Ill-structured Problem Solving Research Articles

Research Trends in the Ill-Structured Problem-Solving of Mathematics Education in Korea

In mathematics education, there has been substantial interest in mathematical problem-solving, which has led to the development of competencies of problem-solving based on the relevance and applicability of mathematical knowledge learned in school to problem-solving in one’s everyday life. This study revisits the development of ill-structured problem-solving and its pedagogical implications with the aim of providing students with a transferable problem-solving experience in which the knowledge they learn in school can be meaningfully employed in a real-world context. To examine the overall trend of research focusing on ill-structured problems or ill-structured problem-solving, this study statistically analyzed the papers published in the field of mathematics education in Korea according to the research period, topic, research method, and mathematics content strands to provide useful insights as descriptive research. More specifically, the ill-structuredness of textbook problems, the process of ill-structured problem-solving and the collaborative problem solving that emerges from ill-structured problem-solving were analyzed more closely. Based on the results, the researchers suggested the directions and implications for mathematical problem-solving in terms of ill-structured problems or problem-solving in mathematics education.

Constructivist gamification environment model designing framework to improve ill-structured problem solving in learning sciences

Constructivist gamification environment model designing framework to improve ill-structured problem solving in learning sciences

Capturing Translation Representation Schema of Students Through Ill-Structured Problems Task

Translation of mathematical representation is one of the important aspects of mathematics problem solving because the accuracy of mathematical representation translation is one of the terms of success in solving a problem. This research purposed to explore how the schema of mathematical representation translation among multiple representations type of junior high school students in solving well-structured problems and ill-structured problems. The participants were 132 8th students in Junior High School (SMP) in Kediri. The participant was then taken two students who completed a step for solving the problems as subjects. This study used qualitative explorative methods, with researchers conducting in-depth interviews with subjects to explore mathematical representation translation processed when solving well-ill social arithmetic problems. Data were analyzed by technique triangulation. Based on data analysis, the researchers found that: 1) both subjects failed to solve ill-structured problems because their translation of mathematical representation didn’t accurate. Subject-1 can’t unpack the source when problem representation. While subject-2 can’t determine equivalence between source representation and target representation, and 2) they found that both subjects have inconsistent representation translation schematic when solving an ill-structured problem. From the founded, the researcher concluded that ill-structured problems must often be given to students to practice their representation translation capabilities. Keywords: Translation, Mathematical Representation, Ill-Structured Problem Solving

A Critical Thinking Profile of Mathematics Education Students in Solving Ill-Structured Problem based on Mathematical Ability

This study aims to describe the critical thinking profile of mathematics education students in solving ill-structured problems based on mathematical ability. The critical thinking profile in solving the described ill-structured problem consists of several stages, namely (1) Analyze; (2) Browse; (3) Create; (4) Decision-making; (5) Evaluate; and (6) List or with the term A-B-C-D-E plus L based on critical thinking skills, namely (1) Interpretation; (2) Analysis; (3) Conclusion; (4) Evaluation; (5) Explanation; and (6) Self-regulation. The subjects of this study consisted of one student of mathematics education who had the high mathematical ability and one student of mathematics education who had the moderate mathematical ability. They were interviewed based on the results of the Ill-Structured problem-solving. This research used a descriptive qualitative approach. The data obtained were validated, then analyzed with several steps, namely: reduction, data presentation, categorization, interpretation, and inference. The results showed that the mathematics education students carried out critical thinking processes in solving ill-structured problems through six (6) stages, namely: Analyze, Browse, Create, Decision-making, Evaluate, and List or with the term A-B-C-D-E plus L, those which refer to the stages of critical thinking skills, including Interpretation, Analysis, Conclusions, Evaluation, Explanation, and Self-regulation.

Comparing metacognitive regulation and socially shared metacognitive regulation in face-to-face and online learning settings in ill-structured problem solving

For collaborative groups to succeed, problem solvers need to agree on what the problem is and how to solve it. In ill-structured problems, the problem solvers switch back and forth between redefining the problem and generating solutions. This lack of parameters and structure implies that solving ill-structured problems is a complicated process, which can present problems in several different phases of problem solving. Efficient metacognitive regulation (MR) and socially shared metacognitive regulation (SSMR) skills benefit ill-structured problem solving. Online environments often lack the necessary social dimension to foster MR and SSMR. In the current article we report on a natural experiment caused by COVID-19 which forced a classroom-based workshop into an online version, thus contrasting face-to-face and audio-synchronous online learning setting in an Educational Sciences course of the Open University of the Netherlands. The student groups were presented with an ill-structured problem during which MR and SSMR processes were analyzed. We found that groups from the online setting demonstrated more MR processes than the face-to-face groups whereas the face-to-face groups engaged in more SSMR than the online groups.

