrated-format materials and were asked to use a computer modeling tool to solve a complex problem about immigration policy. A multivariate analysis of variance was performed with field type as the independent variable, and cognitive load, problem-solving performance, and learner interaction with the computer tool as the dependent variables. The results indicated that there was no significant difference in terms of the amount of cognitive load reported. However, there was a significant difference in terms of learner problem-solving performance. Specifically, field-independent learners outperformed field-dependent learners, and field-mixed learners outperformed field-dependent learners. The results also indicated significant differences in computer interaction between field-independent and field-dependent learners, and between field-mixed and field-dependent learners. The qualitative findings of the study showed that students who interacted poorly with the software were unsure about how to systematically use the affordances of the computer tool to solve the problem, did not have a goal-directed plan or strategy in mind about how to investigate the issue at hand, and had difficulty with testing the immigration policies by appropriately controlling variables in order to collect data to inform decision making. Implications are discussed in terms of designing computer systems that scaffold learners' complex problem solving by considering the cognitive demands of the task.     

The identification,implementation, and evaluation of critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, ‘Math Explorer’, which delivers addition and subtraction word problem-solving instruction for students with learning disabilities at the early elementary level, was designed and developed. Lastly, usability testing was conducted to assess whether Math Explorer was well-designed in terms of the interface for students with learning disabilities. Given the results of the usability testing, this study corroborated the fact that the critical user interface design features and guidelines in mathematics computer-assisted instruction programs would be essential for facilitating the mathematical learning of students with learning disabilities. Implications for practice and future research were discussed.     

Lifelike Pedagogical Agents for Mixed-initiative Problem Solving in Constructivist Learning Environments

Mixed-initiative problem solving lies at the heart of knowledge- based learning environments. While learners are actively engaged in problem-solving activities, learning environments should monitor their progress and provide them with feedback in a manner that contributes to achieving the twin goals of learning effectiveness and learning efficiency. Mixed-initiative interactions are particularly critical for constructivist learning environments in which learners participate in active problem solving. We have recently begun to see the emergence of believable agents with lifelike qualities. Featured prominently in constructivist learning environments, lifelike pedagogical agents could couple key feedback functionalities with a strong visual presence by observing learners' progress and providing them with visually contextualized advice during mixed-initiative problem solving. For the past three years, we have been engaged in a large-scale research program on lifelike pedagogical agents and their role in constructivist learning environments. In the resulting computational framework, lifelike pedagogical agents are specified by(1) a behavior space containing animated and vocal behaviors,(2) a design-centered context model that maintains constructivist problem representations, multimodal advisory contexts, and evolving problem-solving tasks, and(3) a behavior sequencing engine that in realtime dynamically selects and assembles agents' actions to create pedagogically effective, lifelike behaviors.To empirically investigate this framework, it has been instantiated in a full-scale implementation of a lifelike pedagogical agent for Design-A-Plant, a learning environment developed for the domain of botanical anatomy and physiology for middle school students. Experience with focus group studies conducted with middle school students interacting with the implemented agent suggests that lifelike pedagogical agents hold much promise for mixed-initiative learning.     

Factors of problem-solving competency in a virtual chemistry environment: The role of metacognitive knowledge about strategies

The ability to solve complex scientific problems is regarded as one of the key competencies in science education. Until now, research on problem solving focused on the relationship between analytical and complex problem solving, but rarely took into account the structure of problem-solving processes and metacognitive aspects. This paper, therefore, presents a theoretical framework, which describes the relationship between the components of problem solving and strategy knowledge.In order to assess the constructs, we developed a virtual environment which allows students to solve interactive and static problems. 162 students of grade 10 and the upper secondary level completed the tests within a cross-sectional survey. In order to investigate the structure of problem-solving competency, we established measurement models representing different theoretical assumptions, and evaluated model fit statistics by using confirmatory factor analyses.Results show that problem-solving competency in virtual environments comprises to three correlated abilities: achieving a goal state, systematical handling of variables, and solving analytical tasks. Furthermore, our study provides empirical evidence on the distinction between analytical and complex problem solving.Additionally, we found significant differences between students of grades 10 and 12 within the problem-solving subscales, which could be explained by gaming experience and prior knowledge. These findings are discussed from a measurement perspective. Implications for assessing complex problem solving are given.     

