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.

Problemlösning genomsyrar hela läroplanen och är en viktig del av matematik-undervisningen i skolan (Skolverket, 2011a). Att lösa problem kommer naturligt för barn och det är lärarens uppgift att ta vara på den förmågan och hjälpa elever att bli effektiva problemlösare. Förmågan att lösa problem är en viktig kunskap som varje elev har fördel av att kunna (Lester, 1996). Studiens syfte är att undersöka variationen av problemlösnings-strategier som elever använder samt undersöka hur eleverna resonerar när de löser ett problem. 39 elever från två olika skolor i England och Sverige fick lösa ett matematiskt problem och sedan intervjuades 12 av dem med olika lösningsstrategier. Resultatet visade att eleverna använde sig av fyra olika kategorier av lösningsstrategier. De olika kategorierna var: lösningsstrategi genom addition, lösningsstrategi genom addition och subtraktion, lösningsstrategi genom att gissa och resonera, och lösningsstrategi genom att söka mönster. Det fanns även en grupp elever som inte hade någon utläsbar lösningsstrategi. Slutsatsen av studien är att elever behöver explicit undervisning i problemlösning för att till fullo kunna behärska den. / Problemlösning genomsyrar hela läroplanen och är en viktig del av matematik-undervisningen i skolan (Skolverket, 2011a). Att lösa problem kommer naturligt för barn och det är lärarens uppgift att ta vara på den förmågan och hjälpa elever att bli effektiva problemlösare. Förmågan att lösa problem är en viktig kunskap som varje elev har fördel av att kunna (Lester, 1996). Studiens syfte är att undersöka variationen av problemlösnings-strategier som elever använder samt undersöka hur eleverna resonerar när de löser ett problem. 39 elever från två olika skolor i England och Sverige fick lösa ett matematiskt problem och sedan intervjuades 12 av dem med olika lösningsstrategier. Resultatet visade att eleverna använde sig av fyra olika kategorier av lösningsstrategier. De olika kategorierna var: lösningsstrategi genom addition, lösningsstrategi genom addition och subtraktion, lösningsstrategi genom att gissa och resonera, och lösningsstrategi genom att söka mönster. Det fanns även en grupp elever som inte hade någon utläsbar lösningsstrategi. Slutsatsen av studien är att elever behöver explicit undervisning i problemlösning för att till fullo kunna behärska den. Problem solving permeates the Swedish national curriculum and it is an important part of mathematics education (Skolverket, 2011a). To solve problems comes naturally to children and it is the teacher’s task to harvest this ability and help pupils to be effective problem solvers. The ability to solve problems is an important knowledge and if known provides an advantage in life (Lester, 1996). The purpose of this study is to investigate the variation of problem solving strategies that pupil use and to investigate their mathematical reasoning while solving a mathematical problem. 39 pupils from two different schools in England and Sweden got to solve a mathematical problem and then 12 of them, which had different solution strategies, were selected for an interview. The result showed that the pupils used four categories or solving strategies. The categories were: finding a solution though addition, finding a solution though both addition and subtraction, finding a solution though guessing and reasoning and finding a solution though seeking patterns. There was also one group of pupils who did not have a distinguishable solution strategy. The conclusion of this study is that pupils need explicit teaching about problem solving to be able to fully master it.