Designing a Framework to Facilitate Metacognitive Strategy Development in Computer-Mediated Problem-Solving Instruction.

Metacognition is a key component of ill-structured problem solving. As such, there is a need for instructional design guidance for metacognitive skill development. This study addressed this need through the creation of a computer-based interactive content design framework to guide the design of metacognitive scaffolds for ill-structured problem-solving instruction. It utilized a type II design and development research approach and formative design principles to create a comprehensive and generalizable instructional design framework. The framework was composed by synthesizing research and practical literature and evaluated by experts in related fields. Key components of the framework include metacognitive strategies, instructional design strategies, interactive media types, question prompts, and feedback. Instructors, course developers, and other key stakeholders could follow the guidelines proposed in this framework to create metacognitive-based ill-structured problem-solving instruction using e-Learning authoring tools. This study bridges the gap between theory and practice, as well as adds to literature in media research with focusing on utilizing various media types to create effective learning materials.

An exploration of the relationship between argumentative prompts and depth to elicit alternative positions in ill-structured problem solving

An exploration of the relationship between argumentative prompts and depth to elicit alternative positions in ill-structured problem solving

Characteristics of Prospective Student Teacher’s Representation in Solving Ill-Well Algebraic Problems

Mathematical representation is an important aspect of mathematical problem-solving. But prospective student teachers’ ability of a mathematical representation in ill-structured problem solving is still very limited compared to that in well-structured problem-solving. However, ill-structured problems supported mathematical abstraction used in mathematical concept understanding. This study described the characteristics of prospective student teachers’ representations and translation among representation in ill-structured and well-structured social algebraic problem-solving. Thirty Indonesian prospective students teachers have to solve the ill-well algebraic problems by using think-aloud while recorded using a video recorder and the researchers observed by writing on a field note to record the important events. Data were analyzed using a comparative method so that it was obtained the different characteristics of representations between solving ill-structured and well-structured problems. The result showed that verbal and symbolic representations used by subjects to compute, detect and correct an error, and justify their answers in ill-structured problem solving but visual representation only used by the first subject to detect and correct error. The subjects lack to uncover necessary information to solve the ill-Structured problem compared to that of a well-structured problem. It means that representation is important to be studied further because it affected to ill-structured problem ability.

Role-Playing to Enhance Student Ill-Structured Problem-Solving Ability

Role-Playing to Enhance Student Ill-Structured Problem-Solving Ability

Guardrails to Constructing Learning: the Potential of Open Microcredentials to Support Inquiry-Based Learning

Inquiry-based learning has been growing in popularity, but the ill-structured nature of complex problem-solving still has challenges related to how to ensure students learn the content and how to provide feedback. This paper addresses this gap by exploring how open microcredentials can support open-ended learning by providing “guardrails” that simultaneously honor the openness of student inquiry while addressing these challenges. This manuscript begins by exploring the theoretical tenents of IBI and the importance of self-directed learning in ill-structured problem-solving. We then discuss the challenges documented in the literature and how microcredentials could address some of the implementation issues described in the literature.

THE EFFECTS OF INDEXING PROMPTS ON PROBLEM-SOLVING IN CASE LIBRARY LEARNING

Researchers have suggested that case library learning is an effective instructional method that promotes argumentation skills for ill-structured problem-solving. However, little research has examined scaffolding strategies to implement effective case library learning. The aim of this research was to examine the effects of indexing prompts as scaffolds on argumentation skills during problem-solving in case library learning. A quasi-experimental design was employed for the research. A total of 111 first-year students in a university across three sections in a career development course participated in the experiment. Participants were provided with three different indexing prompts: explanation-based indexing prompts (focused on self-explaining anomalies of individual cases), difference-based indexing prompts (focused on self-explaining similarities and differences between cases), and no prompts (allowing spontaneous self-explanations when studying cases). Learners’ argumentation essays comprising initial arguments, counterarguments, and rebuttals were collected. The results found that learners who were prompted to generate mental indices outperformed the learners in the control group when constructing argumentation. More specifically, explanation-based indices were beneficial in making counterarguments and rebuttals, and difference-based indices were helpful when making rebuttals. These findings suggest that indexing cases based on both exploration of the anomalies of each case and comparisons between cases improves argumentation by facilitating case retention, retrieval, and reuse. Keywords: argumentation skills, case library learning, case-based reasoning, indexing prompts.

