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Sample records for algebra problem solving

  1. Maximum/Minimum Problems Solved Using an Algebraic Way

    ERIC Educational Resources Information Center

    Modica, Erasmo

    2010-01-01

    This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…

  2. Maximum/Minimum Problems Solved Using an Algebraic Way

    ERIC Educational Resources Information Center

    Modica, Erasmo

    2010-01-01

    This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…

  3. Algebraic and Geometric Approach in Function Problem Solving

    ERIC Educational Resources Information Center

    Mousoulides, Nikos; Gagatsis, Athanasios

    2004-01-01

    This study explores students algebraic and geometric approach in solving tasks in functions and the relation of these approaches with complex geometric problem solving. Data were obtained from 95 sophomore pre-service teachers, enrolled in a basic algebra course. Implicative statistical analysis was performed to evaluate the relation between…

  4. Algebraic Thinking: A Problem Solving Approach

    ERIC Educational Resources Information Center

    Windsor, Will

    2010-01-01

    Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…

  5. How Problem Solving Can Develop an Algebraic Perspective of Mathematics

    ERIC Educational Resources Information Center

    Windsor, Will

    2011-01-01

    SProblem solving has a long and successful history in mathematics education and is valued by many teachers as a way to engage and facilitate learning within their classrooms. The potential benefit for using problem solving in the development of algebraic thinking is that "it may broaden and develop students' mathematical thinking beyond the…

  6. Strategic differences in algebraic problem solving: neuroanatomical correlates.

    PubMed

    Lee, Kerry; Lim, Zee Ying; Yeong, Stephanie H M; Ng, Swee Fong; Venkatraman, Vinod; Chee, Michael W L

    2007-06-25

    In this study, we built on previous neuroimaging studies of mathematical cognition and examined whether the same cognitive processes are engaged by two strategies used in algebraic problem solving. We focused on symbolic algebra, which uses alphanumeric equations to represent problems, and the model method, which uses pictorial representation. Eighteen adults, matched on academic proficiency and competency in the two methods, transformed algebraic word problems into equations or models, and validated presented solutions. Both strategies were associated with activation of areas linked to working memory and quantitative processing. These included the left frontal gyri, and bilateral activation of the intraparietal sulci. Contrasting the two strategies, the symbolic method activated the posterior superior parietal lobules and the precuneus. These findings suggest that the two strategies are effected using similar processes but impose different attentional demands.

  7. Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving later.

    PubMed

    Hoover, Jerome D; Healy, Alice F

    2017-02-14

    The classic bat-and-ball problem is used widely to measure biased and correct reasoning in decision-making. University students overwhelmingly tend to provide the biased answer to this problem. To what extent might reasoners be led to modify their judgement, and, more specifically, is it possible to facilitate problem solution by prompting participants to consider the problem from an algebraic perspective? One hundred ninety-seven participants were recruited to investigate the effect of algebraic cueing as a debiasing strategy on variants of the bat-and-ball problem. Participants who were cued to consider the problem algebraically were significantly more likely to answer correctly relative to control participants. Most of this cueing effect was confined to a condition that required participants to solve isomorphic algebra equations corresponding to the structure of bat-and-ball question types. On a subsequent critical question with differing item and dollar amounts presented without a cue, participants were able to generalize the learned information to significantly reduce overall bias. Math anxiety was also found to be significantly related to bat-and-ball problem accuracy. These results suggest that, under specific conditions, algebraic reasoning is an effective debiasing strategy on bat-and-ball problem variants, and provide the first documented evidence for the influence of math anxiety on Cognitive Reflection Test performance.

  8. Slower Algebra Students Meet Faster Tools: Solving Algebra Word Problems with Graphing Software

    ERIC Educational Resources Information Center

    Yerushalmy, Michal

    2006-01-01

    The article discusses the ways that less successful mathematics students used graphing software with capabilities similar to a basic graphing calculator to solve algebra problems in context. The study is based on interviewing students who learned algebra for 3 years in an environment where software tools were always present. We found differences…

  9. Problem Solving

    ERIC Educational Resources Information Center

    Kinsella, John J.

    1970-01-01

    Discussed are the nature of a mathematical problem, problem solving in the traditional and modern mathematics programs, problem solving and psychology, research related to problem solving, and teaching problem solving in algebra and geometry. (CT)

  10. Relational Knowledge and Successful Problem Solving in Algebra

    ERIC Educational Resources Information Center

    Chinnappan, Mohan

    2004-01-01

    The quality of knowledge underlying students' algebraic thinking is a major concern of K-12 mathematics teaching and reform-driven curriculum documents. In this paper the author examines this issue by characterizing a group of high school students' algebraic knowledge and patterns of use of that knowledge during the solution of selected problems.…

  11. Continuity in Representation between Children and Adults: Arithmetic Knowledge Hinders Undergraduates' Algebraic Problem Solving

    ERIC Educational Resources Information Center

    McNeil, Nicole M.; Rittle-Johnson, Bethany; Hattikudur, Shanta; Petersen, Lori A.

    2010-01-01

    This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

  12. Primary School Students' Strategies in Early Algebra Problem Solving Supported by an Online Game

    ERIC Educational Resources Information Center

    van den Heuvel-Panhuizen, Marja; Kolovou, Angeliki; Robitzsch, Alexander

    2013-01-01

    In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…

  13. Primary School Students' Strategies in Early Algebra Problem Solving Supported by an Online Game

    ERIC Educational Resources Information Center

    van den Heuvel-Panhuizen, Marja; Kolovou, Angeliki; Robitzsch, Alexander

    2013-01-01

    In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…

  14. Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.

    2015-01-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

  15. Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.

    2015-01-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

  16. Fostering Analogical Transfer: The Multiple Components Approach to Algebra Word Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing

    2012-01-01

    Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated…

  17. Persistent and Pernicious Errors in Algebraic Problem Solving

    ERIC Educational Resources Information Center

    Booth, Julie L.; Barbieri, Christina; Eyer, Francie; Paré-Blagoev, E. Juliana

    2014-01-01

    Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed…

  18. Assessing Algebraic Solving Ability: A Theoretical Framework

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  19. Exploring Algebra Based Problem Solving Methods and Strategies of Spanish-Speaking High School Students

    ERIC Educational Resources Information Center

    Hernandez, Andrea C.

    2013-01-01

    This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking…

  20. Exploring Algebra Based Problem Solving Methods and Strategies of Spanish-Speaking High School Students

    ERIC Educational Resources Information Center

    Hernandez, Andrea C.

    2013-01-01

    This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking…

  1. Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

    ERIC Educational Resources Information Center

    Engerman, Jason; Rusek, Matthew; Clariana, Roy

    2014-01-01

    This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

  2. Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

    ERIC Educational Resources Information Center

    Engerman, Jason; Rusek, Matthew; Clariana, Roy

    2014-01-01

    This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

  3. The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

    ERIC Educational Resources Information Center

    Ng, Swee Fong; Lee, Kerry

    2009-01-01

    Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

  4. Dynamic Assessment of Algebraic Learning in Predicting Third Graders' Development of Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Craddock, Caitlin F.; Hamlett, Carol L.

    2008-01-01

    Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were…

  5. Alternative Representations for Algebraic Problem Solving: When Are Graphs Better than Equations?

    ERIC Educational Resources Information Center

    Mielicki, Marta K.; Wiley, Jennifer

    2016-01-01

    Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

  6. Alternative Representations for Algebraic Problem Solving: When Are Graphs Better than Equations?

    ERIC Educational Resources Information Center

    Mielicki, Marta K.; Wiley, Jennifer

    2016-01-01

    Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

  7. Application of symbolic and algebraic manipulation software in solving applied mechanics problems

    NASA Technical Reports Server (NTRS)

    Tsai, Wen-Lang; Kikuchi, Noboru

    1993-01-01

    As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.

  8. Application of symbolic and algebraic manipulation software in solving applied mechanics problems

    NASA Astrophysics Data System (ADS)

    Tsai, Wen-Lang; Kikuchi, Noboru

    1993-08-01

    As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.

  9. Expert Strategies in Solving Algebraic Structure Sense Problems: The Case of Quadratic Equations

    NASA Astrophysics Data System (ADS)

    Jupri, Al; Sispiyati, R.

    2017-02-01

    Structure sense, an intuitive ability towards symbolic expressions, including skills to interpret, to manipulate, and to perceive symbols in different roles, is considered as a key success in learning algebra. In this article, we report results of three phases of a case study on solving algebraic structure sense problems aiming at testing the appropriateness of algebraic structure sense tasks and at investigating expert strategies dealing with the tasks. First, we developed three tasks on quadratic equations based on the characteristics of structure sense for high school algebra. Next, we validated the tasks to seven experts. In the validation process, we requested these experts to solve each task using two different strategies. Finally, we analyzing expert solution strategies in the light of structure sense characteristics. We found that even if eventual expert strategies are in line with the characteristics of structure sense; some of their initial solution strategies used standard procedures which might pay less attention to algebraic structures. This finding suggests that experts have reconsidered their procedural work and have provided more efficient solution strategies. For further investigation, we consider to test the tasks to high school algebra students and to see whether they produce similar results as experts.

  10. Trade-offs between grounded and abstract representations: evidence from algebra problem solving.

    PubMed

    Koedinger, Kenneth R; Alibali, Martha W; Nathan, Mitchell J

    2008-03-01

    This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade-offs in problem-solving performance. In prior research with high school students solving relatively simple problems, Koedinger and Nathan (2004) demonstrated performance benefits of grounded representations over abstract representations-students were better at solving simple story problems than the analogous equations. This article extends this prior work to examine both simple and more complex problems in two samples of college students. On complex problems with two references to the unknown, a "symbolic advantage" emerged, such that students were better at solving equations than analogous story problems. Furthermore, the previously observed "verbal advantage" on simple problems was replicated. We thus provide empirical support for a trade-off between grounded, verbal representations, which show advantages on simpler problems, and abstract, symbolic representations, which show advantages on more complex problems. 2008 Cognitive Science Society, Inc.

  11. Voila: A visual object-oriented iterative linear algebra problem solving environment

    SciTech Connect

    Edwards, H.C.; Hayes, L.J.

    1994-12-31

    Application of iterative methods to solve a large linear system of equations currently involves writing a program which calls iterative method subprograms from a large software package. These subprograms have complex interfaces which are difficult to use and even more difficult to program. A problem solving environment specifically tailored to the development and application of iterative methods is needed. This need will be fulfilled by Voila, a problem solving environment which provides a visual programming interface to object-oriented iterative linear algebra kernels. Voila will provide several quantum improvements over current iterative method problem solving environments. First, programming and applying iterative methods is considerably simplified through Voila`s visual programming interface. Second, iterative method algorithm implementations are independent of any particular sparse matrix data structure through Voila`s object-oriented kernels. Third, the compile-link-debug process is eliminated as Voila operates as an interpreter.

  12. Solving Our Algebra Problem: Getting All Students through Algebra I to Improve Graduation Rates

    ERIC Educational Resources Information Center

    Schachter, Ron

    2013-01-01

    graduation as well as admission to most colleges. But taking algebra also can turn into a pathway for failure, from which some students never recover. In 2010, a national U.S. Department of Education study…

  13. Solving Our Algebra Problem: Getting All Students through Algebra I to Improve Graduation Rates

    ERIC Educational Resources Information Center

    Schachter, Ron

    2013-01-01

    graduation as well as admission to most colleges. But taking algebra also can turn into a pathway for failure, from which some students never recover. In 2010, a national U.S. Department of Education study…

  14. The Effect of Using the TI-92 on Basic College Algebra Students' Ability To Solve Word Problems.

    ERIC Educational Resources Information Center

    Runde, Dennis C.

    As part of an effort to improve community college algebra students' ability to solve word problems, a study was undertaken at Florida's Manatee Community College to determine the effects of using heuristic instruction (i.e., providing general rules for solving different types of math problems) in combination with the TI-92 calculator. The TI-92…

  15. Conceptual Model-Based Problem Solving That Facilitates Algebra Readiness: An Exploratory Study with Computer-Assisted Instruction

    ERIC Educational Resources Information Center

    Xin, Yan Ping; Si, Luo; Hord, Casey; Zhang, Dake; Cetinas, Suleyman; Park, Joo Young

    2012-01-01

    The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…

  16. Two-Stage Screening for Math Problem-Solving Difficulty Using Dynamic Assessment of Algebraic Learning

    ERIC Educational Resources Information Center

    Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Hamlett, Carol L.; Seethaler, Pamela M.

    2011-01-01

    The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on…

  17. Dynamic Assessment of Algebraic Learning in Predicting Third Graders' Development of Mathematical Problem Solving.

    PubMed

    Fuchs, Lynn S; Compton, Donald L; Fuchs, Douglas; Hollenbeck, Kurstin N; Craddock, Caitlin F; Hamlett, Carol L

    2008-11-01

    Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3(rd) graders' development of mathematics problem solving. In the fall, 122 3(rd)-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities.

  18. Dynamic Assessment of Algebraic Learning in Predicting Third Graders’ Development of Mathematical Problem Solving

    PubMed Central

    Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Craddock, Caitlin F.; Hamlett, Carol L.

    2008-01-01

    Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3rd graders’ development of mathematics problem solving. In the fall, 122 3rd-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities. PMID:19884957

  19. Arithmetic and algebraic problem solving and resource allocation: the distinct impact of fluid and numerical intelligence.

    PubMed

    Dix, Annika; van der Meer, Elke

    2015-04-01

    This study investigates cognitive resource allocation dependent on fluid and numerical intelligence in arithmetic/algebraic tasks varying in difficulty. Sixty-six 11th grade students participated in a mathematical verification paradigm, while pupil dilation as a measure of resource allocation was collected. Students with high fluid intelligence solved the tasks faster and more accurately than those with average fluid intelligence, as did students with high compared to average numerical intelligence. However, fluid intelligence sped up response times only in students with average but not high numerical intelligence. Further, high fluid but not numerical intelligence led to greater task-related pupil dilation. We assume that fluid intelligence serves as a domain-general resource that helps to tackle problems for which domain-specific knowledge (numerical intelligence) is missing. The allocation of this resource can be measured by pupil dilation. Copyright © 2014 Society for Psychophysiological Research.

  20. Effects of Argumentation on Group Micro-Creativity: Statistical Discourse Analyses of Algebra Students' Collaborative Problem Solving

    ERIC Educational Resources Information Center

    Chiu, Ming Ming

    2008-01-01

    The micro-time context of group processes (such as argumentation) can affect a group's micro-creativity (new ideas). Eighty high school students worked in groups of four on an algebra problem. Groups with higher mathematics grades showed greater micro-creativity, and both were linked to better problem solving outcomes. Dynamic multilevel analyses…

  1. A scalable approach to solving dense linear algebra problems on hybrid CPU-GPU systems

    SciTech Connect

    Song, Fengguang; Dongarra, Jack

    2014-10-01

    Aiming to fully exploit the computing power of all CPUs and all graphics processing units (GPUs) on hybrid CPU-GPU systems to solve dense linear algebra problems, in this paper we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, and to accommodate the heterogeneity between CPUs and GPUs. The new heterogeneous tile algorithms are executed upon our decentralized dynamic scheduling runtime system, which schedules a task graph dynamically and transfers data between compute nodes automatically. The runtime system uses a new distributed task assignment protocol to solve data dependencies between tasks without any coordination between processing units. By overlapping computation and communication through dynamic scheduling, we are able to attain scalable performance for the double-precision Cholesky factorization and QR factorization. Finally, our approach demonstrates a performance comparable to Intel MKL on shared-memory multicore systems and better performance than both vendor (e.g., Intel MKL) and open source libraries (e.g., StarPU) in the following three environments: heterogeneous clusters with GPUs, conventional clusters without GPUs, and shared-memory systems with multiple GPUs.

  2. A scalable approach to solving dense linear algebra problems on hybrid CPU-GPU systems

    DOE PAGES

    Song, Fengguang; Dongarra, Jack

    2014-10-01

    Aiming to fully exploit the computing power of all CPUs and all graphics processing units (GPUs) on hybrid CPU-GPU systems to solve dense linear algebra problems, in this paper we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, and to accommodate the heterogeneity between CPUs and GPUs. The new heterogeneous tile algorithms are executed upon our decentralized dynamic scheduling runtime system, which schedules a task graph dynamically and transfers data between compute nodes automatically. The runtime system uses a new distributed task assignment protocol to solve data dependencies between tasksmore » without any coordination between processing units. By overlapping computation and communication through dynamic scheduling, we are able to attain scalable performance for the double-precision Cholesky factorization and QR factorization. Finally, our approach demonstrates a performance comparable to Intel MKL on shared-memory multicore systems and better performance than both vendor (e.g., Intel MKL) and open source libraries (e.g., StarPU) in the following three environments: heterogeneous clusters with GPUs, conventional clusters without GPUs, and shared-memory systems with multiple GPUs.« less

  3. Facilitating Case Reuse during Problem Solving in Algebra-Based Physics

    ERIC Educational Resources Information Center

    Mateycik, Frances Ann

    2010-01-01

    This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual…

  4. New Protocols for Solving Geometric Calculation Problems Incorporating Dynamic Geometry and Computer Algebra Software.

    ERIC Educational Resources Information Center

    Schumann, Heinz; Green, David

    2000-01-01

    Discusses software for geometric construction, measurement, and calculation, and software for numerical calculation and symbolic analysis that allows for new approaches to the solution of geometric problems. Illustrates these computer-aided graphical, numerical, and algebraic methods of solution and discusses examples using the appropriate choice…

  5. New Protocols for Solving Geometric Calculation Problems Incorporating Dynamic Geometry and Computer Algebra Software.

    ERIC Educational Resources Information Center

    Schumann, Heinz; Green, David

    2000-01-01

    Discusses software for geometric construction, measurement, and calculation, and software for numerical calculation and symbolic analysis that allows for new approaches to the solution of geometric problems. Illustrates these computer-aided graphical, numerical, and algebraic methods of solution and discusses examples using the appropriate choice…

  6. Solving a Contextual Problem with the Spreadsheet as an Environment for Algebraic Thinking Development

    ERIC Educational Resources Information Center

    Nobre, Sandra; Amado, Nelia; Carreira, Susana

    2012-01-01

    In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13-14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in…

  7. A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness

    ERIC Educational Resources Information Center

    Xin, Yan Ping; Zhang, Dake; Park, Joo Young; Tom, Kinsey; Whipple, Amanda; Si, Luo

    2011-01-01

    The authors compared a conceptual model-based problem-solving (COMPS) approach with a general heuristic instructional approach for teaching multiplication-division word-problem solving to elementary students with learning problems (LP). The results indicate that only the COMPS group significantly improved, from pretests to posttests, their…

  8. LOGO Teaching Sequences on Strategy in Problem-Solving and Story Problems in Algebra. Teacher's Text and Problems.

    ERIC Educational Resources Information Center

    Lukas, George; And Others

    In order to provide high school students with general problem-solving skills, two LOGO computer-assisted instruction units were developed--one on the methods and strategies for solution and a second on the relation between formal and informal representations of problems. In both cases specific problem contexts were used to give definition and…

  9. Two-stage screening for math problem-solving difficulty using dynamic assessment of algebraic learning.

    PubMed

    Fuchs, Lynn S; Compton, Donald L; Fuchs, Douglas; Hollenbeck, Kurstin N; Hamlett, Carol L; Seethaler, Pamela M

    2011-01-01

    The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on word-problem performance. Logistic regression was conducted to contrast two models. One relied exclusively on the fall test of math word-problem skill to predict word-problem difficulty on the spring outcome (less than the 25th percentile). The second model relied on a combination of the fall test of math word-problem skill and the fall DA to predict the same outcome. Holding sensitivity at 87.5%, the universal screener alone resulted in a high proportion of false positives, which was practically reduced when DA was included in the prediction model. Findings are discussed in terms of a two-stage process for screening students within a responsiveness-to-intervention prevention model.

  10. Intensive Scaffolding in an Intelligent Tutoring System for the Learning of Algebraic Word Problem Solving

    ERIC Educational Resources Information Center

    González-Calero, José Antonio; Arnau, David; Puig, Luis; Arevalillo-Herráez, Miguel

    2015-01-01

    The term intensive scaffolding refers to any set of conceptual scaffolding strategies that always allow the user to find the solution to a problem. Despite the many benefits of scaffolding, some negative effects have also been reported. These are mainly related to the possibility that a student solves the problems without actually engaging in…

  11. Facilitating case reuse during problem solving in algebra-based physics

    NASA Astrophysics Data System (ADS)

    Mateycik, Frances Ann

    This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual clinical interviews were conducted and quantitative examination data were collected to assess students' conceptual understanding, knowledge organization, and problem solving performance on a variety of problem tasks. The study began with a short one-time treatment of two independent, research-based strategies chosen to facilitate case reuse. Exploration of students' perceptions and use of the strategies lead investigators to select one of the two strategies to be implemented over a full semester of focus group interviews. The strategy chosen was structure mapping. Structure maps are defined as visual representations of quantities and their associations. They were created by experts to model the appropriate mental organization of knowledge elements for a given physical concept. Students were asked to use these maps as they were comfortable while problem solving. Data obtained from this phase of our study (Phase I) offered no evidence of improved problem solving schema. The 11 contact hour study was barely sufficient time for students to become comfortable using the maps. A set of simpler strategies were selected for their more explicit facilitation of analogical reasoning, and were used together during two more semester long focus group treatments (Phase II and Phase III of this study). These strategies included the use of a step-by-step process aimed at reducing cognitive load associated with mathematical procedure, direct reflection of principles involved in a given set of problems, and the direct comparison of problem pairs designed to be void of surface similarities (similar objects or object orientations) and sharing

  12. Effects of Modified Schema-Based Instruction on Real-World Algebra Problem Solving of Students with Autism Spectrum Disorder and Moderate Intellectual Disability

    ERIC Educational Resources Information Center

    Root, Jenny Rose

    2016-01-01

    The current study evaluated the effects of modified schema-based instruction (SBI) on the algebra problem solving skills of three middle school students with autism spectrum disorder and moderate intellectual disability (ASD/ID). Participants learned to solve two types of group word problems: missing-whole and missing-part. The themes of the word…

  13. Trade-Offs between Grounded and Abstract Representations: Evidence from Algebra Problem Solving

    ERIC Educational Resources Information Center

    Koedinger, Kenneth R.; Alibali, Martha W.; Nathan, Mitchell J.

    2008-01-01

    This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…

  14. Algebra and Problem-Solving in Down Syndrome: A Study with 15 Teenagers

    ERIC Educational Resources Information Center

    Martinez, Elisabetta Monari; Pellegrini, Katia

    2010-01-01

    There is a common opinion that mathematics is difficult for persons with Down syndrome, because of a weakness in numeracy and in abstract thinking. Since 1996, some single case studies have suggested that new opportunities in mathematics are possible for these students: some of them learned algebra and also learned to use equations in…

  15. Algebra and Problem-Solving in Down Syndrome: A Study with 15 Teenagers

    ERIC Educational Resources Information Center

    Martinez, Elisabetta Monari; Pellegrini, Katia

    2010-01-01

    There is a common opinion that mathematics is difficult for persons with Down syndrome, because of a weakness in numeracy and in abstract thinking. Since 1996, some single case studies have suggested that new opportunities in mathematics are possible for these students: some of them learned algebra and also learned to use equations in…

  16. High-School Students' Approaches to Solving Algebra Problems that Are Posed Symbolically: Results from an Interview Study

    ERIC Educational Resources Information Center

    Huntley, Mary Ann; Davis, Jon D.

    2008-01-01

    A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are…

  17. High-School Students' Approaches to Solving Algebra Problems that Are Posed Symbolically: Results from an Interview Study

    ERIC Educational Resources Information Center

    Huntley, Mary Ann; Davis, Jon D.

    2008-01-01

    A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are…

  18. Fibonacci's Triangle: A Vehicle for Problem Solving.

    ERIC Educational Resources Information Center

    Ouellette, Hugh

    1979-01-01

    A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

  19. Fibonacci's Triangle: A Vehicle for Problem Solving.

    ERIC Educational Resources Information Center

    Ouellette, Hugh

    1979-01-01

    A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

  20. Algebra Word Problem Solving Approaches in a Chemistry Context: Equation Worked Examples versus Text Editing

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing

    2013-01-01

    Text editing directs students' attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three…

  1. Algebra Word Problem Solving Approaches in a Chemistry Context: Equation Worked Examples versus Text Editing

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing

    2013-01-01

    Text editing directs students' attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three…

  2. Solution Strategies, Modes of Representation and Justifications of Primary Five Pupils in Solving Pre Algebra Problems: An Experience of Using Task-Based Interview and Verbal Protocol Analysis

    ERIC Educational Resources Information Center

    Ling, Gan We; Ghazali, Munirah

    2007-01-01

    This descriptive study was aimed at looking into how Primary 5 pupils solve pre-algebra problems concerning patterns and unknown quantities. Specifically, objectives of this study were to describe Primary 5 pupils' solution strategies, modes of representations and justifications in: (a) discovering, describing and using numerical and geometrical…

  3. The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

    PubMed Central

    Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

    2016-01-01

    The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

  4. Some Applications of Algebraic System Solving

    ERIC Educational Resources Information Center

    Roanes-Lozano, Eugenio

    2011-01-01

    Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

  5. Some Applications of Algebraic System Solving

    ERIC Educational Resources Information Center

    Roanes-Lozano, Eugenio

    2011-01-01

    Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

  6. The roles of prefrontal and posterior parietal cortex in algebra problem solving: a case of using cognitive modeling to inform neuroimaging data.

    PubMed

    Danker, Jared F; Anderson, John R

    2007-04-15

    In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments.

  7. Problem Solving through Paper Folding

    ERIC Educational Resources Information Center

    Wares, Arsalan

    2014-01-01

    The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

  8. Junior high school students' cognitive process in solving the developed algebraic problems based on information processing taxonomy model

    NASA Astrophysics Data System (ADS)

    Purwoko, Saad, Noor Shah; Tajudin, Nor'ain Mohd

    2017-05-01

    This study aims to: i) develop problem solving questions of Linear Equations System of Two Variables (LESTV) based on levels of IPT Model, ii) explain the level of students' skill of information processing in solving LESTV problems; iii) explain students' skill in information processing in solving LESTV problems; and iv) explain students' cognitive process in solving LESTV problems. This study involves three phases: i) development of LESTV problem questions based on Tessmer Model; ii) quantitative survey method on analyzing students' skill level of information processing; and iii) qualitative case study method on analyzing students' cognitive process. The population of the study was 545 eighth grade students represented by a sample of 170 students of five Junior High Schools in Hilir Barat Zone, Palembang (Indonesia) that were chosen using cluster sampling. Fifteen students among them were drawn as a sample for the interview session with saturated information obtained. The data were collected using the LESTV problem solving test and the interview protocol. The quantitative data were analyzed using descriptive statistics, while the qualitative data were analyzed using the content analysis. The finding of this study indicated that students' cognitive process was just at the step of indentifying external source and doing algorithm in short-term memory fluently. Only 15.29% students could retrieve type A information and 5.88% students could retrieve type B information from long-term memory. The implication was the development problems of LESTV had validated IPT Model in modelling students' assessment by different level of hierarchy.

