Downloads and Free Reading Options

We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and decycling operations by a new one, called cyclic sliding, which appears to be a more natural choice. We give an analysis of the complexity of our algorithm in terms of fundamental operations with simple elements, so our analysis is valid for every Garside group. This paper intends to be self-contained, not requiring any previous knowledge of prior algorithms, and includes all the details for the algorithm to be implemented on a computer.

This study determined the effects of assigning students from speech classes to one of 14 positive sociometrically determined groups, 14 negative sociometrically determined groups, or 14 randomly determined groups upon individuals' satisfaction with the group and the time needed to solve a specific test problem. All significant differences among the five- and six-person groups showed that individuals in positively oriented groups were more satisfied after solving the problem than those from negatively oriented or randomly assigned groups. Observed differences showed that individuals from random groups were more satisfied than individuals from negative groups. This study indicated that positive sociometric assignment of individuals to problem solving groups produces increased satisfaction. (Author)

The hybrid nature of an electronic meeting system (EMS)-as a communication medium and as a manager of diversity-offers organizations an excellent vehicle for improving group performance, handling stress, and building cohesive teams. This report describes a project that examined the performance and behavior of various decision making groups using an EMS in face-to-face and dispersed settings. Results of this study suggest that the proper task-technology-team fit is a critical factor in determining outcomes. In other words, homogeneous groups needing to discuss issues and resolve ambiguities may require face-to-face meetings, while diverse groups may be able to accomplish the same tasks in dispersed settings using an EMS. However, where the goal is information exchange and uncertainty reduction, lean media such as dispersed EMS may be used just as effectively as any other media by all groups, regardless of their degree of diversity.

The hybrid nature of an electronic meeting system (EMS)-as a communication medium and as a manager of diversity-offers organizations an excellent vehicle for improving group performance, handling stress, and building cohesive teams. This report describes a project that examined the performance and behavior of various decision making groups using an EMS in face-to-face and dispersed settings. Results of this study suggest that the proper task-technology-team fit is a critical factor in determining outcomes. In other words, homogeneous groups needing to discuss issues and resolve ambiguities may require face-to-face meetings, while diverse groups may be able to accomplish the same tasks in dispersed settings using an EMS. However, where the goal is information exchange and uncertainty reduction, lean media such as dispersed EMS may be used just as effectively as any other media by all groups, regardless of their degree of diversity.

Discourse, especially dialogic communication between students in collaborative problem-solving groups, plays a central role in educational reforms informed by learning science. This study examined the quality of discourse in problem-based learning groups in a university course. The study found a low incidence of high quality dialogue (dialogic communication, elaboration and co-construction of ideas, productive disciplinary discourse) in 12 one-hour planning meetings. The most competent students took leadership in groups and made the majority of the conceptual contributions. Although there was a reasonable amount of time spent connecting theories to cases, there was little time spent in high-level analysis and very few instances of true dialogic discourse. The majority of time was devoted to activities involving organizing, planning and logistics and organizing the presentation. There was very little off-task behavior.

Discourse, especially dialogic communication between students in collaborative problem-solving groups, plays a central role in educational reforms informed by learning science. This study examined the quality of discourse in problem-based learning groups in a university course. The study found a low incidence of high quality dialogue (dialogic communication, elaboration and co-construction of ideas, productive disciplinary discourse) in 12 one-hour planning meetings. The most competent students took leadership in groups and made the majority of the conceptual contributions. Although there was a reasonable amount of time spent connecting theories to cases, there was little time spent in high-level analysis and very few instances of true dialogic discourse. The majority of time was devoted to activities involving organizing, planning and logistics and organizing the presentation. There was very little off-task behavior.

This study examined the problem-solving behaviors, strategies, and achievement of college students enrolled in a one-semester college algebra and statistics course, with respect to the content areas of quantitative literacy, connections between algebraic and graphical representations, and mathematical modeling. Four instructional units of this course were chosen, two in which the students were assigned to cooperative-learning groups and two in which the students worked independently. The findings suggest that students who work in cooperative learning groups clearly exhibit important problem-solving behaviors such as persistence and a willingness to explore alternative solutions; however, they still experience difficulty explicating the connections between mathematical actions and/or processes and the related mathematical concepts. (Author)

1 volume (various pagings) : 21 cm

Problem solving task design is not only the design of a non-routine problem to be solves by the students. Our task design also requires a supporting document, the practical worksheet, which would act as a cognitive scaffold for the students in the initial stages of the problem solving process before they can internalize the metacognitive strategies and automate the use of these strategies when faced with a new problem. A further enhancement of the scaffolding that can be provided by the teacher as she facilitates forty or more students working on the practical worksheet is a set of scaffolding cards. In this paper, we describe the cards and the preliminary use of these cards to facilitate problem solving for teachers in a professional development workshop.