Use of a Cornerstone Project to Teach Ill-Structured Software Design in First Year

Contribution: A first-year programming course was redesigned with a large, open-ended robotics project. The course design aligns with best practices for promoting development of students' self-efficacy in solving ill-structured software design problems. Background: From Jonassen's theory, problem-solving outcomes are dependent on the problem structure, complexity, and representation; and the characteristics of the solver. These characteristics are diverse, including knowledge, familiarity, and psychometric qualities of the solver (e.g., self-efficacy and motivation). Thus, better problem-solving outcomes are dependent on the development of these traits, and on the problem characteristics. Intended Outcomes: Pre-2010, course learning activities and assessments overly focused on syntax. The course was redesigned with a focus on ill-structured problem solving and design in high-fidelity problem domains. Application Design: Complex and ill-structured lecture examples, assignments, and exams were redesigned to reinforce the importance of software design and problem solving. An open-ended cornerstone project using robotics was added as a structured means of providing students practice with solving ill-structured and open-ended problems. The assignment and exam questions, with the course cornerstone project, achieve instructional alignment in the course. Findings: The results show that students' self-efficacy improved from start to end of term. The course design achieves several objectives: 1) students learned the requisite programming skills; 2) students developed their self-efficacy in programming and design; and 3) students demonstrated strong problem-solving outcomes.

Promoting learning in online, ill-structured problem solving: The effects of scaffolding type and metacognition level

This study aims to identify the effects of scaffolding type (supportive or reflective) and metacognition level (low or high) on presence, problem-solving performance, and achievement in online ill-structured problem solving. One hundred forty-eight students who enrolled in a college-level course on instructional design participated in this study in South Korea. The course was delivered as eight sessions led by the same instructor using the same content, and four of them were provided with supportive scaffolding, while the other four with reflective scaffolding. All of them were given an ill-structured problem of designing a lesson plan for a three-week project in a web-based learning environment without any face-to-face classes or meetings, and were asked to go through five stages of problem-solving. Metacognition and presence were measured using survey instruments, while problem-solving performance and achievement were measured using a rubric and quiz items, respectively. Data were analyzed using two-way MANOVA and ANCOVA, using pretest scores as a covariate. The results indicated that the reflective scaffolding group scored higher on cognitive and social presence, and also on problem representation, monitoring and evaluation in problem-solving performance than the supportive scaffolding group. The reflective scaffolding group also showed higher achievement than did the supportive scaffolding group. There was a significant interaction effect between scaffolding types and metacognition level on teaching presence and achievement. The results provide implications on the design of scaffolding for online ill-structured problem solving activities in association with learner characteristics.

Enhancing the learning effectiveness of ill-structured problem solving with online co-creation

ABSTRACT Ill-structured problem solving is widely believed to promote learning in higher education but its multiplicity (i.e. multiple solutions and evaluation criteria) is often seen as a challenge to manage. This study shows that the multiplicity can be managed as well as leveraged to enhance learning effectiveness through online co-creation. Three co-creation activities are identified and their effects on different aspects of learning effectiveness are assessed in a study involving 225 tertiary-level students. Results indicate that solution co-creation and solution sharing enhance cognitive learning (e.g. perceived knowledge about a subject topic), while decision co-creation enhances epistemic learning (e.g. perceived understanding of criteria of knowing). The findings demonstrate the value of online co-creation and they pave the way for more research on online co-creation in other collaborative pedagogical practices such as co-skilling.

