Well-structured Problems Research Articles

Methodology and Multicriteria Algorithm for Group Decision Support in Classification Problems

In this work, a Group Decision methodology and algorithm for small collaborating teams is introduced. It is based on a multicriteria algorithm for classification decisions, where aggregation of member preferences is executed at the parameter level. The algorithm applies to relatively well-structured problems guided by a process facilitator. Initially, a set of parameters is proposed by the facilitator to the group and next group members evaluate the proposed parameter set and express their preferences in numeric or linguistic format. Individual preferences are aggregated by appropriate operators, and a set of group parameter values is generated, which is used as input for the classification algorithm. NeXClass multicriteria classification algorithm is used for the classification of alternatives, initially at a training set of alternatives and later at the entire set. Finally, group members evaluate results, and consensus, as well as satisfaction metrics, are calculated. In case of a low acceptance level, problem parameters are reviewed by the facilitator, and the aggregation phase is repeated. The methodology is a valid approach for group decision problems and can be utilized in numerous business environments. The algorithm can be also utilized by software agents in multiagent environments for automated decision-making, given the large volume of agent-based decision-making in various settings today.

Why and how to implement worked examples in upper division theoretical physics

Studying worked examples has been shown by extensive research to be an effective method for learning to solve well-structured problems in physics and mathematics. The effectiveness of learning with worked examples has been demonstrated and documented in many research projects. In this work, we propose a new four-step approach for teaching with worked examples that includes writing explanations and finding and correcting errors. This teaching method can even be implemented in courses in which homework performance constitutes part of the grading system. This four-step approach is illustrated in the context of Lagrangian mechanics, which is ideal for the application of worked examples due to its universal approach to solve problems.

Comparing Students' Problem-Solving Processes on Probability Tasks: Well-Structured and Ill-Structured Tasks

This study aims to describe the differences in the problem-solving abilities of well-structured problems and ill-structured problems models related to the concept of opportunity for Grade VIII junior high school students. Two students with the same mathematical abilities were selected to be subjects according to our research objectives. The results show that the two samples find it more difficult to solve well-structured problems than ill-structured problems. When at the stage of understanding the problem students need to read the questions repeatedly and when asked to retell the students can't do it well. In the questions of the type of well-structured problems subject 1 can only mention what is asked, but it is not appropriate to state the conditions needed to solve the problem and in subject 2 it is found otherwise, while in ill-structured problems it is not appropriate to write down what is known but write down what is asked with precise and knowing the requirements to solve the problem. Subject 1 uses logical and logical reasoning strategies. Then, subject 2 uses a trial and error strategy with logical reasoning. The two subjects carried out problem solving according to plan, carried out the re-checking stage, and were able to find solutions to problems that did not require calculations in them but could not find solutions to problems that contained calculations and had to be solved by utilizing the probability theorem. These results can be used as an evaluation in the learning process or a reference for further research.

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

Editorial: Toyota Production System practices asFast‐and‐Frugalheuristics

Editorial: Toyota Production System practices as<scp>Fast‐and‐Frugal</scp>heuristics

Optimizing expected policy outcomes through creative problem structuring: Police human resource development policy in the southeast Sulawesi regional police, Indonesia

This study aims to investigate the problem structuring process using creative methods to create well-structured problems, and how it can optimize the expected policy outcomes of human resource development in regional police. This study uses a qualitative research method by integrating qualitative data from semi-structured interviews and administrative data. Five informants were purposively selected, four of whom were authorized officials in the field of human resource development at regional police institutions, and the other was a prominent civic organization activist. The interview data were analysed using qualitative interactive models, while directed content analysis was applied to administrative data. The results of the study show that the problem structuring process in human resource development policies for regional police is limited to identifying the main elements of problem definition through the partial use of brainstorming methods and classification analysis. Such a problem structuring process cannot create well-structured problems that optimize expected policy outcomes of human resource development. However, the use of creative problem-solving methods in a comprehensive manner can optimize the expected policy outcomes from the development of more critical and collaborative human resource development in the regional police force.

Improving middle school students' geometry problem solving ability through hands-on experience: An fNIRS study.

Hands-on learning is proposed as a prerequisite for mathematics learning in kindergarten and primary school. However, it remains unclear that whether hands-on experience aids understanding of geometry knowledge for middle school students. We also know little about the neural basis underlying the value of hands-on experience in math education. In this study, 40 right-handed Chinese students (20 boys and 20 girls) with different academic levels were selected from 126 seventh-grade students in the same school, who learnt "Axisymmetric of an Isosceles Triangle" in different learning style (hands-on operation vs. video observation). Half of them operated the concrete manipulatives while the other half watched the instructional videos. The learning-test paradigm and functional near-infrared spectroscopy (fNIRS) technique were used to compare the differences in geometry reasoning involved in solving well-structured problems and ill-structured problems. Behavioral results showed that hands-on experience promoted students' performances of geometry problem-solving. Students with lower academic level were more dependent on hands-on experience than those with higher academic level. The fNIRS results showed that meaningful hands-on experience with concrete manipulatives related to learning contents increased reactivation of the somatosensory association cortex during subsequent reasoning, which helped to improve the problem-solving performance. Hands-on experience also reduced students' cognitive load during the well-structured problem-solving process. These findings contribute to better understand the value of hands-on experience in geometry learning and the implications for future mathematics classroom practices.

