The Adaptive Problem Sensing and Solving (APSS) Model and Its Use for Efficient TRIZ Tool Selection

Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5 children were not able to answer any problems correctly. The results suggest that children can solve a wide range of problems, including problems involving multiplication and division situations, much earlier than generally has been presumed. With only a few exceptions, children's strategies could be characterized as representing or modeling the action or relationships described in the problems. The conception of problem solving as modeling could provide a unifying framework for thinking about problem solving in the primary grades. Modeling offers a parsimonious and coherent way of thinking about children's mathematical problem solving that is relatively straightforward and is accessible to teachers and students alike. The construction of a model or representation of a problem situation is one of the most fundamental problem-solving processes. Many problems can be solved by representing directly the critical features of the problem situation with an equation, a computer program, or a physical or pictorial representation. Modeling also turns out to be a relatively natural problemsolving process for young children. There is an extensive body of research documenting that even before they receive formal instruction in arithmetic, young children can solve a variety of different types of addition and subtraction word problems by directly modeling with counters the different action and relationships described in the problems (Carpenter, 1985;

Background Although the importance of dealing with paradoxes in frame creation in abductive reasoning has been discussed in design research (Dorst, 2011, 2015b), a logical approach to deal with paradoxes in problem solving has been lacking. We raise the following questions: If design reasoning is not random, what is a logical method that could be useful for designers to engage with paradoxes in the problem-solving process? What is a logical principle behind the interplay among complex meanings? Methods We attempt to respond to these questions by proposing “the semiotic square” as a logical method to cope with paradoxes in frame creation in abductive reasoning (Greimas, 1987; Greimas & Rastier, 1968). It is assumed that since meaning is grasped in the relations of difference (Floch, 2001; Greimas, 1983; Greimas & Rastier, 1968), the semiotic square involving contrary, contradictory, and implicative relations may be useful to deal with complex meanings in design reasoning for problem-solving. We present the analysis of a design case based on the semiotic square with a diagram. We attempt to describe a logical principle behind the interplay among complex meanings in frame creation in abductive reasoning by use of the semiotic square. Results The analysis of a design case shows that it is in the logical relations of contradiction, contrariety, and implication that working principles, paradoxes, themes, assumptions behind concrete practices from the problematic situation, and proposals for design solutions may be arranged and better grasped. We found that using the semiotic square in frame creation in abductive reasoning may facilitate the logical development of reasoning about the potential possibilities of design directions because a given meaning may be expanded upon the semiotic square. Conclusions Using the semiotic square in problem-solving does not produce the solution directly, but it might help materialize the abstract process of frame creation in abductive reasoning. By following a logical path of the semiotic square while questioning the logic behind “WHAT + HOW = VALUE” (Dorst, 2011) and abductive reasoning that infers possible preconditions (WHAT + HOW) for the consequence (VALUE), one might find a simpler and easier way to deal with complex meanings from the problematic situation than managing the process without it.

This study investigated social problem solving and cognitive style (field independence-dependence) in a sample of 70 teachers taking a summer course in counseling. To examine social problem solving, protocol analysis was utilized to determine how adults solved ill-defined interpersonal, intrapersonal, complex, and simple problems. Problem situations were scored for eight problem-solving elements (e.g., strategy, evaluation), three problem-solving processes (sequential, wholistic, simultaneous), and three problem-solving styles (analytical, affective, behavioral). Results indicated that participants used more analysis and evaluation of self on intrapersonal problems, whereas on interpersonal problems they employed more evaluation of strategies. On simple problems, participants utilized more strategies, elaborations, and problem statements, whereas on complex problems they utilized more analysis, evaluations, and feeling statements. Educational implications of these results are explored.

