In this paper I argue that the message system of “what counts as valid knowledge” as a definition of the “curriculum” in regards to problem solving as an ability in the Swedish upper elementary school mathematics has changed by empathizing assessment as a tool to control what is being taught. The argument is based on studying syllabus, commentary material, textbooks and national tests published with each of the two reforms 1994 and 2011. I argue that the syllabus, commentary material, textbooks and national tests seen combined express the intended curriculum in a way that correlates better to reality than what is shown by only studying the official curriculum and syllabus. The conclusions of this study are based on analyses using Bernstein’s theory of classification and frame.

Creativity plays an important part in design and problem-solving. While the role of play has enjoyed a great deal of attention in the study of both creativity and problem-solving alike, the overlap between games and the creative problem-solving process has not enjoyed much scholarly attention. This dissertation therefore focuses on exploring the overlap between games and the creative problem-solving process. This exploration seeks to enhance the manner in which the role and function of gameplay within the creative problem-solving process is understood. This study is approached from the viewpoint of a thorough literature review and synthesises insights from design discourse, creativity studies and game design literature. Firstly, this study demonstrates the systemic similarities between games and creative problems. These similarities prove that both systems are capable of generating or allowing the emergence of gameplay. The second aspect focused on is the manner in which gameplay emerges from creative problem-solving and the value that it holds for that process. The third aspect focused on is the role and function of rules in both games and problem-solving in eliciting gameplay. These explorations culminate in a rudimentary framework that describes the manner in which the rules and limitations in a creative problem become established in order to allow gameplay to emerge. Lastly, the paper explores the psychological factors inherent in eliciting gameplay from a creative problem in the form of adopting a lusory attitude. The study ultimately demonstrates the crucial role of gameplay in creative problem-solving and the aspects that influence its emergence. / Dissertation (MA)--University of Pretoria, 2017. / Visual Arts / MA / Unrestricted

In South Africa, the Department of Education (DOE) via its South African Qualifications Authority (SAQA) mandates lecturers particularly at higher education level to deliver students that should be able to think critically and solve problems by the end of their undergraduate journey at any Higher Education Institution (HEI), whether public or private. HEIs have each taken their own approach on how to develop these competencies in their undergraduate students. This qualitative inductive case study focuses on understanding how eleven lecturers teaching at a private HEI in Midrand South Africa facilitate Active Learning in their classes, how they measure the success of Active Learning strategies and the support they have available to them by using semi-structured interviews and class observation data. Some of the findings highlight that these lecturers know exactly what Active Learning is even though most have never been officially trained. Six groups of different Active Learning strategies were identified including different questioning techniques, engagement via reading, engagement via writing, hands-on activities, use of technology and interaction with peers. Even though lecturers believed in Active Learning, evidence substantiating the effectiveness of their teaching methodology was mostly subjective. It was also found that lecturers had more support requirements than current support available and that the majority of current support was in the form of the immediate lecturer community. / Thesis (PhD)--University of Pretoria, 2017. / Science, Mathematics and Technology Education / PhD / Unrestricted

A finite element model is developed to study the stresses in a uniaxially loaded infinite sheet containing an interference-fit fastener. The sheet-fastener interface is modeled using one-dimensional gap elements. The geometry is chosen so that the performance of the gap element can be compared with known theoretical solutions. The fastener is modeled as a disk with thickness equal to that of the sheet. The effect of the fastener exiting the sheet, referred to as edge-stiffening, is neglected in the current study. Plane stress conditions are assumed for the sheet and fastener. Material response is assumed to be elastic after fastener insertion and during subsequent loading. Frictionless and no-slip conditions for the sheet-fastener interface are investigated. These two idealized conditions are expected to bracket the real behavior of the sheet-fastener interface. The ability of the gap element to predict the sheet-fastener separation stress for frictionless and no-slip interface conditions is investigated. Results obtained from the finite element models compare favorably with theoretical solutions. / Master of Science

The purpose of this study is to find out, through observations and focus group interviews, how four different groups in grade four work with and reason about problem solving in mathematics based on George Polyas problem solving model. Questions that are as follows: How do the problem solving activities go in the groups? How do the pupils reason about their problem solving activities? We based our selection from different schools. The results of this study give an insight into better understanding of how pupils work with mathematical problems and how they reason about their problem solving activities. The result also indicates that there is a connection between the pupils problem solving approach and previous research ant theories found in this study.