The Compound Area of Quadrilaterals and Triangles: A Worked Example Based Learning Design

Complex yet hierarchical mathematical material in fact does not mean that the process of schema acquisition and accommodation in long-term memory is easy. For an instance, year seven students learn to solve problems related to the compound area of quadrilaterals and triangles. This problem may be categorized as a well-structured problem, therefore, it might be procedurally obvious to reach the solution, for those who have possessed sufficient prior knowledge of the aspects of the shapes. This study aims to discuss instructional strategy for novices when learning to solve problems like these. Based on a cognitive load theory, the strategy of worked example could be applied effectively for novices. The design of the worked example must be presented in such a way it could minimize extraneous cognitive load. The composite shapes of quadrilateral and triangles might be challenging to be described in an integrated format to avoid the split attention effect. This paper shows how this can be done by using techniques, such as (1) number sequences of the solution steps; (2) different colors for prompting attention resource; (3) less wording, more procedure application; and (4) consistency of layout within overall material. In order to apply these, the instructional designers should follow ADD steps, (1) Analyze the learning content, arrange them accordingly; (2) Design one worked example, evaluate its accuracy and niche; and (3) Develop into several worked example pairs. Two worked example with paired problems have been successfully developed and declare valid. Eventually, it might be suggested that comprehensive consideration when designing worked example that contain pictures should reflects how students use their cognitive resource during learning.

Enhancing ecological hierarchical problem-solving with domain-specific question agendas

ABSTRACT Promoting problem-solving in students is an important aim of secondary science education. There is a mismatch, however, between the complex, ill-structured nature of realistic scientific problems, versus the well-structured problems students are generally confronted with. The current study investigates a teaching-learning strategy that resolves this mismatch by combining a focus on hierarchical problem-solving strategies for complex, authentic problems with the use of domain-specific question agendas that represent scientific perspectives. Three design principles were applied to develop an exemplary lesson series that was implemented in two Dutch pre-university classes. A pre-/post-test research design was followed in which data was collected in the form of sets of student-generated research questions. Additionally, audio recordings of lessons and student interviews were collected and analysed. Results indicate that participating students became more proficient at applying hierarchical problem-solving strategies like (1) reducing complex ecological problems to more manageable subproblems by formulating productive research questions and (2) identifying types of ecological problems by connecting them to domain-specific question agendas (problem-abstraction). A qualitative analysis of the teaching-learning process and student interviews informed potential refinements of the design principles, namely the use of more diverse contexts and a greater focus on collaborative learning.

Classical paradigms versus complexity thinking in engineering education: an essential discussion in the education for sustainable development

PurposeThis paper aims to discuss how the theory of complex thinking can be considered an interesting element in engineering education, especially in the context in which challenges toward sustainable development are multidisciplinary.Design/methodology/approachThis viewpoint synthesizes the main reflections and discussions generated during a process of debate, research and creation of a proposal for an undergraduate engineering course at a higher education institution in Brazil. The literature on engineering education, sustainability and complexity was considered in an integrated way. Debates were conducted considering the authors’ knowledge and experience as professors of engineering courses and researchers in the field of sustainability. A qualitative and reflexive approach was used to organize the main discussions.FindingsThe prevailing classical engineering paradigm trains professionals to think from a Cartesian, reductionist perspective, appropriate for solving well-structured problems with known solution paths and convergent answers. However, addressing sustainability challenges requires a different kind of thinking capable of dealing with situations characterized by uncertainty, emergence and incompleteness of knowledge. Complexity thinking can be useful for this purpose as it provides a broad system approach to deal with ill-defined, ill-structured and unpredictable problems. This study can be understood as a call to researchers and professionals to consider the value and importance of complexity thinking to advance engineering education for sustainability.Originality/valueThe need to overcome the limits of the classical engineering paradigm is emphasized in the context of sustainability. Complex thinking is considered as a path toward a paradigm shift in engineering education for sustainability. It can contribute to the training of professionals to face pressing challenges now and in the future. This viewpoint provides some insights to enhance debates on education engineering.