Part I: The School Psychologist as a Problem Solver: Establishing a Foundation and a Vision. Ervin, Peacock, Merrell, The School Psychologist as a Problem Solver in the 21st Century: Rationale and Role Definition. Hawkins, Barnett, Morrison, Musti-Rao, Choosing Targets for Assessment and Intervention: Improving Important Student Outcomes. Part II: Assessment and Analysis: Focus on Academic Outcomes. VanDerHeyden, Analysis of Universal Academic Data to Plan, Implement, and Evaluate Schoolwide Improvement. Floyd, Assessment of Cognitive Abilities and Cognitive Processes: Issues, Applications, and Fit within a Problem-solving Model: Focusing on Academic Achievement. Marcotte, Hintze, Assessment of Academic Skills in Reading within a Problem-solving Model. Burns, Klingbeil, Assessment of Academic Skills in Math within a Problem-solving Model. Gansle, Noell, Assessment of Academic Skills in Written Expression within a Problem-solving Model. Daly III, Hofstadter, Martinez, Andersen, Selecting Academic Interventions for Individual Students. Part III: Assessment and Analysis: Focus on Social Emotional and Behavioral Outcomes. McIntosh, Reinke, Herman, Schoolwide Analysis of Data for Social Behavior Problems: Assessing Outcomes, Selecting Targets for Intervention, and Identifying Need for Support. Martens, Ardoin, Assessing Disruptive Behavior within a Problem-solving Model. Miller, Assessing Internalizing Problems and Well-being. Jones, Wickstrom, Using Functional Assessment to Select Behavioral Interventions. Part IV: Implementing Prevention and Intervention Strategies. Stoiber, DeSmet, Guidelines for Evidence-based Practice in Selecting Interventions. Howell, Schumann, Proactive Strategies for Promoting Learning. Merrell, Levitt, Gueldner, Proactive Strategies for Promoting Social Competence and Resilience. Linan-Thompson, Vaughn, Evidence-based Reading Instruction: Developing and Implementing Reading Programs at the Core, Supplemental, and Intervention Levels. Chard, Ketterlin-Geller, Jungjohann, Baker, Evidence-based Math Instruction: Developing and Implementing Math Intervention Programs at the Core, Supplemental, and Intervention Levels. McCurdy, Schmitz, Albertson, Evidence-based Written Language Instruction: Teaching Written Language Skills at the Core. MacKay, Andreou, Ervin, Peer-mediated Intervention Strategies. Hoff, Sawka-Miller, Self-management Interventions. Gilbertson, Sonnek, Interventions for Homework Problems. Detrich, Higbee, Teaching Functional Life Skills to Children with Developmental Disabilities: Acquisition, Generalization, and Maintenance. Friman, Volz, Haugen, Parents and School Psychologists as Child Behavior Problem-solving Partners: Helpful Concepts and Applications. Shriver, Allen, Parent Training: Working with Families to Develop and Implement Interventions. Bushman, Peacock, Problem-solving Skills Training: Theory and Practice in the School Setting. Swearer, Givens, Frerichs, Cognitive-Behavioral Interventions for Depression and Anxiety. Kern, Benson, Clemens, Strategies for Working with Severe Challenging and Violent Behavior. DuPaul, Weyandt, Booster, Psychopharmacological Interventions. Part V: Evaluating Interventions. Daly III, Barnett, Kupzyk, Hofstadter, Barkley, Summarizing, Evaluating, and Drawing Inferences from Intervention Data. Noell, Empirical and Pragmatic Issues in Assessing and Supporting Intervention Implementation in Schools. Part VI: Building Systems to Support the Problem-solving Model. Sheridan, Magee, Blevins, Swanger-Gagne, Collaboration across Systems to Support Children and Families. Alsop, Dawson, Schaughency, The School Psychologist's Role in Assisting School Staff in Establishing Systems to Manage, Understand, and Use Data. Rhodes, Implementing the Problem-solving Model with Culturally and Linguistically Diverse Students. Tilly III, Niebling, Rahn-Blakeslee, Making Problem-solving School Psychology Work in Schools.

Active and problem-based learning environments strive to improve students' problem solving skills. To better understand students' problem solving processes and thus guide the structure and development of such environments, we asked students to solve data structures and algorithms problems and to verbalize their thoughts as they solved them. In this paper, we discuss methodological issues associated with the analysis of their verbalizations. We then analyze and discuss the relationship between statistics that describe students' problem solving process and their performance in the course they were taking at the time, either the data structures or algorithms course.