A number of theoretical and practical issues are explored that need to be considered in the design of assessments that use group collaboration to be sure that collaboration works toward, rather than away from, the purpose of the assessment. The traditional purpose of assessment has been to measure individual competence of students in thinking skills and subject matter knowledge. A second purpose can be to measure how well students can perform after they have been given an opportunity to learn from group collaboration. Another purpose is to measure group productivity, and a fourth is to measure student ability to collaborate and function as part of a team. The purpose of the assessment, the goal of group work, and the group processes must be specified clearly and must be measurable. Evaluation procedures and criteria must be consistent with the goal of group work. Students do not automatically know how to work with others, and must be prepared for group assessments. A variety of strategies are suggested for preparation and effective collaboration. (Contains 119 references.) (SLD)

The 1972 publication of the Marland Report by the U.S. Commissioner of Education proposed a multifaceted definition of gifted and talented education, enhancing what traditionally had been a focus on academics. Leadership materialized as a component of giftedness, along with general intellectual ability, specific academic aptitude, creative or productive thinking, visual and performing arts, and psychomotor ability (Foster, 1981; Karnes, Riley, & McGinnis, 1996). States, including but not limited to Indiana, Oklahoma, Texas, Idaho, and Colorado, all define giftedness in their state education codes as including a high or unusual capacity for leadership (Stephens & Karnes, 2000). Definitions of giftedness and subsequently leadership at both the federal and state levels of government present an ongoing struggle between one based on governmental policy and one that can be conceptually and empirically defined (Foster). The inclusion of leadership in state education definitions of giftedness necessitates measures to identify those with leadership qualities; however, few exist. The measurements that are available possess marginal psychometric properties or are not normed for this specific population (Oakland, Falkenberg, & Oakland, 1996).

Social Problem Solving for Child Scale is frequently used to determine behavioral problems of children with their own word and to identify ways of conflict encountered in daily life, and interpersonal relationships in abroad. The primary purpose of this study was to adapt the Wally Child Social Problem-Solving Detective Game Test. In order to determine validity of 6 years old children (208-52% female and 192 male-48%) scale, data exploratory and confirmatory factor analyses were conducted. Exploratory factor analysis (EFA) identified two factor accounting for 46.534% of the variance. The confirmatory factor analyses results indicated that the factor structure was partially consistent with the model. Cronbach Alpha internal consistency coefficients were 0.88 for general scale, were 0.86 and 0.73 for subscales. Spearman-Brown coefficients were 0.80 for general scale, were 0.81 and 0.75 for subscales. The secondary purpose of this study was to determine whether social problem solving of children predicted preschool behavior problem, and gender and socio-cultural level variables predicted social problem solving. The results showed that whereas subscales of social problem solving of the students significantly predicted subscales of preschool behavior problem, gender and socio-cultural level did not significantly predicted social problem solving of children.

For this project, groups of Army captains were tested in a problem solving exercise called VARWARS. Normally in VARWARS exercises, groups use a naturalistic problem solving process characterized by sequential elaboration and development of possible solutions, rather than a concurrent comparison of options. In the first experiment, an attempt was made to induce some groups to use a concurrent option comparison method. It proved possible to increase the likelihood of groups using the method; however, this did not result in an improvement in solution quality. In the second experiment, groups were induced to use a different method, called Early Decision, in which the groups were compelled to select a single candidate solution much sooner than they normally would. The Early Decision process resulted in a significant and substantial improvement in the quality of solutions, compared with both naturalistic and concurrent comparison methods.

Students' frequent exposure to inquiry-based science teaching is presumed more effective than their exposure to traditional didactic instruction in helping improve competence in content knowledge and problem solving. Framed through theoretical perspectives of inquiry-based instruction and culturally relevant pedagogy, this study examines this assumption using TIMSS 2007 US eighth-grade student data. Data analysis revealed three instructional approaches, including more inquiry based, mixed, and practice based, were popularly practiced in classrooms. More inquiry-based instruction was not significantly associated with content and problem solving achievements across Caucasian, African American, and Hispanic American students. The mixed teaching approach had a significant positive relationship for Hispanic American student's content and problem solving achievement. The relationship between practice-based approach with content and problem solving achievements of all three racial/ethnic groups were not significant. This study questions the popular assumption of the effectiveness of science teaching approaches and offers important implications for science teaching reform.

