Ill-defined Problems Research Articles

Connecting Problem-solving Style to Peer Evaluations of Performance in Secondary Cooperative Learning Projects

With an evolving and expanding agricultural industry, it is crucial to provide future professionals with valuable experiences and skills in problem solving, communication, and teamwork. Agricultural summer programs for secondary students, which provide cooperative learning experiences with a focus on group work and problem solving, aim to help meet the current demand of employment in the various disciplines within agriculture. Many of these summer programs offer secondary students opportunities to learn more about agriculture, and gain experiences as they work in teams to consider the agricultural issues they may face upon entering the workforce. While adaption-innovation theory has been used in agribusinesses across the world to provide explanation to how people work together in teams to solve complex ill-defined problems, little is known regarding the degree the theory applies to secondary student learning in groups. This study utilized a quantitative, quasi-experimental design to further explore how high school students’ problem-solving styles impact their perceptions of group members in a cooperative learning experience while participating in the Virginia’s Summer Residential Governor’s School for Agriculture program. The findings and recommendations can assist instructors in providing cooperative learning experiences to their students and further maximize high school student’s experiences in working in teams and solving complex ill-defined problems associated with agricultural issues.

Establishment of a Digital Knowledge Conversion Architecture Design Learning with High User Acceptance

The purpose of this study is to design a knowledge conversion and management digital learning system for architecture design learning, helping students to share, extract, use and create their design knowledge through web-based interactive activities based on socialization, internalization, combination and externalization process in addition to learning in the “design studio” at school. In addition, the technology acceptance model3 is used in this study to measure how students accept the system developed in this study by analyzing the user behavioral and environmental factors that can affect their use of the system. The results of questionnaire surveys based on TAM3 indicate that this digital learning environment based on knowledge management can effectively reduce the challenge of “ill-defined design problems” for students and help to promote better learning results. Therefore, it can be concluded that the knowledge transfer learning system developed in this study is very helpful for learning of architecture design.

A Knowledge Conversion Model Based on the Cognitive Load Theory for Architectural Design Education

The education of architectural design requires balanced curricular arrangements of respectively theoretical knowledge and practical skills to really help students build their knowledge structures, particularly helping them in solving the problems of cognitive load. The purpose of this study is to establish an architectural design knowledge conversion model, helping students to obtain architectural design knowledge through a learning process of knowledge sharing/socialization, extraction, externalization, integration, creation and internalization. This model can help students to effectively solve the problems of cognitive load in the learning process, achieve knowledge construction and storage through meaningful learning, apply their knowledge in their future designs and, ultimately, improve their design capability. This study starts with a literature review on theories of knowledge conversion and cognitive load to establish an architectural design knowledge conversion model complemented with especially designed curricular contents and activities. The model is applied in actual teaching to find out if the application of this model has a positive influence on the students in their learning of architectural design, solving the ill-defined problems in their learning and easing their cognitive load.

Ranking influential spreaders is an ill-defined problem

Finding influential spreaders of information and disease in networks is an important theoretical problem, and one of considerable recent interest. It has been almost exclusively formulated as a node-ranking problem —methods for identifying influential spreaders output a ranking of the nodes. In this work, we show that such a greedy heuristic does not necessarily work: the set of most influential nodes depends on the number of nodes in the set. Therefore, the set of n most important nodes to vaccinate does not need to have any node in common with the set of n + 1 most important nodes. We propose a method for quantifying the extent and impact of this phenomenon. By this method, we show that it is a common phenomenon in both empirical and model networks.

The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

The state-of-the-art in realization of the method of distribution of relaxation times (DRT) as applied to the analysis of data of electrochemical impedance spectroscopy is briefly surveyed. The theoretical fundamentals of the DRT method are described, the methods of solving the Fredholm equation of the 1st order with respect to the unknown DRT function are considered as an ill-defined problem. The Tikhonov regularization method presently considered as the most suitable for solving this equation is discussed. For several numerical experiments, the high resolution of the DRT method and its stability with respect to noise in impedance spectra are demonstrated. Among the problems and limitations of the DRT methods, the choice of the optimal regularization coefficient is considered as the most significant. Particularly, it is shown that in those cases where several relaxation processes with the constant phase angle appear in the response of objects under study to ac disturbances, different regularization coefficients should be selected for each of these elements in order to obtain adequate results.