  9. Characterizing the Development of a Schema for Representing and Solving Algebra Word Problems by Pre-Algebraic Students Engaged in a Structured Diagrammatic Environment

    ERIC Educational Resources Information Center

    Green, Jan

    2009-01-01

    In recent years, the learning of algebra by all students has become a significant national priority (Moses & Cobb, 2001; National Council of Teachers of Mathematics, 2000). Algebra is considered to be a foundational topic in mathematics (Usiskin, 1988) and some have argued that an understanding of algebra is fundamental to success in today's…

  10. Solving Geometric Problems by Using Algebraic Representation for Junior High School Level 3 in Van Hiele at Geometric Thinking Level

    ERIC Educational Resources Information Center

    Suwito, Abi; Yuwono, Ipung; Parta, I. Nengah; Irawati, Santi; Oktavianingtyas, Ervin

    2016-01-01

    This study aims to determine the ability of algebra students who have 3 levels van Hiele levels. Follow its framework Dindyal framework (2007). Students are required to do 10 algebra shaped multiple choice, then students work 15 about the geometry of the van Hiele level in the form of multiple choice questions. The question has been tested levels…

  11. Using CAS to Solve Classical Mathematics Problems

    ERIC Educational Resources Information Center

    Burke, Maurice J.; Burroughs, Elizabeth A.

    2009-01-01

    Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

  12. Using CAS to Solve Classical Mathematics Problems

    ERIC Educational Resources Information Center

    Burke, Maurice J.; Burroughs, Elizabeth A.

    2009-01-01

    Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

  13. Algebra Word Problems: A Review of the Theoretical Models and Related Research Literature.

    ERIC Educational Resources Information Center

    Carifio, James; Nasser, Ramzi

    Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…

  14. Problem Solving. Research Brief

    ERIC Educational Resources Information Center

    Muir, Mike

    2004-01-01

    No longer solely the domain of Mathematics, problem solving permeates every area of today's curricula. Ideally students are applying heuristics strategies in varied contexts and novel situations in every subject taught. The ability to solve problems is a basic life skill and is essential to understanding technical subjects. Problem-solving is a…

  15. The Problems of Problem Solving

    ERIC Educational Resources Information Center

    Watson, Charles E.

    1976-01-01

    Discusses some common pitfalls in problem-solving and outlines three basic approaches to successfully identifying problems and their causes. (Available from Business Horizons, School of Business, Indiana University, Bloomington, Indiana 47401; $2.50, single copy) (Author/JG)

  16. Techniques of Problem Solving.

    ERIC Educational Resources Information Center

    Krantz, Steven G.

    The purpose of this book is to teach the basic principles of problem solving in both mathematical and non-mathematical problems. The major components of the book consist of learning to translate verbal discussion into analytical data, learning problem solving methods for attacking collections of analytical questions or data, and building a…

  17. Group Problem Solving.

    ERIC Educational Resources Information Center

    King, James C.

    1988-01-01

    This pamphlet discusses group problem solving in schools. Its point of departure is that teachers go at problems from a number of different directions and that principals need to capitalize on those differences and bring a whole range of skills and perceptions to the problem-solving process. Rather than trying to get everyone to think alike,…

  18. Techniques of Problem Solving.

    ERIC Educational Resources Information Center

    Krantz, Steven G.

    The purpose of this book is to teach the basic principles of problem solving in both mathematical and non-mathematical problems. The major components of the book consist of learning to translate verbal discussion into analytical data, learning problem solving methods for attacking collections of analytical questions or data, and building a…

  19. Strategies for Problem Solving.

    ERIC Educational Resources Information Center

    Karmos, Joseph S.; Karmos, Ann H.

    Problem-solving skills are becoming increasingly important in the workplace, and more schools are including them in the curriculum. Knowledge of problem solving will be critical to a work force that is dealing with advanced technology, yet many students have yet to master these skills. Based on this premise, this guide attempts to show how…

  20. Teaching through Problem Solving

    ERIC Educational Resources Information Center

    Fi, Cos D.; Degner, Katherine M.

    2012-01-01

    Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

  1. Problem Solving and Intelligence.

    ERIC Educational Resources Information Center

    Resnick, Lauren B.; Glaser, Robert

    This paper argues that a major aspect of intelligence is the ability to solve problems and that careful analysis of problem-solving behavior is a means of specifying many of the psychological processes that make up intelligence. The focus is on the mechanisms involved when, in the absence of complete instruction, a person must "invent" a new…

  2. Problem Solving and Learning

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha

    2009-07-01

    One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts. The limited capacity of short term memory makes the cognitive load high during problem solving tasks, leaving few cognitive resources available for meta-cognition. The abstract nature of the laws of physics and the chain of reasoning required to draw meaningful inferences makes these issues critical. In order to help students, it is crucial to consider the difficulty of a problem from the perspective of students. We are developing and evaluating interactive problem-solving tutorials to help students in the introductory physics courses learn effective problem-solving strategies while solidifying physics concepts. The self-paced tutorials can provide guidance and support for a variety of problem solving techniques, and opportunity for knowledge and skill acquisition.

  3. Chemical Reaction Problem Solving.

    ERIC Educational Resources Information Center

    Veal, William

    1999-01-01

    Discusses the role of chemical-equation problem solving in helping students predict reaction products. Methods for helping students learn this process must be taught to students and future teachers by using pedagogical skills within the content of chemistry. Emphasizes that solving chemical reactions should involve creative cognition where…

  4. Problem Solving by Design

    ERIC Educational Resources Information Center

    Capobianco, Brenda M.; Tyrie, Nancy

    2009-01-01

    In a unique school-university partnership, methods students collaborated with fifth graders to use the engineering design process to build their problem-solving skills. By placing the problem in the context of a client having particular needs, the problem took on a real-world appeal that students found intriguing and inviting. In this article, the…

  5. Problem Solving by Design

    ERIC Educational Resources Information Center

    Capobianco, Brenda M.; Tyrie, Nancy

    2009-01-01

    In a unique school-university partnership, methods students collaborated with fifth graders to use the engineering design process to build their problem-solving skills. By placing the problem in the context of a client having particular needs, the problem took on a real-world appeal that students found intriguing and inviting. In this article, the…

  6. Discovering Steiner Triple Systems through Problem Solving

    ERIC Educational Resources Information Center

    Sriraman, Bharath

    2004-01-01

    An attempt to implement problem solving as a teacher of ninth grade algebra is described. The problems selected were not general ones, they involved combinations and represented various situations and were more complex which lead to the discovery of Steiner triple systems.

  7. Problem Solving in Electricity.

    ERIC Educational Resources Information Center

    Caillot, Michel; Chalouhi, Elias

    Two studies were conducted to describe how students perform direct current (D-C) circuit problems. It was hypothesized that problem solving in the electricity domain depends largely on good visual processing of the circuit diagram and that this processing depends on the ability to recognize when two or more electrical components are in series or…

  8. Problem Solving in Electricity.

    ERIC Educational Resources Information Center

    Caillot, Michel; Chalouhi, Elias

    Two studies were conducted to describe how students perform direct current (D-C) circuit problems. It was hypothesized that problem solving in the electricity domain depends largely on good visual processing of the circuit diagram and that this processing depends on the ability to recognize when two or more electrical components are in series or…

  9. Inquiry and Problem Solving.

    ERIC Educational Resources Information Center

    Thorson, Annette, Ed.

    1999-01-01

    This issue of ENC Focus focuses on the topic of inquiry and problem solving. Featured articles include: (1) "Inquiry in the Everyday World of Schools" (Ronald D. Anderson); (2) "In the Cascade Reservoir Restoration Project Students Tackle Real-World Problems" (Clint Kennedy with Advanced Biology Students from Cascade High…

  10. Programming and Problem Solving.

    ERIC Educational Resources Information Center

    Elias, Barbara P.

    A study was conducted to examine computer programming as a problem solving activity. Thirteen fifth grade children were selected by their teacher from an above average class to use Apple IIe microcomputers. The investigator conducted sessions of 40-50 minutes with the children in groups of two or three. Four problems, incorporating the programming…

  11. Problem Solving Techniques Seminar.

    ERIC Educational Resources Information Center

    Massachusetts Career Development Inst., Springfield.

    This booklet is one of six texts from a workplace literacy curriculum designed to assist learners in facing the increased demands of the workplace. Six problem-solving techniques are developed in the booklet to assist individuals and groups in making better decisions: problem identification, data gathering, data analysis, solution analysis,…

  12. Problem-Solving Software

    NASA Technical Reports Server (NTRS)

    1992-01-01

    CBR Express software solves problems by adapting sorted solutions to new problems specified by a user. It is applicable to a wide range of situations. The technology was originally developed by Inference Corporation for Johnson Space Center's Advanced Software Development Workstation. The project focused on the reuse of software designs, and Inference used CBR as part of the ACCESS prototype software. The commercial CBR Express is used as a "help desk" for customer support, enabling reuse of existing information when necessary. It has been adopted by several companies, among them American Airlines, which uses it to solve reservation system software problems.

  13. Expertise in Problem Solving.

    DTIC Science & Technology

    1981-05-18

    use at each step of the solution process. By contrast, both Issac and Newton contain separate representations of the same physics knowledge for each...representation. Issac . Issac by Gordon Novak (1977) is a program that can read the problem statement. It does this for statics problems only. The key feature of...problem does not generate an efficient solution. Newton . Newton by Johann de Kleer (1977) does not have any language translation facility. It solves

  14. Toward Solving the Problem of Problem Solving: An Analysis Framework

    ERIC Educational Resources Information Center

    Roesler, Rebecca A.

    2016-01-01

    Teaching is replete with problem solving. Problem solving as a skill, however, is seldom addressed directly within music teacher education curricula, and research in music education has not examined problem solving systematically. A framework detailing problem-solving component skills would provide a needed foundation. I observed problem solving…

  15. Toward Solving the Problem of Problem Solving: An Analysis Framework

    ERIC Educational Resources Information Center

    Roesler, Rebecca A.

    2016-01-01

    Teaching is replete with problem solving. Problem solving as a skill, however, is seldom addressed directly within music teacher education curricula, and research in music education has not examined problem solving systematically. A framework detailing problem-solving component skills would provide a needed foundation. I observed problem solving…

  16. Introspection in Problem Solving

    ERIC Educational Resources Information Center

    Jäkel, Frank; Schreiber, Cornell

    2013-01-01

    Problem solving research has encountered an impasse. Since the seminal work of Newell und Simon (1972) researchers do not seem to have made much theoretical progress (Batchelder and Alexander, 2012; Ohlsson, 2012). In this paper we argue that one factor that is holding back the field is the widespread rejection of introspection among cognitive…

  17. Solving Common Mathematical Problems

    NASA Technical Reports Server (NTRS)

    Luz, Paul L.

    2005-01-01

    Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.

  18. Achievement in Problem Solving

    ERIC Educational Resources Information Center

    Friebele, David

    2010-01-01

    This Action Research Project is meant to investigate the effects of incorporating research-based instructional strategies into instruction and their subsequent effect on student achievement in the area of problem-solving. The two specific strategies utilized are the integration of manipulatives and increased social interaction on a regular basis.…

  19. Solving Problems Reductively

    ERIC Educational Resources Information Center

    Armoni, Michal; Gal-Ezer, Judith; Tirosh, Dina

    2005-01-01

    Solving problems by reduction is an important issue in mathematics and science education in general (both in high school and in college or university) and particularly in computer science education. Developing reductive thinking patterns is an important goal in any scientific discipline, yet reduction is not an easy subject to cope with. Still,…

  20. Problem Solving with Patents

    ERIC Educational Resources Information Center

    Moore, Jerilou; Sumrall, William J.

    2008-01-01

    Exploring our patent system is a great way to engage students in creative problem solving. As a result, the authors designed a teaching unit that uses the study of patents to explore one avenue in which scientists and engineers do science. Specifically, through the development of an idea, students learn how science and technology are connected.…

  1. [Problem Solving Activities.

    ERIC Educational Resources Information Center

    Wisconsin Univ. - Stout, Menomonie. Center for Vocational, Technical and Adult Education.

    The teacher directed problem solving activities package contains 17 units: Future Community Design, Let's Build an Elevator, Let's Construct a Catapult, Let's Design a Recreational Game, Let's Make a Hand Fishing Reel, Let's Make a Wall Hanging, Let's Make a Yo-Yo, Marooned in the Past, Metrication, Mousetrap Vehicles, The Multi System…

  2. Problem Solving with Patents

    ERIC Educational Resources Information Center

    Moore, Jerilou; Sumrall, William J.

    2008-01-01

    Exploring our patent system is a great way to engage students in creative problem solving. As a result, the authors designed a teaching unit that uses the study of patents to explore one avenue in which scientists and engineers do science. Specifically, through the development of an idea, students learn how science and technology are connected.…

  3. Problem Solving Using Microcomputers.

    ERIC Educational Resources Information Center

    Demana, Franklin; Waits, Bert

    1987-01-01

    It is argued that microcomputer technology has evolved to the stage that it should be routinely used by mathematics students at all levels. It is shown how the use of microcomputers can change the way problems are solved. Computer-generated graphics are highlighted. (PK)

  4. Solving Problems through Circles

    ERIC Educational Resources Information Center

    Grahamslaw, Laura; Henson, Lisa H.

    2015-01-01

    Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…

  5. Universal Design Problem Solving

    ERIC Educational Resources Information Center

    Sterling, Mary C.

    2004-01-01

    Universal design is made up of four elements: accessibility, adaptability, aesthetics, and affordability. This article addresses the concept of universal design problem solving through experiential learning for an interior design studio course in postsecondary education. Students' experiences with clients over age 55 promoted an understanding of…

  6. Circumference and Problem Solving.

    ERIC Educational Resources Information Center

    Blackburn, Katie; White, David

    The concept of pi is one of great importance to all developed civilization and one that can be explored and mastered by elementary students through an inductive and problem-solving approach. Such an approach is outlined and discussed. The approach involves the following biblical quotation: "And he made a moltin sea ten cubits from one brim to…

  7. Solving Problems in Genetics

    ERIC Educational Resources Information Center

    Aznar, Mercedes Martinez; Orcajo, Teresa Ibanez

    2005-01-01

    A teaching unit on genetics and human inheritance using problem-solving methodology was undertaken with fourth-level Spanish Secondary Education students (15 year olds). The goal was to study certain aspects of the students' learning process (concepts, procedures and attitude) when using this methodology in the school environment. The change…

  8. Universal Design Problem Solving

    ERIC Educational Resources Information Center

    Sterling, Mary C.

    2004-01-01

    Universal design is made up of four elements: accessibility, adaptability, aesthetics, and affordability. This article addresses the concept of universal design problem solving through experiential learning for an interior design studio course in postsecondary education. Students' experiences with clients over age 55 promoted an understanding of…

  9. Solving Problems through Circles

    ERIC Educational Resources Information Center

    Grahamslaw, Laura; Henson, Lisa H.

    2015-01-01

    Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…

  10. Environmental problem solving

    SciTech Connect

    Miller, A.

    1999-06-01

    Human influences create both environmental problems and barriers to effective policy aimed at addressing those problems. In effect, environmental managers manage people as much as they manage the environment. Therefore, they must gain an understanding of the psychological and sociopolitical dimensions of environmental problems that they are attempting to resolve. The author reappraises conventional analyses of environmental problems using lessons from the psychosocial disciplines. The author combines the disciplines of ecology, political sociology and psychology to produce a more adaptive approach to problem-solving that is specifically geared toward the environmental field. Numerous case studies demonstrate the practical application of theory in a way that is useful to technical and scientific professionals as well as to policymakers and planners.

  11. Problem Solving and Reasoning.

    DTIC Science & Technology

    1984-02-01

    Sloan Foundation (HAS). This paper is a draft of a chapter to appear in R. C. Atkinson, R. Herrnstein, G. Lindzey, and R. D. Luce (Eds.), Stevens ...D. Luce (Eds.), Stevens ’ Handbook of Experimental Psychology, (Revised Edition). New York: John Wiley & Sons. PROBLEM SOLVING AND REASONING James G... LaBerge & S. J. Samuels (Eds.), Perception and comprehension. Hillsdale, NJ: Erlbaum. Anderson, J. R. (1982). Acquisition of cognitive skill

  12. A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry

    ERIC Educational Resources Information Center

    Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew

    2012-01-01

    In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

  13. A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry

    ERIC Educational Resources Information Center

    Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew

    2012-01-01

    In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

  14. Planning and Problem Solving

    DTIC Science & Technology

    1982-10-01

    Artificial Intelig ~ence (Vol. III, edited by Paul R. Cohen and’ Edward A.. Feigenbaum)’, The chapter was written B’ Paul Cohen, with contributions... Artificial Intelligence (Vol. III, edited by Paul R. Cohen and EdWard A. Feigenbaum). The chapter was written by Paul R. Cohen, with contributions by Stephen...Wheevoats"EntermdI’ Planning and ProblemSolving by Paul R. Cohen Chaptb-rXV-of Volumec III’of the Handbook of Artificial Intelligence edited by Paul R

  15. Problem Solving Tips for Teachers.

    ERIC Educational Resources Information Center

    O'Daffer, Phares G.

    1984-01-01

    The problem-solving strategy of making an organized list is highlighted, with a problem and suggestions for teaching the strategy. Other suggestions for teaching problem solving are then presented. (MNS)

  16. Fundamentals of the Design and the Operation of an Intelligent Tutoring System for the Learning of the Arithmetical and Algebraic Way of Solving Word Problems

    ERIC Educational Resources Information Center

    Arnau, David; Arevalillo-Herraez, Miguel; Puig, Luis; Gonzalez-Calero, Jose Antonio

    2013-01-01

    Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…

  17. Fundamentals of the Design and the Operation of an Intelligent Tutoring System for the Learning of the Arithmetical and Algebraic Way of Solving Word Problems

    ERIC Educational Resources Information Center

    Arnau, David; Arevalillo-Herraez, Miguel; Puig, Luis; Gonzalez-Calero, Jose Antonio

    2013-01-01

    Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…

  18. The Calculator is a Problem-solving Concept Developer.

    ERIC Educational Resources Information Center

    Comstock, Margaret; Demana, Franklin

    1987-01-01

    How calculators can enhance problem-solving abilities is discussed. Examples of calculator table-building activities that span the gap from arithmetic to algebra in middle schools are given. Percent, area and perimeter, and exponents are the focus. (MNS)

  19. Computer Problem-Solving Coaches

    NASA Astrophysics Data System (ADS)

    Hsu, Leon; Heller, Kenneth

    2005-09-01

    Computers might be able to play an important role in physics instruction by coaching students to develop good problem-solving skills. Building on previous research on student problem solving and on designing computer programs to teach cognitive skills, we are developing a prototype computer coach to provide students with guided practice in solving problems. In addition to helping students become better problem solvers, such programs can be useful in studying how students learn to solve problems and how and if problem-solving skills can be transferred from a computer to a pencil-and-paper environment.

  20. Problem Solving and Beginning Programming.

    ERIC Educational Resources Information Center

    McAllister, Alan

    Based on current models of problem solving within cognitive psychology, this study focused on the spontaneous problem solving strategies used by children as they first learned LOGO computer programming, and on strategy transformations that took place during the problem solving process. The research consisted of a six weeks programming training…

  1. The Identity of Problem Solving

    ERIC Educational Resources Information Center

    Mamona-Downs, Joanna; Downs, Martin

    2005-01-01

    This paper raises issues motivated by considering the "identity" of problem solving. This means that we are concerned with how other mathematics education topics impinge on problem solving, and with themes that naturally arise within the problem-solving agenda. We claim that some of these issues need more attention by educational research, while…

  2. Measuring Family Problem Solving: The Family Problem Solving Diary.

    ERIC Educational Resources Information Center

    Kieren, Dianne K.

    The development and use of the family problem-solving diary are described. The diary is one of several indicators and measures of family problem-solving behavior. It provides a record of each person's perception of day-to-day family problems (what the problem concerns, what happened, who got involved, what those involved did, how the problem…

  3. On a modification of minimal iteration methods for solving systems of linear algebraic equations

    NASA Astrophysics Data System (ADS)

    Yukhno, L. F.

    2010-04-01

    Modifications of certain minimal iteration methods for solving systems of linear algebraic equations are proposed and examined. The modified methods are shown to be superior to the original versions with respect to the round-off error accumulation, which makes them applicable to solving ill-conditioned problems. Numerical results demonstrating the efficiency of the proposed modifications are given.

  4. Numerical stability in problems of linear algebra.

    NASA Technical Reports Server (NTRS)

    Babuska, I.

    1972-01-01

    Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

  5. Numerical stability in problems of linear algebra.

    NASA Technical Reports Server (NTRS)

    Babuska, I.

    1972-01-01

    Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

  6. Problem Solving: Tips for Teachers.

    ERIC Educational Resources Information Center

    O'Daffer, Phares G., Ed.; Schaaf, Oscar

    1986-01-01

    Describes: (1) a computation-oriented problem with procedures and some questions that might be asked of students; (2) four ways to help students develop positive problem-solving attitudes; (3) a strategy game; (4) a multiplication problem; and (5) several questions that will help students develop problem-solving skills. (JN)

  7. Resource Scarcity: Problems Technology Cannot Solve; Problems Technology Can Solve.

    ERIC Educational Resources Information Center

    Meadows, Dennis; Castle, Emery N.

    1979-01-01

    Lists resource problems technology can and cannot solve, and emphasizes the need for considering and restructuring the social environments and institutions as well as developing new technologies. (CK)

  8. Problem Solving Tips for Teachers.

    ERIC Educational Resources Information Center

    O'Daffer, Phares G.

    1985-01-01

    The focus is on the problem-solving strategy of find a pattern, with a problem explored to illustrate how to use the strategy. Other tips concern classroom climate, checking skills, research, and type of problems. (MNS)

  9. The Effect of Strategy on Problem Solving: An FMRI Study

    ERIC Educational Resources Information Center

    Newman, Sharlene D.; Pruce, Benjamin; Rusia, Akash; Burns, Thomas, Jr.

    2010-01-01

    fMRI was used to examine the differential effect of two problem-solving strategies. Participants were trained to use both a pictorial/spatial and a symbolic/algebraic strategy to solve word problems. While these two strategies activated similar cortical regions, a number of differences were noted in the level of activation. These differences…

  10. The Effect of Strategy on Problem Solving: An FMRI Study

    ERIC Educational Resources Information Center

    Newman, Sharlene D.; Pruce, Benjamin; Rusia, Akash; Burns, Thomas, Jr.

    2010-01-01

    fMRI was used to examine the differential effect of two problem-solving strategies. Participants were trained to use both a pictorial/spatial and a symbolic/algebraic strategy to solve word problems. While these two strategies activated similar cortical regions, a number of differences were noted in the level of activation. These differences…

  11. Problem Solving Tips for Teachers.

    ERIC Educational Resources Information Center

    O'Daffer, Phares G.

    1984-01-01

    Presents a problem-solving activity in which students first guess and then check their answer. Also presents an activity to help students develop skill in understanding the question in a problem and a suggestion to help develop a classroom climate conducive to problem-solving. (JN)

  12. Technological Problem Solving: A Proposal.

    ERIC Educational Resources Information Center

    Waetjen, Walter B.

    Examination of newer technology education materials reveals two recurring themes: one relates to curriculum content, familiarizing students with technology, and another to a technique of classroom instruction, i.e., problem solving. A problem-solving framework for technical education has the following components: (1) define the problem; (2)…

  13. Solving Transportation Problems via Aggregation,

    DTIC Science & Technology

    1984-07-01

    AD-A144 219 SOLVING TRANSPORTATION PROBLEMS VIA AGGREGATION (U) i/l GEORGIA INST OF TECH ATLANTA PRODUCTION AND DISTRIBUTION RESEARCH CENTER R W...10 July 1984 SOLVING TRANSPORTATION PROBLEMS VIA AGGREGATION by" 4 Richard W. Taylort C. M. Shettytt PDRC 84-10 DTIC E L - TE~ School of Business...c UoaOO48--17 Rpouto spritein whol or pr for ny prpos of he U S. overment Abstract Solving Transportation Problems Via Aggregation 0

  14. Paving a Way to Algebraic Word Problems Using a Nonalgebraic Route

    ERIC Educational Resources Information Center

    Amit, Miriam; Klass-Tsirulnikov, Bella

    2005-01-01

    A three-stage model for algebraic word problem solving is developed in which students' understanding of the intrinsic logical structure of word problems is strengthened by connecting real-life problems and formal mathematics. (Contains 3 figure.)

  15. Algebraic solution of the synthesis problem for coded sequences

    SciTech Connect

    Leukhin, Anatolii N

    2005-08-31

    The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations for a given code dimension is solved. It is pointed out that the problem of synthesis of PC sequences is related to the fundamental problems of discrete mathematics and, first of all, to a number of combinatorial problems, which can be solved, as the number factorisation problem, by algebraic methods by using the theory of Galois fields and groups. (fourth seminar to the memory of d.n. klyshko)

  16. Problem Solving Style, Creative Thinking, and Problem Solving Confidence

    ERIC Educational Resources Information Center

    Houtz, John C.; Selby, Edwin C.

    2009-01-01

    Forty-two undergraduate and graduate students completed VIEW: An Assessment of Problem Solving Style, the non-verbal Torrance Test Thinking Creatively with Pictures, and the Problem Solving Inventory (PSI). VIEW assesses individuals' orientation to change, manner of processing, and ways of deciding, while the Torrance test measures several…

  17. Algebraic approach to solve tt dilepton equations

    SciTech Connect

    Sonnenschein, Lars

    2005-11-01

    The set of nonlinear equations describing the standard model kinematics of the top quark antiquark production system in the dilepton decay channel has at most a fourfold ambiguity due to two not fully reconstructed neutrinos. Its most precise solution is of major importance for measurements of top quark properties like the top quark mass and tt spin correlations. Simple algebraic operations allow one to transform the nonlinear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be analytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree 16. The number of its real solutions is determined analytically by means of Sturm's theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary bracketing.

  18. Student Difficulties in Mathematizing Word Problems in Algebra

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul

    2016-01-01

    To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization,…

  19. Student Difficulties in Mathematizing Word Problems in Algebra

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul

    2016-01-01

    To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization,…

  20. Problem Solving Tips for Teachers.

    ERIC Educational Resources Information Center

    O'Daffer, Phares G.

