The ten step problem solving is created to capture and resolve all issues that arise with designing, developing, manufacturing and delivering a new vehicle produce. These steps will provide a common process, which effectively defines and resolves concerns and prevents their recurrence. Step 1: Prepare for the process Step 2: Establish Team Step 3: Describe the Problem Step 4: Develop short term containment action Step 5: Define and verify root cause and escape point Step 6: Choose and verify permanent corrective actions Step 7: Implement and validate permanent corrective actions Step 8: Prevent recurrence Step 9: Recognize team and individual contributions Step 10: Benchmarking The ten step problem solving process is an enhancement to 6-sigma process that is currently used by many manufacturers. Consumer Driven 6-Sigma is a tool that significantly improves customer satisfaction and shareholder value by reducing variability in every aspect of the business. It builds on existing processes, provides additional tools, and offers a disciplined approach to focus on meeting customer expectations. 6-Sigma helps on finding out where the variability is in a process, and then provides the tools to reduce variability and make the process better.

The aim of this study is to explore different graders¡¦ concept of unknown and performance in solving equations in concrete situations. In recent years of early algebra research in the United States (Carraher, Schliemann, & Schwartz, in press), it was found that through systematic teaching, low and middle graders¡¦ algebra performance was better than the same or even higher graders without teaching. Therefore, semi-structured interview was adopted to collect data on three cases: a second-grader, a fifth-grader and a seventh-grader who were using textbooks that follow Grade one-nine Integrated Coordinate Curriculum in SY89. The interview questions included addition and subtraction CHANGE problems, as well as multiplication and division EQUAL GROUPS problems; with natural numbers below 20, and given in four types: one-step, two-steps mixed, relating two unknowns and comparing two unknowns. Data analysis was conducted by referring to three sources of data: protocols from interviews, children¡¦s problem-solving records and interviewer¡¦s observation records. Research findings were: all three cases that received guidance could use equations to express problems; ¡§Undoing¡¨ was the most frequently used problem-solving strategy; both second and fifth graders could simplify expressions by number properties in concrete situations; both fifth and seventh graders could check if answers were reasonable; the meaning of equal sign developed from ¡§finding the results of¡¨ to ¡§equality in measures¡¨; and, individual differences in ¡§trial and error substitution¡¨ among three cases. Such results were consistent to that of Carraher. It is suggested that, introducing early algebra in the elementary school is helpful to children¡¦s learning of formal algebra in the junior high school.

This study employed thinking aloud and semi-structured interviews to explore problem-solving representations, problem-solving processes, and problem-solving strategies of six grade seven students on word problems of linear equation in one variable. The instrument of the study was a researcher-designed test with literal, graphics and/or symbolic descriptions and was examined and revised by three senior secondary mathematics teachers. According to their mathematics scores of 3rd midterm exam last semester, students were divided into three achievement groups¡Ð¡Ðlow achievement group (the lowest 27%)¡Amiddle achievement group (46%) and high achievement group (the highest 27%). One subject was selected from each of middle and high achievement groups of three grade seven classes. Six subjects, in total, had taken thinking aloud training for three weeks, and then they took the paper and pencil test individually with a follow-up interview. All the processes of individual tests and interviews were video recorded. The videotapes were transcribed and provided the major evidence of the analyses of participants¡¦ performances of problem-solving processes, their problem-solving representations, and their problem-solving strategies. The results of problem-solving representation, problem-solving process, and problem-solving strategy were reported separately as follows: (1)Problem-solving representation. Participants applied literal, algebraic and numeral representations to solve one-variable leaner equation problems more often than used graphic one. (2)Problem-solving process. (a)When graphic representation was applied in this test, the time of problem solving could be shortened effectively. (b)The times that Participants repeat to read and analyze the topic increased relatively in the topics with more writing narration. (c)In more than one half of the fault problem-solving cases, the three stages of exploration, implementation, and planning were administered simultaneously. (d)The more verification was applied during participant¡¦s problem-solving process, his/her opportunity of success was higher. (e)Verification was often administered in problems with complex computations or questionable topics. (f)The relevance was higher between problem content and daily life, the opportunity of success was higher. (g)The time that the high achievement group used to solve problems was shorter than the middle achievement group used, and the opportunity of success was also higher than the middle achievement group. (3)Problem-solving strategy. (a)The problem-solving strategies applied by participants of high achievement group were more consistent, and the problem-solving strategies among participants of middle achievement group were more diverse. (b)The problem-solving strategies that participants often used to solve word problems of linear equations in one variable were translating the word problem into an equation, simplification of equation by collecting terms, using inverse operations, and properties of equality.