Many schools have problem-solving teams that support teachers by helping identify and resolve students' academic and social problems. Although research is limited, it has been found that teams sometimes fail to implement problem-solving processes with fidelity, which may hinder the resolution of problems. We developed the Team-Initiated Problem Solving (TIPS) model to guide problem-solving processes of Positive Behavior Interventions and Supports (PBIS) Teams and the Decision Observation, Recording, and Analysis (DORA) instrument for measuring the fidelity of TIPS implementation. We conducted a TIPS Workshop for four elementary school PBIS Teams in North Carolina and Oregon and used DORA to assess the teams' implementation of TIPS processes in subsequent meetings. We found DORA was successful at allowing us to gather measures of fidelity of implementation, and that teams implemented TIPS processes with fidelity following the workshop. Limitations of these findings as well as implications for future research and practice are provided.

The learning model is one of the most important things in the learning and learning process. A good learning model will make students more enthusiastic in learning because the model is interesting and effective. The purpose of this study was to analyze the comparison of learning models of problem based learning and problem solving models with student problem solving on cube and block material on the skill process in elementary schools. The method used in this study is a quantitative method with a comparative type. The population of this study was 72 students from two schools, included 40 women and 32 men as students, were the subjects studied. The instruments used are student process skills observation sheets and learning questionnaire models. Data collection techniques used in this study were questionnaires and observation sheets. The data analysis technique used is purposive sampling. The results of the description can be said that based on the T test it can be said that the problem-solving learning model is superior to the problem-based learning model. From the results of the T test for the learning model of students' science process skills, it can be seen that there are differences in the learning model.

In this study, it is aimed to determine the problem-solving success of primary school third grade students according to their reading skills and their difficulties in problem solving process. The data were obtained through the reading comprehension text consisting of a total of 12 questions for the reading skills of the participants and six open-ended questions for mathematics problem solving skills. In the study, a case study (a qualitative one) was used because it was aimed to determine the difficulties faced by the students in problem solving stages and to investigate the behaviors in problem solving process according to their level of reading comprehension skills. With this aim, the interviews were conducted with the participant students consists of six third grade students, who represent high-middle-low group depending on the level of reading comprehension, selected from a total of ninety-third grade students in the province of Kocaeli in 2018-2019 academic year. The obtained data were analyzed using descriptive statistics. According to the results of the study, it was understood that the students with low level of reading comprehension had problems in all stages of problem solving while the students with high level of reading comprehension were successful in all problem-solving stages. Besides, these students had problems in controlling the solution and problem formation stages in general according to the level of reading comprehension. Additionally, the results were discussed in the light of the literature and suggestions were made for the difficulties in problem solving depending on the level of reading comprehension.

This chapter examines a type of problem posing that has received little attention in the mathematics education literature. Silver (For the Learning of Mathematics 14:19–28, 1994) defined within-solution problem posing as “problem formulation or reformulation [that] occurs within the process of problem solving” (p. 19). Our analysis documents and explains the role that within-solution problem posing plays during problem solving, focusing on episodes of students from two grade levels: (a) Two fourth-grade students solving a multiplication task, and (b) A mathematics education graduate student solving a number array task. Our research examines: (a) How problem posing evolves from the students’ ongoing interpretations of problematic situations, and (b) How these posed problems contribute to the students’ problem solving. The results provide an explanation of how problem posing and problem solving coevolve in the course of solution activity and thus indicate the beneficial role that problem posing can play in the solution of mathematics problems.

In modern societies, life itself is a problem solving. OCSE-PISA defined the problem-solving competence as the capacity to engage in cognitive processing to understand and solve problem situations where a method of solution is not immediately obvious. Hence in teaching Mathematics, and in general scientific subjects, it becomes important to adopt new methods centred on student learning, which are able not only to deliver knowledge but also to enhance the competence in problem solving. It is essential to start from simulated real-life problem situations in order to explain new concepts, since it enables students to understand the application of Mathematics as well as to enhance their ability to regulate problem-solving processes. The University of Turin has adopted problem solving digital methodologies using a virtual learning environment integrated with an advanced computing environment, automatic assessment and a web conference system. This set of technologies promote interaction among students and help teachers guide and coach their students in creating, conjecturing, exploring, testing and verifying. In the Erasmus+ Project SMART – Science and Mathematics Advanced Research in good Teaching - the University of Turin shared these methodologies with other European partners (Strategic Partnership Key action). The aim of this exchange of best practices is to obtain Mathematics and Science teachers who are more involved in the methodology and consequently students who are better equipped to develop coherent mental representations of problem situations, more flexible in incorporating feedback and in reflecting. In the paper, examples of interactive material produced and tested in the Project are presented and the results of the experience are discussed.

