Hundred Chart Challenge

Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. In this month's Problem Solvers Solutions, readers have a window into students' number and operation sense in the early elementary grades. Second and third graders were presented with problem-solving tasks using a hundred chart consisting of two number cards and a challenge card aligned to an addition or subtraction structure. Drawing on the structure of the hundred chart and prior knowledge, students were able to articulate their solution strategies.

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Which lake is bigger?

Teaching Children Mathematics ◽

10.5951/teacchilmath.23.4.0212 ◽

2016 ◽

Vol 23 (4) ◽

pp. 212-214

Author(s):

Reagan Bachour ◽

Sarah Braun ◽

Andrew M. Tyminski

Keyword(s):

Problem Solving ◽

Elementary Students ◽

Third Graders ◽

Early Elementary ◽

Area And Perimeter ◽

Problem Solvers

Each month, this section of the problem solvers department showcases students' in-depth thinking and discusses classroom results of using problems from previous issues of Teaching Children Mathematics. In these solutions to the November 2015 problem, readers have a window into early elementary students' problem solving and understanding of measurement. Third graders were presented with tasks using maps of two lakes and various manipulatives to determine the bigger lake. Students discovered and were able to articulate that identifying the bigger lake depends on the attributes, area, and perimeter explored and that different attributes could result in different solutions.

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Relationship of Arithmetic Problem Solving and Reflective—Impulsive Cognitive Styles in Third-Grade Students

Psychological Reports ◽

10.2466/pr0.1999.85.1.179 ◽

1999 ◽

Vol 85 (1) ◽

pp. 179-186 ◽

Cited By ~ 2

Author(s):

Jose I. Navarro ◽

Manuel Aguilar ◽

Concha Alcalde ◽

Richard Howell

Keyword(s):

Problem Solving ◽

Cognitive Style ◽

Cognitive Styles ◽

Third Graders ◽

Arithmetic Problem ◽

Third Grade Students ◽

Mathematical Problems ◽

Figure Test ◽

Problem Solvers ◽

Relationship Of

Different individuals approach mathematical problems in a variety of ways, with these different approaches also reflected in over-all cognitive styles. This investigation had two purposes, first, to determine whether good and poor arithmetic problem solvers differ substantially in cognitive style, and second, to determine whether the students, after training in techniques of solving arithmetic problems, improve their performance with no significant change in cognitive style. A total of 98 third graders participated (mean age 8.1 yr.; 50 boys, 48 girls). The Matching Familiar Figure Test was used to classify the students by cognitive style as either Reflective or Impulsive. Students also were given training with different problem-solving exercises for different arithmetic problems. The training program in problem-solving strategies did not improve performance on arithmetic problems for Reflective students; however, Impulsive students' performance did improve after training.

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Systems thinking, a consilience of values and logic

Human Systems Management ◽

10.3233/hsm-2005-24402 ◽

2005 ◽

Vol 24 (4) ◽

pp. 259-274

Author(s):

Sameer Kumar ◽

Thomas Ressler ◽

Mark Ahrens

Keyword(s):

Decision Making ◽

Problem Solving ◽

Systems Thinking ◽

Qualitative Reasoning ◽

Colleges And Universities ◽

Decision Makers ◽

Modern World ◽

Problem Solving Process ◽

Problem Solvers

This article is an appeal to incorporate qualitative reasoning into quantitative topics and courses, especially those devoted to decision-making offered in colleges and universities. Students, many of whom join professional workforce, must become more systems thinkers and decision-makers than merely problem-solvers. This will entail discussion of systems thinking, not just reaching “the answer”. Managers will need to formally and forcefully discuss objectives and values at each stage of the problem-solving process – at the start, during the problem-solving stage, and at the interpretation of the results stage – in order to move from problem solving to decision-making. The authors suggest some methods for doing this, and provide examples of why doing so is so important for decision-makers in the modern world.

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Good problem solvers? Leveraging knowledge sharing mechanisms and management support

Journal of Knowledge Management ◽

10.1108/jkm-05-2018-0290 ◽

2019 ◽

Vol 23 (6) ◽

pp. 1017-1038 ◽

Cited By ~ 2

Author(s):

Ambra Galeazzo ◽

Andrea Furlan

Keyword(s):