    1984-01-01

    The strategy of making a table is highlighted. A problem is given and the procedure for setting up and using the table are explained. Other suggestions for teaching problem solving are also included. (MNS)

  1. Problem Solving, Scaffolding and Learning

    ERIC Educational Resources Information Center

    Lin, Shih-Yin

    2012-01-01

    Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…

  2. Learning Impasses in Problem Solving

    NASA Technical Reports Server (NTRS)

    Hodgson, J. P. E.

    1992-01-01

    Problem Solving systems customarily use backtracking to deal with obstacles that they encounter in the course of trying to solve a problem. This paper outlines an approach in which the possible obstacles are investigated prior to the search for a solution. This provides a solution strategy that avoids backtracking.

  3. Creative Thinking and Problem Solving.

    ERIC Educational Resources Information Center

    Lacy, Grace

    The booklet considers the nature of creativity in children and examines classroom implications. Among the topics addressed are the following: theories about creativity; research; developments in brain research; the creative process; creative problem solving; the Structure of Intellect Problem Solving (SIPS) model; a rationale for creativity in the…

  4. Difficulties in Genetics Problem Solving.

    ERIC Educational Resources Information Center

    Tolman, Richard R.

    1982-01-01

    Examined problem-solving strategies of 30 high school students as they solved genetics problems. Proposes a new sequence of teaching genetics based on results: meiosis, sex chromosomes, sex determination, sex-linked traits, monohybrid and dihybrid crosses (humans), codominance (humans), and Mendel's pea experiments. (JN)

  5. Creative Thinking and Problem Solving.

    ERIC Educational Resources Information Center

    Lacy, Grace

    The booklet considers the nature of creativity in children and examines classroom implications. Among the topics addressed are the following: theories about creativity; research; developments in brain research; the creative process; creative problem solving; the Structure of Intellect Problem Solving (SIPS) model; a rationale for creativity in the…

  6. A Personal Problem Solving Inventory.

    ERIC Educational Resources Information Center

    Heppner, P. Paul; Petersen, Chris H.

    Few studies have explicitly attended to the personal problem-solving process within the counseling literature, perhaps due in part to the dearth of relevant assessment instruments. To examine the dimensions underlying the applied problem-solving process, an exploratory factor analysis was conducted using data collected from four samples of college…

  7. Difficulties in Genetics Problem Solving.

    ERIC Educational Resources Information Center

    Tolman, Richard R.

    1982-01-01

    Examined problem-solving strategies of 30 high school students as they solved genetics problems. Proposes a new sequence of teaching genetics based on results: meiosis, sex chromosomes, sex determination, sex-linked traits, monohybrid and dihybrid crosses (humans), codominance (humans), and Mendel's pea experiments. (JN)

  8. Problem Solving, Scaffolding and Learning

    ERIC Educational Resources Information Center

    Lin, Shih-Yin

    2012-01-01

    Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…

  9. The Future Problem Solving Program.

    ERIC Educational Resources Information Center

    Crabbe, Anne B.

    1989-01-01

    Describes the Future Problem Solving Program, in which students from the U.S. and around the world are tackling some complex challenges facing society, ranging from acid rain to terrorism. The program uses a creative problem solving process developed for business and industry. A sixth-grade toxic waste cleanup project illustrates the process.…

  10. Adaptive Problem Solving

    DTIC Science & Technology

    2017-03-01

    Auckland Private Bag 92019 Auckland, 1142 New Zealand Name of Principal Investigators (Co-PI): Patricia J. Riddle - e-mail address : pat...Auckland, 1142 New Zealand Period of Performance: 5/27/2015 – 11/26/2016 Abstract: We have implemented a system, MSP, that given a specific problem...since 2014. Thus, we cannot compare MSP against a new set of competitors on a new set of problems. However, we can compare it against RIDA* on the

  11. Modeling Applied to Problem Solving

    NASA Astrophysics Data System (ADS)

    Pawl, Andrew; Barrantes, Analia; Pritchard, David E.

    2009-10-01

    Modeling Applied to Problem Solving (MAPS) is a pedagogy that helps students transfer instruction to problem solving in an expert-like manner. Declarative and Procedural syllabus content is organized and learned (not discovered) as a hierarchy of General Models. Students solve problems using an explicit Problem Modeling Rubric that begins with System, Interactions and Model (S.I.M.). System and Interactions are emphasized as the key to a strategic description of the system and the identification of the appropriate General Model to apply to the problem. We have employed the pedagogy in a three-week review course for students who received a D in mechanics. The course was assessed by a final exam retest as well as pre and post C-LASS surveys, yielding a one standard deviation improvement in the students' ability to solve final exam problems and a statistically significant positive shift in 7 of the 9 categories in the C-LASS.

  12. Children Solve Problems.

    ERIC Educational Resources Information Center

    De Bono, Edward

    A group of children were presented with several tasks, including the invention of a sleep machine and a machine to weigh elephants. The tasks were chosen to involve the children in coping with problems of a distinct character. A study of the children's drawings and interpretations shows that children's thinking ability is not very different from…

  13. Understanding Students' Problem-Solving Knowledge through Their Writing

    ERIC Educational Resources Information Center

    Steele, Diana F.

    2007-01-01

    This article describes a teaching experiment conducted in a seventh-grade classroom. It explores ways that students used four types of problem-solving knowledge through writing their responses to algebraic problems. The problems were presented to students in the geometric contexts of growth and change and size and shape. It was found that writing…

  14. Teaching Representation and Solution of Algebraic Word Problems to Learning Disabled Adolescents.

    ERIC Educational Resources Information Center

    Hutchinson, Nancy; Hemingway, Peter

    The dual purpose of this study was (1) to design instruction in problem representation and solution of algebraic word problems in order to improve the algebraic problem solving skills of learning disabled (LD) adolescents; and (2) to devise and evaluate the effectiveness of instructional procedures for teaching LD adolescents to represent and…

  15. Solving A Corrosion Problem

    NASA Technical Reports Server (NTRS)

    1979-01-01

    The corrosion problem, it turned out, stemmed from the process called electrolysis. When two different metals are in contact, an electrical potential is set up between them; when the metals are surrounded by an electrolyte, or a conducting medium, the resulting reaction causes corrosion, often very rapid corrosion. In this case the different metals were the copper grounding system and the ferry's aluminum hull; the dockside salt water in which the hull was resting served as the electrolyte. After identifying the source of the trouble, the Ames engineer provided a solution: a new wire-and-rod grounding system made of aluminum like the ferry's hull so there would no longer be dissimilar metals in contact. Ames research on the matter disclosed that the problem was not unique to the Golden Gate ferries. It is being experienced by many pleasure boat operators who are probably as puzzled about it as was the Golden Gate Transit Authority.

  16. Solving bearing overheating problems

    SciTech Connect

    Jendzurski, T.

    1995-05-08

    Overheating is a major indicator, along with vibration and noise, of an underlying problem affecting a bearing or related components. Because normal operating temperatures vary widely from one application to another, no single temperature is a reliable sign of overheating in every situation. By observing an application when it is running smoothly, a technician can establish a benchmark temperature for a particular bearing arrangement. Wide deviations from this accepted norm generally indicate troublesome overheating. The list of possible causes of over-heating ranges from out-of-round housings and oversize shaft diameters to excessive lubrication and bearing preloading. These causes fall into two major categories: improper or faulty lubrication and mechanical problems, such as incorrect fits and tolerances. These are discussed along with solutions.

  17. Problem Solving and Reasoning

    DTIC Science & Technology

    1988-01-01

    response fre- of homework or test problems that the class was lems were esented quencies in two tasks. Findings that fit this working on at the time...psychological models were th this students who receive these tasks as homework simpler, and the inferences about processes ved by assignments and...quantitative relations study of children from kindergarten through and stud, nts must be able to choose formulas third grade. The versions differ in

  18. Irrelevance in Problem Solving

    NASA Technical Reports Server (NTRS)

    Levy, Alon Y.

    1992-01-01

    The notion of irrelevance underlies many different works in AI, such as detecting redundant facts, creating abstraction hierarchies and reformulation and modeling physical devices. However, in order to design problem solvers that exploit the notion of irrelevance, either by automatically detecting irrelevance or by being given knowledge about irrelevance, a formal treatment of the notion is required. In this paper we present a general framework for analyzing irrelevance. We discuss several properties of irrelevance and show how they vary in a space of definitions outlined by the framework. We show how irrelevance claims can be used to justify the creation of abstractions thereby suggesting a new view on the work on abstraction.

  19. Supporting Problem Solving in PBL

    ERIC Educational Resources Information Center

    Jonassen, David

    2011-01-01

    Although the characteristics of PBL (problem focused, student centered, self-directed, etc.) are well known, the components of a problem-based learning environment (PBLE) and the cognitive scaffolds necessary to support learning to solve different kinds of problems with different learners is less clear. This paper identifies the different…

  20. Student Problem-Solving Behaviors

    NASA Astrophysics Data System (ADS)

    Harper, Kathleen A.

    2006-04-01

    Kathy Harper is director of undergraduate curriculum development in the physics department at The Ohio State University. She has been involved in local and national workshops for in-service teachers and conducts research in student problem solving.

  1. Problem Solving with General Semantics.

    ERIC Educational Resources Information Center

    Hewson, David

    1996-01-01

    Discusses how to use general semantics formulations to improve problem solving at home or at work--methods come from the areas of artificial intelligence/computer science, engineering, operations research, and psychology. (PA)

  2. Solving Toda field theories and related algebraic and differential properties

    NASA Astrophysics Data System (ADS)

    Nie, Zhaohu

    2012-12-01

    Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld-Sokolov gauge is used. The main objective of this paper is to carry out this approach of solving the Toda field theories for the classical Lie algebras, following Balog et al. (1990) [5]. In this process, we discover and prove some algebraic identities for principal minors of special matrices. The known elegant solutions of Leznov (1980) [10] fit in our scheme in the sense that they are the general solutions to our conditions discovered in this solving process. To prove this, we find and prove some differential identities for iterated integrals. It can be said that altogether our paper gives complete mathematical proofs for Leznov's solutions.

  3. Working Memory and Literacy as Predictors of Performance on Algebraic Word Problems

    ERIC Educational Resources Information Center

    Lee, Kerry; Ng, Swee-Fong; Ng, Ee-Lynn; Lim, Zee-Ying

    2004-01-01

    Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient…

  4. Students' Problem Solving and Justification

    ERIC Educational Resources Information Center

    Glass, Barbara; Maher, Carolyn A.

    2004-01-01

    This paper reports on methods of students' justifications of their solution to a problem in the area of combinatorics. From the analysis of the problem solving of 150 students in a variety of settings from high-school to graduate study, four major forms of reasoning evolved: (1) Justification by Cases, (2) Inductive Argument, (3) Elimination…

  5. Quantitative Reasoning in Problem Solving

    ERIC Educational Resources Information Center

    Ramful, Ajay; Ho, Siew Yin

    2015-01-01

    In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

  6. Promote Problem-Solving Discourse

    ERIC Educational Resources Information Center

    Bostic, Jonathan; Jacobbe, Tim

    2010-01-01

    Fourteen fifth-grade students gather at the front of the classroom as their summer school instructor introduces Jonathan Bostic as the mathematics teacher for the week. Before examining any math problems, Bostic sits at eye level with the students and informs them that they will solve problems over the next four days by working individually as…

  7. Customer-centered problem solving.

    PubMed

    Samelson, Q B

    1999-11-01

    If there is no single best way to attract new customers and retain current customers, there is surely an easy way to lose them: fail to solve the problems that arise in nearly every buyer-supplier relationship, or solve them in an unsatisfactory manner. Yet, all too frequently, companies do just that. Either we deny that a problem exists, we exert all our efforts to pin the blame elsewhere, or we "Band-Aid" the problem instead of fixing it, almost guaranteeing that we will face it again and again.

  8. Robot, computer problem solving system

    NASA Technical Reports Server (NTRS)

    Becker, J. D.

    1972-01-01

    The development of a computer problem solving system is reported that considers physical problems faced by an artificial robot moving around in a complex environment. Fundamental interaction constraints with a real environment are simulated for the robot by visual scan and creation of an internal environmental model. The programming system used in constructing the problem solving system for the simulated robot and its simulated world environment is outlined together with the task that the system is capable of performing. A very general framework for understanding the relationship between an observed behavior and an adequate description of that behavior is included.

  9. Identification of Strategies Used by Fifth Graders To Solve Mathematics Word Problems.

    ERIC Educational Resources Information Center

    Palomares, Julio Cesar Arteaga; Hernandez, Jose Guzman

    When students confront arithmetic or algebraic word problems, they develop ideas and notations during the processes of solving them by using various arithmetic strategies. Those ideas and notations are the basis for solving that type of problems. Is it possible to aid the development of students' algebraic thinking during their transition from…

  10. Mathematical problem solving by analogy.

    PubMed

    Novick, L R; Holyoak, K J

    1991-05-01

    We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.

  11. Problem? "No Problem!" Solving Technical Contradictions

    ERIC Educational Resources Information Center

    Kutz, K. Scott; Stefan, Victor

    2007-01-01

    TRIZ (pronounced TREES), the Russian acronym for the theory of inventive problem solving, enables a person to focus his attention on finding genuine, potential solutions in contrast to searching for ideas that "may" work through a happenstance way. It is a patent database-backed methodology that helps to reduce time spent on the problem,…

  12. Problem? "No Problem!" Solving Technical Contradictions

    ERIC Educational Resources Information Center

    Kutz, K. Scott; Stefan, Victor

    2007-01-01

    TRIZ (pronounced TREES), the Russian acronym for the theory of inventive problem solving, enables a person to focus his attention on finding genuine, potential solutions in contrast to searching for ideas that "may" work through a happenstance way. It is a patent database-backed methodology that helps to reduce time spent on the problem,…

  13. Problem Solving Does Not Have To Be a Problem.

    ERIC Educational Resources Information Center

    Barb, Cynthia; Quinn, Anne Larson

    1997-01-01

    Highlights the argument that states that problem solving is much more than just solving problems, by focusing on problem-solving history, George Polya's view of problem solving, Asians' successful use of multiple intuitive solutions, and other examples. (ASK)

  14. Quantum Computing: Solving Complex Problems

    ScienceCinema

    DiVincenzo, David [IBM Watson Research Center

    2016-07-12

    One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.

  15. Human Problem Solving in 2006

    ERIC Educational Resources Information Center

    Pizlo, Zygmunt

    2007-01-01

    This paper presents a bibliography of a little more than 100 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Compendex databases. Only journal papers, books and dissertations are included. The topics include human development, education, neuroscience, research in applied…

  16. Time Out for Problem Solving.

    ERIC Educational Resources Information Center

    Champagne, Audrey B.; And Others

    Teachers in elementary schools, supervisors of instruction, and other educational practitioners are the primary audience for this publication. The paper presents philosophical, psychological, and practical reasons for including a problem-solving approach in elementary school instruction. It draws on the writings of John Dewey, Jean Piaget, James…

  17. Human Problem Solving in 2012

    ERIC Educational Resources Information Center

    Funke, Joachim

    2013-01-01

    This paper presents a bibliography of 263 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Academic Premier data-base. Journal papers, book chapters, and dissertations are included. The topics include human development, education, neuroscience, and research in applied settings. It…

  18. Human Problem Solving in 2008

    ERIC Educational Resources Information Center

    Pizlo, Zygmunt

    2008-01-01

    This paper presents a bibliography of more than 200 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo database. Journal papers, book chapters, books and dissertations are included. The topics include human development, education, neuroscience, research in applied settings, as well as…

  19. Human Problem Solving in 2008

    ERIC Educational Resources Information Center

    Pizlo, Zygmunt

    2008-01-01

    This paper presents a bibliography of more than 200 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo database. Journal papers, book chapters, books and dissertations are included. The topics include human development, education, neuroscience, research in applied settings, as well as…

  20. Robot computer problem solving system

    NASA Technical Reports Server (NTRS)

    Becker, J. D.

    1972-01-01

    Continuing research is reported in a program aimed at the development of a robot computer problem solving system. The motivation and results are described of a theoretical investigation concerning the general properties of behavioral systems. Some of the important issues which a general theory of behavioral organization should encompass are outlined and discussed.

  1. Teaching through Collaborative Problem Solving.

    ERIC Educational Resources Information Center

    Blandford, A. E.

    1994-01-01

    Discussion of a prototype intelligent education system called WOMBAT (Weighted Objectives Method by Arguing with the Tutor) focuses on dialogue and negotiation in collaborative problem solving. The results of a formative evaluation, in which the system was used by 10 subjects who commented on various aspects of the design, are presented. (Contains…

  2. Error Patterns in Problem Solving.

    ERIC Educational Resources Information Center

    Babbitt, Beatrice C.

    Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…

  3. Gender and Mathematical Problem Solving.

    ERIC Educational Resources Information Center

    Duffy, Jim; Gunther, Georg; Walters, Lloyd

    1997-01-01

    Studied the relationship between gender and mathematical problem solving in 83 male and 76 female high achieving Canadian 12-year-olds. Gender differences were found on the Canadian Test of Basic Skills but not on the GAUSS assessment. Implications for the discussion of the origin of gender differences in mathematics are discussed. (SLD)

  4. Customer Service & Team Problem Solving.

    ERIC Educational Resources Information Center

    Martin, Sabrina Budasi

    This curriculum guide provides materials for a six-session, site-specific training course in customer service and team problem solving for the Claretian Medical Center. The course outline is followed the six lesson plans. Components of each lesson plan include a list of objectives, an outline of activities and discussion topics for the lesson,…

  5. Solving the problem of writing.

    PubMed

    Ferguson, D

    1995-04-01

    This paper explores the difficulties which some students appear to encounter with written work and recommends the teaching of a problem-solving approach. Exploration of the skills necessary for writing, e.g. language skills and memory functions, highlights the structured format of cognitive processes. Most study skill packages emphasise the need for planning and organising work. It may be that students require more detailed help and guidance in such skills. This paper promotes the teaching to students of a problem-solving approach to written work. We all solve problems every day, many we are completely unaware of. This approach seeks to harness these transferable skills and utilise them in a new area. It can be applied at a macro and at a micro level, i.e. the entire essay/project/report may be planned utilising this approach and then each section or paragraph further planned in the same manner. The use of a mnemonic further aids the student in developing and applying the problem solving approach to written work.

  6. Robot computer problem solving system

    NASA Technical Reports Server (NTRS)

    Becker, J. D.; Merriam, E. W.

    1974-01-01

    The conceptual, experimental, and practical phases of developing a robot computer problem solving system are outlined. Robot intelligence, conversion of the programming language SAIL to run under the THNEX monitor, and the use of the network to run several cooperating jobs at different sites are discussed.

  7. Robot computer problem solving system

    NASA Technical Reports Server (NTRS)

    Becker, J. D.; Merriam, E. W.

    1974-01-01

    The conceptual, experimental, and practical aspects of the development of a robot computer problem solving system were investigated. The distinctive characteristics were formulated of the approach taken in relation to various studies of cognition and robotics. Vehicle and eye control systems were structured, and the information to be generated by the visual system is defined.

  8. Human Problem Solving in 2006

    ERIC Educational Resources Information Center

    Pizlo, Zygmunt

    2007-01-01

    This paper presents a bibliography of a little more than 100 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Compendex databases. Only journal papers, books and dissertations are included. The topics include human development, education, neuroscience, research in applied…

  9. Gender and Mathematical Problem Solving.

    ERIC Educational Resources Information Center

    Duffy, Jim; Gunther, Georg; Walters, Lloyd

    1997-01-01

    Studied the relationship between gender and mathematical problem solving in 83 male and 76 female high achieving Canadian 12-year-olds. Gender differences were found on the Canadian Test of Basic Skills but not on the GAUSS assessment. Implications for the discussion of the origin of gender differences in mathematics are discussed. (SLD)

  10. Human Problem Solving in 2012

    ERIC Educational Resources Information Center

    Funke, Joachim

    2013-01-01

    This paper presents a bibliography of 263 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Academic Premier data-base. Journal papers, book chapters, and dissertations are included. The topics include human development, education, neuroscience, and research in applied settings. It…

  11. Teaching Math. Extending Problem Solving.

    ERIC Educational Resources Information Center

    May, Lola

    1996-01-01

    Describes four teaching activities to help children extend math problem-solving skills by using their own questions. Activities involve using a chart and symbols to develop equations adding up to 12, going on an imaginary shopping trip, using shapes to represent dollar amounts, using the date on a penny to engage in various mathematical…

  12. Time Out for Problem Solving.

    ERIC Educational Resources Information Center

    Champagne, Audrey B.; And Others

    Teachers in elementary schools, supervisors of instruction, and other educational practitioners are the primary audience for this publication. The paper presents philosophical, psychological, and practical reasons for including a problem-solving approach in elementary school instruction. It draws on the writings of John Dewey, Jean Piaget, James…

  13. Integrating Study Skills and Problem Solving into Remedial Mathematics

    ERIC Educational Resources Information Center

    Cornick, Jonathan; Guy, G. Michael; Beckford, Ian

    2015-01-01

    Students at a large urban community college enrolled in seven classes of an experimental remedial algebra programme, which integrated study skills instruction and collaborative problem solving. A control group of seven classes was taught in a traditional lecture format without study skills instruction. Student performance in the course was…

  14. Reversible Reasoning and the Working Backwards Problem Solving Strategy

    ERIC Educational Resources Information Center

    Ramful, Ajay

    2015-01-01

    Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

  15. A Study of Student Interactions during Asynchronous Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Cooper, Thomas E.

    2009-01-01

    This study was conducted to investigate the quality and nature of the students' interactions during asynchronous online problem solving in two sections of College Algebra taught by the author. In a shared-work section, students worked independently for an initial phase and had access to classmates' work during a follow-up phase. Students in the…

  16. Reversible Reasoning and the Working Backwards Problem Solving Strategy

    ERIC Educational Resources Information Center

    Ramful, Ajay

    2015-01-01

    Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

  17. Practical algorithms for algebraic and logical correction in precedent-based recognition problems

    NASA Astrophysics Data System (ADS)

    Ablameyko, S. V.; Biryukov, A. S.; Dokukin, A. A.; D'yakonov, A. G.; Zhuravlev, Yu. I.; Krasnoproshin, V. V.; Obraztsov, V. A.; Romanov, M. Yu.; Ryazanov, V. V.

    2014-12-01

    Practical precedent-based recognition algorithms relying on logical or algebraic correction of various heuristic recognition algorithms are described. The recognition problem is solved in two stages. First, an arbitrary object is recognized independently by algorithms from a group. Then a final collective solution is produced by a suitable corrector. The general concepts of the algebraic approach are presented, practical algorithms for logical and algebraic correction are described, and results of their comparison are given.

  18. Solving the generalized Langevin equation with the algebraically correlated noise

    NASA Astrophysics Data System (ADS)

    Srokowski, T.; Płoszajczak, M.

    1998-04-01

    We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.

  19. Genetics problem solving and worldview

    NASA Astrophysics Data System (ADS)

    Dale, Esther

    The research goal was to determine whether worldview relates to traditional and real-world genetics problem solving. Traditionally, scientific literacy emphasized content knowledge alone because it was sufficient to solve traditional problems. The contemporary definition of scientific literacy is, "The knowledge and understanding of scientific concepts and processes required for personal decision-making, participation in civic and cultural affairs and economic productivity" (NRC, 1996). An expanded definition of scientific literacy is needed to solve socioscientific issues (SSI), complex social issues with conceptual, procedural, or technological associations with science. Teaching content knowledge alone assumes that students will find the scientific explanation of a phenomenon to be superior to a non-science explanation. Formal science and everyday ways of thinking about science are two different cultures (Palmer, 1999). Students address this rift with cognitive apartheid, the boxing away of science knowledge from other types of knowledge (Jedege & Aikenhead, 1999). By addressing worldview, cognitive apartheid may decrease and scientific literacy may increase. Introductory biology students at the University of Minnesota during fall semester 2005 completed a written questionnaire-including a genetics content-knowledge test, four genetic dilemmas, the Worldview Assessment Instrument (WAI) and some items about demographics and religiosity. Six students responded to the interview protocol. Based on statistical analysis and interview data, this study concluded the following: (1) Worldview, in the form of metaphysics, relates to solving traditional genetic dilemmas. (2) Worldview, in the form of agency, relates to solving traditional genetics problems. (3) Thus, worldview must be addressed in curriculum, instruction, and assessment.

  20. Teaching Problem Solving through Children's Literature.

    ERIC Educational Resources Information Center

    Forgan, James W.

    This book helps general and special education teachers empower students in grades K-4 to independently solve problems by teaching them how characters in children's literature books solved similar problems. Students are also taught a problem solving strategy that they can apply to solve problems in any situation. The book contains ready-to-use…

  1. Modeling Applied to Problem Solving

    NASA Astrophysics Data System (ADS)

    Pawl, Andrew; Barrantes, Analia; Pritchard, David E.

    2009-11-01

    We describe a modeling approach to help students learn expert problem solving. Models are used to present and hierarchically organize the syllabus content and apply it to problem solving, but students do not develop and validate their own Models through guided discovery. Instead, students classify problems under the appropriate instructor-generated Model by selecting a system to consider and describing the interactions that are relevant to that system. We believe that this explicit System, Interactions and Model (S.I.M.) problem modeling strategy represents a key simplification and clarification of the widely disseminated modeling approach originated by Hestenes and collaborators. Our narrower focus allows modeling physics to be integrated into (as opposed to replacing) a typical introductory college mechanics course, while preserving the emphasis on understanding systems and interactions that is the essence of modeling. We have employed the approach in a three-week review course for MIT freshmen who received a D in the fall mechanics course with very encouraging results.

  2. Solving the Dark Matter Problem

    ScienceCinema

    Baltz, Ted

    2016-07-12

    Cosmological observations have firmly established that the majority of matter in the universe is of an unknown type, called 'dark matter'. A compelling hypothesis is that the dark matter consists of weakly interacting massive particles (WIMPs) in the mass range around 100 GeV. If the WIMP hypothesis is correct, such particles could be created and studied at accelerators. Furthermore they could be directly detected as the primary component of our galaxy. Solving the dark matter problem requires that the connection be made between the two. We describe some theoretical and experimental avenues that might lead to this connection.