As part of an ongoing effort to better understand student problem-solving processes to openended problems, we have coded 14 mechanical engineering projects (representing about 60 journals) according to abstraction level, design activity, planning, and reporting. We also developed quantitative outcome measures that are reported in a separate submission to this conference. We then developed a computer model of the journal data that correlates 12 key process variables to design outcomes, and conducted a computer design of experiments to extract the effects that the process variables have on the response variables (i.e., project outcomes). In this paper we report the results of this modeling effort and discuss their implications for the general model of engineering problem-solving presented in various forms in many engineering textbooks. Our results suggest modifications to the engineering problem-solving model to make it more suitable for engineering students. Solving open-ended problems is arguably the cornerstone of the engineering endeavor. Employers look for engineers who are effective at solving open-ended problems. Engineering accreditation demands evidence that students can tackle open-ended problems proficiently. Much faculty effort is devoted to improving student skills in this area. The basic process model used for these kinds of problems starts with identification of need, then goes through information gathering, idea generation, evaluation and selection steps—in other words, a basic design process model. Our three-year study of student design processes suggests that the general model for engineering problem-solving may require some tweaking to make it a more effective model for engineering students. Over the decades, numerous models have been proposed to describe “the engineering design process.” However, few of these have been empirically validated or experimentally verified. Most have been developed through personal experience and accumulation of anecdotes. Furthermore, few models explicitly consider student processes relative to project outcomes. Our work attempts to further our understanding of problem-solving processes by gathering data from actual projects (one in which the participants have real stakes) in large enough sample sizes to enable statistical modeling that directly links design process to outcome. In this study, we analyzed data collected from 14 student mechanical engineering design projects, relating design process variables to project outcomes using statistical techniques. Our aim was to better understand what process characteristics tend to be associated with good design outcomes.

Cognitive item generation, rooted from the theory-based measurement paradigm, requires formulating an elaborated theory of the measured construct, upon which task features that are linked to cognitive variables underlying such theory can be systematically analyzed and manipulated. Cast from the perspective of problem solving as an agent – situation interactive process, both cognitive processes of algebra story problem solving and task affordance of such problems are systematically analyzed in this article. Specifically, an algebra story problem is considered as a particular quantitative structure embedded in a verbally-stated realistic situation. Three different types of representations, i.e., a textbase, a situational model and a quantitative model, need to be formed during the four phases of algebra story problem solving including translation, integration, planning and execution, which are further mediated by the schematic knowledge possessed by the problem-solver. Correspondingly, Task features that are associated with syntactic/semantic relations, quantitative elements as well as their structures, and problem situations are analyzed and synthesized based on a broad range of relevant literature. It is evident from the current analysis that subsequent research should focus on empirical studies to link the set of cognitive variables and task features for such problems, as well as to evaluate the generalizability of such linkages across the targeted domain in order for item generation of algebra story problem to lay on a solidly scientific foundation.

Learning and problem solving are intimately related: problem solving determines the knowledge requirements of the reasoner which learning must fulfill, and learning enables improved problem-solving performance. Different models of problem solving, however, recognize different knowledge needs, and, as a result, set up different learning tasks. Some recent models analyze problem solving in terms of generic tasks, methods, and subtasks. These models require the learning of problem-solving concepts such as new tasks and new task decompositions. We view reflection as a core process for learning these problem-solving concepts. In this paper, we identify the learning issues raised by the task-structure framework of problem solving. We view the problem solver as an abstract device, and represent how it works in terms of a structure-behavior-function model which specifies how the knowledge and reasoning of the problem solver results in the accomplishment of its tasks. We describe how this model enables reflection, and how model-based reflection enables the reasoner to adapt its task structure to produce solutions of better quality. The Autognostic system illustrates this reflection process.KeywordsConceptual RelationProblem SolverTask StructureReflective LearningApplicability CriterionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Background:Problem solving is not simply a process that ends when an answer is found; it is a scientific process that evolves from understanding the problem to evaluating the solution. This process is affected by several factors. Among these, one of the most substantial is belief. The purpose of this study was to evaluate the beliefs of high school students according to their explanations in the problem solving process.Materials and methods:A case study was carried out with five students. Each of the students’ problem solving processes was examined by means of clinical interviews and three problems were presented to the students.Results:The results illustrate that the students who thought problem solving should be a short process and that they could address it by memorization of rules also believed that problem solving is difficult.Conclusions:This study concludes that not only beliefs affect the problem solving process, but also personal factors such as life experiences.

