Strategies and Precise Vocabulary Knowledge: Exploring the Relationships Among Mathematics Vocabulary, Problem Solving, and Confidence

In this action research study I focused on my eighth grade pre-algebra students’ abilities to attack problems with enthusiasm and self confidence whether they completely understand the concepts or not. I wanted to teach them specific strategies and introduce and use precise vocabulary as a part of the problem solving process in hopes that I would see students’ confidence improve as they worked with mathematics. I used non-routine problems and concept-related open-ended problems to teach and model problem solving strategies. I introduced and practiced communication with specific and precise vocabulary with the goal of increasing student confidence and lowering student anxiety when they were faced with mathematics problem solving. I discovered that although students were working more willingly on problem solving and more inclined to attempt word problems using the strategies introduced in class, they were still reluctant to use specific vocabulary as they communicated to solve problems. As a result of this research, my style of teaching problem solving will evolve so that I focus more specifically on strategies and use precise vocabulary. I will spend more time introducing strategies and necessary vocabulary at the beginning of the year and continue to focus on strategies and process in order to lower my students’ anxiety and thus increase their self confidence when it comes to doing mathematics, especially problem solving.

Problem Solving Policing: Views of Citizens and Citizens Expectations in Germany

For the last two decades American police experts developed new police philosophies in order to tackle more successful the increasing crime problems. Community Policing tries to improve the cooperation between the population and the police and to increase the trust in the police. A crucial factor is a meaningful cooperation between the police and the citizens. Problem Oriented Policing aims at structural changes in the organisation and the procedures of the police in public. The police have to investigate the hidden problems and conflicts of an individual offence and to create proactive and long term concepts for the social area of conflicts beyond the specific case. It is doubtful whether these philosophies can be implemented in Germany since the legality principle prohibits meaningful, trustworthy relationships between citizens and police officers. However, if one examines the results of surveys on citizens views and expectations towards the police one finds that the majority of the German citizens favour the postulates of community and problem oriented policing. They expect through these measures an improvement of their life situation in the community and the feelings of safety. If one takes these results seriously one has to question if the legality principle is still appropriate. It seems to hamper new, more promising policing styles which seem to improve life of it's citizens and reflect what the citizens want and expect from their police force.

The Effect of Proximity, Explicitness, and Representation of Basic Science Information on Student Clinical Problem-Solving

Problem: Medical and veterinary students memorize facts but then have difficulty applying those facts in clinical problem solving. Cognitive engineering research suggests that the inability of medical and veterinary students to infer concepts from facts may be due in part to specific features of how information is represented and organized in educational materials. First, physical separation of pieces of information may increase the cognitive load on the student. Second, information that is necessary but not explicitly stated may also contribute to the student’s cognitive load. Finally, the types of representations – textual or graphical – may also support or hinder the student’s learning process. This may explain why students have difficulty applying biomedical facts in clinical problem solving. Purpose: To test the hypothesis that three specific aspects of expository text – the patial distance between the facts needed to infer a rule, the explicitness of information, and the format of representation – affected the ability of students to solve clinical problems. Setting: The study was conducted in the parasitology laboratory of a college of veterinary medicine in Texas. Sample: The study subjects were a convenience sample consisting of 132 second-year veterinary students who matriculated in 2007. The age of this class upon admission ranged from 20-52, and the gender makeup of this class consisted of approximately 75% females and 25% males. Results: No statistically significant difference in student ability to solve clinical problems was found when relevant facts were placed in proximity, nor when an explicit rule was stated. Further, no statistically significant difference in student ability to solve clinical problems was found when students were given different representations of material, including tables and concept maps. Findings: The findings from this study indicate that the three properties investigated – proximity, explicitness, and representation – had no statistically significant effect on student learning as it relates to clinical problem-solving ability. However, ad hoc observations as well as findings from other researchers suggest that the subjects were probably using rote learning techniques such as memorization, and therefore were not attempting to infer relationships from the factual material in the interventions, unless they were specifically prompted to look for patterns. A serendipitous finding unrelated to the study hypothesis was that those subjects who correctly answered questions regarding functional (non-morphologic) properties, such as mode of transmission and intermediate host, at the family taxonomic level were significantly more likely to correctly answer clinical case scenarios than were subjects who did not correctly answer questions regarding functional properties. These findings suggest a strong relationship (p < .001) between well-organized knowledge of taxonomic functional properties and clinical problem solving ability. Recommendations: Further study should be undertaken investigating the relationship between knowledge of functional taxonomic properties and clinical problem solving ability. In addition, the effect of prompting students to look for patterns in instructional material, followed by the effect of factors that affect cognitive load such as proximity, explicitness, and representation, should be explored.

A Language to Formalize and to Operationalize Problem-solving Strategies of Structured Knowledge Models

This paper describes a proposal of a language called Link which has been designed to formalize and operationalize problem solving strategies. This language is used within a software environment called KSM (Knowledge Structure Manager) which helps developers in formulating and operationalizing structured knowledge models. The paper presents both its syntax and dynamics, and gives examples of well-known problem-solving strategies of reasoning formulated using this language.