  3. Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2014-01-01

    Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

  4. Disciplinary Foundations for Solving Interdisciplinary Scientific Problems

    ERIC Educational Resources Information Center

    Zhang, Dongmei; Shen, Ji

    2015-01-01

    Problem-solving has been one of the major strands in science education research. But much of the problem-solving research has been conducted on discipline-based contexts; little research has been done on how students, especially individuals, solve interdisciplinary problems. To understand how individuals reason about interdisciplinary problems, we…

  5. Disciplinary Foundations for Solving Interdisciplinary Scientific Problems

    ERIC Educational Resources Information Center

    Zhang, Dongmei; Shen, Ji

    2015-01-01

    Problem-solving has been one of the major strands in science education research. But much of the problem-solving research has been conducted on discipline-based contexts; little research has been done on how students, especially individuals, solve interdisciplinary problems. To understand how individuals reason about interdisciplinary problems, we…

  6. King Oedipus and the Problem Solving Process.

    ERIC Educational Resources Information Center

    Borchardt, Donald A.

    An analysis of the problem solving process reveals at least three options: (1) finding the cause, (2) solving the problem, and (3) anticipating potential problems. These methods may be illustrated by examining "Oedipus Tyrannus," a play in which a king attempts to deal with a problem that appears to be beyond his ability to solve, and…

  7. Problem Solving with the Elementary Youngster.

    ERIC Educational Resources Information Center

    Swartz, Vicki

    This paper explores research on problem solving and suggests a problem-solving approach to elementary school social studies, using a culture study of the ancient Egyptians and King Tut as a sample unit. The premise is that problem solving is particularly effective in dealing with problems which do not have one simple and correct answer but rather…

  8. Research on Computers and Problem Solving.

    ERIC Educational Resources Information Center

    Burton, John K.; And Others

    1988-01-01

    Eight articles review and report on research involving computers and problem solving skills. Topics discussed include research design; problem solving skills and programing languages, including BASIC and LOGO; computer anxiety; diagnostic programs for arithmetic problems; and relationships between ability and problem solving scores and between…

  9. Graphing as a Problem-Solving Strategy.

    ERIC Educational Resources Information Center

    Cohen, Donald

    1984-01-01

    The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)

  10. Teaching DICOM by problem solving.

    PubMed

    Noumeir, Rita; Pambrun, Jean-François

    2012-10-01

    The Digital Imaging and Communications in Medicine (DICOM) is the standard for encoding and communicating medical imaging information. It is used in radiology as well as in many other imaging domains such as ophthalmology, dentistry, and pathology. DICOM information objects are used to encode medical images or information about the images. Their usage outside of the imaging department is increasing, especially with the sharing of medical images within Electronic Health Record systems. However, learning DICOM is long and difficult because it defines and uses many specific abstract concepts that relate to each other. In this paper, we present an approach, based on problem solving, for teaching DICOM as part of a graduate course on healthcare information. The proposed approach allows students with diversified background and no software development experience to grasp a large breadth of knowledge in a very short time.

  11. Robot computer problem solving system

    NASA Technical Reports Server (NTRS)

    Merriam, E. W.; Becker, J. D.

    1973-01-01

    A robot computer problem solving system which represents a robot exploration vehicle in a simulated Mars environment is described. The model exhibits changes and improvements made on a previously designed robot in a city environment. The Martian environment is modeled in Cartesian coordinates; objects are scattered about a plane; arbitrary restrictions on the robot's vision have been removed; and the robot's path contains arbitrary curves. New environmental features, particularly the visual occlusion of objects by other objects, were added to the model. Two different algorithms were developed for computing occlusion. Movement and vision capabilities of the robot were established in the Mars environment, using LISP/FORTRAN interface for computational efficiency. The graphical display program was redesigned to reflect the change to the Mars-like environment.

  12. Rees algebras, Monomial Subrings and Linear Optimization Problems

    NASA Astrophysics Data System (ADS)

    Dupont, Luis A.

    2010-06-01

    In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.

  13. How to encourage university students to solve physics problems requiring mathematical skills: the 'adventurous problem solving' approach

    NASA Astrophysics Data System (ADS)

    DeMul, Frits F. M.; Batlle, Cristina Martin i.; DeBruijn, Imme; Rinzema, Kees

    2004-01-01

    Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential expressions and multi-dimensional integrations, and the Gauss and Ampère laws learnt in electromagnetism courses. To enhance those skills in a quick and efficient way we have developed 'Integrating Mathematics in University Physics', in which students are provided with a selection of problems (exercises) that explicitly deal with the relation between physics and mathematics. The project is based on computer-assisted instruction (CAI), and available via the Internet (http://tnweb.tn.utwente.nl/onderwijs/; or http://www.utwente.nl/; search or click to: CONECT). Normally, in CAI a predefined student-guiding sequence for problem solving is used (systematic problem solving). For self-learning this approach was found to be far too rigid. Therefore, we developed the 'adventurous problem solving' (APS) method. In this new approach, the student has to find the solution by developing his own problem-solving strategy in an interactive way. The assessment of mathematical answers to physical questions is performed using a background link with an algebraic symbolic language interpreter. This manuscript concentrates on the subject of APS.

  14. Creative Problem Solving for Social Studies.

    ERIC Educational Resources Information Center

    Weiss, Steve; Kinney, Mark; And Others

    1980-01-01

    This article discusses techniques for integrating real problem solving and decision making into secondary social studies programs. Approaches to creative problem solving are presented, and various systematic decision making programs currently available for classroom use are identified. (Author/RM)

  15. Temporal Reasoning and Problem Solving

    DTIC Science & Technology

    1992-01-28

    Engineering Applications of Artificial Intelligence and Expert...Keretho. "Efficient Propagation Algorithms for Temporal Interval Algebra," International Conference on Industrial and Engineering Applications of Artificial Intelligence and...Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, June 1991. 12

  16. Key Contextual Features of Algebra Word Problems: A Theoretical Model and Review of the Literature.

    ERIC Educational Resources Information Center

    Nasser, Ramzi; Carifio, James

    One of the four algebra word problem structures found in K-12 textbooks is the propositional relation structure (Mayer, 1982). This type of problem asks students to establish equivalences between the variables or noun referents in the problem. The literature available indicates that students have inordinate difficulties, when trying to solve a…

  17. Community-powered problem solving.

    PubMed

    Gouillart, Francis; Billings, Douglas

    2013-04-01

    Traditionally, companies have managed their constituencies with specific processes: marketing to customers, procuring from vendors, developing HR policies for employees, and so on. The problem is, such processes focus on repeatability and compliance, so they can lead to stagnation. Inviting your constituencies to collectively help you solve problems and exploit opportunities--"co-creation"--is a better approach. It allows you to continually tap the skills and insights of huge numbers of stakeholders and develop new ways to produce value for all. The idea is to provide stakeholders with platforms (physical and digital forums) on which they can interact, get them to start exploring new experiences and connections, and let the system grow organically. A co-creation initiative by a unit of Becton, Dickinson and Company demonstrates how this works. A global leader in syringes, BD set out to deepen its ties with hospital customers and help them reduce the incidence of infections from unsafe injection and syringe disposal practices. The effort began with a cross-functional internal team, brought in the hospital procurement and supply managers BD had relationships with, and then reached out to hospitals' infection-prevention and occupational health leaders. Eventually product designers, nurses, sustainability staffers, and even hospital CFOs were using the platform, contributing data that generated new best practices and reduced infections.

  18. Process Inquiry: Analysis of Oral Problem-Solving Skills in Mathematics of Engineering Students

    ERIC Educational Resources Information Center

    Trance, Naci John C.

    2013-01-01

    This paper presents another effort in determining the difficulty of engineering students in terms of solving word problems. Students were presented with word problems in algebra. Then, they were asked to solve the word problems orally; that is, before they presented their written solutions, they were required to explain how they understood the…

  19. Flowing toward Correct Contributions during Group Problem Solving: A Statistical Discourse Analysis

    ERIC Educational Resources Information Center

    Chiu, Ming Ming

    2008-01-01

    Groups that created more correct ideas (correct contributions or CCs) might be more likely to solve a problem, and students' recent actions (micro-time context) might aid CC creation. 80 high school students worked in groups of 4 on an algebra problem. Groups with higher mathematics grades or more CCs were more likely to solve the problem. Dynamic…

  20. Flowing toward Correct Contributions during Group Problem Solving: A Statistical Discourse Analysis

    ERIC Educational Resources Information Center

    Chiu, Ming Ming

    2008-01-01

    Groups that created more correct ideas (correct contributions or CCs) might be more likely to solve a problem, and students' recent actions (micro-time context) might aid CC creation. 80 high school students worked in groups of 4 on an algebra problem. Groups with higher mathematics grades or more CCs were more likely to solve the problem. Dynamic…

  1. Strategies for Teaching Learning Disabled Adolescents Algebraic Problems.

    ERIC Educational Resources Information Center

    Hutchinson, Nancy L.

    1987-01-01

    The article details an instructional procedure (based on the effective instruction research) to enable learning disabled adolescents to master three types of algebraic word problems: relational problems, proportion problems, and problems with two variables and two equations. (Author/DB)

  2. Application of the Group Algebra of the Problem of the Tail σ-ALGEBRA of a Random Walk on a Group and the Problem of Ergodicity of a Skew-Product Action

    NASA Astrophysics Data System (ADS)

    Ismagilov, R. S.

    1988-02-01

    Two problems in measure theory are considered: that of the tail C*-algebra of a random walk on a group, and that of ergodicity of a skew-product action. These problems are solved in a uniform way by using Banach algebras and harmonic analysis on a group. Bibliography: 22 titles.

  3. Strategies for Problem Solving. Revised Edition.

    ERIC Educational Resources Information Center

    Karmos, Joseph S.; Karmos, Ann H.

    This manual provides a comprehensive approach to problem solving; it is written in narrative style with numerous examples. The guide is organized in eight sections that cover the following topics: (1) problem-solving overview (with suggested readings and recommendations for schools); (2) a five-step model for solving problems; (3) strategies for…

  4. Problem Solving Appraisal of Delinquent Adolescents.

    ERIC Educational Resources Information Center

    Perez, Ruperto M.; And Others

    The study investigated the following: (1) the relationship of problem solving appraisal to narcissistic vulnerability, locus of control, and depression; (2) the differences in problem solving appraisal, locus of control, and depression in first-time and repeat offenders; and (3) the prediction of problem solving appraisal by narcissistic…

  5. Perspectives on Problem Solving and Instruction

    ERIC Educational Resources Information Center

    van Merrienboer, Jeroen J. G.

    2013-01-01

    Most educators claim that problem solving is important, but they take very different perspective on it and there is little agreement on how it should be taught. This article aims to sort out the different perspectives and discusses problem solving as a goal, a method, and a skill. As a goal, problem solving should not be limited to well-structured…

  6. Kindergarten Students Solving Mathematical Word Problems

    ERIC Educational Resources Information Center

    Johnson, Nickey Owen

    2013-01-01

    The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…

  7. A Component Analysis of Mathematical Problem Solving.

    ERIC Educational Resources Information Center

    Schwieger, Ruben Don

    The purpose of this study was the construction of a theoretical model for analyzing mathematical problem solving. A list of general problem-solving abilities was generated through a literature search. This list was narrowed to eight basic abilities pertinent to mathematics problem solving. Each of these was operationally defined and exemplified in…

  8. Developing Creativity through Collaborative Problem Solving

    ERIC Educational Resources Information Center

    Albert, Lillie R.; Kim, Rina

    2013-01-01

    This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

  9. Kindergarten Students Solving Mathematical Word Problems

    ERIC Educational Resources Information Center

    Johnson, Nickey Owen

    2013-01-01

    The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…

  10. Developing Creativity through Collaborative Problem Solving

    ERIC Educational Resources Information Center

    Albert, Lillie R.; Kim, Rina

    2013-01-01

    This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

  11. The Important Thing about Teaching Problem Solving

    ERIC Educational Resources Information Center

    Roberts, Sally K.

    2010-01-01

    The author teaches a content course in problem solving for middle school teachers. During the course, teacher candidates have the opportunity to confront their insecurities as they actively engage in solving math problems using a variety of strategies. As the semester progresses, they add new strategies to their problem-solving arsenal and…

  12. Collis-Romberg Mathematical Problem Solving Profiles.

    ERIC Educational Resources Information Center

    Collis, K. F.; Romberg, T. A.

    Problem solving has become a focus of mathematics programs in Australia in recent years, necessitating the assessment of students' problem-solving abilities. This manual provides a problem-solving assessment and teaching resource package containing four elements: (1) profiles assessment items; (2) profiles diagnostic forms for recording individual…

  13. Collis-Romberg Mathematical Problem Solving Profiles.

    ERIC Educational Resources Information Center

    Collis, K. F.; Romberg, T. A.

    Problem solving has become a focus of mathematics programs in Australia in recent years, necessitating the assessment of students' problem-solving abilities. This manual provides a problem-solving assessment and teaching resource package containing four elements: (1) profiles assessment items; (2) profiles diagnostic forms for recording individual…

  14. Physics Problem Solving Research Using Protocols.

    ERIC Educational Resources Information Center

    Brekke, Stewart E.

    This paper presents an overview of research on physics problem solving using verbal protocols. It asserts that the understanding of physics problem solving strategies enables researchers to write computer programs, which can automatically solve physics problems without the users having to be experts in physics. This, in turn, can generate more…

  15. LEGO Robotics: An Authentic Problem Solving Tool?

    ERIC Educational Resources Information Center

    Castledine, Alanah-Rei; Chalmers, Chris

    2011-01-01

    With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the…

  16. Does Early Algebraic Reasoning Differ as a Function of Students' Difficulty with Calculations versus Word Problems?

    PubMed

    Powell, Sarah R; Fuchs, Lynn S

    2014-08-01

    According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2(nd)- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty.

  17. Does Early Algebraic Reasoning Differ as a Function of Students’ Difficulty with Calculations versus Word Problems?

    PubMed Central

    Powell, Sarah R.; Fuchs, Lynn S.

    2014-01-01

    According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044

  18. Stabilization: A Descriptive Framework for Problem Solving

    NASA Astrophysics Data System (ADS)

    Savrda, Sherry L.

    2006-12-01

    An alternative description of problem solving was tested against the think-aloud protocols of twelve introductory calculus-based physics students. Think-aloud protocols are transcripts of problem-solving sessions during which participants are asked to verbalize their thoughts as they attempt to solve a problem. The stabilization model tested considers perceptions of problem difficulty to be related to four primary factors: categorization, goal interpretation, resource relevance, and complexity. A fifth superordinate factor, stabilization, considers the shifting relationships between the four primary factors over the problem-solving process. Problem solving is then described in terms of a search for a stable relationship among the four primary factors. Results from the study to be presented suggest that with further refinement, the stabilization model could be an effective alternative model of problem solving. Results related to the observed problem-solving processes undertaken by the participants will also be presented.

  19. A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

    PubMed

    Benhammouda, Brahim

    2016-01-01

    Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

  20. Teaching Conceptual Model-Based Word Problem Story Grammar to Enhance Mathematics Problem Solving

    ERIC Educational Resources Information Center

    Xin, Yan Ping; Wiles, Ben; Lin, Yu-Ying

    2008-01-01

    Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching "word problem (WP) story grammar" on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or…

  1. Solving a System of Nonlinear Algebraic Equations You Only Get Error Messages--What to Do Next?

    ERIC Educational Resources Information Center

    Shacham, Mordechai; Brauner, Neima

    2017-01-01

    Chemical engineering problems often involve the solution of systems of nonlinear algebraic equations (NLE). There are several software packages that can be used for solving NLE systems, but they may occasionally fail, especially in cases where the mathematical model contains discontinuities and/or regions where some of the functions are undefined.…

  2. Preconditioning projection methods for solving algebraic linear systems

    NASA Astrophysics Data System (ADS)

    García-Palomares, Ubaldo

    1999-09-01

    Numerical experiments have shown that projection methods are robust for solving the problem of finding a point satisfying a linear system of n variables and m equations; however, their qualities of convergence depend on certain parameters: an n n symmetric positive definite matrix M, and a vector u with m components. We are concerned here with the choice of M. Through a link with Conjugate Gradient methods we determine an expedient M. Preliminary numerical results on a hard 3D partial differential equation are highly promising. We solve a discretized system that could not be solved by conventional methods. We also give hints on how to adapt our findings to the solution of a linear system of inequalities. This is the first stage of a forthcoming research.

  3. On modification of certain methods of the conjugate direction type for solving rectangular systems of linear algebraic equations

    NASA Astrophysics Data System (ADS)

    Yukhno, L. F.

    2007-12-01

    The use of modifications of certain well-known methods of the conjugate direction type for solving systems of linear algebraic equations with rectangular matrices is examined. The modified methods are shown to be superior to the original versions with respect to the round-off accumulation; the advantage is especially large for ill-conditioned matrices. Examples are given of the efficient use of the modified methods for solving certain fairly large ill-conditioned problems.

  4. Solving Large-scale Eigenvalue Problems in SciDACApplications

    SciTech Connect

    Yang, Chao

    2005-06-29

    Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an overview of the recent development of eigenvalue computation in the context of two SciDAC applications. We emphasize the importance of Krylov subspace methods, and point out its limitations. We discuss the value of alternative approaches that are more amenable to the use of preconditioners, and report the progression using the multi-level algebraic sub-structuring techniques to speed up eigenvalue calculation. In addition to methods for linear eigenvalue problems, we also examine new approaches to solving two types of non-linear eigenvalue problems arising from SciDAC applications.

  5. Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

    ERIC Educational Resources Information Center

    Mairing, Jackson Pasini

    2017-01-01

    Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

  6. Problem solving using soft systems methodology.

    PubMed

    Land, L

    This article outlines a method of problem solving which considers holistic solutions to complex problems. Soft systems methodology allows people involved in the problem situation to have control over the decision-making process.

  7. Curricular Reforms That Improve Students' Attitudes and Problem-Solving Performance

    ERIC Educational Resources Information Center

    Teodorescu, Raluca E.; Bennhold, Cornelius; Feldman, Gerald; Medsker, Larry

    2014-01-01

    We present the most recent steps undertaken to reform the introductory algebra-based course at The George Washington University. The reform sought to help students improve their problem-solving performance. Our pedagogy relies on didactic constructs such as the" GW-ACCESS problem-solving protocol," "instructional sequences" and…

  8. Understanding Undergraduates’ Problem-Solving Processes †

    PubMed Central

    Nehm, Ross H.

    2010-01-01

    Fostering effective problem-solving skills is one of the most longstanding and widely agreed upon goals of biology education. Nevertheless, undergraduate biology educators have yet to leverage many major findings about problem-solving processes from the educational and cognitive science research literatures. This article highlights key facets of problem-solving processes and introduces methodologies that may be used to reveal how undergraduate students perceive and represent biological problems. Overall, successful problem-solving entails a keen sensitivity to problem contexts, disciplined internal representation or modeling of the problem, and the principled management and deployment of cognitive resources. Context recognition tasks, problem representation practice, and cognitive resource management receive remarkably little emphasis in the biology curriculum, despite their central roles in problem-solving success. PMID:23653710

  9. The Problem Life Solves (Invited)

    NASA Astrophysics Data System (ADS)

    Shock, E.

    2013-12-01

    After forming, planets start the long process of dissipating energy into space. Early on, accretionary processes provide sufficient kinetic energy to raise temperatures enough to drive chemical systems rapidly toward equilibrium, maximizing the release of chemical energy. Eventually heat is dissipated, temperatures drop, and outer portions of planets cool enough to slow the rates of chemical reactions. As reaction rates slow to the scale of geologic time, chemical energy becomes trapped in assemblages of planetary materials far from equilibrium. Numerous examples are provided by chondritic meteorites, which show that activation energy barriers allow chemical energy to remain trapped for most of the age of the solar system even if heat dissipation is efficient -- and perhaps as a direct consequence. Activation energies that inhibit favorable reactions can be overcome by catalysis, which permits chemical systems to attain lower energy states. Catalysis in planets serves to continue the release of energy into space begun by heat dissipation. This implies that there is an overall thermodynamic drive for catalysis to appear as planets cool. Reasons why catalysis emerges in some cases and not others may depend on interactions of cooling rates and compositions but the specifics are murky at present. Life is a particularly efficient catalyst, and its emergence on a planet helps solve the problem generated by the catastrophic decrease in reaction rates during cooling. The single example we have of life on Earth got its start catalyzing oxidation-reduction reactions arranged in states far from equilibrium by geologic processes. On the pre-photosynthetic Earth the boldest biosignatures were redox processes occurring at rates that could only be explained by catalysis, and specifically by catalytic processes that have no abiotic mechanism. Biologically enhanced rates of redox reactions persist to the present, and maintain the biogeochemical cycles that permit the photosynthetic

  10. Learning to Solve Problems in Primary Grades

    ERIC Educational Resources Information Center

    Whitin, Phyllis; Whitin, David J.

    2008-01-01

    Problem solving lies at the heart of mathematical learning. Children need opportunities to write, discuss, and solve problems on a regular basis. The problems must incorporate grade-appropriate content and be "accessible and engaging to the students, building on what they know and can do." Teachers also play a key role in establishing a classroom…

  11. Computer Games Teach Problem-Solving.

    ERIC Educational Resources Information Center

    Clayson, James

    1982-01-01

    The difficulty many students have in solving complex problems stems not from a lack of mathematical skill but from an inability to visualize the problem. An appropriately-structured computer game may assist students in achieving this visualization and in solving problems better. A heuristic approach in programing one game is provided. (Author/JN)

  12. Distributed problem solving by pilots and dispatchers

    NASA Technical Reports Server (NTRS)

    Orasanu, Judith; Wich, Mike; Fischer, Ute; Jobe, Kim; Mccoy, Elaine; Beatty, Roger; Smith, Phil

    1993-01-01

    The study addressed the following question: Are flight planning problems solved differently by PILOTS and DISPATCHERS when they work alone versus when they work together? Aspect of their performance that were of interest include the following: Problem perception and definition; Problem solving strategies and information use; Options considered; Solution and rational; and errors.

  13. New Perspectives on Human Problem Solving

    ERIC Educational Resources Information Center

    Goldstone, Robert L.; Pizlo, Zygmunt

    2009-01-01

    In November 2008 at Purdue University, the 2nd Workshop on Human Problem Solving was held. This workshop, which was a natural continuation of the first workshop devoted almost exclusively to optimization problems, addressed a wider range of topics that reflect the scope of the "Journal of Problem Solving." The workshop was attended by 35…

  14. New Perspectives on Human Problem Solving

    ERIC Educational Resources Information Center

    Goldstone, Robert L.; Pizlo, Zygmunt

    2009-01-01

    In November 2008 at Purdue University, the 2nd Workshop on Human Problem Solving was held. This workshop, which was a natural continuation of the first workshop devoted almost exclusively to optimization problems, addressed a wider range of topics that reflect the scope of the "Journal of Problem Solving." The workshop was attended by 35…

  15. Mobile serious games for collaborative problem solving.

    PubMed

    Sanchez, Jaime; Mendoza, Claudia; Salinas, Alvaro

    2009-01-01

    This paper presents the results obtained from the implementation of a series of learning activities based on mobile serious games (MSG) for the development of problem-solving and collaborative skills in Chilean 8th grade students. Three MSGs were developed and played by teams of four students, who had to solve the problems posed by the game collaboratively. The data shows that the experimental group had a higher perception of their own skills of collaboration and of the plan execution dimension of problem solving than the control group, providing empirical evidence regarding the contribution of MSGs to the development of collaborative problem-solving skills.

  16. Cultivating Problem Solving Skills via a New Problem Categorization Scheme

    NASA Astrophysics Data System (ADS)

    Harper, Kathleen A.; Freuler, Richard J.; Demel, John T.

    2007-01-01

    When one looks at STEM disciplines as a whole, the need for effective problem solving skills is a commonality. However, studies indicate that the bulk of students who graduate from problem-solving intensive programs display little increase in their problem solving abilities. Also, there is little evidence for transfer of general skills from one subject area to another. Furthermore, the types of problems typically encountered in introductory STEM courses do not often cultivate the skills students will need when solving "real-world" problems. Initial efforts to develop and implement an interdisciplinary problem categorization matrix as a tool for instructional design are described. The matrix, which is independent of content, shows promise as a means for promoting useful problem-solving discussion among faculty, designing problem-solving intensive courses, and instructing students in developing real-world problem solving skills.

  17. Problem-Solving Test: Pyrosequencing

    ERIC Educational Resources Information Center

    Szeberenyi, Jozsef

    2013-01-01

    Terms to be familiar with before you start to solve the test: Maxam-Gilbert sequencing, Sanger sequencing, gel electrophoresis, DNA synthesis reaction, polymerase chain reaction, template, primer, DNA polymerase, deoxyribonucleoside triphosphates, orthophosphate, pyrophosphate, nucleoside monophosphates, luminescence, acid anhydride bond,…

  18. Problem-Solving Test: Pyrosequencing

    ERIC Educational Resources Information Center

    Szeberenyi, Jozsef

    2013-01-01

    Terms to be familiar with before you start to solve the test: Maxam-Gilbert sequencing, Sanger sequencing, gel electrophoresis, DNA synthesis reaction, polymerase chain reaction, template, primer, DNA polymerase, deoxyribonucleoside triphosphates, orthophosphate, pyrophosphate, nucleoside monophosphates, luminescence, acid anhydride bond,…

  19. Common Core: Solve Math Problems

    ERIC Educational Resources Information Center

    Strom, Erich

    2012-01-01

    The new common core standards for mathematics demand that students (and teachers!) exhibit deeper conceptual understanding. That's music to the ears of education professor John Tapper, who says teachers have overemphasized teaching procedures--and getting right answers. In his new book, "Solving for Why," he makes a powerful case for moving beyond…

  20. Strengthening Programs through Problem Solving.

    ERIC Educational Resources Information Center

    Dyer, Jim

    1993-01-01

    Describes a secondary agricultural education program that was a dumping ground for academically disadvantaged students. Discusses how such a program can be improved by identifying problems and symptoms, treating problems, and goal setting. (JOW)

  1. Strengthening Programs through Problem Solving.

    ERIC Educational Resources Information Center

    Dyer, Jim

    1993-01-01

    Describes a secondary agricultural education program that was a dumping ground for academically disadvantaged students. Discusses how such a program can be improved by identifying problems and symptoms, treating problems, and goal setting. (JOW)

  2. Disciplinary Foundations for Solving Interdisciplinary Scientific Problems

    NASA Astrophysics Data System (ADS)

    Zhang, Dongmei; Shen, Ji

    2015-10-01

    Problem-solving has been one of the major strands in science education research. But much of the problem-solving research has been conducted on discipline-based contexts; little research has been done on how students, especially individuals, solve interdisciplinary problems. To understand how individuals reason about interdisciplinary problems, we conducted an interview study with 16 graduate students coming from a variety of disciplinary backgrounds. During the interviews, we asked participants to solve two interdisciplinary science problems on the topic of osmosis. We investigated participants' problem reasoning processes and probed in their attitudes toward general interdisciplinary approach and specific interdisciplinary problems. Through a careful inductive content analysis of their responses, we studied how disciplinary, cognitive, and affective factors influenced their interdisciplinary problems-solving. We found that participants' prior discipline-based science learning experiences had both positive and negative influences on their interdisciplinary problem-solving. These influences were embodied in their conceptualization of the interdisciplinary problems, the strategies they used to integrate different disciplinary knowledge, and the attitudes they had toward interdisciplinary approach in general and specific interdisciplinary problems. This study sheds light on interdisciplinary science education by revealing the complex relationship between disciplinary learning and interdisciplinary problem-solving.