This study aims to investigate problem-solving differences between real groups and nominal groups.

This study aims to investigate problem-solving differences between real groups and nominal groups.

Full study of small group communication must include consideration of task and socio-emotional dimensions, especially in relation to group problem solving. Thirty small groups were tested for their reactions in various "ad hoc" conflict resolution situations. Instructions to the groups were (1) no problem-solving instructions (control), (2) reflective thinking instructions, (3) conflict management instructions, and (4) instructions combining reflective thinking and conflict management. Posttesting yielded group satisfaction, perception of tension, and expression of disagreement. Results showed that there were no significant differences among the various groups and approaches. These findings contradict earlier published research using managed conflict instruction. (CH)

To determine what factors either alone or together interact to create ethnic variations in mental health care use in the State of Hawaii, a study interviewed subjects who were randomly selected from the higher income area of Diamond Head/Kahala and the lower income area of Kalihi/Palama. Ethnic groups studied included Caucasian, Japanese, Chinese, Filipino, and Hawaiian/part Hawaiian. The interviewees were of the same sex and ethnic extraction as the persons they interviewed. Responses indicated the following: (1) no significant differences among ethnic groups on what constitutes a "problem" but significant ethnic differences in the quality and the ranking of problems experienced; (2) no significant ethnic differences in the occurrence of stress symptoms during either the open-ended or the structured portions of the interview; (3) no significant differences between ethnic groups in regard to help-seeking behaviors; (4) significantly more male worry and sleeplessness over job-related problems but significantly more female depression, anger, and physical distress from family problems; and (5) no significant group differences in the level of satisfaction with help received. Appendixes include listings of respondents' occupations by ethnic group, types and frequency of problems, and frequencies of help-seeking behaviors cited. (HOD)

One of the most interesting questions about a group is if its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists and geometers, and is the target of intensive current research. We look at the braid group from a topological point of view (rather than a geometrical one). The braid group is defined by the action of diffeomorphisms on the fundamental group of a punctured disk. We exploit the topological definition of the braid group in order to give a new approach for solving its word problem. Our algorithm is faster, in comparison with known algorithms, for short braid words with respect to the number of generators combining the braid, and it is almost independent of the number of strings in the braids. Moreover, the algorithm is based on a new computer presentation of the elements of the fundamental group of a punctured disk. This presentation can be used also for other algorithms.

One of the most interesting questions about a group is if its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists and geometers, and is the target of intensive current research. We look at the braid group from a topological point of view (rather than a geometrical one). The braid group is defined by the action of diffeomorphisms on the fundamental group of a punctured disk. We exploit the topological definition of the braid group in order to give a new approach for solving its word problem. Our algorithm is faster, in comparison with known algorithms, for short braid words with respect to the number of generators combining the braid, and it is almost independent of the number of strings in the braids. Moreover, the algorithm is based on a new computer presentation of the elements of the fundamental group of a punctured disk. This presentation can be used also for other algorithms.

Click here to view the University of Florida catalog record

The purpose of this exploratory study was to examine the problem-solving behaviors and perceptions of (n=27) seventh-grade students as they worked on solving a mathematical problem within a small-group setting. An assessment system was developed that allowed for this analysis. To assess problem-solving behaviors within a small group a Group Problem Solving Assessment Instrument was developed. To assess student perceptions a stimulated-recall interview was used. Data were obtained through videotapes of the students working in small groups and audiotapes of stimulated-recall interviews of the individual students. The results suggest the importance of higher level processes used when students talk about the problem with their peers. A continuous interplay of talking about the problem and doing the problem appeared to be necessary for successful problem solving and maximum student involvement. Perceptions, particularly those of higher and lower-ability students, provided an understanding of the observed problem-solving behaviors within groups. The assessment system shows promise of being a powerful tool for examining the internal dynamics of mathematical problem solving in a small-group setting. Contains 25 references. (Author)