The role of computational logic as a hinge paradigm among deduction, problem solving, programming, and parallelism

This paper presents some brief considerations on the role of Computational Logic in the construction of Artificial Intelligence systems and in programming in general. It does not address how the many problems in AI can be solved but, rather more modestly, tries to point out some advantages of Computational Logic as a tool for the AI scientist in his quest. It addresses the interaction between declarative and procedural views of programs (deduction and action), the impact of the intrinsic limitations of logic, the relationship with other apparently competing computational paradigms, and finally discusses implementation-related issues, such as the efficiency of current implementations and their capability for efficiently exploiting existing and future sequential and parallel hardware. The purpose of the discussion is in no way to present Computational Logic as the unique overall vehicle for the development of intelligent systems (in the firm belief that such a panacea is yet to be found) but rather to stress its strengths in providing reasonable solutions to several aspects of the task.

School and community : partners in problem-solving /

Includes bibliographical references.

Post-war economic policy and planning. Preliminary report of the Special committee on post-war economic policy and planning, pursuant to S.Res.102, a resolution creating a Special committee on post-war economic policy and planning ... [and Report[s]].

Submitted by Mr. George.

The role of software tools in influencing creative problem solving in engineering design and education

Creativity is increasingly recognised as an essential component of engineering design. This paper describes an exploratory study into the nature and importance of creativity in engineering design problem solving in relation to the possible impact of software design tools. The first stage of the study involved an empirical investigation in the form of a case study of the use of standard CAD tool sets and the development of a systems engineering software support tool. It was found that there were several ways in which CAD influenced the creative process, including enhancing visualisation and communication, premature fixation, circumscribed thinking and bounded ideation. The tool development experience uncovered the difficulty in supporting creative processes from the developer's perspective. The issues were the necessity of making assumptions, achieving a balance between structure and flexibility, and the pitfalls of satisfying user wants and needs. The second part of the study involved the development of a model of the creative problem solving process in engineering design. This provided a possible explanation for why purpose designed engineering software tools might encourage an analytical problem solving approach and discourage a more creative approach.

A study of the problem solving strategies used by expert and novice designers

This research project focused upon the design strategies adopted by expert and novice designers. It was based upon a desire to compare the design problem solving strategies of novices, in this case key stage three pupils studying technolgy within the United Kingdom National Curriculum, with designers who could be considered to have developed expertise. The findings helped to provide insights into potential teaching strategies to suit novice designers. Verbal protocols were made as samples of expert and novice designers solved a design problem and talked aloud as they worked. The verbalisations were recorded on video tape. The protocols were transcribed and segmented, with each segment being assigned to a predetermined coding system which represented a model of design problem solving. The results of the encoding were analysed and consideration was also given to the general design strategy and heuristics used by the expert and novice designers. The drawings and models produced during the generation of the protocols were also analysed and considered. A number of significant differences between the problem solving strategies adopted by the expert and novice designers were identified. First of all, differences were observed in the way expert and novice designers used the problem statement and solution validation during the process. Differences were also identified in the way holistic solutions were generated near the start of the process, and also in the cycles of exploration and the processes of integration. The way design and technological knowledge was used provided further insights into the differences between experts and novices, as did the role of drawing and modelling during the process. In more general terms, differences were identified in the heuristics and overall design strategies adopted by the expert and novice designers. The above findings provided a basis for discussing teaching strategies appropriate for novice designers. Finally, opportunities for future research were discussed.

A systems and cybernetic perspective on complex problem solving

This thesis is concerned with Organisational Problem Solving. The work reflects the complexities of organisational problem situations and the eclectic approach that has been necessary to gain an understanding of the processes involved. The thesis is structured into three main parts. Part I describes the author's understanding of problems and suitable approaches. Chapter 2 identifies the Transcendental Realist (TR) view of science (Harre 1970, Bhaskar 1975) as the best general framework for identifying suitable approaches to complex organisational problems. Chapter 3 discusses the relationship between Checkland's methodology (1972) and TR. The need to generate iconic (explanatory) models of the problem situation is identified and the ability of viable system modelling to supplement the modelling stage of the methodology is explored in Chapter 4. Chapter 5 builds further on the methodology to produce an original iconic model of the methodological process. The model characterises the mechanisms of organisational problem situations as well as desirable procedural steps. The Weltanschauungen (W's) or "world views" of key actors is recognised as central to the mechanisms involved. Part II describes the experience which prompted the theoretical investigation. Chapter 6 describes the first year of the project. The success of this stage is attributed to the predominance of a single W. Chapter 7 describes the changes in the organisation which made the remaining phase of the project difficult. These difficulties are attributed to a failure to recognise the importance of differing W's. Part III revisits the theoretical and organisational issues. Chapter 8 identifies a range of techniques embodying W's which are compatible with .the framework of Part I and which might usefully supplement it. Chapter 9 characterises possible W's in the sponsoring organisation. Throughout the work, an attempt 1s made to reflect the process as well as the product of the author's leaving.

Minority influence and optimal problem-solving

An analogous thinking task was used to test Nemeth's Convergent–Divergent theory of majority and minority influence. Participants read a (base) problem and one of three solutions (one of which is considered the ‘best' solution). They then generated solutions to a second (target) problem which shared similar structural features to the first problem. Due to the similarities between problems, the solution given to the first problem can be used as an analogy in solving the second. In contrast to Nemeth's theory, when the solution to the base problem was endorsed by a numerical majority there was not an increase in analogy-transfer in solving the target problem. However, in support of Nemeth's theory, when the base solution was supported by a numerical minority then the participants were more likely to generate the ‘best' solution to the target problem regardless of which base solution they were given. Copyright © 1999 John Wiley & Sons, Ltd.