Three issues from studies of primary children's addition are identif ied and investigated with children between 6 and 8 years old. The first is why descriptions of strategy use der i ved from chronometr ic studies vary so much from those based on observation and interview. The second and third concern the factors influencing strategy choice and are the relation between procedural and conceptual knowledge and characteristics of the sum. Whereas reaction time studies have been interpreted as showing that primary schoolchildren predominantly use one strategy, counting on from the larger addend (COL), interview and observation studies suggest each child uses a variety of strategies. In Experiment (1) children were given a large set of single digit additions and both their reaction times (RT) and their overt behaviour recorded. The best predictor of RT was a model based on COL. The tactic of recording both RTs and observations was continued in Experiments (2) and (3) and in Experiment (4) children were interviewed as well as timed. The major concern, however, was to investigate why children so rarely use decomposition (ie analysing a given sum into a known number fact and counting on the difference). To this end children were presented with number facts and asked to read them out prior to doing the sum. The relation between the given number fact and the sum was varied and the effect on RT determined. Presenting a number fact that was the same or a commuted version of the sum had major effects on observed and reported strategy and overall response latency. When the number facts differed by 1 or 2 from the sum children typically ignored them. Overall the utility of chronometric studies for identifying strategy use was questioned as there was much variation between studies in the best fitting RT model. Also, apart from COL, no RT model of a specific strategy made adequate predictions. Experiments (5) and (6) explored whether children do not use decomposition because they do not understand it. Awareness of the potential use of decomposition was assessed by presenting number facts and asking how these would help do particular sums. In Experiment (5), which was conducted with the participants in Experiment (4), the children were also asked to select which number facts would be useful. The same children who so rarely used decomposition demonstrated that they understood how to use it. How children's use of COL was related to understanding of commutativity was tested in Experiment (7). While children who used COL often typicallY passed commutativity tests there were some who did not.The influence of problem characteristics on strategy use was tested in Experiment (8) by using sums with very large second addends (eg 2 + 95). Every child who attempted these sums used the COL strategy on them whereas many never used COL on the more traditionally used single digit additions, but counted on from the first digit instead. This implies that the common practice of classifying children's strategy use on the basis of how they solve single digit sums may be misleading. In reviewing these and other findings it is concluded that what children know about number and addition strategies may bear little relation to how they solve simple addition sums. The explanation of why children choose a particular strategy may lie instead in the amount of 'cognitive effort' that is involved.

A dissertation submitted to the Department of Mathematics, Science, and Technology in fulfilment of the requirements for the degree of Master of Education (Mathematics Education) in the Faculty of Education at the University of Zululand, 2019. / Algebra is a mathematical concept that explains the rules of symbol operations, equations, and inequality. Algebra is a combination of logic and language; hence common mistakes and conceptions are either attributed to logic or language problems, or both. There is also ongoing debate about the fact that learners come to class with different ideas that result in errors and misconceptions when they solve algebraic equations and expressions. Based on this debate concerning both errors and misconceptions in solving algebraic equations and expressions, the purpose of this study was to investigate the errors and misconceptions committed by learners when learning Algebra. The study answered the following research questions: What are the types and the sources of errors and misconceptions committed by Grade 9 learners in Algebra learning? How do the types and the sources of errors and misconceptions influence errors in Grade 9 learners’ cognition when learning Algebra? Which strategies work to avoid errors? What are the sources of the errors and misconceptions in Algebra? Unlike the predominant existing studies, which are urban-based, this study was based in rural schools in the King Cetshwayo District of UMlalazi and Mtunzini Municipality. The structure of the observed learning outcome (SOLO) theory was adopted to observe, examine and analyse learners’ misconceptions in rural-based secondary schools.