Applying decision-making techniques to Civil Engineering Projects

Multi-Criteria Decision-Making (MCDM) techniques are found to be useful tools in project managers’ hands to overcome decision-making (DM) problems in Civil Engineering Projects (CEPs). The main contribution of this paper includes selecting and studying the popular MCDM techniques that uses different and wide ranges of data types in CEPs. A detailed study including advantages and pitfalls of using the Analytic Hierarchy Process (AHP) and Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) is introduced. Those two techniques are selected for the purpose of forming a package that covers most available data types in CEPs. The results indicated that AHP has a structure which simplifies complicated problems, while Fuzzy TOPSIS uses the advantages of linguistic variables to solve the issue of undocumented data and ill-defined problems. Furthermore, AHP is a simple technique that depends on pairwise comparisons of factors and natural attributes, beside it is preferable for widely spread hierarchies. On the other hand, Fuzzy TOPSIS needs more information but works well for the one-tier decision tree as well as it shows more flexibility to work in fuzzy environments. The two techniques have the facility to be integrated and combined in a new module to support most of the decisions required in CEPs.

Problem Space Matters: The Development of Creativity and Intelligence in Primary School Children

Previous research showed that in primary school, children’s intelligence develops continually, but creativity develops more irregularly. In this study, the development of intelligence, measured traditionally, i.e., operating within well-defined problem spaces (Standard Progressive Matrices) was compared with the development of intelligence operating in ill-defined problem spaces (Creative Reasoning Task) and the development of creativity (Test of Creative Thinking-Drawing Production), in primary school children (N = 175) across four grade levels. Results showed that problem space matters: Traditional intelligence test scores increased regularly with grade level, whereas creativity, as well as intelligence operating in an ill-defined problem space, developed irregularly but similarly. This suggests that when creativity is fostered, intelligence’s ability to operate in ill-defined problem space may be fostered, likewise.

Resolving Wicked Problems: Appositional Reasoning and Sketch Representation

The influence of a design education upon reasoning in response to ill-defined design problems was examined through a comparative protocol study of design and non-design students. A statistical analysis compared distributions of and transitions between the activities naming, framing, moving, and reflecting. Design student protocols were characterized by significantly increased activity associated with reasoning between problem definition and solution ideation. In contrast, participants lacking any formal design education or experience indicated significantly increased reasoning towards problem definition, with little evidence of ideation. A subsequent qualitative comparison identifies sketching as a potential driver for both increased solution-focused activity and greater iteration between problem definition and solution ideation. Implications for design ability, sketching and appositional bridge-building between problem definition and solution ideation are discussed.

Very short-term reactive forecasting of the solar ultraviolet index using an extreme learning machine integrated with the solar zenith angle

Exposure to erythemally-effective solar ultraviolet radiation (UVR) that contributes to malignant keratinocyte cancers and associated health-risk is best mitigated through innovative decision-support systems, with global solar UV index (UVI) forecast necessary to inform real-time sun-protection behaviour recommendations. It follows that the UVI forecasting models are useful tools for such decision-making. In this study, a model for computationally-efficient data-driven forecasting of diffuse and global very short-term reactive (VSTR) (10-min lead-time) UVI, enhanced by drawing on the solar zenith angle (θs) data, was developed using an extreme learning machine (ELM) algorithm. An ELM algorithm typically serves to address complex and ill-defined forecasting problems. UV spectroradiometer situated in Toowoomba, Australia measured daily cycles (0500–1700h) of UVI over the austral summer period. After trialling activations functions based on sine, hard limit, logarithmic and tangent sigmoid and triangular and radial basis networks for best results, an optimal ELM architecture utilising logarithmic sigmoid equation in hidden layer, with lagged combinations of θs as the predictor data was developed. ELM’s performance was evaluated using statistical metrics: correlation coefficient (r), Willmott’s Index (WI), Nash-Sutcliffe efficiency coefficient (ENS), root mean square error (RMSE), and mean absolute error (MAE) between observed and forecasted UVI. Using these metrics, the ELM model’s performance was compared to that of existing methods: multivariate adaptive regression spline (MARS), M5 Model Tree, and a semi-empirical (Pro6UV) clear sky model. Based on RMSE and MAE values, the ELM model (0.255, 0.346, respectively) outperformed the MARS (0.310, 0.438) and M5 Model Tree (0.346, 0.466) models. Concurring with these metrics, the Willmott’s Index for the ELM, MARS and M5 Model Tree models were 0.966, 0.942 and 0.934, respectively. About 57% of the ELM model’s absolute errors were small in magnitude (±0.25), whereas the MARS and M5 Model Tree models generated 53% and 48% of such errors, respectively, indicating the latter models’ errors to be distributed in larger magnitude error range. In terms of peak global UVI forecasting, with half the level of error, the ELM model outperformed MARS and M5 Model Tree. A comparison of the magnitude of hourly-cumulated errors of 10-min lead time forecasts for diffuse and global UVI highlighted ELM model’s greater accuracy compared to MARS, M5 Model Tree or Pro6UV models. This confirmed the versatility of an ELM model drawing on θsdata for VSTR forecasting of UVI at near real-time horizon. When applied to the goal of enhancing expert systems, ELM-based accurate forecasts capable of reacting quickly to measured conditions can enhance real-time exposure advice for the public, mitigating the potential for solar UV-exposure-related disease.