THE EFFECT OF GIVING ILL-STRUCTURED MATH PROBLEM AND WELL-STRUCTURED MATH PROBLEM ON THE SELF-EFFICACY OF JUNIOR HIGH SCHOOL STUDENTS

This study aimed to determine the effect of giving ill-structured problems and well-structured problems to students' self-efficacy. The study population was class VIII students at Junior High School 1 Ngawen Blora which consisted of an experimental class and a control class with the selection of samples using purposive sampling technique. This research is a quantitative research with a comparative problem formulation that compares the increase in self-efficacy between students who are given well-structured math problems and ill-structured math problems. The data analysis technique used was t-test dependent and t-test independent. The results showed that: 1) there is an effect of giving ill-structured math problems on students' self-efficacy at a significant level of 0.05; 2) there isn’t an effect of giving well-structured math problems on students' self-efficacy at a significant level of 0.05; 3) there is a difference in changes in student self-efficacy between giving ill-structured math problems and giving well-structured math problems at a significant level of 0.05

The Effects of Self-Regulated Learning Support on Learners’ Task Performance and Cognitive Load in Computer Programing

This study explores the effect of self-regulated learning support on learners’ cognitive load and problem-solving performance, considering cases from well-structured to ill-structured tasks in a computer programing course. Sixty-seven undergraduate students in a computer programing fundamentals course were randomly assigned into one of two groups: (1) experimental group ( N = 34; received self-regulated learning support) and (2) control group ( N = 33). Participants in both groups were asked to solve programing problems using Python over 3 weeks, and their cognitive load levels were measured after each week. The results showed that novice learners’ self-regulated learning skills can be influenced by learning support, which contributes to solving complex problems. The results also suggest that, given the sequence of tasks (i.e., basic and advanced well-structured and ill-structured problems), self-regulated learning support may require time to be effective. The germane load of the experimental group was higher for well-structured problems than that of the control group. Using logistic regression, the two groups were differentiated through different variables measured in this study, which showed a high predictive explanatory power. The results provide implications for designing self-regulated learning support for programing courses, using problem-based learning in association with problem-solving skills, self-regulated learning skills, and cognitive load management.

Exploring Agency in Capstone Design Problem Framing

<strong>Background:</strong> Because of prior experience solving well-structured problems that have single, correct answers, students often struggle to direct their own design work and may not understand the need to frame ill-structured design problems. <strong>Purpose: </strong>Framing agency—defined as making decisions that are consequential to framing design problems and learning through this process—sheds light on students’ treatment of design problems; by framing, we mean the various actions designers take to understand, define, and bound the problem. Using the construct framing agency, we sought to characterize design team discourse to detect whether students treated design problems as ill- or well-structured and examine the consequences of this treatment. <strong>Method: </strong>Data were collected through extended participant observation of a capstone design course in a biomedical engineering program at a large research university. Data included audio and video records of design team meetings over the course of framing and solving industry-sponsored problems. For this paper, we analyzed three cases using sociolinguistic content analysis to characterize framing agency and compared the cases to illuminate the nuances of framing agency. <strong>Results: </strong>All teams faced impasses; one team navigated the impasse by framing the problem, whereas the others treated the problem as given. We identified markers of agency in students’ discourse, including tentative language, personal pronouns, and sharing ownership. <strong>Conclusions:</strong> Framing agency clarifies the kinds of learning experiences students need in order to overcome past experiences dominated by solving archetypical well-structured problems with predetermined solutions.

Learning to Frame Complex Sustainability Challenges in Place: Explorations Into a Transdisciplinary “Challenge Lab” Curriculum

Complex sustainability challenges may never be fully solved, rather requiring continuous, adaptive, and reflexive responses over time. Engagement of this nature departs from well-structured problems that entail expected solutions; here, focus shifts toward ill-structured or ill-defined issues characterized by wickedness. In the context of complex challenges, inadequate or absent framing has performative implications on action. By overlooking the value of framing, eventual responses may not only fall short; they may even displace, prolong, or exacerbate situations by further entrenching unsustainability. In educational settings, we know little about how curriculum designs support challenge framing, and how students experience and learn framing processes. In this paper we explore a transdisciplinary “Challenge Lab” (C-Lab) curriculum from a perspective of challenge framing. When considering framing in higher education, we turn to the agenda in education for, as and with sustainable development to be problem-solving, solutions-seeking or challenge-driven. We introduce framing as a boundary object for transformative praxis, where sustainability is held to be complex and contextual. This study is qualitative and case-based, designed to illuminate processes of and experiences into sustainability challenge framing in a transdisciplinary learning setting. Methodologically, we draw from student reflective diaries that span the duration of a curriculum design. We structure our results with the support of three consecutive lenses for understanding “curriculum”: intended, enacted, and experienced curriculum. First, we present and describe a C-Lab approach at the level of ambition and design. Here it is positioned as a student-centered space, process, and institutional configuration, working with framing and re-framing complex sustainability challenges in context. Second, we present a particular C-Lab curriculum design that unfolded in 2020. Third, we illustrate the lived experiences and practical realities of participating in C-Lab as students and as teachers. We reflect upon dilemmas that accompany challenge framing in C-Lab and discuss the methodological implications of this study. Finally, we point toward fruitful research avenues that may extend understandings of challenge framing in higher education.