Besides the traditional face-to-face learning medium, online media are now available for students in various learning environments. The delivery of coursework through online media is on the increase in colleges and universities. However, research on the use of online learning media in beginning collegiate level foundational mathematics courses for non-mathematics and non-science majors is limited. Therefore, the purpose of this study was to investigate, within a foundational mathematics course, connections between media used for instruction in hybrid and online enhanced face-to-face learning environments and students’ media preferences. The online Web Course Tools (WebCT) Vista template used in this study was designed by the researcher and her colleague as a part of the hybrid fellowship project for a two-year college. Applying transactional distance theory and engagement theory, designers carefully analyzed each concept and determined which concepts would be delivered most effectively in each learning medium. This study was quantitative in nature. During Fall 2005, thirty-eight students in the Introduction to Mathematical Modeling course at a community college in the southeast participated in the final study. Students in the hybrid sections comprised the treatment group while students in the online face-to-face section comprised the control group. Throughout the semester, all students were asked to respond to questions on the following instruments: Assignment Feedback, Quiz Feedback, Test Feedback, and Project Feedback. Chi-Square analysis showed that significant differences were found in the majority of items on the Test Feedback instrument related to the linear and quadratic modules. In general, the treatment group preferred online learning at least half of the time and believed online resources provide the basic resources for learning the subject matter. Students’ written responses from the treatment group indicated that both online learner-content interactions, and in-class learner-instructor interactions supplemented the learning of mathematics. The control group preferred predominantly face-to-face learning and believed that learning primarily took place in a physical setting. The findings showed that the proportion of students who completed the course using the hybrid and face-to-face learning environments was not significantly different. Therefore, the data showed the success rate for both learning environments was about the same.

No description available.

Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2016 / The advent of a new mathematics curriculum in South Africa requires a sound Pedagogical Content Knowledge (PCK) for both novice and experienced educators. Central to this is the challenge of identifying and exploring “rich and appropriate” contexts that may serve as “scaffolds” in the understanding and internalization of school level mathematics concepts. This exploratory, inductive study focused on a real-life irrigation technology in the farming sector with a view to “exploring” the general school level mathematics concepts that might be “grounded” in the machine’s mobility and water spread mechanisms. Data was generated through two stages of theoretical and practical approaches. This was in accordance with Alasuutari’s (1993) phases of simplification of observations and “solving the enigma” during an exploratory research project. In the theoretical approach, the operations of a linear move irrigation machine and a circular move center pivot irrigation system were mimicked through sketches which were explored for the general school level mathematics concepts embedded therein. The practical approach centrally focused on hands-on activities that aimed at verifying the theoretical mathematics models that were perceived to explain how the CPIS moves and spread water across the entire irrigation field. An intense observation of the actual Centre Pivot Irrigation System (CPIS) at the research site formed the spine of the latter data collection stage. Finally a document analysis, which focused on mathematics documents such as the National Curriculum Statement and Curriculum and Assessment Policy Statement documents for grades R-12, was done to ascertain the school level at which the grounded general mathematics concepts are applicable. The findings of this study indicated that certain mathematics concepts might be “constructed” and consolidated in the CPIS context or setting.

Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2017 / The qualitative study reported here was aimed at documenting and describing how agency is enacted through students‟ interactions in a mathematics classroom. A case study design was adopted and focused on a grade 11 mathematics class with all the students being participants. These participants were purposefully selected as they formed the class which was allocated to me for dayto-day mathematics teaching. The research question which the study sought to address was: how is agency enacted through students‟ interactions in a mathematics classroom? The classroom in which data was generated adopted a sociocultural perspective as a referent for its practice. Due to this perspective, agency was thus employed as conceptualised by Pickering (1995). Data was generated through interviews and participant observation. However, the interviews were not employed in their „tradition‟ view, but were mostly like focus-group interviews in nature. Data also emerged from classroom discussions, when students in their groups, worked through learning activities. These interactions together with the interviews were audio recorded. Meanwhile, observation data was recorded in a researcher journal in which entries were made after each lesson. Data was analysed following Polkinghorne‟s (1995) narrative analysis of eventful data. During the analysis the researcher listened to the audio records a number of times, and then transcribed all the audio into text. This was followed by reading through the textual data which led to a selection of excerpts used in data analysis. It was found that agency was enacted during student-material interactions, as students engaged in the „dance of agency‟ when deciding on learning a new approach or using an old one to respond to questions. Furthermore, agency was enacted during student-student interactions when students initiated either group or whole class discussion and they were able to sustain the discussions to completion without the teacher‟s intrusion. Finally, during teacher-student interactions, students accounted for their actions and shared their experience and decision making process.