Long-term trends accentuate the import of creative and critical thinking skills developed by design thinking and ill-defined questions

The economic, financial, and political trends such as stagnating standards of living, fiscal pressure, and an escalating mistrust of government were set in motion during the 1960s and 1970s. Due to the duration of the trends, the magnitude, but not the nature, of the challenges confronting the health care, nonprofit and public sectors has changed. Consequently, with the exception of adding topics relating to strategies for securing voluntary compliance and effectively interacting with constituents who are increasingly angry and opposed to government intervention, the Great Recession and subsequent Age of Austerity do not appreciably affect the Master in Public Administration (MPA) curriculum’s content. However, the intractable nature of the challenges accompanying the trends places a premium on cultivating the students’ critical thinking and creative skills. Meeting this challenge necessitates the adoption of learning strategies that shift to students a greater share of the responsibility for learning. One of the options for achieving the outcome is to provide students with the foundational materials and an ill-defined problem that, in conjunction with design thinking, maximizes the students’ freedom to independently define the problem, identify the requisite information for analysis, and develop solutions. The article provides examples of the learning strategy that has been applied in several courses.

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.

Strehler-Mildvan correlation is a degenerate manifold of Gompertz fit

Gompertz empirical law of mortality is often used in practical research to parametrize survival fraction as a function of age with the help of just two quantities: the Initial Mortality Rate (IMR) and the Gompertz exponent, inversely proportional to the Mortality Rate Doubling Time (MRDT). The IMR is often found to be inversely related to the Gompertz exponent, which is the dependence commonly referred to as Strehler-Mildvan (SM) correlation. In this paper, we address fundamental uncertainties of the Gompertz parameters inference from experimental Kaplan-Meier plots and show, that a least squares fit often leads to an ill-defined non-linear optimization problem, which is extremely sensitive to sampling errors and the smallest systematic demographic variations. Therefore, an analysis of consequent repeats of the same experiments in the same biological conditions yields the whole degenerate manifold of possible Gompertz parameters. We find that whenever the average lifespan of species greatly exceeds MRDT, small random variations in the survival records produce large deviations in the identified Gompertz parameters along the line, corresponding to the set of all possible IMR and MRDT values, roughly compatible with the properly determined value of average lifespan in experiment. The best fit parameters in this case turn out to be related by a form of SM correlation. Therefore, we have to conclude that the combined property, such as the average lifespan in the group, rather than IMR and MRDT values separately, may often only be reliably determined via experiments, even in a perfectly homogeneous animal cohort due to its finite size and/or low age-sampling frequency, typical for modern high-throughput settings. We support our findings with careful analysis of experimental survival records obtained in cohorts of C. elegans of different sizes, in control groups and under the influence of experimental therapies or environmental conditions. We argue that since, SM correlation may show up as a consequence of the fitting degeneracy, its appearance is not limited to homogeneous cohorts. In fact, the problem persists even beyond the simple Gompertz mortality law. We show that the same degeneracy occurs exactly in the same way, if a more advanced Gompertz-Makeham aging model is employed to improve the modeling. We explain how SM type of relation between the demographic parameters may still be observed even in extremely large cohorts with immense statistical power, such as in human census datasets, provided that systematic historical changes are weak in nature and lead to a gradual change in the mean lifespan.

Doctors as Makers.

Traditional skills and expertise are not enough to prepare future physicians for the complexity, instability, and uncertainty of clinical practice. Responding and making meaning from ill-defined or unusual problems calls for, even demands, creativity. In this article, the author suggests expanding the traditional role of doctor as science-using, evidence-based practitioner to include that of doctor as a "maker" (creator) and artist. Such a reimagining requires a shift in how we view medical knowledge and patients' stories, as well as a new appreciation for "not-knowing" as a generative, creative space in medicine. Creative thinking deserves a central place in the training of doctors, driven by a reconceptualization of the traditional educational model to include medical disciplines, humanities scholars, artists, and designers.