Transformational Leadership ◽

Problem Solving ◽

Knowledge Sharing ◽

Hierarchical Linear Modeling ◽

Shop Floor ◽

Management Support ◽

Linear Modeling ◽

Content Type ◽

Problem Solvers ◽

Good Problem

Purpose Organizational learning relies on problem-solving as a way to generate new knowledge. Good problem solvers should adopt a problem-solving orientation (PSO) that analyzes the causes of problems to arrive at an effective solution. The purpose of this paper is to investigate this relevant, though underexplored, topic by examining two important antecedents of PSO: knowledge sharing mechanisms and transformational leaders’ support. Design/methodology/approach Hierarchical linear modeling analyses were performed on a sample of 131 workers in 12 plants. A questionnaire was designed to collect data from shop-floor employees. Knowledge sharing was measured using the mechanisms of participative practices and standardized practices. Management support was assessed based on the extent to which supervisors engaged in transformational leadership. Findings Knowledge sharing mechanisms are an antecedent of PSO behavior, but management support measured in terms of transformational leadership is not. However, transformational leadership affects the use of knowledge sharing mechanisms that, in turn, is positively related to PSO behavior. Practical implications The research provides practical guidance for practitioners to understand how to manage knowledge in the workplace to promote employees’ PSO behaviors. Originality/value Though problem-solving activities are intrinsic in any working context, PSO is still very much underrepresented and scarcely understood in knowledge management studies. This study fills this gap by investigating the antecedents of PSO behavior.

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The Effects of Context-based Problem-solving Tasks on Students’ Interest and Metacognitive Experiences

Open Education Studies ◽

10.1515/edu-2020-0118 ◽

2020 ◽

Vol 2 (1) ◽

pp. 112-125

Author(s):

Marcela Pozas ◽

Patrick Löffler ◽

Wolfgang Schnotz ◽

Alexander Kauertz

Keyword(s):

Problem Solving ◽

Prior Knowledge ◽

Situational Interest ◽

Analysis Of Covariance ◽

Task Characteristics ◽

Factor Analyses ◽

Subject Factor ◽

Problem Solving Process ◽

High Track ◽

Metacognitive Experiences

AbstractPrior knowledge, motivational factors, and metacognition have been long considered basic elements for successful problem-solving process. However, the interplay of these variables with context-based task characteristics has rarely been explored in research. The present study aimed at investigating how context-based task characteristics influence these three elements, and further expands to explore potential differentiated effects across physics’ topics. A multivariate analysis of covariance was conducted with 232 participants from high-track schools in Germany to investigate the effects of task characteristics and task topic with regard to their motivational and metacognitive variables. Overall results indicated that students’ situational interest and estimate of solution correctness decrease through time as a result from their interaction with the tasks characteristics. Furthermore, between-subject factor analyses revealed important differences across the task topics of mechanics and thermodynamics. Finally, the covariate of prior knowledge was positively significant across all analyses. The findings demonstrate the importance of appropriate design of context-based tasks to positively influence students’ motivation and metacognitive processing. Implications of the results, as well as further lines of research are discussed.

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Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

International Education Studies ◽

10.5539/ies.v10n1p1 ◽

2016 ◽

Vol 10 (1) ◽

pp. 1 ◽

Cited By ~ 2

Author(s):

Jackson Pasini Mairing

Keyword(s):

Problem Solving ◽

Procedural Knowledge ◽

Mental Image ◽

Research Subjects ◽

Maximum Score ◽

Mathematical Problems ◽

Problem Solving Strategies ◽

Thinking Process ◽

Problem Solvers ◽

Holistic Rubric

Solving problem 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 the thinking process of naive problem solvers based on heuristic of Polya. The researcher gave two problems to students at grade XI from one of high schools in Palangka Raya, Indonesia. The research subjects were two students with problem solving scores of 0 or 1 for both problems (naive problem solvers). The score was determined by using a holistic rubric with maximum score of 4. Each subject was interviewed by the researcher separately based on the subject’s solution. The results showed that the naive problem solvers read the problems for several times in order to understand them. The naive problem solvers could determine the known and the unknown if they were written in the problems. However, they faced difficulties when the information in the problems should be processed in their mindsto construct a mental image. The naive problem solvers were also failed to make an appropriate plan because they did not have a problem solving schema. The schema was constructed by the understanding of the problems, conceptual and procedural knowledge of the relevant concepts, knowledge of problem solving strategies, and previous experiences in solving isomorphic problems.

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Effectiveness of a Problem-Solving Training Program

Psychological Reports ◽

10.2466/pr0.1995.76.2.507 ◽

1995 ◽

Vol 76 (2) ◽

pp. 507-514 ◽

Cited By ~ 7

Author(s):

Johan W. Wege ◽

André T. Möller

Keyword(s):

Problem Solving ◽

Training Program ◽

Undergraduate Students ◽

Internal Control ◽

Self Efficacy ◽

Group Analysis ◽

External Control ◽

Problem Solving Skills ◽

Control Orientation ◽

Problem Solvers

The relationship between problem-solving efficiency, defined in terms of the quality of alternative soludons selected, and measures of behavioral competence (self-efficacy and locus of control) was investigated as well as the effectiveness of a problem-solving training program. Subjects were 29 undergraduate students assigned to an effective ( n = 16) and an ineffective ( n = 13) problem-solving group. Analysis indicated that the ineffective problem-solvers appraised their problem-solving skills more negatively and reported low self-efficacy expectations and an external control orientation. Problem-solving training led to improved general self-efficacy expectancies, greater confidence in problem-solving, a more internal control orientation, and improved problem-solving skills. These improvements were maintained at follow-up after two months.

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