  3. Applying Cooperative Techniques in Teaching Problem Solving

    ERIC Educational Resources Information Center

    Barczi, Krisztina

    2013-01-01

    Teaching how to solve problems--from solving simple equations to solving difficult competition tasks--has been one of the greatest challenges for mathematics education for many years. Trying to find an effective method is an important educational task. Among others, the question arises as to whether a method in which students help each other might…

  4. Does Early Algebraic Reasoning Differ as a Function of Students' Difficulty with Calculations versus Word Problems?

    ERIC Educational Resources Information Center

    Powell, Sarah R.; Fuchs, Lynn S.

    2014-01-01

    According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…

  5. Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.

    PubMed

    Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu

    2012-01-01

    Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

  6. Problem Solving, Patterns, Probability, Pascal, and Palindromes.

    ERIC Educational Resources Information Center

    Hylton-Lindsay, Althea Antoinette

    2003-01-01

    Presents a problem-solving activity, the birth order problem, and several solution-seeking strategies. Includes responses of current and prospective teachers and a comparison of various strategies. (YDS)

  7. Indoor Air Quality Problem Solving Tool

    EPA Pesticide Factsheets

    Use the IAQ Problem Solving Tool to learn about the connection between health complaints and common solutions in schools. This resource provides an easy, step-by-step process to start identifying and resolving IAQ problems found at your school.

  8. Problem Posing and Solving with Mathematical Modeling

    ERIC Educational Resources Information Center

    English, Lyn D.; Fox, Jillian L.; Watters, James J.

    2005-01-01

    Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

  9. Problem Solving, Patterns, Probability, Pascal, and Palindromes.

    ERIC Educational Resources Information Center

    Hylton-Lindsay, Althea Antoinette

    2003-01-01

    Presents a problem-solving activity, the birth order problem, and several solution-seeking strategies. Includes responses of current and prospective teachers and a comparison of various strategies. (YDS)

  10. Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

    ERIC Educational Resources Information Center

    Aljaberi, Nahil M.; Gheith, Eman

    2016-01-01

    This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…

  11. Pen Pals: Practicing Problem Solving

    ERIC Educational Resources Information Center

    Lampe, Kristen A.; Uselmann, Linda

    2008-01-01

    This article describes a semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. (Contains 6 figures.)

  12. Problem Solving & Comprehension. Fourth Edition.

    ERIC Educational Resources Information Center

    Whimbey, Arthur; Lochhead, Jack

    This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

  13. Do TEFL Articles Solve Problems?

    ERIC Educational Resources Information Center

    Edge, Julian

    1985-01-01

    Discusses the problem which English-as-a-foreign-language (EFL) teacher trainees who are nonnative English speakers have in reading articles about EFL teaching methods. As a solution to this problem, the author produced a worksheet for the students to fill in while reading the articles which followed Hoey's…

  14. Pen Pals: Practicing Problem Solving

    ERIC Educational Resources Information Center

    Lampe, Kristen A.; Uselmann, Linda

    2008-01-01

    This article describes a semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. (Contains 6 figures.)

  15. Trigonometric problem cases well solved

    NASA Astrophysics Data System (ADS)

    Schröer, H.

    2001-10-01

    Content of the book are trigonometric problems that can be found scarely in the technical literature. It begins with using trigonometric functions to horizon and height. Interesting pure mathematical problems about tangent, inscribed tetragon and parallelogram follow. In chapter 6 is a generalization of Euclid's theorem fo the right-angled triangle. The next themes are exterior circle and incircle. In chapter 9 an unusual proof of the cosine law for sides is given. Further treated problems are the distance of two stars and eclipses. The aim group consists of mathematicians, natural scientists and technicians(also teacher) who have to do professionally with trigonometric problems and (or)who are interested in trigonometric problems. There is an english and a german edition.

  16. Solving global optimization problems on GPU cluster

    SciTech Connect

    Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya

    2016-06-08

    The paper contains the results of investigation of a parallel global optimization algorithm combined with a dimension reduction scheme. This allows solving multidimensional problems by means of reducing to data-independent subproblems with smaller dimension solved in parallel. The new element implemented in the research consists in using several graphic accelerators at different computing nodes. The paper also includes results of solving problems of well-known multiextremal test class GKLS on Lobachevsky supercomputer using tens of thousands of GPU cores.

  17. Problem Solving Strategies among Primary School Teachers

    ERIC Educational Resources Information Center

    Yew, Wun Thiam; Lian, Lim Hooi; Meng, Chew Cheng

    2017-01-01

    The purpose of this article was to examine problem solving strategies among primary school teachers. The researchers employed survey research design to examine their problem solving strategies. The participants of this study consisted of 120 primary school teachers from a public university in Peninsula Malaysia who enrolled in a 4-year Graduating…

  18. Could HPS Improve Problem-Solving?

    ERIC Educational Resources Information Center

    Coelho, Ricardo Lopes

    2013-01-01

    It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students' careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem…

  19. Measuring Problem Solving Skills in "Portal 2"

    ERIC Educational Resources Information Center

    Shute, Valerie J.; Wang, Lubin

    2013-01-01

    This paper examines possible improvement to problem solving skills as a function of playing the video game "Portal 2." Stealth assessment is used in the game to evaluate students' problem solving abilities--specifically basic and flexible rule application. The stealth assessment measures will be validated against commonly accepted…

  20. Conceptual Problem Solving in High School Physics

    ERIC Educational Resources Information Center

    Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

    2015-01-01

    Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an…

  1. Solving Problems in Genetics II: Conceptual Restructuring

    ERIC Educational Resources Information Center

    Orcajo, Teresa Ibanez; Aznar, Mercedes Martinez

    2005-01-01

    This paper presents the results of part of an investigation carried out with fourth-level Spanish secondary education students (15 years old), in which we implemented a teaching unit based on problem-solving methodology as an investigation to teach genetics and human inheritance curricular contents. By solving open problems, the students…

  2. Computer-Based Assessment of Problem Solving.

    ERIC Educational Resources Information Center

    Baker, E. L.; Mayer, R. E.

    1999-01-01

    Examines the components required to assess student problem solving in technology environments. Discusses the purposes of testing, provides an example demonstrating the difference between retention and transfer, defines and analyzes problem solving, and explores techniques and standards for measuring the quality of student understanding. Contains…

  3. Taking "From Scratch" out of Problem Solving

    ERIC Educational Resources Information Center

    Brown, Wayne

    2007-01-01

    Solving problems and creating processes and procedures from the ground up has long been part of the IT department's way of operating. IT staffs will continue to encounter new problems to solve and new technologies to be implemented. They also must involve their constituents in the creation of solutions. Nonetheless, for many issues they no longer…

  4. Strategies for Solving Word Problems in Science.

    ERIC Educational Resources Information Center

    Garrigan, George A.

    1997-01-01

    Reviews the approaches presented in the Self-Paced Study of Strategies Useful for Solving Word Problems in the Physical and Biological Sciences that can be used by students to successfully solve word problems encountered in any entry-level science course. Describes the topics covered in five "study sessions" that allow the students to practice the…

  5. Creativity and Insight in Problem Solving

    ERIC Educational Resources Information Center

    Golnabi, Laura

    2016-01-01

    This paper analyzes the thought process involved in problem solving and its categorization as creative thinking as defined by psychologist R. Weisberg (2006). Additionally, the notion of insight, sometimes present in unconscious creative thinking and often leading to creative ideas, is discussed in the context of geometry problem solving. In…

  6. Student Modeling Based on Problem Solving Times

    ERIC Educational Resources Information Center

    Pelánek, Radek; Jarušek, Petr

    2015-01-01

    Student modeling in intelligent tutoring systems is mostly concerned with modeling correctness of students' answers. As interactive problem solving activities become increasingly common in educational systems, it is useful to focus also on timing information associated with problem solving. We argue that the focus on timing is natural for certain…

  7. Guiding Young Children in Successful Problem Solving.

    ERIC Educational Resources Information Center

    Lee, Kil S.

    1982-01-01

    A list of heuristics for elementary school children is provided. Two examples which are viewed to demonstrate the conscientious and creative use of problem-solving strategies by fourth graders are detailed. Suggestions for teachers on how to help pupils develop their problem-solving abilities are included. (MP)

  8. A Multivariate Model of Physics Problem Solving

    ERIC Educational Resources Information Center

    Taasoobshirazi, Gita; Farley, John

    2013-01-01

    A model of expertise in physics problem solving was tested on undergraduate science, physics, and engineering majors enrolled in an introductory-level physics course. Structural equation modeling was used to test hypothesized relationships among variables linked to expertise in physics problem solving including motivation, metacognitive planning,…

  9. Problem-Solving Rules for Genetics.

    ERIC Educational Resources Information Center

    Collins, Angelo

    The categories and applications of strategic knowledge as these relate to problem solving in the area of transmission genetics are examined in this research study. The role of computer simulations in helping students acquire the strategic knowledge necessary to solve realistic transmission genetics problems was emphasized. The Genetics…

  10. Facilitating Problem Solving in High School Chemistry.

    ERIC Educational Resources Information Center

    Gabel, Dorothy L.; Sherwood, Robert D.

    This paper reported the results of a study designed to determine whether certain instructional strategies are superior to others in teaching problem solving to high school chemistry students. The effectiveness of four instructional strategies for teaching problem solving to students of various proportional reasoning ability, verbal and visual…

  11. Metacognition: Student Reflections on Problem Solving

    ERIC Educational Resources Information Center

    Wismath, Shelly; Orr, Doug; Good, Brandon

    2014-01-01

    Twenty-first century teaching and learning focus on the fundamental skills of critical thinking and problem solving, creativity and innovation, and collaboration and communication. Metacognition is a crucial aspect of both problem solving and critical thinking, but it is often difficult to get students to engage in authentic metacognitive…

  12. Problem Solving in the Middle Grades.

    ERIC Educational Resources Information Center

    Malloy, Carol E.; Guild, D. Bruce

    2000-01-01

    Describes the mathematics curriculum proposed by the Principles and Standards for School Mathematics (PSSM)in which students build new mathematical knowledge through problem-solving. Compares the role of PSSM problem solving with that in the 1989 curriculum standards. (YDS)

  13. Dynamic Problem Solving: A New Assessment Perspective

    ERIC Educational Resources Information Center

    Greiff, Samuel; Wustenberg, Sascha; Funke, Joachim

    2012-01-01

    This article addresses two unsolved measurement issues in dynamic problem solving (DPS) research: (a) unsystematic construction of DPS tests making a comparison of results obtained in different studies difficult and (b) use of time-intensive single tasks leading to severe reliability problems. To solve these issues, the MicroDYN approach is…

  14. Problem Solving Interactions on Electronic Networks.

    ERIC Educational Resources Information Center

    Waugh, Michael; And Others

    Arguing that electronic networking provides a medium which is qualitatively superior to the traditional classroom for conducting certain types of problem solving exercises, this paper details the Water Problem Solving Project, which was conducted on the InterCultural Learning Network in 1985 and 1986 with students from the United States, Mexico,…

  15. Can Television Enhance Children's Mathematical Problem Solving?

    ERIC Educational Resources Information Center

    Fisch, Shalom M.; And Others

    1994-01-01

    A summative evaluation of "Square One TV," an educational mathematics series produced by the Children's Television Workshop, shows that children who regularly viewed the program showed significant improvement in solving unfamiliar, complex mathematical problems, and viewers showed improvement in their mathematical problem-solving ability…

  16. Could HPS Improve Problem-Solving?

    ERIC Educational Resources Information Center

    Coelho, Ricardo Lopes

    2013-01-01

    It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students' careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem…

  17. Dynamic Problem Solving: A New Assessment Perspective

    ERIC Educational Resources Information Center

    Greiff, Samuel; Wustenberg, Sascha; Funke, Joachim

    2012-01-01

    This article addresses two unsolved measurement issues in dynamic problem solving (DPS) research: (a) unsystematic construction of DPS tests making a comparison of results obtained in different studies difficult and (b) use of time-intensive single tasks leading to severe reliability problems. To solve these issues, the MicroDYN approach is…

  18. Mathematical Problem Solving through Sequential Process Analysis

    ERIC Educational Resources Information Center

    Codina, A.; Cañadas, M. C.; Castro, E.

    2015-01-01

    Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

  19. Emotion dysregulation, problem-solving, and hopelessness.

    PubMed

    Vatan, Sevginar; Lester, David; Gunn, John F

    2014-04-01

    A sample of 87 Turkish undergraduate students was administered scales to measure hopelessness, problem-solving skills, emotion dysregulation, and psychiatric symptoms. All of the scores from these scales were strongly associated. In a multiple regression, hopelessness scores were predicted by poor problem-solving skills and emotion dysregulation.

  20. Problem Solving Software for Math Classes.

    ERIC Educational Resources Information Center

    Troutner, Joanne

    1987-01-01

    Described are 10 computer software programs for problem solving related to mathematics. Programs described are: (1) Box Solves Story Problems; (2) Safari Search; (3) Puzzle Tanks; (4) The King's Rule; (5) The Factory; (6) The Royal Rules; (7) The Enchanted Forest; (8) Gears; (9) The Super Factory; and (10) Creativity Unlimited. (RH)

  1. Student Modeling Based on Problem Solving Times

    ERIC Educational Resources Information Center

    Pelánek, Radek; Jarušek, Petr

    2015-01-01

    Student modeling in intelligent tutoring systems is mostly concerned with modeling correctness of students' answers. As interactive problem solving activities become increasingly common in educational systems, it is useful to focus also on timing information associated with problem solving. We argue that the focus on timing is natural for certain…

  2. Metacognition: Student Reflections on Problem Solving

    ERIC Educational Resources Information Center

    Wismath, Shelly; Orr, Doug; Good, Brandon

    2014-01-01

    Twenty-first century teaching and learning focus on the fundamental skills of critical thinking and problem solving, creativity and innovation, and collaboration and communication. Metacognition is a crucial aspect of both problem solving and critical thinking, but it is often difficult to get students to engage in authentic metacognitive…

  3. Creativity and Insight in Problem Solving

    ERIC Educational Resources Information Center

    Golnabi, Laura

    2016-01-01

    This paper analyzes the thought process involved in problem solving and its categorization as creative thinking as defined by psychologist R. Weisberg (2006). Additionally, the notion of insight, sometimes present in unconscious creative thinking and often leading to creative ideas, is discussed in the context of geometry problem solving. In…

  4. Problem Solving Under Time-Constraints.

    ERIC Educational Resources Information Center

    Richardson, Michael; Hunt, Earl

    A model of how automated and controlled processing can be mixed in computer simulations of problem solving is proposed. It is based on previous work by Hunt and Lansman (1983), who developed a model of problem solving that could reproduce the data obtained with several attention and performance paradigms, extending production-system notation to…

  5. Interpersonal Problem Solving in Preschool Aged Children.

    ERIC Educational Resources Information Center

    Swanson, Arthur J.; Siegel, Lawrence J.

    This study was designed as a partial replication and extension of the research on interpersonal problem solving in preschool children by Shure and Spivack. Fifteen well-adjusted and 14 impulsive children from Head Start Centers were administered the Preschool Interpersonal Problem Solving test (PIPS) under either incentive or no incentive…

  6. A Multivariate Model of Physics Problem Solving

    ERIC Educational Resources Information Center

    Taasoobshirazi, Gita; Farley, John

    2013-01-01

    A model of expertise in physics problem solving was tested on undergraduate science, physics, and engineering majors enrolled in an introductory-level physics course. Structural equation modeling was used to test hypothesized relationships among variables linked to expertise in physics problem solving including motivation, metacognitive planning,…

  7. Students' Metaphors for Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Yee, Sean P.

    2012-01-01

    The purpose of this study was to determine the metaphors used by students to describe mathematical problem solving. This study focused on identifying how students interpret and perceive mathematical problem solving via conceptual metaphors (Lakoff and Johnson, 2003). These perceptions and interpretations were coded and analyzed qualitatively and…

  8. The Functions of Pictures in Problem Solving

    ERIC Educational Resources Information Center

    Elia, Iliada; Philippou, George

    2004-01-01

    In the present study, we assert that pictures serve four functions in problem solving: decorative, representational, organizational and informational. We, therefore, investigate the effects of pictures based on their functions in mathematical problem solving (MPS), by high achievement students of Grade 6 in Cyprus, in a communication setting. A…

  9. The Process of Solving Complex Problems

    ERIC Educational Resources Information Center

    Fischer, Andreas; Greiff, Samuel; Funke, Joachim

    2012-01-01

    This article is about Complex Problem Solving (CPS), its history in a variety of research domains (e.g., human problem solving, expertise, decision making, and intelligence), a formal definition and a process theory of CPS applicable to the interdisciplinary field. CPS is portrayed as (a) knowledge acquisition and (b) knowledge application…

  10. Solving Problems in Genetics II: Conceptual Restructuring

    ERIC Educational Resources Information Center

    Orcajo, Teresa Ibanez; Aznar, Mercedes Martinez

    2005-01-01

    This paper presents the results of part of an investigation carried out with fourth-level Spanish secondary education students (15 years old), in which we implemented a teaching unit based on problem-solving methodology as an investigation to teach genetics and human inheritance curricular contents. By solving open problems, the students…

  11. Mathematics Teachers Circle around Problem Solving

    ERIC Educational Resources Information Center

    Fernandes, Anthony; Koehler, Jacob; Reiter, Harold

    2011-01-01

    Making problem solving a central part of teaching may be challenging to teachers who have limited experiences in learning and teaching mathematics in this way. Math Teachers' Circles were developed with the aim of establishing a "culture of problem solving" among middle school mathematics teachers. This culture could then be carried back into…

  12. Scaffolding Online Argumentation during Problem Solving

    ERIC Educational Resources Information Center

    Oh, S.; Jonassen, D. H.

    2007-01-01

    In this study, constraint-based argumentation scaffolding was proposed to facilitate online argumentation performance and ill-structured problem solving during online discussions. In addition, epistemological beliefs were presumed to play a role in solving ill-structured diagnosis-solution problems. Constraint-based discussion boards were…

  13. Taking "From Scratch" out of Problem Solving

    ERIC Educational Resources Information Center

    Brown, Wayne

    2007-01-01

    Solving problems and creating processes and procedures from the ground up has long been part of the IT department's way of operating. IT staffs will continue to encounter new problems to solve and new technologies to be implemented. They also must involve their constituents in the creation of solutions. Nonetheless, for many issues they no longer…

  14. Teaching Problem-Solving. Informal Series/43.

    ERIC Educational Resources Information Center

    Ross, John A.; Maynes, Florence J.

    This monograph is designed to provide practical classroom suggestions, including sample lesson plans, to show how teachers can improve the problem-solving competence of students at all educational and ability levels. The examples provided show that problem-solving instruction can be integrated with teaching the content of particular topics. While…

  15. Teaching Problem Solving: An Instructional Design Strategy.

    ERIC Educational Resources Information Center

    Ross, John A.; Maynes, Florence J.

    1983-01-01

    Instructional design strategy for improving problem solving is presented. The strategy entails selecting an appropriate domain of problem-solving tasks, learning hierarchies, teaching methods and assembling of learning materials, and designing teacher training and evaluation. Obstacles to be overcome and directions for future research are…

  16. Teaching and Learning through Problem Solving

    ERIC Educational Resources Information Center

    Ollerton, Mike

    2007-01-01

    In this article, the author relates some problem solving work with primary schools to Department for Children, Schools, and Families (DfES) support. In four primary schools in the West Midlands, the focus was teaching mathematics through problem solving, based on materials published on the DfES "standards" website. The author noticed…

  17. Mathematical Problem Solving through Sequential Process Analysis

    ERIC Educational Resources Information Center

    Codina, A.; Cañadas, M. C.; Castro, E.

    2015-01-01

    Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

  18. Mathematical Problem Solving. Issues in Research.

    ERIC Educational Resources Information Center

    Lester, Frank K., Jr., Ed.; Garofalo, Joe, Ed.

    This set of papers was originally developed for a conference on Issues and Directions in Mathematics Problem Solving Research held at Indiana University in May 1981. The purpose is to contribute to the clear formulation of the key issues in mathematical problem-solving research by presenting the ideas of actively involved researchers. An…

  19. Self-appraised social problem solving abilities, emotional reactions and actual problem solving performance.

    PubMed

    Shewchuk, R M; Johnson, M O; Elliott, T R

    2000-07-01

    Self-report measures of social problem solving abilities have yet to be associated with objective problem solving performance in any consistent manner. In the present study, we investigated the relation of social problem solving abilities--as measured by the Social Problem Solving Skills Inventory--Revised (SPSI-R [Maydeu-Olivares, A. & D'Zurilla, T. J. (1996). A factor analytic study of the Social Problem Solving Inventory: an integration of theory and data. Cognitive Therapy and Research, 20, 115-133])--to performance on a structured problem solving task. Unlike previous studies, we examined the relation of problem solving skills to performance curves observed in repeated trials, while controlling for affective reactions to each trial. Using hierarchical modeling techniques, a negative problem orientation was significantly predictive of performance and this effect was not mediated by negative affectivity. Results are discussed as they pertain to contemporary models of social problem solving.

  20. Clifford algebra approach to the coincidence problem for planar lattices.

    PubMed

    Rodríguez, M A; Aragón, J L; Verde-Star, L

    2005-03-01

    The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square, rectangular and rhombic lattices are worked out in detail. One of the aims of this work is to show the potential usefulness of Clifford algebra in crystallography. The power of Clifford algebra for expressing geometric ideas is exploited here and the procedure presented can be generalized to higher dimensions.

  1. The effects of cumulative practice on mathematics problem solving.

    PubMed

    Mayfield, Kristin H; Chase, Philip N

    2002-01-01

    This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.

  2. Solving a problem by analogy

    NASA Astrophysics Data System (ADS)

    Easton, Don

    1999-03-01

    This note is a description of a student solution to a problem. I found the solution exciting because it exemplifies the kind of solution by analogy that Feynman describes in The Feynman Lectures on Physics.

  3. Problem-solving competency of nursing graduates.

    PubMed

    Uys, Leana R; Van Rhyn, Lily L; Gwele, Nomthandaso S; McInerney, Patricia; Tanga, Tobeka

    2004-12-01

    This paper reports a study describing and evaluating the outcomes of problem-based learning (PBL) programmes in nursing schools in South Africa in terms of the competence of graduates to solve problem in actual clinical settings, and comparing this competence with that of graduates from non-PBL programmes. The nursing literature tends to equate problem-solving with patient-centred problems or the nursing process. However, it is also a skill used in managing the work role, working in a team and managing a health care unit. Problem-solving refers to the process of selectively attending to information in a patient care setting. The investigation of problem-solving in nursing is complicated by the complex relationships between different cognitive processes. A qualitative evaluation study, descriptive and comparative in nature, was carried out. In-depth interviews were held with graduates and their supervisors, asking them to identify problem-solving incidents in which they had been involved. Template analysis style and Benner's interpretive approach were used to analyse the data. The majority of the incidents described by the graduates (84%) were graded at the advanced beginner level or above. The majority of incidents at the novice level came from the non-PBL group. 'Using people skills' and 'being assertive' were the two problem-solving strategies most often used. The PBL group fared better than the non-problem-based group in the level of their problem-solving ability. The findings of this study suggest that further research is warranted into the problem-solving abilities of PBL graduates, their personal development over time and at different stages of practice. In addition, it would be interesting to follow the development of their problem-solving abilities over time.

  4. Collection of solved problems in physics

    NASA Astrophysics Data System (ADS)

    Koupilová, ZdeÅka; Mandíková, Dana; Snětinová, Marie

    2017-01-01

    To solve physics problems is a key ability which students should reach during their physics education. Ten years ago we started to develop a Collection of fully solved problems. The structure of problems' solutions is specially designed to substitute tutor's help during lesson and encourage students to solve at least some parts of a problem independently. Nowadays the database contains about 770 fully solved problems in physics in Czech, more than 100 problems in Polish and more than 140 problems in English. Other problems are still being translated. Except for physics problems, the Collection has also a mathematical part, which contains more than 300 fully solved problems in mathematics. This paper follows the presentation of the Collection of solved problems from previous years and introduces a new interface of the Collection, its enhanced functionality, new topics, newly created interface for teachers, user feedback and plans for future development. The database is placed at the website of the Department of Physics Education, Faculty of Mathematics and Physics, Charles University in Prague, the links are: http://reseneulohy.cz/fyzika (Czech version); http://www.physicstasks.eu/ (English version).

  5. Reflection on problem solving in introductory and advanced physics

    NASA Astrophysics Data System (ADS)

    Mason, Andrew J.

    Reflection is essential in order to learn from problem solving. This thesis explores issues related to how reflective students are and how we can improve their capacity for reflection on problem solving. We investigate how students naturally reflect in their physics courses about problem solving and evaluate strategies that may teach them reflection as an integral component of problem-solving. Problem categorization based upon similarity of solution is a strategy to help them reflect about the deep features of the problems related to the physics principles involved. We find that there is a large overlap between the introductory and graduate students in their ability to categorize. Moreover, introductory students in the calculus-based courses performed better categorization than those in the algebra-based courses even though the categorization task is conceptual. Other investigations involved exploring if reflection could be taught as a skill on individual and group levels. Explicit self-diagnosis in recitation investigated how effectively students could diagnose their own errors on difficult problems, how much scaffolding was necessary for this purpose, and how effective transfer was to other problems employing similar principles. Difficulty in applying physical principles and difference between the self-diagnosed and transfer problems affected performance. We concluded that a sustained intervention is required to learn effective problem-solving strategies. Another study involving reflection on problem solving with peers suggests that those who reflected with peers drew more diagrams and had a larger gain from the midterm to final exam. Another study in quantum mechanics involved giving common problems in midterm and final exams and suggested that advanced students do not automatically reflect on their mistakes. Interviews revealed that even advanced students often focus mostly on exams rather than learning and building a robust knowledge structure. A survey was

  6. "Playing the Game" of Story Problems: Coordinating Situation-Based Reasoning with Algebraic Representation

    ERIC Educational Resources Information Center

    Walkington, Candace; Sherman, Milan; Petrosino, Anthony

    2012-01-01

    This study critically examines a key justification used by educational stakeholders for placing mathematics in context--the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were…

  7. Preservice Teachers' Algebraic Reasoning and Symbol Use on a Multistep Fraction Word Problem

    ERIC Educational Resources Information Center

    Cullen, Amanda L.; Tobias, Jennifer M.; Safak, Elif; Kirwan, J. Vince; Wessman-Enzinger, Nicole M.; Wickstrom, Megan H.; Baek, Jae M.