이 연구의 목적은 소프트웨어 교육을 위하여 컴퓨팅 사고력 기반의 소프트웨어 수업모형으로써 실생활을 소재로 하는 문제해결 모형을 개발하고, 이 모형을 실생활 문제에 적용해 봄으로써 모형의 적용 가능성을 확인하는데 있다. 컴퓨팅사고의 개념과 하위요소를 탐색하였고, 연구 주제와 관련된 선행 연구를 조사 및 분석하였다. 모형 개발을 위하여 CT-PS(Computational Thinking based Problem Solving)모형을 탐색하였고, 이 모형을 토대로 CT-RLPS(Computational Thinking based Real Life Problem Solving) 모형을 제안하였다. 이 모형의 타당도를 검증하기 위하여 모형의 7가지 측면에 대해 12명의 소프트웨어교육 전문가를 대상으로 타당성 및 의견 조사를 실시하였다. 조사 결과에 대해 CVR분석을 통해 기준값보다 낮은 항목이 발견되었고, 전문가 의견 분석 및 종합을 통해 타당도가 낮은 이유를 발견할 수 있었다. CVR분석 및 전문가 의견을 토대로 모형을 수정 및 보완하여 최종 CT-RLPS모형을 제안하였다. 모형의 실생활 문제적용 가능성을 확인하기 위하여 실생활 문제의 조건을 탐색하였고, ‘체험학습장소 설문조사하기’문제에 모형을 적용하여 문제 해결을 시도한 결과 모형의 적용가능 성을 확인할 수 있었다. CT-RLPS모형의 이용자는 이 사례를 참고하여 다른 실생활 문제에 모형을 적용할 수 있다. 마지막으로 CT-RLPS 모형 이용의 수월성을 높이기 위하여 이 모형을 실생활 문제에 적용할 때 유의해야 할 점을 제시하였다. 결론적으로 CT-RLPS모형은 ‘문제 분석 및 분해’, ‘설계’, ‘구현’의 3단계로 구성되고, 각 단계의 하위 요소를 실생활 문제에 적용함으로써 컴퓨팅사고를 훈련할 수 있을 것으로 기대한다.The purpose of this research is to develop a real-life problem solving model based on computational thinking and to confirm the applicability of the model by applying this model to real problems. We explored the concept and sub-elements of computational thinking, investigated and analyzed prior research related to research themes. In order to develop a model, we searched for CT-PS(Computational Thinking based Problem Solving) model and proposed CT-RLPS(Computational Thinking based Real-Life Problem Solving) model based on this model. In order to verify the validity of this model, we conducted a validity and opinion survey for 12 software education experts on seven aspects of the model. As for the results of the survey, items lower than the reference value were discovered through CVR analysis, and it was possible to discover reasons of the low validity through the analysis and synthesis of expert opinions. We modified and complemented the model based on CVR analysis and opinion of experts, and proposed the final CT-RLPS model. We explored the conditions of the real-life problems in order to confirm the applicability of the model to the real-life problem. And we applied this model to the problem Surveying the place for active learning in school and tried solving the problem, and as a result we could confirm the applicability of the model. A user of the CTR-PS model can apply the model to the other real-life problems with reference to this case. Finally, we presented points to be noted when applying this model to real-life problems in order to improve the excellence of using the CT-RLPS model, In conclusion, the CT-RLPS model consists of three stages of Analysis and Decomposition of Problems , Design , Implementation , and we expect students to train the computational thinking by applying sub-elements of each stage to real-life issues.