Designing Crowdcritique Systems for Formative Feedback

Intelligent tutors based on expert systems often struggle to provide formative feedback on complex, ill-defined problems where answers are unknown. Hybrid crowdsourcing systems that combine the intelligence of multiple novices in face-to-face settings might provide an alternate approach for providing intelligent formative feedback. The purpose of this study was to develop empirically grounded design principles for crowdcritique systems that provide intelligent formative feedback on complex, ill-defined problems. In this design research project, we iteratively developed and tested a crowdcritique system through 3 studies of 43 novice problem solvers in 3 formal and informal learning environments. We collected observations, interviews, and surveys and used a grounded theory approach to develop and test socio-technical design principles for crowdcritique systems. The project found that to provide formative feedback on ill-defined problems, crowdcritique systems should provide a combination of technical features including: quick invite tools; formative framing; a public, near-synchronous social media interface; critique scaffolds; “like” system; community hashtags; analysis tools and “to do” lists; along with social practices including: prep/write-first/write-last script and critique training. Such a system creates a dual-channel conversation that increases the volume of quality critique by grounding comments, scaffolding and recording critique, and reducing production blocking. Such a design provides the benefits of both face-to-face critique and computer-support in both formal and informal learning environments while reducing the orchestration burden on instructors.

WeChat: a new clinical teaching tool for problem-based learning.

Problem-based learning (PBL) is an instructional student-centered approach which utilizes carefully constructed real-world, ill-defined problems as a context for students to extend their prior experiences and knowledge through discussion and self-directed and collaborative learning that fosters the development of problem-solving and reasoning skills.1 Compared with traditional lecture-dominant teaching and learning approaches, PBL prompts students to actively engage not only in knowledge construction and develop competencies across multiple contexts,2,3 but also in self-directed learning and general work-related skills.4 PBL has a large contribution to medical education, but it has limitations. It is considered less effective than traditional learning methods because it is time-consuming.5 Other obstacles to the popularity of PBL include a predominating uncertainty about the breadth and depth of learning without a syllabus, concerns about overlooking things, and the high self-motivation required.6 So implementations of PBL is highly desirable. It is well known that Facebook and Twitter are introduced into medical education in colleges and universities in the western countries,7 achieving great success. Recently, Chinese medical educators are actively exploring new teaching methods to adapt to the social development. New media, WeChat,8 have been widely utilized in medical schools and exert a positive influence. WeChat is the most popular platform visited daily by university students in China. It is currently recognized as the best social networking site used by people of all ages and professions in China. WeChat is connecting more than a half billion Chinese people now. Apart from free chat, WeChat’s large-scale network platform hosts a vast amount of user-generated data, including text, voice call, video, and images. Group chat is perfect for professional online discussion. Its characteristics of convenience, promptness, and good cross-platform support enrich and simplify the communication model to offer WeChat application users communication that is more prompt.9 WeChat, owing to its immediate communication and source sharing, break the spatial and temporal limitations and change the teaching mode of the traditional classroom, making communication more convenient. The teaching mode of WeChat combined with PBL Ethics Review is used for a ongoing prospective study comparing WeChat-PBL and PBL. It is not necessary to the present descriptive study. The teacher divides all students into several WeChat groups with 3-4 students per group. After obtaining written agreement from patients, the teacher collects their clinical data, including basic information, chief complaint, symptoms, signs, and laboratory examinations. These data are presented in words. Imaging data and surgery materials are presented in images and video, respectively. The teacher delivers the materials and questions to the WeChat groups before class. The students research this material individually and then discuss the questions with each other in their small WeChat group. They can communicate and exchange ideas with their WeChat group colleagues to solve the problems. One representative of each group shows their discussion and conclusions in a slide show to the classroom. The teacher makes comments about their work. Students can further discuss their experiences after class to enhance the teaching effects.

Inverting the Nakanishi Integral Relation for a Bound State Euclidean Bethe–Salpeter Amplitude

The extraction of the weight function g of the Nakanishi integral representation of the Bethe–Salpeter amplitude is investigated. We studied the numerical inversion of the discretized Nakanishi kernel in the case of an Euclidean bound state. The discretized kernel is regularized by adding the identity operator times a small regularisation parameter \({\varepsilon}\) to avoid numerically unstabilities. We have found that the weight function g as well as the associated light-front valence wave function are unstable against variation of \({\varepsilon}\). These results suggest that the extraction of the Nakanishi weight function from an Euclidean amplitude, is an ill-defined problem. Without further assumptions on the solution or/and without developing more elaborate methods, the Nakanishi weight function, as well as the corresponding light-front valence wave function, cannot be safely determined.