The purpose of the research is to explore second graders' concept of number development and quantitative reasoning. For this purpose, there were two stages of trials for the children. The first trial was concrete objects. After three months, the children participated in the second trial of half concrete objects. Since understanding the process of solving problems in children is necessary, the researcher observed how children used strategies to discriminate numerosity. After that, the researcher interviewed some students. The research sample came from second graders in Taiwan and Hawaii elementary schools. Twenty students participated in each place. In addition, it was observed whether numerical discrimination strategy in children is the same as in adults. The sample included 20 adults. The result of the research showed that Taiwanese and Hawaiian children reached up to a 90% rate of correct answers in the trial of real objects. However, in the trial of half concrete objects, the rate of correct answers was down to 65%, especially when children compared two quantities of 5:6 ratios. As for strategy, the strategies of the children who gave correct answers were the same as the adults who gave completely correct answers. Because their discrimination was not influenced by distance effect, they could judge the numbers correctly. However, the children who got 90% correct answers were impacted by distance effect, but not influenced by the size of the object. The research suggests that teachers give children real objects to estimate or discriminate the quantities of numbers in their lives. (Contains 2 tables.)

In introductory psychology courses, the desire to cover content can conflict with the desire to acquaint students with psychological thinking processes. The IDEAL method is a group problem solving quiz technique which addresses both of these goals. In the process, instructors choose key concepts from a given reading and divide the class into groups of four to six students. Each member of each group then chooses a concept to specialize in, completing concept sheets which compare and contrast their concept to other assigned concepts. Groups then determine how to apply their understandings of their concepts to common situations, such as when an individual decides to accompany a group to an event that they do not believe will be enjoyable. Testing is conducted in essentially the same format, with quizzes evaluated on the basis of how aspects of the scenario exemplify the concept in action or how the students apply the concept to the scenario in order to address the question. The advantages of this method for psychology classes are that it makes use of student learning and gives them practice with problem solving, critical thinking, and group interaction skills while teaching the content of the subject area. A disadvantage is that the amount of material covered must be reduced to allow for time spent on problem solving techniques and teamwork skills. A sample concept sheet is appended. (TGI)

In introductory psychology courses, the desire to cover content can conflict with the desire to acquaint students with psychological thinking processes. The IDEAL method is a group problem solving quiz technique which addresses both of these goals. In the process, instructors choose key concepts from a given reading and divide the class into groups of four to six students. Each member of each group then chooses a concept to specialize in, completing concept sheets which compare and contrast their concept to other assigned concepts. Groups then determine how to apply their understandings of their concepts to common situations, such as when an individual decides to accompany a group to an event that they do not believe will be enjoyable. Testing is conducted in essentially the same format, with quizzes evaluated on the basis of how aspects of the scenario exemplify the concept in action or how the students apply the concept to the scenario in order to address the question. The advantages of this method for psychology classes are that it makes use of student learning and gives them practice with problem solving, critical thinking, and group interaction skills while teaching the content of the subject area. A disadvantage is that the amount of material covered must be reduced to allow for time spent on problem solving techniques and teamwork skills. A sample concept sheet is appended. (TGI)

It can be difficult to find adequate strategies when teaching problem solving in a standard based mathematics classroom. The purpose of this study was to improve students' problem solving skills and attitudes through differentiated instruction when working on lengthy performance tasks in cooperative groups. This action research studied for 15 days whether students in a treatment group (n = 28), who were grouped by learning styles (auditory, kinesthetic, and visual), would display greater ability learning the standards or display better attitudes towards problem solving when compared to a control group (n = 28) who were grouped in random cooperative groups. When the qualitative and quantitative data were analyzed, the results demonstrated that the treatment group did not show significant gains when compared to random cooperative groups. The following are appended: (1) Instructional Unit Plan: Quadratic Investigations; (2) Peer-Review Instructional Plan Rubric; (3) Unit 5 Math I Test: Factoring and Solving Quadratics; (4) Student Problem Solving Attitudes Scale; (5) Performance Task Answer Sheet; (6) Product Grading Rubric; (7) Learning Channel Preference; (8) Learning Style Menu; (9) Note Taking for Reflective Journal; (10) Reflective Journal Prompts; and (11) Learning Style Survey. (Contains 12 tables.)

Twelve groups of five to seven college students each were randomly formed and assigned one of two decision-making tasks as part of a study of the relational, or control, dimension of interpersonal communication. Group discussions were recorded and transcribed for analysis of act, interact, and double interact patterns. Results indicated significant variance of interaction patterns with the difficulty of the task, a nonsignificant relationship between interaction structure and performance outputs, a tendency for interaction structure to increase as the level of analysis moved from the act to the interact to the double interact, and, in contrast to existing data, smaller interaction structure values and more one-upmanship. (Author/AA)