Reframing Architecture through Design

Reframing Architecture through Design

Investigating how university students collaborate to compose physics problems through structured tasks

Traditionally, scholars in physics education research have focused on students solving well-structured learning activities at the university. However, due to their constrained nature, these problems hinder collaboration and idea generation. In order to encourage student collaboration and decision making demands among undergraduate students in an introductory physics course, we utilized a real-world problem where groups were asked to compose a well-structured physics problem for younger learners. In this study we explored how they collaborated in composing physics problems. Data collection consisted of audio recording of the group discussions while they were collaborating to develop their physics problems and their respective problem solutions. Through interviews, we accessed participants’ perceptions of the task and related challenges. Results suggest that composing problems is an opportunity for participants to propose ideas and make decisions regarding the goals of the problem, concepts and procedures, contextual details, and magnitudes and units to introduce in their activities. Further, participants valued the open-ended nature of the task and recognized its benefits in utilizing physics ideas into context, which in turn enabled collaboration in a way not experienced by them with traditional well-structured problems. These findings shed light on the nature of composing physics problems in undergraduate courses, where participants assume a different role by facing a real-world activity that encourages expertise through physics-related communication and writing.Received 7 January 2020Accepted 25 January 2021DOI:https://doi.org/10.1103/PhysRevPhysEducRes.17.010120Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesScientific reasoning & problem solvingProfessional TopicsLower undergraduate studentsPhysics Education Research

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.

The Use of Metacognitive Strategies in Solving Mathematical Problems

The ability to solve mathematical problems is useful not only for the absorption of knowledge, but also for the formation of thinking and attitude in solving the problems. This research was conducted to describe the metacognitive strategies that students undertake when solving mathematical problems. Metacognitive strategy is one of the methods used in problem solving that emphasizes to build the well-structured of thinking, by deciding what to do and where to go in realizing and overcoming obstacles. Data obtained through problem solving by the subject and then analyzed qualitatively. Through the application of metacognitive strategies, a systematic and well-structured problem solving is implemented based on the logical thinking steps, and allows to the right solution. For students, metacognitive strategies are very important to build a strong foundation of thinking and to be applied in various situations and levels of complexity problems.

Social networks and academic performance in physics: Undergraduate cooperation enhances ill-structured problem elaboration and inhibits well-structured problem solving

For several decades, scholars have studied cooperation and its outcomes in the educational context. Yet, we lack a complete understanding of how different instructional strategies impact the relationship between cooperation and learning. Here we studied how different instructional strategies led to different social configurations and their differences in individual academic performance in an experiment with 82 first-year students from an introductory physics course. Surprisingly, we found that students who actively seek out information on multiple peers are less likely to achieve good performance on well-structured (algebra-based) problems, whereas, for ill-structured (real-world-like) problems, this effect depended on the features of the learning environment. Besides, we observed that good performance on ill and well-structured problems responded to different social network configurations. In a highly clustered network (which contains redundant information), students performed well-structured problems better than ill-structured problems. In contrast, students with access to network structural holes (which enable access to more diverse information) performed ill-structured problems better than well-structured problems. Finally, ill-structured problems could promote creative thinking, provided that instructors guide the solving process and motivate students to engage in the appropriate cognitive demands these problems entail. Our results suggest that teaching and instructional strategies play an important role in cooperative learning; therefore, educators implementing cooperative learning methods have to accompany them with adequate instructional strategy.

Karakteristik Kemampuan Siswa SMA dalam Menyelesaikan Well dan Ill Structured Problems pada Pembelajaran Fisika

One effort to improve the quality of learning physics is by developing abilities in problem solving. Problem solving abilities are complex cognitive activities using thought processes. For students, by knowing problem solving abilities, they can do self-reflection and have learning motivation to change for the better. For teachers, knowing students' abilities in problem solving can be used as a guide for designing learning strategies and evaluations that are suitable for improving problem solving skills. For this reason, it is necessary to identify problem solving abilities of high school students. Methods of research data collection using tests and interviews. Tests for measuring problem solving abilities are categorized as ill-structured problems and well-structured problems. The results showed that students were better able to solve well-structured problems than ill-structured problems. The ability of students to solve well-structured problems and ill-structured problems, most of them are included in the category of novice and only a small proportion are categorized as expert. The novice and expert characteristics based on the results of the study is described in detail in the part of discussion.