APPROACHES IN DESIGN EDUCATION: THE ROLE OF PATTERNS AND SCENARIOS IN THE DESIGN STUDIO

The studio is the educational setting where architectural students dedicate a large part of their study career working individually and in groups. Supporting students with adequate methods to deal with ill-defined problems in the design studio is a major challenge for design education. Whereas different approaches such as using design patterns and developing scenarios are reported to improve the design activity, they were never investigated in the design studio. An empirical investigation was conducted in order to explore whether and how scenarios and patterns can help students in developing a useful knowledge base and enhance their abilities to solve design problems in the design studio. Students were requested to solve a series of design problems using these educational methods, while working individually and as a team. They were asked to produce as many design ideas as possible, while in the team setting were instructed to think aloud. The data assessed is gathered from surveys, problem solving sessions, and interviews. Thus, qualitative and quantitative analyses had to be done to find out about the different impact of the two methods in design. The results showed that as an educational approach, patterns aided in defining problems and analyzing idea solutions, mainly from a technical and functional perspective. Scenarios, on the other hand, were helpful to generate new ideas, and to enhance design creativity. Independently of the pedagogical method used in the design studio, working in teams showed to be central to enrich and enhance many aspects of the design activity. The findings have important implications for intervention programs in the design studio. Key words: design thinking, design studio, design education, educational setting, problem solving session, students teamwork.

Using Architecture Design Studio Pedagogies to Enhance Engineering Education

Problem-Based Learning pedagogies that require high levels of inquiry and hands-on engagement can enhance studentlearning in engineering. Such pedagogies lie at the core of studio-based design education, having been used to teacharchitects since the Renaissance. Today, design assignments and studio-based learning formats are finding their way intoengineering programs, often as part of larger movements to implement Student-Centered, Problem-Based Learning (PBL)pedagogies. This spectrum of pedagogies is mutually supportive, as illustrated in the University of Michigan’sSmartSurfaces course where students majoring in engineering, art and design, and architecture collaborate on wickedlycomplex and ill-defined design problems. In SmartSurfaces and other similar PBL environments, students encountercomplex, trans-disciplinary, open-ended design prompts that have timely social relevance.Analyzing data generated in studio-based PBL courses like SmartSurfaces can help educators evaluate and trackstudents’ intellectual growth. This paper presents a rubric for measuring students’ development of increasingly refinedepistemological understanding (regarding knowledge and how it is created, accessed, and used). The paper illustratesuse ofthe tool in evaluating blogs created by students in SmartSurfaces, which in turn provides evidence to help validate therubric and suggest avenues for future refinement. The overall result of the exploratory study reported here is to provideevidence of positive change among students who learn in PBL environments and to provide educators with a preliminarytool for assessing design-related epistemological development. Findings of this study indicate design-based education canhave powerful effects and collaborating across disciplines can help engineering students advance in valuable ways.

The Downstream Consequences of Problem-Solving Mindsets: How Playing with LEGO Influences Creativity

Business leaders, governments, and scholars are increasingly recognizing the importance of creativity. Recent trends in technology and education, however, suggest that many people are facing fewer opportunities to engage in creative thought as they increasingly solve well-defined (vs. ill-defined) problems. Using three studies that involve real problem-solving activities (e.g., putting together a LEGO kit), the authors examine the mindset created by addressing such well-defined problems. The studies demonstrate the negative downstream impact of such a mindset on both creative task performance and tendency to choose to engage in creative tasks. The research has theoretical implications for the creativity and mindset literature streams as well as substantive insights for managers and public policy makers.

Toward an Understanding of Development of Learning to Solve Ill-Defined Problems in an Online Context: A Multi-Year Qualitative Exploratory Study

The case study is a classic tool used in several educational programs that emphasizes solving of ill-defined problems. Though it has been used in classroom-based teaching and educators have developed a rich repertoire of methods, its use in online courses presents different challenges. To explore factors that develop skills in solving ill-defined problems, I present results of a seven-year study seeking to develop tools for facilitating and assessing skills for case studies in an online graduate class. This study began with the introduction of a classroom-based case method into an online graduate class. Over the following years, I used three sources of data to make changes to the design of the course with respect to case studies: feedback from students, feedback from colleagues, and measurement of student performance. Findings suggest the following general approaches may work better in online classes involving case studies in particular, and more broadly in courses that teach solving of ill-defined problems: 1) immersion (or the use of drills) to support trial and error learning especially given the additional distractions of an online setting as compared to attending classes on campus; 2) structure to facilitate learning as it involves building skills based on absorptive capacity that students acquire from skills learned earlier; 3) social learning to enhance trial and error learning; 4) inductive learning that may be more appropriate to online teaching as compared to deductive learning; 5) provision of structure instead of participation by the instructor may encourage self-discovery of methods to solve ill-defined problems in an online context.