This research examines problem definition as the first step in a sequential problem solving process. Seventy-seven managers in four diverse organizations were studied to determine common characteristics of problem definers. Among the variables considered as differentiating problem definers from non-problem definers were cognitive style, personal need characteristics, preference for ideation, experience, level of management, and type and level of education. Six hypotheses were tested using the following instruments: the Problem Solving Inventory, the Myers-Briggs Type Indicator Schedule, the Preference for Ideation Scale, the Edwards Personal Preference Schedule, a Problem Definition Exercise, and a Personal Data Questionnaire. Among the managers studied, only twelve were found to be problem definers. Such small numbers severely limit the ability to generalize about problem definers. However, it is possible that problem definers are scarce in organizations. In terms of cognitive style, problem definers were primarily thinking types who preferred evaluation to ideation in dealing with problems, making judgmental decisions on the basis of collected facts. Problem definers were not predominant at lower levels of the organization. One-third of the problem definers held upper level management positions while another one-fourth were responsible for specialized activities within their organizations, overseeing special projects and individuals much like upper level managers. Sixty-eight of the problem definers had non-business educations with none having more than a bachelors degree. As knowledge and judgment on which to base evaluation expands, managers may become less adept at defining problems and more adept at selecting and implementing alternatives. Several tentative hypotheses can be tested in future research including: 1) determining whether problem definers are scarce in organizations, 2) determining whether problem definers are more prevalent in some types of organizations than others, 3) verifying unique cognitive and personal need characteristics, 4) determining whether non-managers rather than managers have problem defining skills.

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<p>Denna studie handlar om elevers strategier för att lösa matematiska textuppgifter i årskurs 1. Undersökningen har gjorts genom intervjuer och observationer. Tjugo elever har deltagit i undersökningen, de kommer från två olika skolor i Kalmar kommun. Första analysen var intervjuer, som spelades in med hjälp av en diktafon. Genom denna analys kunde vi dela in textuppgifterna i två olika kategorier, problem eller rutinuppgift. I resultatet visade det sig att det fanns de elever som hade svårt med förståelsen av textuppgifterna och ansåg att uppgiften var ett problem. Dock fanns det de elever som lätt kunde ange ett svar och sedan på ett utförligt sätt förklara sitt genomförande under intervjun. Andra fasen av intervjuanalysen var att identifiera vilka strategier eleverna använde för att lösa textuppgifterna. Det visade sig att eleverna använde sig av tre av de fyra räknesätten som strategier för att lösa textuppgifterna. Andra analysen fokuserades på observationerna som gjordes vid intervjutillfällena. Vid observationen användes ingen teknisk utrustning, utan allt skrevs ner under intervjutillfället. När vi analyserade observationen visade det sig att eleverna använde andra strategier, som fingerräkning och gester, utöver räknesätten för att lösa textuppgifterna. I undersökningen ansåg vi att det var elever som hade svårt för olika begrepp, exempelvis hel och halv. Detta kan bero på att de inte gått igenom detta i sin matematik undervisning. Användningen av textuppgifter i matematik visade sig vara nästan helt osynliga enligt en av lärarna som vi samtalade med.</p> / <p>This study deals with pupils in first grade and how they solve text tasks in mathematics and which strategies they are using. To find out about this we have performed interviews and observations. We interviewed twenty pupils from two different schools in Kalmar municipality, Sweden. Firstly we analyzed the interviews; these were recorded with a dictaphone. Thanks to the analysis we could divide answer from the tasks into two categories, problem or routine task. The result showed that there were pupils who had problems understanding the text tasks and therefore found them to be problems. However there were pupils that gave a correct answer and a good explanation of how they solved the tasks during the interviews. Then we looked at the answers from the pupils when they solved the tasks. We could see that the pupils used three of the four rules of arithmetic. The second analysis focused on the observations that were done during the interviews. We did not use any technical device. When we looked at the observations we could see that the pupils were using other strategies besides the rules of arithmetic’s to solve the tasks. In the study we found that some pupils had difficulties with some concepts such as whole and half. This might be because they had not gone through those concepts in their math education. The use of text tasks in math was almost completely invisible according to one of the teachers we spoke to.</p>