An inquiry of synergy structure and its effect on ill-structured problem solving

An inquiry of synergy structure and its effect on ill-structured problem solving

The effect of sustained vs. faded scaffolding on students’ argumentation in ill-structured problem solving

Research suggests that scaffolding is an important element when gaining problem-solving skills. However, very little research has investigated the role of fading and explored its implications in the context of deep learning. To address this gap, we investigated the effects of fading question prompts on argumentation as learners were given two fading schedules, (1) sustained scaffold schedule, and (2) faded scaffold schedule. We employed three different measurements of argumentation quality to triangulate the results. When using the rubric assessment method, we found no significant differences between the two conditions in argumentation quality. However, when using learning analytics to examine the conceptual linkages of students' knowledge structure, we found that students in the sustained scaffolding condition performed significantly better than the students in the faded condition. The results indicated that (a) scaffolds should not be faded before students have acquired the necessary problem-solving processes and (b) that novices might need a fuller set of scaffolds for a longer period to support their problem-solving performance. Implications for theory and methods are discussed.

Student Learning of Complex Earth Systems: A Model to Guide Development of Student Expertise in Problem-Solving

ABSTRACTEngaging students in problem-solving concerning environmental issues in near-surface complex Earth systems involves developing student conceptualization of the Earth as a system and applying that scientific knowledge to the problems using practices that model those used by professionals. In this article, we review geoscience education research related to student learning and ill-structured problem-solving in the classroom. This article has two main goals: (1) to propose a model that applies the National Research Council (NRC, 2012) Science and Engineering Practices to students engaged with authentic, ill-structured problems centered on environmental issues and complex near-surface Earth systems (CNSES), and (2) analyze existing literature in the field of ill-structured problem-solving in CNSES to validate the proposed model. Eleven research studies met the inclusion and exclusion criteria. Although none of the selected articles met every component of the model, many of the papers only lacked a few components. We suggest the proposed model will help to alleviate student difficulties in the classroom that arise from lack of background knowledge and enthusiasm about the course or problem, and help guide the design of instructional activities that seek to engage geoscience students in authentic environmental problems.

Research Projects in Physics: A Mechanism for Teaching Ill-Structured Problem Solving

Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or ill-structured, problems, similar to the types of problems students might face in their professional lives. Given the national discourse on educational system reform aligned with 21st century skills, including problem solving, it is critical to provide educational experiences that help students learn to solve all types of problems, including ill-structured problems.

Do cases teach themselves? A comparison of case library prompts in supporting problem-solving during argumentation

Theorists have argued instructional strategies that emphasize ill-structured problem solving are an effective means to support higher order learning skills such as argumentation. However, argumentation is often difficult because novices lack the expertise or experience needed to solve contextualized problems. One way to supplement this lack of experience is through case-library learning environments that provide detailed stories of expert problem solving. In the current study, participants were provided three different variations of case libraries when solving an argumentation task: case library with no prompts, case library with retain prompt (focused on understanding an individual case), and case library with retrieval/reuse prompt (focused on understanding similarities with others cases in the case library). This study found that the no prompt and case library with retain prompts outperformaed the case library with retrieval/reuse prompts. The finding was found on measurements of counterclaim and overall holistic scores on the transfer task. The findings suggest the design of the cases within the library impacts how the participants adopted the case as a vicarious experience and transferred the experience to solve problems.

Instructional Scaffolding To Support Ill-Structured Problem Solving: A Review

Provision of an alternative instructional platform has encouraged students’ involvement in online social collaborative learning that could potentially enhance problem-solving (PS) skill. There are many types of scaffoldings proposed by researchers to inculcate this skill; however, concern arises as a result of an ill-defined problem. Besides being complex than a well-defined problem, its uniqueness originates from the integration of domains in a problem and multiple solutions that can be generated out of it. This study aims to identify the dominant type of scaffold used to guide ill-defined PS, to determine the common platform used and the education level where ill-defined PS is mostly studied. The search and review of relevant articles were done through online databases, journals and Google Scholar search engine using keywords of scaffolding problem solving, ill-structured problem, scaffolding ill-defined problem and support in PS. The findings revealed that metacognitive scaffolding (MS) is dominant in supporting ill-structured PS. MS assists in realigning the thinking of an individual to ensure proactive measures taken in the process of PS. Nevertheless, majority of the previous studies of MS were carried out in higher institutions instead of schools and within formal platform e.g., Learning Management System (LMS). Thus it is hoped that this review will give insights for educators to inculcate MS and improve PS skill in schools and through the use of new platform of social media.