    2017-01-01

    Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

  8. Diagrams Benefit Symbolic Problem-Solving

    ERIC Educational Resources Information Center

    Chu, Junyi; Rittle-Johnson, Bethany; Fyfe, Emily R.

    2017-01-01

    Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

  9. Problem Solving with Generic Algorithms and Computers.

    ERIC Educational Resources Information Center

    Larson, Jay

    Success in using a computer in education as a problem-solving tool requires a change in the way of thinking or of approaching a problem. An algorithm, i.e., a finite step-by-step solution to a problem, can be designed around the data processing concepts of input, processing, and output to provide a basis for classifying problems. If educators…

  10. Problem Solving with Generic Algorithms and Computers.

    ERIC Educational Resources Information Center

    Larson, Jay

    Success in using a computer in education as a problem-solving tool requires a change in the way of thinking or of approaching a problem. An algorithm, i.e., a finite step-by-step solution to a problem, can be designed around the data processing concepts of input, processing, and output to provide a basis for classifying problems. If educators…

  11. Problem-Solving Analysis and Business Writing.

    ERIC Educational Resources Information Center

    Myrsiades, Linda Suny

    Problem solving skills such as patterning facts, locating problems, separating problems and solutions, and presenting effective written products are essential to success in the business community. Facts can be patterned using a grid relating a problem's effect at the individual, group, situational, and organizational level. Such a grid tests each…

  12. Tracking children's mental states while solving algebra equations.

    PubMed

    Anderson, John R; Betts, Shawn; Ferris, Jennifer L; Fincham, Jon M

    2012-11-01

    Behavioral and function magnetic resonance imagery (fMRI) data were combined to infer the mental states of students as they interacted with an intelligent tutoring system. Sixteen children interacted with a computer tutor for solving linear equations over a six-day period (days 0-5), with days 1 and 5 occurring in an fMRI scanner. Hidden Markov model algorithms combined a model of student behavior with multi-voxel imaging pattern data to predict the mental states of students. We separately assessed the algorithms' ability to predict which step in a problem-solving sequence was performed and whether the step was performed correctly. For day 1, the data patterns of other students were used to predict the mental states of a target student. These predictions were improved on day 5 by adding information about the target student's behavioral and imaging data from day 1. Successful tracking of mental states depended on using the combination of a behavioral model and multi-voxel pattern analysis, illustrating the effectiveness of an integrated approach to tracking the cognition of individuals in real time as they perform complex tasks. Copyright © 2011 Wiley Periodicals, Inc.

  13. Robot, computer problem solving system

    NASA Technical Reports Server (NTRS)

    Becker, J. D.; Merriam, E. W.

    1973-01-01

    The TENEX computer system, the ARPA network, and computer language design technology was applied to support the complex system programs. By combining the pragmatic and theoretical aspects of robot development, an approach is created which is grounded in realism, but which also has at its disposal the power that comes from looking at complex problems from an abstract analytical point of view.

  14. Causality in Solving Economic Problems

    ERIC Educational Resources Information Center

    Robinson, A. Emanuel; Sloman, Steven A.; Hagmayer, York; Hertzog, Christopher K.

    2010-01-01

    The role of causal beliefs in people's decisions when faced with economic problems was investigated. Two experiments are reported that vary the causal structure in prisoner's dilemma-like economic situations. We measured willingness to cooperate or defect and collected justifications and think-aloud protocols to examine the strategies that people…

  15. Solving the wrong hierarchy problem

    SciTech Connect

    Blinov, Nikita; Hook, Anson

    2016-06-29

    Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and Z2-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. Lastly, we show this mechanism postdicts the top Yukawa to be within 1σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.

  16. Solving the wrong hierarchy problem

    DOE PAGES

    Blinov, Nikita; Hook, Anson

    2016-06-29

    Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and Z2-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs massmore » by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. Lastly, we show this mechanism postdicts the top Yukawa to be within 1σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.« less

  17. Solving the wrong hierarchy problem

    NASA Astrophysics Data System (ADS)

    Blinov, Nikita; Hook, Anson

    2016-06-01

    Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and Z_2 -symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z_2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. We show this mechanism postdicts the top Yukawa to be within 1 σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.

  18. Sour landfill gas problem solved

    SciTech Connect

    Nagl, G.; Cantrall, R.

    1996-05-01

    In Broward County, Fla., near Pompano Beach, Waste Management of North America (WMNA, a subsidiary of WMX Technologies, Oak Brook, IL) operates the Central Sanitary Landfill and Recycling Center, which includes the country`s largest landfill gas-to-energy plant. The landfill consists of three collection sites: one site is closed, one is currently receiving garbage, and one will open in the future. Approximately 9 million standard cubic feet (scf) per day of landfill gas is collected from approximately 300 wells spread over the 250-acre landfill. With a dramatic increase of sulfur-containing waste coming to a South Florida landfill following Hurricane Andrew, odors related to hydrogen sulfide became a serious problem. However, in a matter of weeks, an innovative desulfurization unit helped calm the landfill operator`s fears. These very high H{sub 2}S concentrations caused severe odor problems in the surrounding residential area, corrosion problems in the compressors, and sulfur dioxide (SO{sub 2}) emission problems in the exhaust gas from the turbine generators.

  19. Assertiveness and problem solving in midwives.

    PubMed

    Yurtsal, Zeliha Burcu; Özdemir, Levent

    2015-01-01

    Midwifery profession is required to bring solutions to problems and a midwife is expected to be an assertive person and to develop midwifery care. This study was planned to examine the relationship between assertiveness and problem-solving skills of midwives. This cross-sectional study was conducted with 201 midwives between July 2008 and February 2009 in the city center of Sivas. The Rathus Assertiveness Schedule (RAS) and Problem Solving Inventory (PSI) were used to determine the level of assertiveness and problem-solving skills of midwives. Statistical methods were used as mean, standard deviation, percentage, Student's T, ANOVA and Tukey HSD, Kruskal Wallis, Fisher Exact, Pearson Correlation and Chi-square tests and P < 0.05. The RAS mean scores and the PSI mean scores showed statistically significant differences in terms of a midwife's considering herself as a member of the health team, expressing herself within the health care team, being able to say "no" when necessary, cooperating with her colleagues, taking part in problem-solving skills training. A statistically significant negative correlation was found between the RAS and PSI scores. The RAS scores decreased while the problem-solving scores increased (r: -0451, P < 0.01). There were significant statistical differences between assertiveness levels and problem solving skills of midwives, and midwives who were assertive solved their problems better than did others. Assertiveness and problem-solving skills training will contribute to the success of the midwifery profession. Midwives able to solve problems, and display assertive behaviors will contribute to the development of midwifery profession.

  20. Assertiveness and problem solving in midwives

    PubMed Central

    Yurtsal, Zeliha Burcu; Özdemir, Levent

    2015-01-01

    Background: Midwifery profession is required to bring solutions to problems and a midwife is expected to be an assertive person and to develop midwifery care. This study was planned to examine the relationship between assertiveness and problem-solving skills of midwives. Materials and Methods: This cross-sectional study was conducted with 201 midwives between July 2008 and February 2009 in the city center of Sivas. The Rathus Assertiveness Schedule (RAS) and Problem Solving Inventory (PSI) were used to determine the level of assertiveness and problem-solving skills of midwives. Statistical methods were used as mean, standard deviation, percentage, Student's T, ANOVA and Tukey HSD, Kruskal Wallis, Fisher Exact, Pearson Correlation and Chi-square tests and P < 0.05. Results: The RAS mean scores and the PSI mean scores showed statistically significant differences in terms of a midwife's considering herself as a member of the health team, expressing herself within the health care team, being able to say “no” when necessary, cooperating with her colleagues, taking part in problem-solving skills training. A statistically significant negative correlation was found between the RAS and PSI scores. The RAS scores decreased while the problem-solving scores increased (r: -0451, P < 0.01). Conclusions: There were significant statistical differences between assertiveness levels and problem solving skills of midwives, and midwives who were assertive solved their problems better than did others. Assertiveness and problem-solving skills training will contribute to the success of the midwifery profession. Midwives able to solve problems, and display assertive behaviors will contribute to the development of midwifery profession. PMID:26793247

  1. Synthesizing Huber's Problem Solving and Kolb's Learning Cycle: A Balanced Approach to Technical Problem Solving

    ERIC Educational Resources Information Center

    Kamis, Arnold; Khan, Beverly K.

    2009-01-01

    How do we model and improve technical problem solving, such as network subnetting? This paper reports an experimental study that tested several hypotheses derived from Kolb's experiential learning cycle and Huber's problem solving model. As subjects solved a network subnetting problem, they mapped their mental processes according to Huber's…

  2. The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework

    ERIC Educational Resources Information Center

    Carlson, Marilyn P.; Bloom, Irene

    2005-01-01

    This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…

  3. I Can Problem Solve: An Interpersonal Cognitive Problem-Solving Program. Intermediate Elementary Grades.

    ERIC Educational Resources Information Center

    Shure, Myrna B.

    Designed for teachers of intermediate elementary grades to enable children to learn how to solve the problems they have with others, the underlying goal of the program is to help children develop problem-solving skills so that they learn how to think, not what to think. The interpersonal cognitive problem-solving (ICPS) program includes both…

  4. The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework

    ERIC Educational Resources Information Center

    Carlson, Marilyn P.; Bloom, Irene

    2005-01-01

    This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…

  5. Lesion mapping of social problem solving

    PubMed Central

    Colom, Roberto; Paul, Erick J.; Chau, Aileen; Solomon, Jeffrey; Grafman, Jordan H.

    2014-01-01

    Accumulating neuroscience evidence indicates that human intelligence is supported by a distributed network of frontal and parietal regions that enable complex, goal-directed behaviour. However, the contributions of this network to social aspects of intellectual function remain to be well characterized. Here, we report a human lesion study (n = 144) that investigates the neural bases of social problem solving (measured by the Everyday Problem Solving Inventory) and examine the degree to which individual differences in performance are predicted by a broad spectrum of psychological variables, including psychometric intelligence (measured by the Wechsler Adult Intelligence Scale), emotional intelligence (measured by the Mayer, Salovey, Caruso Emotional Intelligence Test), and personality traits (measured by the Neuroticism-Extraversion-Openness Personality Inventory). Scores for each variable were obtained, followed by voxel-based lesion–symptom mapping. Stepwise regression analyses revealed that working memory, processing speed, and emotional intelligence predict individual differences in everyday problem solving. A targeted analysis of specific everyday problem solving domains (involving friends, home management, consumerism, work, information management, and family) revealed psychological variables that selectively contribute to each. Lesion mapping results indicated that social problem solving, psychometric intelligence, and emotional intelligence are supported by a shared network of frontal, temporal, and parietal regions, including white matter association tracts that bind these areas into a coordinated system. The results support an integrative framework for understanding social intelligence and make specific recommendations for the application of the Everyday Problem Solving Inventory to the study of social problem solving in health and disease. PMID:25070511

  6. The ideal science student and problem solving

    NASA Astrophysics Data System (ADS)

    Sullivan, Florence R.

    2005-09-01

    The purpose of this dissertation was to examine the relationship between students' social mental models of the ideal science student, science epistemological beliefs, problem solving strategies used, and problem solving ability in a robotics environment. Participants were twenty-six academically advanced eleven and twelve year old students attending the Center for Talented Youth summer camp. Survey data was collected from the students including demographic background, views of the ideal science student, and science epistemological beliefs. Students also solved a robotics challenge. This problem solving session was videotaped and students were asked to think aloud as they solved the problem. Two social mental models were identified, a traits-based social mental model and a robust social mental model. A significant association was found between social mental model group and strategy usage. The robust social mental model group is more likely to use domain specific strategies than the traits-based group. Additionally, the robust social mental model group achieved significantly higher scores on their final solution than the traits-based social mental model group. Science epistemological beliefs do not appear to be associated with students' social mental model of the ideal science student. While students with a puzzle-solver view of science were more likely to use domain specific strategies in the planning phase of the problem solving session, there was no significant difference in problem solving ability between this group and students who have a dynamic view of the nature of science knowledge. This difference in strategy usage and problem solving performance may be due to a difference in the students' views of learning and cognition. The robust social mental model group evidenced a situative view of learning and cognition. These students made excellent use of the tools available in the task environment. The traits-based social mental model group displayed an

  7. Solving the Telomere Replication Problem

    PubMed Central

    Maestroni, Laetitia; Matmati, Samah; Coulon, Stéphane

    2017-01-01

    Telomeres are complex nucleoprotein structures that protect the extremities of linear chromosomes. Telomere replication is a major challenge because many obstacles to the progression of the replication fork are concentrated at the ends of the chromosomes. This is known as the telomere replication problem. In this article, different and new aspects of telomere replication, that can threaten the integrity of telomeres, will be reviewed. In particular, we will focus on the functions of shelterin and the replisome for the preservation of telomere integrity. PMID:28146113

  8. Could HPS Improve Problem-Solving?

    NASA Astrophysics Data System (ADS)

    Coelho, Ricardo Lopes

    2013-05-01

    It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students' careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem solving could be improved by means of HPS. Three typical problems in introductory courses of mechanics—the inclined plane, the simple pendulum and the Atwood machine—are taken as the object of the present study. The solving strategies of these problems in the eighteenth and nineteenth century constitute the historical component of the study. Its philosophical component stems from the foundations of mechanics research literature. The use of HPS leads us to see those problems in a different way. These different ways can be tested, for which experiments are proposed. The traditional solving strategies for the incline and pendulum problems are adequate for some situations but not in general. The recourse to apparent weights in the Atwood machine problem leads us to a new insight and a solving strategy for composed Atwood machines. Educational implications also concern the development of logical thinking by means of the variety of lines of thought provided by HPS.

  9. Problem Solving through an Optimization Problem in Geometry

    ERIC Educational Resources Information Center

    Poon, Kin Keung; Wong, Hang-Chi

    2011-01-01

    This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

  10. Problem Solving through an Optimization Problem in Geometry

    ERIC Educational Resources Information Center

    Poon, Kin Keung; Wong, Hang-Chi

    2011-01-01

    This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

  11. Solving inversion problems with neural networks

    NASA Technical Reports Server (NTRS)

    Kamgar-Parsi, Behzad; Gualtieri, J. A.

    1990-01-01

    A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

  12. Towards Automated Training of Legal Problem Solving.

    ERIC Educational Resources Information Center

    Muntjewerff, Antoinette J.

    An examination of Dutch research on legal case solving revealed that few law students get systematic instruction or testing in the technique of legal problem solving. The research being conducted at the Department of Computer Science and Law at the University of Amsterdam focuses on identifying the different functions in legal reasoning tasks in…

  13. Purdue Elementary Problem-Solving Inventory.

    ERIC Educational Resources Information Center

    Purdue Univ., Lafayette, IN. Educational Research Center.

    This inventory was designed to assess the general problem solving ability of disadvantaged elementary school children from various ethnic backgrounds and grade levels. Twelve tasks are included in the inventory: sensing the problem, identifying the problem, asking questions, guessing causes, clarification of goals, judging if more information is…

  14. Collaborative Problem Solving in Shared Space

    ERIC Educational Resources Information Center

    Lin, Lin; Mills, Leila A.; Ifenthaler, Dirk

    2015-01-01

    The purpose of this study was to examine collaborative problem solving in a shared virtual space. The main question asked was: How will the performance and processes differ between collaborative problem solvers and independent problem solvers over time? A total of 104 university students (63 female and 41 male) participated in an experimental…

  15. Solving Problems with the Percentage Bar

    ERIC Educational Resources Information Center

    van Galen, Frans; van Eerde, Dolly

    2013-01-01

    At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…

  16. Conceptual problem solving in high school physics

    NASA Astrophysics Data System (ADS)

    Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

    2015-12-01

    Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers' implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.

  17. Organizational Structure and Complex Problem Solving

    ERIC Educational Resources Information Center

    Becker, Selwyn W.; Baloff, Nicholas

    1969-01-01

    The problem-solving efficiency of different organization structures is discussed in relation to task requirements and the appropriate organizational behavior, to group adaptation to a task over time, and to various group characteristics. (LN)

  18. Problem Solving under Time-Constraints,

    DTIC Science & Technology

    2014-09-26

    to interruptions. Data from the simulation is compared to data from college students doing the same task. Keywords include: Thinking ; problem solving; dual tasks; computer simulation; production systems; arithmetic.

  19. Physics: Quantum problems solved through games

    NASA Astrophysics Data System (ADS)

    Maniscalco, Sabrina

    2016-04-01

    Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210

  20. Solving the Langevin equation with stochastic algebraically correlated noise

    NASA Astrophysics Data System (ADS)

    Płoszajczak, M.; Srokowski, T.

    1997-05-01

    The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.

  1. Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R

    ERIC Educational Resources Information Center

    Actuarial Foundation, 2013

    2013-01-01

    "Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…

  2. Teaching Problem Solving without Modeling through "Thinking Aloud Pair Problem Solving."

    ERIC Educational Resources Information Center

    Pestel, Beverly C.

    1993-01-01

    Reviews research relevant to the problem of unsatisfactory student problem-solving abilities and suggests a teaching strategy that addresses the issue. Author explains how she uses teaching aloud problem solving (TAPS) in college chemistry and presents evaluation data. Among the findings are that the TAPS class got fewer problems completely right,…

  3. Review on solving the forward problem in EEG source analysis

    PubMed Central

    Hallez, Hans; Vanrumste, Bart; Grech, Roberta; Muscat, Joseph; De Clercq, Wim; Vergult, Anneleen; D'Asseler, Yves; Camilleri, Kenneth P; Fabri, Simon G; Van Huffel, Sabine; Lemahieu, Ignace

    2007-01-01

    solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem. PMID:18053144

  4. Innovative problem solving by wild spotted hyenas.

    PubMed

    Benson-Amram, Sarah; Holekamp, Kay E

    2012-10-07

    Innovative animals are those able to solve novel problems or invent novel solutions to existing problems. Despite the important ecological and evolutionary consequences of innovation, we still know very little about the traits that vary among individuals within a species to make them more or less innovative. Here we examine innovative problem solving by spotted hyenas (Crocuta crocuta) in their natural habitat, and demonstrate for the first time in a non-human animal that those individuals exhibiting a greater diversity of initial exploratory behaviours are more successful problem solvers. Additionally, as in earlier work, we found that neophobia was a critical inhibitor of problem-solving success. Interestingly, although juveniles and adults were equally successful in solving the problem, juveniles were significantly more diverse in their initial exploratory behaviours, more persistent and less neophobic than were adults. We found no significant effects of social rank or sex on success, the diversity of initial exploratory behaviours, behavioural persistence or neophobia. Our results suggest that the diversity of initial exploratory behaviours, akin to some measures of human creativity, is an important, but largely overlooked, determinant of problem-solving success in non-human animals.

  5. The Effects of Schema-Broadening Instruction on Second Graders' Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study

    ERIC Educational Resources Information Center

    Fuchs, Lynn S.; Zumeta, Rebecca O.; Schumacher, Robin Finelli; Powell, Sarah R.; Seethaler, Pamela M.; Hamlett, Carol L.; Fuchs, Douglas

    2010-01-01

    The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which…

  6. Development of a problem solving evaluation instrument; untangling of specific problem solving assets

    NASA Astrophysics Data System (ADS)

    Adams, Wendy Kristine

    The purpose of my research was to produce a problem solving evaluation tool for physics. To do this it was necessary to gain a thorough understanding of how students solve problems. Although physics educators highly value problem solving and have put extensive effort into understanding successful problem solving, there is currently no efficient way to evaluate problem solving skill. Attempts have been made in the past; however, knowledge of the principles required to solve the subject problem are so absolutely critical that they completely overshadow any other skills students may use when solving a problem. The work presented here is unique because the evaluation tool removes the requirement that the student already have a grasp of physics concepts. It is also unique because I picked a wide range of people and picked a wide range of tasks for evaluation. This is an important design feature that helps make things emerge more clearly. This dissertation includes an extensive literature review of problem solving in physics, math, education and cognitive science as well as descriptions of studies involving student use of interactive computer simulations, the design and validation of a beliefs about physics survey and finally the design of the problem solving evaluation tool. I have successfully developed and validated a problem solving evaluation tool that identifies 44 separate assets (skills) necessary for solving problems. Rigorous validation studies, including work with an independent interviewer, show these assets identified by this content-free evaluation tool are the same assets that students use to solve problems in mechanics and quantum mechanics. Understanding this set of component assets will help teachers and researchers address problem solving within the classroom.

  7. Cognitive Load in Algebra: Element Interactivity in Solving Equations

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

    2015-01-01

    Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

  8. Cognitive Load in Algebra: Element Interactivity in Solving Equations

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

    2015-01-01

    Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

  9. Collaborative Everyday Problem Solving: Interpersonal Relationships and Problem Dimensions

    ERIC Educational Resources Information Center

    Strough, Jonell; Patrick, Julie Hicks; Swenson, Lisa M.; Cheng, Suling; Barnes, Kristi A.

    2003-01-01

    Older adults' preferred partners for collaborative everyday problem solving and the types of everyday problems solved alone and with others were examined in a sample of community dwelling older adults (N = 112, M age = 71.86 yrs., SD = 5.92 yrs.). Family members (i.e., spouses, adult children) were the most frequently nominated partners for…

  10. Developing and Validating Sets of Algebra Word Problems.

    ERIC Educational Resources Information Center

    Nasser, Ramzi; Carifio, James

    The validation of key contextual features of algebra word problems was studied in two phases. In the first phase, five experts were asked to assess the appropriateness of the concepts in the problems and the adequacy of the assignment of the contextual features to the problems. In the second phase, construct validity was established by having 6…

  11. The "Mathnet" Format on "SQUARE ONE": Children's Informal Problem Solving, Understanding of Mathematical Concepts, and Ideas and Attitudes about Mathematics.

    ERIC Educational Resources Information Center

    Schauble, Leona; Peel, Tina

    Problem solving is a main topic in mathematics education, and considerable headway has been made in identifying the processes involved in solving well-formed problems like algebra word problems, mathematical algorithms, and logical puzzles like the Tower of Hanoi. The "Mathnet" format of the SQUARE ONE TV program, however, requires…

  12. Lesion mapping of social problem solving.

    PubMed

    Barbey, Aron K; Colom, Roberto; Paul, Erick J; Chau, Aileen; Solomon, Jeffrey; Grafman, Jordan H

    2014-10-01

    Accumulating neuroscience evidence indicates that human intelligence is supported by a distributed network of frontal and parietal regions that enable complex, goal-directed behaviour. However, the contributions of this network to social aspects of intellectual function remain to be well characterized. Here, we report a human lesion study (n = 144) that investigates the neural bases of social problem solving (measured by the Everyday Problem Solving Inventory) and examine the degree to which individual differences in performance are predicted by a broad spectrum of psychological variables, including psychometric intelligence (measured by the Wechsler Adult Intelligence Scale), emotional intelligence (measured by the Mayer, Salovey, Caruso Emotional Intelligence Test), and personality traits (measured by the Neuroticism-Extraversion-Openness Personality Inventory). Scores for each variable were obtained, followed by voxel-based lesion-symptom mapping. Stepwise regression analyses revealed that working memory, processing speed, and emotional intelligence predict individual differences in everyday problem solving. A targeted analysis of specific everyday problem solving domains (involving friends, home management, consumerism, work, information management, and family) revealed psychological variables that selectively contribute to each. Lesion mapping results indicated that social problem solving, psychometric intelligence, and emotional intelligence are supported by a shared network of frontal, temporal, and parietal regions, including white matter association tracts that bind these areas into a coordinated system. The results support an integrative framework for understanding social intelligence and make specific recommendations for the application of the Everyday Problem Solving Inventory to the study of social problem solving in health and disease. © The Author (2014). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved

  13. Spatial Visualization in Physics Problem Solving

    ERIC Educational Resources Information Center

    Kozhevnikov, Maria; Motes, Michael A.; Hegarty, Mary

    2007-01-01

    Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two-dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics-naive students were administered kinematics problems and…

  14. Problem-Solving Exercises and Evolution Teaching

    ERIC Educational Resources Information Center

    Angseesing, J. P. A.

    1978-01-01

    It is suggested that the work of Kammerer provides suitable material, in the form of case studies on which to base discussions of Lamarckism versus Darwinism. A set of structured problems is described as an example of possible problem-solving exercises, and further experiments to extend Kammerer's work are outlined. (Author/MA)

  15. Problem-Solving Exercises and Evolution Teaching

    ERIC Educational Resources Information Center

    Angseesing, J. P. A.

    1978-01-01

    It is suggested that the work of Kammerer provides suitable material, in the form of case studies on which to base discussions of Lamarckism versus Darwinism. A set of structured problems is described as an example of possible problem-solving exercises, and further experiments to extend Kammerer's work are outlined. (Author/MA)

  16. Pose and Solve Varignon Converse Problems

    ERIC Educational Resources Information Center

    Contreras, José N.

    2014-01-01

    The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

  17. Solving Problems of Practice in Education.

    ERIC Educational Resources Information Center

    Boyd, Robert D.; Menlo, Allen

    1984-01-01

    Discusses the many complexities involved in the translation of scientific information in the social sciences into forms usable for solving problems of practice in education. Prescribes a series of stages to be followed from the advent of a practitioner's situational problem to the design of a response to it. (Author/JN)

  18. Personality, Problem Solving, and Adolescent Substance Use

    ERIC Educational Resources Information Center

    Jaffee, William B.; D'Zurilla, Thomas J.

    2009-01-01

    The major aim of this study was to examine the role of social problem solving in the relationship between personality and substance use in adolescents. Although a number of studies have identified a relationship between personality and substance use, the precise mechanism by which this occurs is not clear. We hypothesized that problem-solving…

  19. Problem-Solving: Scaling the "Brick Wall"

    ERIC Educational Resources Information Center

    Benson, Dave

    2011-01-01

    Across the primary and secondary phases, pupils are encouraged to use and apply their knowledge, skills, and understanding of mathematics to solve problems in a variety of forms, ranging from single-stage word problems to the challenge of extended rich tasks. Amongst many others, Cockcroft (1982) emphasised the importance and relevance of…

  20. Complex Problem Solving in a Workplace Setting.

    ERIC Educational Resources Information Center

    Middleton, Howard

    2002-01-01

    Studied complex problem solving in the hospitality industry through interviews with six office staff members and managers. Findings show it is possible to construct a taxonomy of problem types and that the most common approach can be termed "trial and error." (SLD)

  1. Reinventing the Wheel: Design and Problem Solving

    ERIC Educational Resources Information Center

    Blasetti, Sean M.