Detta arbete handlar om matematikens historia i matematikundervisningen på gymnasienivå. Huvudsyftet är att undersöka hur matematiklärare kan integrera historiska aspekter i sina lektioner och att ge konkreta förslag för hur detta kan göras. Arbetet belyser framför allt en integrering med hjälp av problemlösning, där problem väljs ut så att de både har relevans för ämnesplanerna och kan kopplas till viktiga matematiker i historien samt hur matematik genom tiderna har utvecklats. Frågor som har besvarats är vilka historiskt kända matematikproblem som kan fungera som diskussionsunderlag i klassrummet och hur den undervisande läraren skulle kunna kommentera dessa problem för att synliggöra de bakomliggande historiska kopplingarna. Förslagen på problem och kopplingarna sammanställs i ett kompendium som är tänkt att läsas av matematiklärare på gymnasiet. Metoderna som använts för att producera kompendiet är dels litteraturstudium av tidigare arbeten om matematik och matematikdidaktik i samband med matematikens historia, dels kvalitativa intervjuer med erfarna matematiklärare på gymnasiet. De intervjuade lärarna fick se valda delar i ett prototypiskt kompendium och ge synpunkter samt förbättringsförslag för att det färdiga kompendiet skulle kunna fungera väl för den tänkta målgruppen. Trots att kompendiet inte är en lärobok har det bearbetats för att hålla en god pedagogisk kvalité. Kompendiet ska förmedla matematikens historia på ett koncist och tydligt sätt, där de involverade matematikproblemen och historiska kopplingarna ska upplevas som både intressanta och betydelsefulla för en matematiklärare. / This master thesis deals with the use of the history of mathematics in teaching mathematics in Swedish gymnasium schools. A "gymnasium" in Sweden (not to be confused with a gymnastics school) is a type of school which consists of three years, after nine years of elementary school. The main focus of this thesis is to investigate how mathematics teachers can integrate historical aspects of mathematics into their classes, and to give concrete examples of such integration. This thesis illustrates, above all, an integration of mathematics history with problem solving, where problems are selected so that they are relevant to the syllabus and can be connected to important mathematicians in history as well as how mathematics itself has evolved through the ages. The questions to be answered in this thesis concern which mathematical problems that may serve as a basis for discussion in the classroom and how teachers may illuminate the historical connections contained in each discussed problem. The proposed problems and connections are compiled in a compendium which is meant to be read by mathematics teachers teaching at gymnasiums. The methods which have been used to produce the compendium are partly literature study of earlier works about mathematics and mathematics didactics in relation to mathematical history, partly qualitative interviews with experienced mathematics teachers at gymnasiums. The interviewed teachers read selected parts of the prototypal compendium and gave opinions and suggestions of improvement so that the final compendium would work well for the meant target group. Despite the fact that the compendium is not a textbook, a certain pedagogical quality is to be attained. The compendium should convey the history of mathematics in a clear and concise manner, where the involved mathematical problems and historical connections should be experienced as interesting and meaningful for mathematics teachers.

Collaborative problem solving (CPS) is a critical competency, because much of the work people do occurs in a social context involving direct collaboration. Meanwhile, schools are being pressured to reduce the amount of time devoted to large-scale assessments, and to adopt more natural or authentic assessments. It may be possible to address both these issues at once, if collaboration experiences are viewed as opportunities to assess student achievement.However, several issues arise in evaluating individuals’ problem solving skills in a collaborative context: (1) collaborative learning outcomes may obscure individuals’ contributions, making it difficult to isolate individuals’ performance; (2) outcome-based measures may ignore the processes of individuals’ or groups’ problem solving, thus leading to inaccurate estimations of individuals’ or groups’ knowledge, abilities and skills; and (3) prior evaluative focus of CPS research has usually been on social aspects of collaboration rather than domain-relevant cognitive skills. Therefore, the present study aimed to develop a process-based scoring rubric to evaluate individual student achievement in problem solving using collaboration process data. Furthermore, this study explored how group ability composition affects group performance and individual learning gains. The content domain was solving mathematical combinatorics and probability word problems. Participants included 306 Chinese high school students, who performed the following three tasks in order: (1) an individual pretest with seven problems; (2) a collaborative task with three problems; and (3) an individual posttest with seven problems. The results were as follows: First, a four-indicator scoring rubric was developed to evaluate student achievement in solving combinatorics and probability problems using collaboration process data. Evidence suggested that the scoring rubric can be considered reliable and valid in terms of being used as an individual assessment and a teaching tool. Thus, this scoring rubric may provide insights useful for developing relevant performance assessments on more complex and authentic performance tasks. Second, significant differences were found in group performance among dyads as a function of the group’s minimum student ability. Third, students working in dyads with higher maximum or average ability tended to gain more after collaboration. Finally, certain collaborative problem solving behaviors could be linked to individual learning gains.

En problemlösningsuppgift kan innehålla både naturligt språk och symbolspråk. Det kan ställa till det för elever som har svårt för att skifta mellan de olika språken, men även för de som har svårt för läsningen i stort. Denna studie syftar till att granska läsförståelsens betydelse när elever ska arbeta med problemlösningsuppgifter inom matematiken. Frågor som ställs för att besvara syftet är: Vad säger forskningen om läsförståelsens betydelse för att kunna förstå ett problem inom matematisk problemlösning och Vad säger forskningen om läsförståelsens betydelse för att kunna tolka ett problem inom matematisk problemlösning?  Granskningen gjordes genom en litteraturstudie där publikationer från olika delar av världen studerats. Studierna visar att sambandet mellan läsförståelse och matematisk problemlösning är stark. Det framkom även att ett bristande ordförråd påverkar möjligheterna för elever att kunna förstå och tolka ett problem. Ovan nämnt redogörs för och diskuteras. Avslutningsvis lyfts förslag för vidare forskning inom ämnesområdet fram.

Presents real-life and day-to-day examples of service delivery problems which will be familiar to all readers. Then provides practical re-engineering solutions to remedy the problems. The vignettes illustrating the problems are all real-life cases based on the experiences of the authors, and the solutions they propose are also based on their encounters with service providers as educators and consultants, and talks to business audiences by both parties.

To turn today’s challenges and threats into fruitful opportunities, marketing organizations must move away from their traditional modus operandi of closed system approach to an open system where employees, customers, procedures, processes, vendors, and strategies are viewed interdependently. This article presents a systematic and synergistic practical framework grounded in an open system. A case study is employed to illustrate the application of the framework and to demonstrate how it can benefit organizations in attaining desirable outcomes.