Denna studie syftar till att undersöka i vilka spontana lektyper inomhus, förskolebarn uttrycker matematiska begrepp. Bakgrunden till studien är att vi anser att matematikarbetet på förskolan ska utgå från barnens perspektiv och då har leken en viktig betydelse. Leken ses som en central del för matematiklärandet och begreppsbildningen och därför är förskolan en lämplig plats för denna studie. Om barnen redan på förskolan skapar ett intresse och börjar använda matematiska begrepp gynnar det även den begreppsanvändning som krävs i skolan. Med inspiration av ett etnografiskt förhållningssätt har det genomförts observationer på två förskoleavdelningar, vid sju tillfällen på varje avdelning. Avsikten har varit att observera barns matematiska begreppsanvändning i den spontana leken. Vid observationerna har ett särskilt framtaget observationsschema använts för att dokumentera vilka lektyper och matematiska begrepp som observerats. Resultatet visar att olika lektyper stimulerar olika begrepp och de begrepp som uttrycks mest är jämförelseord. De lektyper som framkom i resultatet är; rollek, bygglek, lego, spel, bilar, figurer, dockor och övrigt. Avslutningsvis diskuteras resultatet och metoden i förhållande till litteraturen och våra egna tankar. Tre teman är framtagna i resultatdiskussionen; språket, leken och miljön med utgångspunkt i barnens begreppsanvändning och lektyperna. / This study aims to examine in which spontaneous play indoors, children in preschool expresses mathematical concepts. The background to the study is our belief that the mathematics work in preschool should be assumed from the children's perspective and that play has an important role in that work. The spontaneous play are a central part of mathematics learning and conception and therefore is preschool an appropriate place for this study. If children in preschool at an early stage creates an interest and begin using mathematical concepts if also favors the concept of use, that required in school. Inspired by an ethnographic approach, there have been observations of two preschool departments, on seven occasions in each department. The intention has been to observe children's mathematical concepts used in the spontaneous play. At the observations, a designed observation chart has been used to record the play types and mathematical concepts observed. The result shows that different play types stimulate different concepts, and the concepts that are mostly expressed are comparison words. The play types that emerged in the result are; role play, construction play, lego, games, cars, figures, dolls and others. To sum up, we discuss the result and the method in relation to the literature and our own thoughts. Three themes are produced in the result discussion; language, play and the environment on the basis of children's concepts of use and play types.

Detta examensarbete är en studie om matematik i vardagssituationer i en svensk förskola. Syftet med min studie var att undersöka vilken matematik som uppstår i av- och påklädningssituationer. Ytterligare ville jag ta reda på hur pedagoger arbetar för att lyfta fram och stimulera barnen för att upptäcka matematiken i dessa situationer. Jag har valt att göra en kvalitativ studie. I den empiriska undersökningen använder jag ostrukturerade observationer av pedagoger tillsammans med barnen i tamburen, som kompletteras med löpande protokoll. De kvalitativa intervjuerna med pedagogerna, som var inblandade i undersökningen, användes för att styrka det som observationerna visade. Resultaten visar att en del pedagoger använde av- och påklädningssituationerna för att synliggöra matematiska begrepp. I samtal med barnen utryckte de sig medvetet på ett matematiskt språk och förklarade begrepp för barnen i de situationer det behövdes.

No description available.

Syftet med denna studie är att undesöka vilket matematiskt innehåll förskollärare synliggör vid användning av bilderboken Lilla nollan och dom andra. För att besvara studiens frågeställningar har både observationer och kvalitativa intervjuer använts. Två förskollärare från en förskola valdes ut. Barnen som deltog vid observationerna var 4-5 år gamla. Resultatet visar att förskollärarna synliggör ett brett matematiskt innehåll i den ovannämnda bilderboken. De fokuserar på siffror, räkneramsan, räknar antal och jämför form och storlek. Samtal om siffran 0 och dess betydelse förs med barnen. De reflekterar och resonerar tillsammans med barnen över olika matematiska företeelser som de möter i bilderboken med stöd av dess bilder. Förskollärarna ger också flera exempel på hur barnen har utvecklat matematiska begrepp. De tar även tillvara på den mångfald och den variation av matematik som bilderboken erbjuder. / The purpose of this study is to investigate which mathematical contents preeschool teachers visible when using the picture book Little O and all the others. In order to answer the study questions, both observations and qualitative interviews have been used. Two preeschool teachers from one preeschool were selected. The children who participated in the observations were  4-5 years old. The results show that preeschool teachers reveal a broad mathematical content in the above mentioned picture book. They focus on numbers, countingchants, counting numbers and compare the shape and size. Conversations about the number 0 and the importance of it takes place. They reflect and resonate with the children of different mathematical phenomena they encounter in the picture book by virtue of its images. Preeschool teachers also give several examples of how the children have developed mathematical concepts. They also utilize both the diversity and the variety of mathematics that the picture book offers.