    2010-01-01

    This article describes a design problem that not only takes students through the technological design process, but it also provides them with real-world problem-solving experience as it relates to the manufacturing and engineering fields. It begins with a scenario placing the student as a custom wheel designer for an automotive manufacturing…

  2. Reasoning by Analogy in Solving Comparison Problems.

    ERIC Educational Resources Information Center

    English, Lyn D.

    1998-01-01

    Investigates 10-year-old children's abilities to reason by analogy in solving addition and subtraction comparison problems involving unknown compare sets and unknown reference sets. Children responded in a consistent manner to the tasks involving the basic addition problems, indicating substantial relational knowledge of these but responded in an…

  3. Complex Problem Solving in a Workplace Setting.

    ERIC Educational Resources Information Center

    Middleton, Howard

    2002-01-01

    Studied complex problem solving in the hospitality industry through interviews with six office staff members and managers. Findings show it is possible to construct a taxonomy of problem types and that the most common approach can be termed "trial and error." (SLD)

  4. Teacher Learning on Problem-Solving Teams

    ERIC Educational Resources Information Center

    Gregory, Anne

    2010-01-01

    Problem-solving teams address student difficulties. Teams comprised of teachers, specialists, and administrators identify the student problem, develop individualized interventions, and assess student change. Teacher experiences of teams are understudied. In a prospective, mixed-method study conducted in the United States, 34 teachers were followed…

  5. Reinventing the Wheel: Design and Problem Solving

    ERIC Educational Resources Information Center

    Blasetti, Sean M.

    2010-01-01

    This article describes a design problem that not only takes students through the technological design process, but it also provides them with real-world problem-solving experience as it relates to the manufacturing and engineering fields. It begins with a scenario placing the student as a custom wheel designer for an automotive manufacturing…

  6. Using Bibliotherapy To Teach Problem Solving.

    ERIC Educational Resources Information Center

    Forgan, James W.

    2002-01-01

    This article discusses how students with high-incidence disabilities can benefit from using bibliotherapy by learning to become proactive problem solvers. A sample lesson plan is presented based on a teaching framework for bibliotherapy and problem solving that contains the elements of prereading, guided reading, post-reading discussion, and a…

  7. Teaching Teamwork and Problem Solving Concurrently

    ERIC Educational Resources Information Center

    Goltz, Sonia M.; Hietapelto, Amy B.; Reinsch, Roger W.; Tyrell, Sharon K.

    2008-01-01

    Teamwork and problem-solving skills have frequently been identified by business leaders as being key competencies; thus, teaching methods such as problem-based learning and team-based learning have been developed. However, the focus of these methods has been on teaching one skill or the other. A key argument for teaching the skills concurrently is…

  8. Metaphor and analogy in everyday problem solving.

    PubMed

    Keefer, Lucas A; Landau, Mark J

    2016-11-01

    Early accounts of problem solving focused on the ways people represent information directly related to target problems and possible solutions. Subsequent theory and research point to the role of peripheral influences such as heuristics and bodily states. We discuss how metaphor and analogy similarly influence stages of everyday problem solving: Both processes mentally map features of a target problem onto the structure of a relatively more familiar concept. When individuals apply this structure, they use a well-known concept as a framework for reasoning about real world problems and candidate solutions. Early studies found that analogy use helped people gain insight into novel problems. More recent research on metaphor goes further to show that activating mappings has subtle, sometimes surprising effects on judgment and reasoning in everyday problem solving. These findings highlight situations in which mappings can help or hinder efforts to solve problems. WIREs Cogn Sci 2016, 7:394-405. doi: 10.1002/wcs.1407 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

  9. Model Formulation for Physics Problem Solving. Draft.

    ERIC Educational Resources Information Center

    Novak, Gordon S., Jr.

    The major task in solving a physics problem is to construct an appropriate model of the problem in terms of physical principles. The functions performed by such a model, the information which needs to be represented, and the knowledge used in selecting and instantiating an appropriate model are discussed. An example of a model for a mechanics…

  10. Analogy Generation in Scientific Problem Solving.

    ERIC Educational Resources Information Center

    Clement, John

    The spontaneous use of analogies in problem-solving occurs when a subject first spontaneously shifts his attention to a situation (B) which differs in some significant way from an original problem situation (A), and then tries to apply findings from B to A. This paper describes research on the process with 10 scientifically trained subjects…

  11. Solving Math Word Problems: A Software Roundup.

    ERIC Educational Resources Information Center

    Eiser, Leslie

    1988-01-01

    Reviewed are 11 software packages for the Apple II computer designed to help teach elementary and secondary school children how to solve mathword problems. Included in the review are hardware requirements, price, grade level, use of graphics, kinds of problems, tools provided, strengths, and weaknesses of each program. (CW)

  12. Using Programmable Calculators to Solve Electrostatics Problems.

    ERIC Educational Resources Information Center

    Yerian, Stephen C.; Denker, Dennis A.

    1985-01-01

    Provides a simple routine which allows first-year physics students to use programmable calculators to solve otherwise complex electrostatic problems. These problems involve finding electrostatic potential and electric field on the axis of a uniformly charged ring. Modest programing skills are required of students. (DH)

  13. Scientific Problem Solving by Expert Systems.

    ERIC Educational Resources Information Center

    Good, Ron

    1984-01-01

    Human expert problem-solving in science is defined and used to account for scientific discovery. These ideas are used to describe BACON.5, a machine expert problem solver that discovers scientific laws using data-driver heuristics and "expectations" such as symmetry. Implications of BACON.5 type research for traditional science education…

  14. Dreams and creative problem-solving.

    PubMed

    Barrett, Deirdre

    2017-06-22

    Dreams have produced art, music, novels, films, mathematical proofs, designs for architecture, telescopes, and computers. Dreaming is essentially our brain thinking in another neurophysiologic state-and therefore it is likely to solve some problems on which our waking minds have become stuck. This neurophysiologic state is characterized by high activity in brain areas associated with imagery, so problems requiring vivid visualization are also more likely to get help from dreaming. This article reviews great historical dreams and modern laboratory research to suggest how dreams can aid creativity and problem-solving. © 2017 New York Academy of Sciences.

  15. Problem solving and decisionmaking: An integration

    NASA Technical Reports Server (NTRS)

    Dieterly, D. L.

    1980-01-01

    An attempt was made to redress a critical fault of decisionmaking and problem solving research-a lack of a standard method to classify problem or decision states or conditions. A basic model was identified and expanded to indicate a possible taxonomy of conditions which may be used in reviewing previous research or for systematically pursuing new research designs. A generalization of the basic conditions was then made to indicate that the conditions are essentially the same for both concepts, problem solving and decisionmaking.

  16. Analytical derivation: An epistemic game for solving mathematically based physics problems

    NASA Astrophysics Data System (ADS)

    Bajracharya, Rabindra R.; Thompson, John R.

    2016-06-01

    Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

  17. Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving

    ERIC Educational Resources Information Center

    Bostic, Jonathan D.; Pape, Stephen J.; Jacobbe, Tim

    2016-01-01

    This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

  18. The Effect of Learning Environments Based on Problem Solving on Students' Achievements of Problem Solving

    ERIC Educational Resources Information Center

    Karatas, Ilhan; Baki, Adnan

    2013-01-01

    Problem solving is recognized as an important life skill involving a range of processes including analyzing, interpreting, reasoning, predicting, evaluating and reflecting. For that reason educating students as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum.…

  19. Students' Errors in Solving the Permutation and Combination Problems Based on Problem Solving Steps of Polya

    ERIC Educational Resources Information Center

    Sukoriyanto; Nusantara, Toto; Subanji; Chandra, Tjang Daniel

    2016-01-01

    This article was written based on the results of a study evaluating students' errors in problem solving of permutation and combination in terms of problem solving steps according to Polya. Twenty-five students were asked to do four problems related to permutation and combination. The research results showed that the students still did a mistake in…

  20. Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving

    ERIC Educational Resources Information Center

    Bostic, Jonathan D.; Pape, Stephen J.; Jacobbe, Tim

    2016-01-01

    This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

  1. The development and nature of problem-solving among first-semester calculus students

    NASA Astrophysics Data System (ADS)

    Dawkins, Paul Christian; Mendoza Epperson, James A.

    2014-08-01

    This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving

  2. Enhancing chemistry problem-solving achievement using problem categorization

    NASA Astrophysics Data System (ADS)

    Bunce, Diane M.; Gabel, Dorothy L.; Samuel, John V.

    The enhancement of chemistry students' skill in problem solving through problem categorization is the focus of this study. Twenty-four students in a freshman chemistry course for health professionals are taught how to solve problems using the explicit method of problem solving (EMPS) (Bunce & Heikkinen, 1986). The EMPS is an organized approach to problem analysis which includes encoding the information given in a problem (Given, Asked For), relating this to what is already in long-term memory (Recall), and planning a solution (Overall Plan) before a mathematical solution is attempted. In addition to the EMPS training, treatment students receive three 40-minute sessions following achievement tests in which they are taught how to categorize problems. Control students use this time to review the EMPS solutions of test questions. Although problem categorization is involved in one section of the EMPS (Recall), treatment students who received specific training in problem categorization demonstrate significantly higher achievement on combination problems (those problems requiring the use of more than one chemical topic for their solution) at (p = 0.01) than their counterparts. Significantly higher achievement for treatment students is also measured on an unannounced test (p = 0.02). Analysis of interview transcripts of both treatment and control students illustrates a Rolodex approach to problem solving employed by all students in this study. The Rolodex approach involves organizing equations used to solve problems on mental index cards and flipping through them, matching units given when a new problem is to be solved. A second phenomenon observed during student interviews is the absence of a link in the conceptual understanding of the chemical concepts involved in a problem and the problem-solving skills employed to correctly solve problems. This study shows that explicit training in categorization skills and the EMPS can lead to higher achievement in complex problem-solving

  3. Problem-Solving Transfer Among Programming Languages

    DTIC Science & Technology

    1990-06-04

    stable from programming in the first language to in the second. In other words, the transfer on subsequent drafts was mainly manifested as fewer drafts...substantial transfer from solving a problem in the first language (LISP or PROLOG) to solving it in the second language (PROLOG or LISP) in terms of time...transfer a lot of the algorithmic knowledge gained from programming in the first language to in the second. We will refer this type of transfer as

  4. Why students still can't solve physics problems after solving over 2000 problems

    NASA Astrophysics Data System (ADS)

    Byun, Taejin; Lee, Gyoungho

    2014-09-01

    This study investigates the belief that solving a large number of physics problems helps students better learn physics. We investigated the number of problems solved, student confidence in solving these problems, academic achievement, and the level of conceptual understanding of 49 science high school students enrolled in upper-level physics classes from Spring 2010 to Summer 2011. The participants solved an average of 2200 physics problems before entering high school. Despite having solved so many problems, no statistically significant correlation was found between the number of problems solved and academic achievement on either a mid-term or physics competition examination. In addition, no significant correlation was found between the number of physics problems solved and performance on the Force Concept Inventory (FCI). Lastly, four students were selected from the 49 participants with varying levels of experience and FCI scores for a case study. We determined that their problem solving and learning strategies was more influential in their success than the number of problems they had solved.

  5. AI tools in computer based problem solving

    NASA Technical Reports Server (NTRS)

    Beane, Arthur J.

    1988-01-01

    The use of computers to solve value oriented, deterministic, algorithmic problems, has evolved a structured life cycle model of the software process. The symbolic processing techniques used, primarily in research, for solving nondeterministic problems, and those for which an algorithmic solution is unknown, have evolved a different model, much less structured. Traditionally, the two approaches have been used completely independently. With the advent of low cost, high performance 32 bit workstations executing identical software with large minicomputers and mainframes, it became possible to begin to merge both models into a single extended model of computer problem solving. The implementation of such an extended model on a VAX family of micro/mini/mainframe systems is described. Examples in both development and deployment of applications involving a blending of AI and traditional techniques are given.

  6. AI tools in computer based problem solving

    NASA Technical Reports Server (NTRS)

    Beane, Arthur J.

    1988-01-01

    The use of computers to solve value oriented, deterministic, algorithmic problems, has evolved a structured life cycle model of the software process. The symbolic processing techniques used, primarily in research, for solving nondeterministic problems, and those for which an algorithmic solution is unknown, have evolved a different model, much less structured. Traditionally, the two approaches have been used completely independently. With the advent of low cost, high performance 32 bit workstations executing identical software with large minicomputers and mainframes, it became possible to begin to merge both models into a single extended model of computer problem solving. The implementation of such an extended model on a VAX family of micro/mini/mainframe systems is described. Examples in both development and deployment of applications involving a blending of AI and traditional techniques are given.

  7. Problem solving in a distributed environment

    NASA Technical Reports Server (NTRS)

    Rashid, R. F.

    1980-01-01

    Distributed problem solving is anayzed as a blend of two disciplines: (1) problem solving and ai; and (2) distributed systems (monitoring). It may be necessary to distribute because the application itself is one of managing distributed resources (e.g., distributed sensor net) and communication delays preclude centralized processing, or it may be desirable to distribute because a single computational engine may not satisfy the needs of a given task. In addition, considerations of reliability may dictate distribution. Examples of multi-process language environment are given.

  8. Problem solving in a distributed environment

    NASA Technical Reports Server (NTRS)

    Rashid, R. F.

    1980-01-01

    Distributed problem solving is anayzed as a blend of two disciplines: (1) problem solving and ai; and (2) distributed systems (monitoring). It may be necessary to distribute because the application itself is one of managing distributed resources (e.g., distributed sensor net) and communication delays preclude centralized processing, or it may be desirable to distribute because a single computational engine may not satisfy the needs of a given task. In addition, considerations of reliability may dictate distribution. Examples of multi-process language environment are given.

  9. Problem solving with genetic algorithms and Splicer

    NASA Technical Reports Server (NTRS)

    Bayer, Steven E.; Wang, Lui

    1991-01-01

    Genetic algorithms are highly parallel, adaptive search procedures (i.e., problem-solving methods) loosely based on the processes of population genetics and Darwinian survival of the fittest. Genetic algorithms have proven useful in domains where other optimization techniques perform poorly. The main purpose of the paper is to discuss a NASA-sponsored software development project to develop a general-purpose tool for using genetic algorithms. The tool, called Splicer, can be used to solve a wide variety of optimization problems and is currently available from NASA and COSMIC. This discussion is preceded by an introduction to basic genetic algorithm concepts and a discussion of genetic algorithm applications.

  10. Problem solving with genetic algorithms and Splicer

    NASA Technical Reports Server (NTRS)

    Bayer, Steven E.; Wang, Lui

    1991-01-01

    Genetic algorithms are highly parallel, adaptive search procedures (i.e., problem-solving methods) loosely based on the processes of population genetics and Darwinian survival of the fittest. Genetic algorithms have proven useful in domains where other optimization techniques perform poorly. The main purpose of the paper is to discuss a NASA-sponsored software development project to develop a general-purpose tool for using genetic algorithms. The tool, called Splicer, can be used to solve a wide variety of optimization problems and is currently available from NASA and COSMIC. This discussion is preceded by an introduction to basic genetic algorithm concepts and a discussion of genetic algorithm applications.

  11. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    ERIC Educational Resources Information Center

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  12. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    ERIC Educational Resources Information Center

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  13. Insightful Problem Solving in an Asian Elephant

    PubMed Central

    Foerder, Preston; Galloway, Marie; Barthel, Tony; Moore, Donald E.; Reiss, Diana

    2011-01-01

    The “aha” moment or the sudden arrival of the solution to a problem is a common human experience. Spontaneous problem solving without evident trial and error behavior in humans and other animals has been referred to as insight. Surprisingly, elephants, thought to be highly intelligent, have failed to exhibit insightful problem solving in previous cognitive studies. We tested whether three Asian elephants (Elephas maximus) would use sticks or other objects to obtain food items placed out-of-reach and overhead. Without prior trial and error behavior, a 7-year-old male Asian elephant showed spontaneous problem solving by moving a large plastic cube, on which he then stood, to acquire the food. In further testing he showed behavioral flexibility, using this technique to reach other items and retrieving the cube from various locations to use as a tool to acquire food. In the cube's absence, he generalized this tool utilization technique to other objects and, when given smaller objects, stacked them in an attempt to reach the food. The elephant's overall behavior was consistent with the definition of insightful problem solving. Previous failures to demonstrate this ability in elephants may have resulted not from a lack of cognitive ability but from the presentation of tasks requiring trunk-held sticks as potential tools, thereby interfering with the trunk's use as a sensory organ to locate the targeted food. PMID:21876741

  14. Extending problem-solving procedures through reflection.

    PubMed

    Anderson, John R; Fincham, Jon M

    2014-11-01

    A large-sample (n=75) fMRI study guided the development of a theory of how people extend their problem-solving procedures by reflecting on them. Both children and adults were trained on a new mathematical procedure and then were challenged with novel problems that required them to change and extend their procedure to solve these problems. The fMRI data were analyzed using a combination of hidden Markov models (HMMs) and multi-voxel pattern analysis (MVPA). This HMM-MVPA analysis revealed the existence of 4 stages: Encoding, Planning, Solving, and Responding. Using this analysis as a guide, an ACT-R model was developed that improved the performance of the HMM-MVPA and explained the variation in the durations of the stages across 128 different problems. The model assumes that participants can reflect on declarative representations of the steps of their problem-solving procedures. A Metacognitive module can hold these steps, modify them, create new declarative steps, and rehearse them. The Metacognitive module is associated with activity in the rostrolateral prefrontal cortex (RLPFC). The ACT-R model predicts the activity in the RLPFC and other regions associated with its other cognitive modules (e.g., vision, retrieval). Differences between children and adults seemed related to differences in background knowledge and computational fluency, but not to the differences in their capability to modify procedures.

  15. Solving the hard problem of Bertrand's paradox

    SciTech Connect

    Aerts, Diederik; Sassoli de Bianchi, Massimiliano

    2014-08-15

    Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox contains two different problems: an “easy” problem and a “hard” problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non-ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible “ways of selecting” an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible “ways of selecting” an interaction, which we call a universal average. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.

  16. Representations in Problem Solving: A Case Study with Optimization Problems

    ERIC Educational Resources Information Center

    Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

    2009-01-01

    Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

  17. Representations in Problem Solving: A Case Study with Optimization Problems

    ERIC Educational Resources Information Center

    Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

    2009-01-01

    Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

  18. A Conceptual Approach to Physics Problem Solving

    NASA Astrophysics Data System (ADS)

    Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

    2010-10-01

    Students in introductory physics courses treat problem solving as an exercise in manipulating equations, symbols, and quantities with the goal of obtaining the correct answer. Although this approach is efficient for getting answers, it is far from optimal for learning how conceptual knowledge is applied in the problem-solving process. The goal of this study is to refine and evaluate an approach that encourages students to begin by writing a strategic analysis of a problem based on principles and procedures, and then to follow with a documented problem solution that exhibits, side-by-side, how concepts and equations go together in a solution. We will discuss the implementation and effectiveness of this approach in four local high school classrooms.

  19. Assessing Affect after Mathematical Problem Solving Tasks: Validating the Chamberlin Affective Instrument for Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Chamberlin, Scott A.; Powers, Robert A.

    2013-01-01

    The focus of the article is the validation of an instrument to assess gifted students' affect after mathematical problem solving tasks. Participants were 225 students identified by their district as gifted in grades four to six. The Chamberlin Affective Instrument for Mathematical Problem Solving was used to assess feelings, emotions, and…

  20. Preschoolers' Cooperative Problem Solving: Integrating Play and Problem Solving

    ERIC Educational Resources Information Center

    Ramani, Geetha B.; Brownell, Celia A.

    2014-01-01

    Cooperative problem solving with peers plays a central role in promoting children's cognitive and social development. This article reviews research on cooperative problem solving among preschool-age children in experimental settings and social play contexts. Studies suggest that cooperative interactions with peers in experimental settings are…

  1. Understanding Individual Problem-Solving Style: A Key to Learning and Applying Creative Problem Solving

    ERIC Educational Resources Information Center

    Treffinger, Donald J.; Selby, Edwin C.; Isaksen, Scott G.

    2008-01-01

    More than five decades of research and development have focused on making the Creative Problem Solving process and tools accessible across a wide range of ages and contexts. Recent evidence indicates that when individuals, in both school and corporate settings, understand their own style of problem solving, they are able to learn and apply process…

  2. I Can Problem Solve (ICPS): Interpersonal Cognitive Problem Solving for Young Children.

    ERIC Educational Resources Information Center

    Shure, Myrna B.

    1993-01-01

    Teachers of preschool and kindergarten children from low-income families used the I Can Problem Solve (ICPS) program to help the children learn to think through and solve typical interpersonal problems with peers and adults. Compared to nontrained controls, the children exhibited fewer instances of impulsive and inhibited behaviors as observed in…

  3. I Can Problem Solve: An Interpersonal Cognitive Problem Solving Program. Kindergarten and Primary Grades.

    ERIC Educational Resources Information Center

    Shure, Myrna B.

    Designed for teachers of kindergarten and the primary grades to enable children to learn how to solve the problems they have with others, the underlying goal of the program is to help children develop problem-solving skills so that they learn how to think, not what to think. The 89 lessons are adaptable for various levels of ability throughout the…

  4. I Can Problem Solve: An Interpersonal Cognitive Problem-Solving Program. Preschool.

    ERIC Educational Resources Information Center

    Shure, Myrna B.

    Designed for teachers of preschool to enable children to learn how to solve the problems they have with others, the underlying goal of the program is to help children develop problem-solving skills so that they learn how to think, not what to think. Originally developed for four-year-old children in a preschool setting, most three-year-old…

  5. Understanding Individual Problem-Solving Style: A Key to Learning and Applying Creative Problem Solving

    ERIC Educational Resources Information Center

    Treffinger, Donald J.; Selby, Edwin C.; Isaksen, Scott G.

    2008-01-01

    More than five decades of research and development have focused on making the Creative Problem Solving process and tools accessible across a wide range of ages and contexts. Recent evidence indicates that when individuals, in both school and corporate settings, understand their own style of problem solving, they are able to learn and apply process…

  6. Problem-Framing: A perspective on environmental problem-solving

    NASA Astrophysics Data System (ADS)

    Bardwell, Lisa V.

    1991-09-01

    The specter of environmental calamity calls for the best efforts of an involved public. Ironically, the way people understand the issues all too often serves to discourage and frustrate rather than motivate them to action. This article draws from problem-solving perspectives offered by cognitive psychology and conflict management to examine a framework for thinking about environmental problems that promises to help rather than hinder efforts to address them. Problem-framing emphasizes focusing on the problem definition. Since how one defines a problem determines one's understanding of and approach to that problem, being able to redefine or reframe a problem and to explore the “problem space” can help broaden the range of alternatives and solutions examined. Problem-framing incorporates a cognitive perspective on how people respond to information. It explains why an emphasis on problem definition is not part of people's typical approach to problems. It recognizes the importance of structure and of having ways to organize that information on one's problem-solving effort. Finally, problem-framing draws on both cognitive psychology and conflict management for strategies to manage information and to create a problem-solving environment that not only encourages participation but can yield better approaches to our environmental problems.

  7. Secondary Pre-Service Teachers' Algebraic Reasoning about Linear Equation Solving

    ERIC Educational Resources Information Center

    Alvey, Christina; Hudson, Rick A.; Newton, Jill; Males, Lorraine M.

    2016-01-01

    This study analyzes the responses of 12 secondary pre-service teachers on two tasks focused on reasoning when solving linear equations. By documenting the choices PSTs made while engaging in these tasks, we gain insight into how new teachers work mathematically, reason algebraically, communicate their thinking, and make pedagogical decisions. We…

  8. Laplace transform approach for solving integral equations using computer algebra system

    NASA Astrophysics Data System (ADS)

    Paneva-Konovska, Jordanka; Nikolova, Yanka

    2016-12-01

    The Laplace transform method, along with Computer Algebra Systems (CAS) "Maple" v. 13, are extremely successfully applied for solving a class of integral equations with an arbitrary order, including fractional order integral equations. The combining of both powerful approaches allows students more quickly, enjoyable and thoroughly to master the material.

  9. Solving Problems of Ice-Blocked Drainage.

    DTIC Science & Technology

    1984-09-01

    operations. These techniques may allow ice to form, but will slow down its formation or will maintain an unfrozen opening so that drainage flow can -0...Hampshire 03755 Solving problems of ice-blocked 0 drainage 0 - *O 0 Kevin L. Carey % - S 0 Introduction Once the processes that lead to ice-blocked drainage ...facili- ties are understood (Ice-Blocked Drainage : Problems and - , Processes, Cold Regions Technical Digest No. 83-2), it is pos- sible to work out

  10. Appendix M. Research Utilization and Problem Solving

    ERIC Educational Resources Information Center

    Jung, Charles

    The Research Utilization and Problem Solving (RUPS) Model--an instructional system designed to provide the needed competencies for an entire staff to engage in systems analysis and systems synthesis procedures prior to assessing educational needs and developing curriculum to meet the needs identified--is intended to facilitate the development of…

  11. Assessing Mathematical Problem Solving Using Comparative Judgement

    ERIC Educational Resources Information Center

    Jones, Ian; Swan, Malcolm; Pollitt, Alastair

    2015-01-01

    There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

  12. Young Children's Drawings in Problem Solving

    ERIC Educational Resources Information Center

    Bakar, Kamariah Abu; Way, Jennifer; Bobis, Janette

    2016-01-01

    This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

  13. Solving Wicked Problems through Action Learning

    ERIC Educational Resources Information Center

    Crul, Liselore

    2014-01-01

    This account of practice outlines the Oxyme Action Learning Program which was conducted as part of the Management Challenge in my final year of the MSc in Coaching and Behavioral Change at Henley Business School. The central research questions were: (1) how action learning can help to solve wicked problems and (2) what the effect of an action…

  14. Design and Problem Solving in Technology Education.

    ERIC Educational Resources Information Center

    Custer, Rodney L.

    1999-01-01

    Collectively, technological literacy embraces everything from intelligent consumerism to concerns about environmental degradation, ethics, and elitism. Technological problem solving can have social, ecological, or technological goals and may be categorized by four types: invention, design, trouble shooting, and procedures. Every citizen should be…

  15. Facilitating Problem Solving in High School Chemistry.

    ERIC Educational Resources Information Center

    Gabel, Dorothy L.