This thesis reports about Laotian students’ understanding of the concepts of mechanics, and students’ activities when solving physics problems in groups. Totally, more than 1,000 first year university students from three universities in Laos have been tested using two versions of the Force Concept Inventory (FCI) over a period of three years. The Force Concept Inventory was developed in the USA to test students’ understanding of mechanics concepts. The contexts of some questions were unfamiliar for Laotian students and therefore another Laotian version was constructed. We found that Lao students obtained a low score on the FCI. The average scores of the post-test ranged from 21% to 26% over the three years. The introduction of the Laotian version resulted in just a small improvement of the score but it helped the students to read and understand the questions more quickly. It was difficult to perceive from the answers to the FCI if the students used alternative conceptions however, in video recordings it could be seen that some students did use well-known alternative conceptions. In many cases, students seemed to use their everyday life experiences to find the answers to the FCI questions instead of referring to physics concepts. Group discussions were introduced in tutorial sessions for first year students. There were two types of group discussions. In the first type 29 groups solved end-of-chapter problems and three groups were recorded. One group described the physics theory of the problem before they selected equations and successfully solved the problem. Students in this group were not afraid to raise disagreements; they asked questions and took turns answering them which resulted in a fruitful discussion. The other two groups made the major mistake of not considering that the object moved with constant speed. Students suggested equations to use without giving any arguments based on physics theory. Both groups got stuck and needed help from the teacher. It was found that the problem solving strategy in the physics textbook did not include the important step of describing the physics theory and could actually encourage students to start looking for equations without first describing the physics. In the second type of group discussions 52 groups discussed qualitative multiple-choice questions. Seven groups were recorded and 14 students and three teachers were interviewed. In the group discussions most students co-constructed an answer. However, the students in general did not seem to come to an understanding of the physics concepts and the follow-up discussion in class was essential for a better understanding. To improve the discussions, the students need more time and should also be taught about working in groups. The thesis is concluded with a section on the implications for education in physics in Lao PDR.

The purpose of this study was to examine the impact of computer instruction on the near transfer and far transfer of a means-end analysis problem solving strategy.

No description available.

This study investigated the effect of a blended-learning approach in the learning of problem-solving skills in a first-level distance education physics module. A problem-solving type of instruction with explicit teaching of a problem-solving strategy was implemented in the module, which was presented through correspondence, online using an in-house learning management system as well as two face-to- face discussion classes. The study used the ex post facto research design with stratified sampling to investigate the possible cause-effect relationship between the blended-learning approach and the problem-solving performance. The number of problems attempted, the mean frequency of using strategy in problem solving and the achievement marks of the three strata were compared using inferential statistics. The finding of the study indicated that the blended-learning approach had no statistically significant effect in the learning of problem-solving skills in a distance education module. / Educational Studies / M. Ed. (Open and Distance Learning)

The aim of the research was to understand the kind of relationship that exists among officers and other stakeholders in prevention of crime, regarding the purposes of fighting crime in the Zambezi region. This research would want to determine the strength of the relationships and the roles of trust between the police and society to address the research question which exactly refers to what is to be investigated. A qualitative design was used, an approach that involved the analysing and interpreting texts as well as interviews. The study established that there is a poor relationship among stakeholders who actually maintain law and order and that the majority of them were the main contributing factors for the poor implementation of community policing which resulted in poor crime prevention as well. Community policing can only be effectively implemented under the mandate and function of community policing forums as stipulated in the Namibian Police Act 19 of 1990. / Police Practice / M. Tech. (Policing)

This study investigated the effect of a blended-learning approach in the learning of problem-solving skills in a first-level distance education physics module. A problem-solving type of instruction with explicit teaching of a problem-solving strategy was implemented in the module, which was presented through correspondence, online using an in-house learning management system as well as two face-to- face discussion classes. The study used the ex post facto research design with stratified sampling to investigate the possible cause-effect relationship between the blended-learning approach and the problem-solving performance. The number of problems attempted, the mean frequency of using strategy in problem solving and the achievement marks of the three strata were compared using inferential statistics. The finding of the study indicated that the blended-learning approach had no statistically significant effect in the learning of problem-solving skills in a distance education module. / Educational Studies / M. Ed. (Open and Distance Learning)