Denna studie handlar om elevers strategier för att lösa matematiska textuppgifter i årskurs 1. Undersökningen har gjorts genom intervjuer och observationer. Tjugo elever har deltagit i undersökningen, de kommer från två olika skolor i Kalmar kommun. Första analysen var intervjuer, som spelades in med hjälp av en diktafon. Genom denna analys kunde vi dela in textuppgifterna i två olika kategorier, problem eller rutinuppgift. I resultatet visade det sig att det fanns de elever som hade svårt med förståelsen av textuppgifterna och ansåg att uppgiften var ett problem. Dock fanns det de elever som lätt kunde ange ett svar och sedan på ett utförligt sätt förklara sitt genomförande under intervjun. Andra fasen av intervjuanalysen var att identifiera vilka strategier eleverna använde för att lösa textuppgifterna. Det visade sig att eleverna använde sig av tre av de fyra räknesätten som strategier för att lösa textuppgifterna. Andra analysen fokuserades på observationerna som gjordes vid intervjutillfällena. Vid observationen användes ingen teknisk utrustning, utan allt skrevs ner under intervjutillfället. När vi analyserade observationen visade det sig att eleverna använde andra strategier, som fingerräkning och gester, utöver räknesätten för att lösa textuppgifterna. I undersökningen ansåg vi att det var elever som hade svårt för olika begrepp, exempelvis hel och halv. Detta kan bero på att de inte gått igenom detta i sin matematik undervisning. Användningen av textuppgifter i matematik visade sig vara nästan helt osynliga enligt en av lärarna som vi samtalade med. / This study deals with pupils in first grade and how they solve text tasks in mathematics and which strategies they are using. To find out about this we have performed interviews and observations. We interviewed twenty pupils from two different schools in Kalmar municipality, Sweden. Firstly we analyzed the interviews; these were recorded with a dictaphone. Thanks to the analysis we could divide answer from the tasks into two categories, problem or routine task. The result showed that there were pupils who had problems understanding the text tasks and therefore found them to be problems. However there were pupils that gave a correct answer and a good explanation of how they solved the tasks during the interviews. Then we looked at the answers from the pupils when they solved the tasks. We could see that the pupils used three of the four rules of arithmetic. The second analysis focused on the observations that were done during the interviews. We did not use any technical device. When we looked at the observations we could see that the pupils were using other strategies besides the rules of arithmetic’s to solve the tasks. In the study we found that some pupils had difficulties with some concepts such as whole and half. This might be because they had not gone through those concepts in their math education. The use of text tasks in math was almost completely invisible according to one of the teachers we spoke to.

The purpose of this research is to study the mathematical problem solving processes, strategy use and success factors of middle grade gifted and talented (GT) elementary school students. This research is based on 9 mathematical problems edited by the author and divided into the following categories: ¡§numbers and quantity,¡¨ ¡§shape and space,¡¨ and ¡§logical thinking.¡¨ Seven GT students from Ta-Tung elementary school in Kaohsiung were selected as target students in the study. Besides, the seven students were translated into original cases using a thinking aloud method. Here are the conclusions: First of all, when facing non-traditional problems, GT students may use different problem solving steps to solve different problems and may not show all detailed steps for every single problem. The same types of problems may not have the same problem solving steps. Missing any single step would have no impact on the answers. Problem solving sequence may not fully follow the traditional 5-step sequence: study the problem, analyze, plan, execute, and verify, and, instead, may dynamically adjust the steps according to the thinking. Secondly, GT students¡¦ problem solving strategy includes more or less the following 19 methods: trial and error, tabling, looking for all possibilities, a combination of numbers, listing all possible answers, classifying the length of each side, classifying graphics, classifying points, adding extra numbers (the triangle problem), drawing, identifying rules and repetition, summarizing, forward solving, backward solving, remainder theory, polynomials, organizing data, direct solving, and making tallies. Finally, problem solving success factors are tightly coupled with problem solving knowledge, mathematical capability, and problem solving behavior. Problem solving knowledge includes knowledge of language, understanding, basic models, strategy use, and procedural knowledge. Instances of mathematical capability are capability of abstraction, generalization, calculation, logical thinking, express thinking, reverse thinking, dynamic thinking, memorizing, and space concept. Problem solving behavior includes the sense of understanding the problem and mathematical structure, keeping track of all possible pre-conditions, good understanding of the relationship between the problems and the objectives, applying related knowledge or formulas, verifying the accuracy of the answers, and resilience for problem solving. In addition to discussing the research results, future directions and recommendations for teaching mathematics for GT and regular students are highlighted.

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Pupils' difficulties in solving selected word problems from TIMSS research. (Diploma Thesis.) Abstract The theoretical part of the diploma thesis describes international comparative surveys, namely PISA and TIMSS, and analyses results of Czech pupils. Some areas are distinguished in which our pupils were unsuccessful and from them, the area of word problems and their mathematisation was selected for further work. Next, a solving strategy is characterised and some relevant research from this area is given. The core of the work lies in the experimental part whose goal was to find out what strategies pupils use when solving selected problems from TIMSS research and why they fail in them, via the analysis of pupils' written solutions complemented by interviews with them. Causes of failure of our pupils in these problems in TIMSS 2007 are looked for in mistakes pupils make, while it is also followed in what phase of the solving process they appear. The participants of research were pupils of Grade 9 of a primary school who solved three selected word problems from TIMSS research. Their written solutions were complemented by interviews with the experimenter focused on their mistakes and lack of clarity of the solutions. Four pupils participated in a pilot study. The atomic analysis of their solutions confirmed...