    The major purpose of this study was to determine whether certain types of instructional strategies (factor-label method, use of analogies, use of diagrams, and proportionality) were superior to others in teaching problem solving in four topics (mole concept, gas laws, stoichiometry, and molarity). Also of major interest was whether particular…

  16. Problem Solving. Workplace Education Program Curriculum.

    ERIC Educational Resources Information Center

    Burkhart, Jennifer

    The BUILD Program (Businesses United to Increase Literacy Development) was conducted from June 1991 through December 1992 as a cooperative workplace literacy program joining Arapahoe Community College and four companies in Littleton, Colorado. This document consists of three modules for the problem-solving and computer learning systems classes of…

  17. General Problem Solving: Navy Requirements and Solutions.

    DTIC Science & Technology

    1985-03-01

    Applied Mathematical Problem Solving, ERIC Clearinghouse for Science, Mathematics and Environmental Education , Columbus, Ohio, 1979. Bourne, Lyle...Mathematics and Environmental Education , Columbus, Ohio, 1979. Lewis, Clayton and Mack, Robert L. "The Role of Abduction in Learning to Use a

  18. Raise the Bar on Problem Solving

    ERIC Educational Resources Information Center

    Englard, Lisa

    2010-01-01

    In a 1981 diagnostic test, the Ministry of Education in Singapore found its country facing a challenge: Only 46 percent of students in grades 2-4 could solve word problems that were presented without such key words as "altogether" or "left." Yet today, according to results from the Trends in International Mathematics and…

  19. Problem-Solving Strategies for Career Planning.

    ERIC Educational Resources Information Center

    McBryde, Merry J.; Karr-Kidwell, PJ

    The need for new expertise in problem solving in the work setting has emerged as a woman's issue because work outside the home has become a primary means for personal goal attainment for about half the women in the United States and because traditional career patterns and norms are ineffective. Career planning is the process of individual career…

  20. Problem Solving and Behavior Therapy Revisited

    ERIC Educational Resources Information Center

    Nezu, Arthur M.

    2004-01-01

    Over three decades ago, D'Zurilla and Goldfried (1971) published a seminal article delineating a model of problem-solving training geared to enhance social competence and decrease psychological distress. Since that time, a substantial amount of research has been conducted to test various hypotheses that this model has engendered. Much of this…

  1. ADHD and Problem-Solving in Play

    ERIC Educational Resources Information Center

    Borg, Suzanne

    2009-01-01

    This paper reports a small-scale study to determine whether there is a difference in problem-solving abilities, from a play perspective, between individuals who are diagnosed as ADHD and are on medication and those not on medication. Ten children, five of whom where on medication and five not, diagnosed as ADHD predominantly inattentive type, were…

  2. Conceptual Structures in Mathematical Problem Solving.

    ERIC Educational Resources Information Center

    Cifarelli, Victor

    The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

  3. Facilitating Problem Solving in High School Chemistry.

    ERIC Educational Resources Information Center

    Gabel, Dorothy L.; Sherwood, Robert D.

    1983-01-01

    Investigated superiority of instructional strategies (factor-label method, proportionality, use of analogies, use of diagrams) in teaching problem-solving related to mole concept, gas laws, stoichiometry, and molarity. Also investigated effectiveness of strategies for students (N=609) with different verbal-visual preferences, proportional…

  4. Problem-Solving Interaction in GFL Videoconferencing

    ERIC Educational Resources Information Center

    Hoshii, Makiko; Schumacher, Nicole

    2016-01-01

    This paper reports on the interaction between upper intermediate German as a Foreign Language (GFL) learners in Tokyo and prospective GFL teachers in Berlin in an online videoconferencing environment. It focuses on the way problems in comprehension and production are brought up and solved in the subsequent interaction. Our findings illustrate that…

  5. Mental Imagery in Creative Problem Solving.

    ERIC Educational Resources Information Center

    Polland, Mark J.

    In order to investigate the relationship between mental imagery and creative problem solving, a study of 44 separate accounts reporting mental imagery experiences associated with creative discoveries were examined. The data included 29 different scientists, among them Albert Einstein and Stephen Hawking, and 9 artists, musicians, and writers,…

  6. Student Problem Solving in High School Genetics.

    ERIC Educational Resources Information Center

    Stewart, James

    1983-01-01

    Describes set of specific steps (procedural knowledge) used when solving monohybrid/dihybrid cross problems and extent to which students could justify execution of each step in terms of their conceptual knowledge of genetics and meiosis. Implications for genetics instruction are discussed. (JN)

  7. Quickfire Challenges to Inspire Problem Solving

    ERIC Educational Resources Information Center

    Harper, Suzanne R.; Cox, Dana C.

    2017-01-01

    In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

  8. ADHD and Problem-Solving in Play

    ERIC Educational Resources Information Center

    Borg, Suzanne

    2009-01-01

    This paper reports a small-scale study to determine whether there is a difference in problem-solving abilities, from a play perspective, between individuals who are diagnosed as ADHD and are on medication and those not on medication. Ten children, five of whom where on medication and five not, diagnosed as ADHD predominantly inattentive type, were…

  9. A SURVEY OF PROBLEM-SOLVING COURSES.

    ERIC Educational Resources Information Center

    EDWARDS, M.O.

    TO DETERMINE THE DESIRABILITY OF HAVING ITS OWN CREATIVITY COURSE, THE STANFORD RESEARCH INSTITUTE SURVEYED 43 ORGANIZATIONS ON THEIR PROBLEM SOLVING COURSES. FIFTEEN INDUSTRIAL CORPORATIONS, FOUR CONSULTING FIRMS, A GOVERNMENT AGENCY, A RESEARCH CORPORATION, AND NINE COLLEGES AND UNIVERSITIES RESPONDED WITH SPECIFIC INFORMATION ON COURSE LENGTH…

  10. On Teaching Problem Solving in School Mathematics

    ERIC Educational Resources Information Center

    Pehkonen, Erkki; Näveri, Liisa; Laine, Anu

    2013-01-01

    The article begins with a brief overview of the situation throughout the world regarding problem solving. The activities of the ProMath group are then described, as the purpose of this international research group is to improve mathematics teaching in school. One mathematics teaching method that seems to be functioning in school is the use of open…

  11. How Instructional Designers Solve Workplace Problems

    ERIC Educational Resources Information Center

    Fortney, Kathleen S.; Yamagata-Lynch, Lisa C.

    2013-01-01

    This naturalistic inquiry investigated how instructional designers engage in complex and ambiguous problem solving across organizational boundaries in two corporations. Participants represented a range of instructional design experience, from novices to experts. Research methods included a participant background survey, observations of…

  12. Problem Solving in Biology: A Methodology

    ERIC Educational Resources Information Center

    Wisehart, Gary; Mandell, Mark

    2008-01-01

    A methodology is described that teaches science process by combining informal logic and a heuristic for rating factual reliability. This system facilitates student hypothesis formation, testing, and evaluation of results. After problem solving with this scheme, students are asked to examine and evaluate arguments for the underlying principles of…

  13. Raise the Bar on Problem Solving

    ERIC Educational Resources Information Center

    Englard, Lisa

    2010-01-01

    In a 1981 diagnostic test, the Ministry of Education in Singapore found its country facing a challenge: Only 46 percent of students in grades 2-4 could solve word problems that were presented without such key words as "altogether" or "left." Yet today, according to results from the Trends in International Mathematics and…

  14. Partial Metacognitive Blindness in Collaborative Problem Solving

    ERIC Educational Resources Information Center

    Ng, Kit Ee Dawn

    2010-01-01

    This paper investigates the impact of group dynamics on metacognitive behaviours of students (aged 13-14) during group collaborative problem solving attempts involving a design-based real-world applications project. It was discovered that group dynamics mediated the impact of metacognitive judgments related red flag situations and metacognitive…

  15. Creating Environments for Peaceful Problem Solving

    ERIC Educational Resources Information Center

    Lamm, Sandra; Groulx, Judith G.; Hansen, Cindy; Patton, Mary Martin; Slaton, Anna Jimenez

    2006-01-01

    For may early childhood teachers, angry voices of children are heard all too often. When children focus on protecting themselves and surviving conflicts, they miss out on the joys and opportunities the early childhood program has to offer. Without the ability to solve problems in their interactions with others, children are not able to peacefully…

  16. Complex Problem Solving--More than Reasoning?

    ERIC Educational Resources Information Center

    Wustenberg, Sascha; Greiff, Samuel; Funke, Joachim

    2012-01-01

    This study investigates the internal structure and construct validity of Complex Problem Solving (CPS), which is measured by a "Multiple-Item-Approach." It is tested, if (a) three facets of CPS--"rule identification" (adequateness of strategies), "rule knowledge" (generated knowledge) and "rule application"…

  17. Teaching, Learning and Assessing Statistical Problem Solving

    ERIC Educational Resources Information Center

    Marriott, John; Davies, Neville; Gibson, Liz

    2009-01-01

    In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and…

  18. Should Children Learn to Solve Problems?

    ERIC Educational Resources Information Center

    Watras, Joseph

    2011-01-01

    In this comparative essay, the author discusses the opposing educational theories of John Dewey and Gregory Bateson. While Dewey believed that the scientific method was the dominant method of solving problems and thereby acquiring knowledge that mattered, Bateson warned that this one-sided approach would lead to actions that could destroy the…

  19. Problem-Solving Test: Tryptophan Operon Mutants

    ERIC Educational Resources Information Center

    Szeberenyi, Jozsef

    2010-01-01

    This paper presents a problem-solving test that deals with the regulation of the "trp" operon of "Escherichia coli." Two mutants of this operon are described: in mutant A, the operator region of the operon carries a point mutation so that it is unable to carry out its function; mutant B expresses a "trp" repressor protein unable to bind…

  20. Why Some Communities Can Solve Their Problems.

    ERIC Educational Resources Information Center

    Mathews, David

    1989-01-01

    Effective communities are well-educated about themselves, have a better understanding of public information, talk through public issues to generate shared knowledge, appreciate the difference between public opinion and public judgment, and believe in public leadership as the key to using public power to solve community problems. (SK)

  1. Problem-solving for better health.

    PubMed

    Smith, B; Barnett, S; Collado, D; Connor, M; DePasquale, J; Gross, L; McDermott, V; Sykes, A

    1994-01-01

    An outline is given of an approach to the health-for-all goals which involves optimizing resource use, prioritizing people's well-being, achieving excellence and a measurable impact at all levels of care, and solving health problems in a broad developmental context.

  2. Instruction Emphasizing Effort Improves Physics Problem Solving

    ERIC Educational Resources Information Center

    Li, Daoquan

    2012-01-01

    Effectively using strategies to solve complex problems is an important educational goal and is implicated in successful academic performance. However, people often do not spontaneously use the effective strategies unless they are motivated to do so. The present study was designed to test whether educating students about the importance of effort in…

  3. Accelerated Developmental Arithmetic Using Problem Solving

    ERIC Educational Resources Information Center

    Guy, G. Michael; Cornick, Jonathan; Holt, Robert J.; Russell, Andrew S. H.

    2015-01-01

    After many years of extremely low success rates, a radical new design of the first semester arithmetic remedial course was implemented and studied. Students at a large urban community college could take a traditional semester-long traditional lecture-based remedial arithmetic course or a new accelerated 4-week 20-hour problem-solving based…

  4. Student Problem Solving in High School Genetics.

    ERIC Educational Resources Information Center

    Stewart, James

    1983-01-01

    Describes set of specific steps (procedural knowledge) used when solving monohybrid/dihybrid cross problems and extent to which students could justify execution of each step in terms of their conceptual knowledge of genetics and meiosis. Implications for genetics instruction are discussed. (JN)

  5. Teaching, Learning and Assessing Statistical Problem Solving

    ERIC Educational Resources Information Center

    Marriott, John; Davies, Neville; Gibson, Liz

    2009-01-01

    In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and…

  6. Nanomedicine: Problem Solving to Treat Cancer

    ERIC Educational Resources Information Center

    Hemling, Melissa A.; Sammel, Lauren M.; Zenner, Greta; Payne, Amy C.; Crone, Wendy C.

    2006-01-01

    Many traditional classroom science and technology activities often ask students to complete prepackaged labs that ensure that everyone arrives at the same "scientifically accurate" solution or theory, which ignores the important problem-solving and creative aspects of scientific research and technological design. Students rarely have the…

  7. Complex Problem Solving--More than Reasoning?

    ERIC Educational Resources Information Center

    Wustenberg, Sascha; Greiff, Samuel; Funke, Joachim

    2012-01-01

    This study investigates the internal structure and construct validity of Complex Problem Solving (CPS), which is measured by a "Multiple-Item-Approach." It is tested, if (a) three facets of CPS--"rule identification" (adequateness of strategies), "rule knowledge" (generated knowledge) and "rule application"…

  8. How Instructional Designers Solve Workplace Problems

    ERIC Educational Resources Information Center

    Fortney, Kathleen S.; Yamagata-Lynch, Lisa C.

    2013-01-01

    This naturalistic inquiry investigated how instructional designers engage in complex and ambiguous problem solving across organizational boundaries in two corporations. Participants represented a range of instructional design experience, from novices to experts. Research methods included a participant background survey, observations of…

  9. Problem-Solving Test: Tryptophan Operon Mutants

    ERIC Educational Resources Information Center

    Szeberenyi, Jozsef

    2010-01-01

    This paper presents a problem-solving test that deals with the regulation of the "trp" operon of "Escherichia coli." Two mutants of this operon are described: in mutant A, the operator region of the operon carries a point mutation so that it is unable to carry out its function; mutant B expresses a "trp" repressor protein unable to bind…

  10. Collaborative Problem Solving Methods towards Critical Thinking

    ERIC Educational Resources Information Center

    Yin, Khoo Yin; Abdullah, Abdul Ghani Kanesan; Alazidiyeen, Naser Jamil

    2011-01-01

    This research attempts to examine the collaborative problem solving methods towards critical thinking based on economy (AE) and non economy (TE) in the SPM level among students in the lower sixth form. The quasi experiment method that uses the modal of 3X2 factorial is applied. 294 lower sixth form students from ten schools are distributed…

  11. Nanomedicine: Problem Solving to Treat Cancer

    ERIC Educational Resources Information Center

    Hemling, Melissa A.; Sammel, Lauren M.; Zenner, Greta; Payne, Amy C.; Crone, Wendy C.

    2006-01-01

    Many traditional classroom science and technology activities often ask students to complete prepackaged labs that ensure that everyone arrives at the same "scientifically accurate" solution or theory, which ignores the important problem-solving and creative aspects of scientific research and technological design. Students rarely have the…

  12. Problem Solving in Chemistry Using Eureka.

    ERIC Educational Resources Information Center

    Chau, F. T.; Chik, Andy S. W.

    1989-01-01

    Discusses a software package that allows the user to solve mathematical problems, analyze data, plot graphs, and to examine mathematical models. Presents the attributes of the program and the available mathematical functions. Provides an example of pH calculations. (MVL)

  13. Stoichiometric Problem Solving in High School Chemistry.

    ERIC Educational Resources Information Center

    Schmidt, Hans-Jurgen

    The purpose of this descriptive study was to create and test questions on stoichiometry with number ratios for quick mental calculations and to identify students' problem-solving strategies. The present study was a component of a more comprehensive investigation in which 7,441 German senior high school students were asked to work on 154 test items…

  14. Solving Wicked Problems through Action Learning

    ERIC Educational Resources Information Center

    Crul, Liselore

    2014-01-01

    This account of practice outlines the Oxyme Action Learning Program which was conducted as part of the Management Challenge in my final year of the MSc in Coaching and Behavioral Change at Henley Business School. The central research questions were: (1) how action learning can help to solve wicked problems and (2) what the effect of an action…

  15. Facilitating problem solving in high school chemistry

    NASA Astrophysics Data System (ADS)

    Gabel, Dorothy L.; Sherwood, Robert D.

    The major purpose for conducting this study was to determine whether certain instructional strategies were superior to others in teaching high school chemistry students problem solving. The effectiveness of four instructional strategies for teaching problem solving to students of various proportional reasoning ability, verbal and visual preference, and mathematics anxiety were compared in this aptitude by treatment interaction study. The strategies used were the factor-label method, analogies, diagrams, and proportionality. Six hundred and nine high school students in eight schools were randomly assigned to one of four teaching strategies within each classroom. Students used programmed booklets to study the mole concept, the gas laws, stoichiometry, and molarity. Problem-solving ability was measured by a series of immediate posttests, delayed posttests and the ACS-NSTA Examination in High School Chemistry. Results showed that mathematics anxiety is negatively correlated with science achievement and that problem solving is dependent on students' proportional reasoning ability. The factor-label method was found to be the most desirable method and proportionality the least desirable method for teaching the mole concept. However, the proportionality method was best for teaching the gas laws. Several second-order interactions were found to be significant when mathematics anxiety was one of the aptitudes involved.

  16. Facilitating Problem Solving in High School Chemistry.

    ERIC Educational Resources Information Center

    Gabel, Dorothy L.; Sherwood, Robert D.

    1983-01-01

    Investigated superiority of instructional strategies (factor-label method, proportionality, use of analogies, use of diagrams) in teaching problem-solving related to mole concept, gas laws, stoichiometry, and molarity. Also investigated effectiveness of strategies for students (N=609) with different verbal-visual preferences, proportional…

  17. Effective Practices (Part 4): Problem Solving.

    ERIC Educational Resources Information Center

    Moursund, Dave

    1996-01-01

    Discusses the use of computers to help with problem solving. Topics include information science, including effective procedure and procedural thinking; templates; artificially intelligent agents and expert systems; and applications in education, including the goal of computer literacy for all students, and integrated software packages such as…

  18. Predicting Positive Self-Efficacy in Group Problem Solving.

    ERIC Educational Resources Information Center

    Wolf, Kay N.

    1997-01-01

    A study of 288 hospital employees engaged in problem-solving groups found that previous group problem-solving experience, educational level, work expertise, and problem-solving confidence were the best predictors of self-efficacy. (SK)

  19. Problem solving stages in the five square problem

    PubMed Central

    Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael

    2015-01-01

    According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory. PMID:26300794

  20. Problem solving stages in the five square problem.

    PubMed

    Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael

    2015-01-01

    According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory.

  1. Optimal Planning and Problem-Solving

    NASA Technical Reports Server (NTRS)

    Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg

    2008-01-01

    CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

  2. Discovering the structure of mathematical problem solving.

    PubMed

    Anderson, John R; Lee, Hee Seung; Fincham, Jon M

    2014-08-15

    The goal of this research is to discover the stages of mathematical problem solving, the factors that influence the duration of these stages, and how these stages are related to the learning of a new mathematical competence. Using a combination of multivariate pattern analysis (MVPA) and hidden Markov models (HMM), we found that participants went through 5 major phases in solving a class of problems: A Define Phase where they identified the problem to be solved, an Encode Phase where they encoded the needed information, a Compute Phase where they performed the necessary arithmetic calculations, a Transform Phase where they performed any mathematical transformations, and a Respond Phase where they entered an answer. The Define Phase is characterized by activity in visual attention and default network regions, the Encode Phase by activity in visual regions, the Compute Phase by activity in regions active in mathematical tasks, the Transform Phase by activity in mathematical and response regions, and the Respond phase by activity in motor regions. The duration of the Compute and Transform Phases were the only ones that varied with condition. Two features distinguished the mastery trials on which participants came to understand a new problem type. First, the duration of late phases of the problem solution increased. Second, there was increased activation in the rostrolateral prefrontal cortex (RLPFC) and angular gyrus (AG), regions associated with metacognition. This indicates the importance of reflection to successful learning. Copyright © 2014 Elsevier Inc. All rights reserved.

  3. An efficient algorithm for solving the gravity problem of finding a density in a horizontal layer

    NASA Astrophysics Data System (ADS)

    Akimova, Elena N.; Martyshko, Peter S.; Misilov, Vladimir E.; Kosivets, Rostislav A.

    2016-06-01

    An efficient algorithm for solving the inverse gravity problem of finding a variable density in a horizontal layer using gravitational data is constructed. After the discretization and approximation, the problem reduces to solving a system of linear algebraic equations. The idea of this algorithm is based on exploiting the block-Toeplitz structure of coefficients matrix. Utilizing this algorithm drastically reduces the memory usage, as well as the computation time. The algorithm was parallelized and implemented using the Uran supercomputer. A model problem with synthetic gravitational data was solved.

  4. Status Effects in Group Problem Solving: Group and Individual Level Analyses.

    ERIC Educational Resources Information Center

    Chiu, Ming Ming

    Eighty ninth graders who solved an algebra problem in groups of four showed status effects at the individual level. The students had filled out preactivity questionnaires about mathematical status and social status and a postactivity leadership questionnaire. Hierarchical regressions and path analyses show that, at the group level, solution score…

  5. Tracking Problem Solving by Multivariate Pattern Analysis and Hidden Markov Model Algorithms

    ERIC Educational Resources Information Center

    Anderson, John R.

    2012-01-01

    Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application…

  6. Tracking Problem Solving by Multivariate Pattern Analysis and Hidden Markov Model Algorithms

    ERIC Educational Resources Information Center

    Anderson, John R.

    2012-01-01

    Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application…

  7. Geogebra for Solving Problems of Physics

    NASA Astrophysics Data System (ADS)

    Kllogjeri, Pellumb; Kllogjeri, Adrian

    Today is highly speed progressing the computer-based education, which allowes educators and students to use educational programming language and e-tutors to teach and learn, to interact with one another and share together the results of their work. In this paper we will be concentrated on the use of GeoGebra programme for solving problems of physics. We have brought an example from physics of how can be used GeoGebra for finding the center of mass(centroid) of a picture(or system of polygons). After the problem is solved graphically, there is an application of finding the center of a real object(a plate)by firstly, scanning the object and secondly, by inserting its scanned picture into the drawing pad of GeoGebra window and lastly, by finding its centroid. GeoGebra serve as effective tool in problem-solving. There are many other applications of GeoGebra in the problems of physics, and many more in different fields of mathematics.

  8. The Effects of Schema-Broadening Instruction on Second Graders' Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study.

    PubMed

    Fuchs, Lynn S; Zumeta, Rebecca O; Schumacher, Robin Finelli; Powell, Sarah R; Seethaler, Pamela M; Hamlett, Carol L; Fuchs, Douglas

    2010-06-01

    The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students' word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students' emerging algebraic reasoning.

  9. The Effects of Schema-Broadening Instruction on Second Graders’ Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study

    PubMed Central

    Fuchs, Lynn S.; Zumeta, Rebecca O.; Schumacher, Robin Finelli; Powell, Sarah R.; Seethaler, Pamela M.; Hamlett, Carol L.; Fuchs, Douglas

    2010-01-01

    The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders’ word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students’ word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students’ emerging algebraic reasoning. PMID:20539822

  10. Students' Images of Problem Contexts when Solving Applied Problems

    ERIC Educational Resources Information Center

    Moore, Kevin C.; Carlson, Marilyn P.

    2012-01-01

    This article reports findings from an investigation of precalculus students' approaches to solving novel problems. We characterize the images that students constructed during their solution attempts and describe the degree to which they were successful in imagining how the quantities in a problem's context change together. Our analyses revealed…

  11. Giant Story Problems: Reading Comprehension through Math Problem Solving.

    ERIC Educational Resources Information Center

    Goularte, Renee

    Primary students solve "oversized" story problems using drawings, equations, and written responses, helping them understand the links between the language of story problems and the numerical representations of matching equations. The activity also includes oral language and reflective writing, thus bringing together a variety of language…

  12. A microgenetic study of insightful problem solving.

    PubMed

    Luwel, Koen; Siegler, Robert S; Verschaffel, Lieven

    2008-03-01

    An eight-session microgenetic study of acquisition of an insightful problem-solving strategy was conducted. A total of 35 second graders who did not use this insightful strategy initially were assigned to two groups that differed in the frequency of problems likely to facilitate discovery and generalization of the strategy. Children in the facilitative problems group discovered the insightful strategy earlier, used it more often subsequently, and transferred it more often to novel problems than did those in the nonfacilitative problems group. Children generally discovered the insightful strategy on the most facilitative items and extended it progressively to items on which its advantages were smaller but still substantial. The results indicate that experience outside the experimental situation, as well as experience inside the experimental situation, influences use of new strategies.

  13. A connectionist model for diagnostic problem solving

    NASA Technical Reports Server (NTRS)

    Peng, Yun; Reggia, James A.

    1989-01-01

    A competition-based connectionist model for solving diagnostic problems is described. The problems considered are computationally difficult in that (1) multiple disorders may occur simultaneously and (2) a global optimum in the space exponential to the total number of possible disorders is sought as a solution. The diagnostic problem is treated as a nonlinear optimization problem, and global optimization criteria are decomposed into local criteria governing node activation updating in the connectionist model. Nodes representing disorders compete with each other to account for each individual manifestation, yet complement each other to account for all manifestations through parallel node interactions. When equilibrium is reached, the network settles into a locally optimal state. Three randomly generated examples of diagnostic problems, each of which has 1024 cases, were tested, and the decomposition plus competition plus resettling approach yielded very high accuracy.

  14. Human Problem Solving in Fault Diagnosis Tasks

    DTIC Science & Technology

    1986-04-01

    W - FPFag-kx~~ff~P~xNA F MMIP Research Note 86-33 cc HUMAN PROBLEM SOLVING IN FAULT DIAGNOSIS TASKS J U William B. Rouse and Ruston M. Hunt Center...V -m ... 1 Ira wli W - -. W .: m.4.. . W - r - j ; - R 7T._ W77 m- UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Date Entered) REPORT...ii SECURITY CLASSIFICATION OF THIS PAGE( W "en Data Entered) ,.-... 2

  15. Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

    ERIC Educational Resources Information Center

    Parulekar, Satish J.

    2006-01-01

    Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

  16. Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

    ERIC Educational Resources Information Center

    Parulekar, Satish J.

    2006-01-01

    Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

  17. Comprehension and computation in Bayesian problem solving

    PubMed Central

    Johnson, Eric D.; Tubau, Elisabet

    2015-01-01

    Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point. PMID:26283976

  18. Comprehension and computation in Bayesian problem solving.

    PubMed

    Johnson, Eric D; Tubau, Elisabet

    2015-01-01

    Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on "transparent" Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point.

  19. Exploiting Quantum Resonance to Solve Combinatorial Problems

    NASA Technical Reports Server (NTRS)

    Zak, Michail; Fijany, Amir

    2006-01-01

    Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

  20. Mathematical Problem Solving: A Review of the Literature.

    ERIC Educational Resources Information Center

    Funkhouser, Charles

    The major perspectives on problem solving of the twentieth century are reviewed--associationism, Gestalt psychology, and cognitive science. The results of the review on teaching problem solving and the uses of computers to teach problem solving are included. Four major issues related to the teaching of problem solving are discussed: (1)…