>Magister Scientiae - MSc / Students frequently leave first-year physical science classes with a dual set of physical laws in mind- the equations to be applied to qualitative problems and the entrenched set of concepts, many erroneous, to be applied to qualitative, descriptive, or explanatory problems. It is in this sense that the emphasis of this study is on ‘change’ rather than acquisition. Thus, a blend of theoretical framework was considered according to the aim of the study. Of immediate relevance in this regard within the “constructivist paradigm” are: Posner, Strike, Hewson and Gertzog’s (1982) conceptual change theory and the revised Bloom’s Taxonomy. Moreover, the very shift or restructuring of existing knowledge, concepts or schemata is what distinguishes conceptual change from other types of learning, and provides students with a more fruitful conceptual framework to solve problems, explain phenomena, and function in the world (Biemans & Simons, 1999; Davis, 2011). A quasi-experimental design was adopted to explore pre-service teachers’ conceptual and procedural difficulties in solving mathematical problems in physical science. Sixteen second and third year pre-service teachers in one of the historically black universities in the Western Cape, South Africa, participated in the study. Two inseparable concepts of basic mechanics, work-energy concepts were taught and used for data collection. Data were collected using questionnaires, Physical Science Achievement Test (PSAT), Multiple Reflective Questions (MRQ) and an interview. An explicit problem solving strategy (IDEAL strategy versus maths-in-science instructional model) was taught in the intervention sessions for duration of three weeks to the experimental group (E-group). IDEAL strategy placed emphasis on drill and practice heuristics that helped the pre-service teachers’ (E-group) understanding of problem-solving. Reinforcing heuristics of this IDEAL strategy include breaking a complex problem into sub-problems. Defining and representing problem (e.g. devising a plan-using Free-Body-Diagram) was part of the exploring possible strategies of the IDEAL. More details on IDEAL strategy are discussed in Chapter 3. The same work-energy concepts were taught to the control group (C-group) using lecture-demonstration method. A technique (i.e. revised taxonomy table for knowledge and cognitive process dimension) was used to categorize and analyse the level of difficulties for each item tested (e.g. D1 = minor difficulty, D2 = major difficulty, and D3 = atypical difficulty

>Magister Scientiae - MSc / Students frequently leave first-year physical science classes with a dual set of physical laws in mind- the equations to be applied to qualitative problems and the entrenched set of concepts, many erroneous, to be applied to qualitative, descriptive, or explanatory problems. It is in this sense that the emphasis of this study is on ‘change’ rather than acquisition. Thus, a blend of theoretical framework was considered according to the aim of the study. Of immediate relevance in this regard within the “constructivist paradigm” are: Posner, Strike, Hewson and Gertzog’s (1982) conceptual change theory and the revised Bloom’s Taxonomy. Moreover, the very shift or restructuring of existing knowledge, concepts or schemata is what distinguishes conceptual change from other types of learning, and provides students with a more fruitful conceptual framework to solve problems, explain phenomena, and function in the world (Biemans & Simons, 1999; Davis, 2011). A quasi-experimental design was adopted to explore pre-service teachers’ conceptual and procedural difficulties in solving mathematical problems in physical science. Sixteen second and third year pre-service teachers in one of the historically black universities in the Western Cape, South Africa, participated in the study. Two inseparable concepts of basic mechanics, work-energy concepts were taught and used for data collection. Data were collected using questionnaires, Physical Science Achievement Test (PSAT), Multiple Reflective Questions (MRQ) and an interview. An explicit problem solving strategy (IDEAL strategy versus maths-in-science instructional model) was taught in the intervention sessions for duration of three weeks to the experimental group (E-group). IDEAL strategy placed emphasis on drill and practice heuristics that helped the pre-service teachers’ (E-group) understanding of problem-solving. Reinforcing heuristics of this IDEAL strategy include breaking a complex problem into sub-problems. Defining and representing problem (e.g. devising a plan-using Free-Body-Diagram) was part of the exploring possible strategies of the IDEAL. More details on IDEAL strategy are discussed in Chapter 3. The same work-energy concepts were taught to the control group (C-group) using lecture-demonstration method