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.     

Advancing young adolescents’ hypothesis-development performance in a computer-supported and problem-based learning environment

Hypothesis development is a complex cognitive activity, but one that is critical as a means of reducing uncertainty during ill-structured problem solving. In this study, we examined the effect of metacognitive scaffolds in strengthening hypothesis development. We also examined the influence of hypothesis development on young adolescents’ problem-solving performance. Data was collected from sixth-grade students (N = 172) using a computer-supported problem-based learning environment, Animal Investigator. The findings of the study indicated that participants using metacognitive scaffolds developed significantly better hypotheses and that hypothesis-development performance was predictive of solution-development performance. This article discusses further educational implications of the findings and future research.     

Improving problem solving ability in mathematics by using a mathematical model: A computerized approach

The present study investigates the improvement of students’ mathematical performance by using a mathematical model through a computerized approach. We had developed an intervention program and 11 years students worked independently on a mathematical model in order to improve their self-representation in mathematics, to self-regulate their performance and consequently to improve their problem solving ability. The emphasis of using the specific model was on dividing the problem solving procedure into stages, the concentration on the students’ cognitive processes at each stage and the self-regulation of those cognitive processes in order to overcome cognitive obstacles. The use of the computer offered the opportunity to give students general comments, hints and feedback without the involvement of their teachers. Students had to communicate with a cartoon animation presenting a human being who faced difficulties and cognitive obstacles during problem solving procedure. Three tools were constructed for pre- and post-test (self-representation, mathematical performance and self-regulation). There were administered to 255 students (11 years old), who constituted the experimental and the control group. Results confirmed that providing students with the opportunity to self-reflect on their learning behavior when they encounter obstacles in problem solving is one possible way to enhance students’ self-regulation and consequently their mathematical performance.     

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.     

Can experts' explanations help students develop program design skills?

This paper reports and experimental investigation of the effectiveness of case studies for teaching programming. A case study provides an “expert commentary” on the complex problem-solving skills used in constructing a solution to a computer programming problem as well as one or more worked-out solutions to the problem. To conduct the investigation, we created case studies of programming problems and evaluated what high school students in ten Pascal programming courses learned from them. We found that the expert's commentary on the decisions and activities required to solve a programming problem helped students gain integrated understanding of programming. Furthermore, the expert's commentary imparted more integrated understanding of programming than did the worked-out solution to the problem without the expert's explanation. These results support the contention that explicit explanations can help students learn complex problem-solving skills.We developed case studies for teaching students to solve programming problems for the same reasons that they have been developed in other disciplines. The case method for teaching complex problem solving was first used at Harvard College in 1870 and has permeated curricula for business, law and medicine across the country. These disciplines turned to the case method to communicate the complexity of real problems, to illustrate the process of dealing with this complexity and to teach analysis and decision making skills appropriate for these problems.     

The impact of goal specificity and goal type on learning outcome and cognitive load

Two hundred and thirty three 15-year old students conducted experiments within a computer-based learning environment. They were provided with different goals according to an experimental 2 × 2 design with goal specificity (nonspecific goals versus specific goals) and goal type (problem solving goals versus learning goals) as factors. We replicated the findings of other researchers that nonspecific problem solving goals lead to lower cognitive load and better learning than specific problem solving goals. For learning goals, however, we observed this goal specificity effect only on cognitive load but not on learning outcome. Results indicate that the goal specificity affects the element interactivity of a task and cognitive load with both, problem solving goals or learning goals. But differences in overall cognitive load are not sufficient for explaining differences in learning outcome. Additionally, differences in strategy use come into play. Specific problem solving goals seem to restrict students to use a problem solving strategy whereas nonspecific problem solving goals or learning goals allow students to use a learning strategy. We conclude that in order to foster learning, students must be provided with goals that allow them to use a learning strategy. Additionally, providing them with nonspecific goals decreases cognitive load and, thus, enables students to learn with less effort.