No description available.

<p>The primordial purpose of our studies has been carrying out a detailed research to describe methods or work procedures in the teaching and application of the mathematics, at a school based or alignment on the mathematics instruction. To be able to study the pupils in their development of the mathematical thinking.</p><p>We have carried out a detailed investigation, in the previously mentioned school using the ethnography observation methods directly in the place of the facts. Where it was possible to verify that the mathematics lessons were a consequences of the methods or work procedures which made us deduce that this school did every possible effort to stimulate all the pupils to be better and particularly talented pupils individually to develop one’s talent by means of the following results:</p><p>· Develop the logical thinking</p><p>· The self-critical ability</p><p>· The attitude of the teacher/communication</p><p>· A positive work atmosphere</p><p>· Organization of the school and the class</p><p>· Formation of the theoretical knowledge</p><p>Keywords</p><p>Mathematical thinking.</p><p>Pupils</p><p>Independent school</p>

The primordial purpose of our studies has been carrying out a detailed research to describe methods or work procedures in the teaching and application of the mathematics, at a school based or alignment on the mathematics instruction. To be able to study the pupils in their development of the mathematical thinking. We have carried out a detailed investigation, in the previously mentioned school using the ethnography observation methods directly in the place of the facts. Where it was possible to verify that the mathematics lessons were a consequences of the methods or work procedures which made us deduce that this school did every possible effort to stimulate all the pupils to be better and particularly talented pupils individually to develop one’s talent by means of the following results: · Develop the logical thinking · The self-critical ability · The attitude of the teacher/communication · A positive work atmosphere · Organization of the school and the class · Formation of the theoretical knowledge Keywords Mathematical thinking. Pupils Independent school

More than half a century ago, Piaget concluded from an investigation of children’s representational thinking about the nature of space that the development of children’s representational thought is topological before it is Euclidean. This conclusion, commonly referred to as the “topological primacy thesis,” has essentially been rejected. By giving emphasis to the ideas that develop rather than the order in which they develop, this work set out to develop a new form of non-metric geometry from young children’s early and intuitive topological, or at least non-metric, ideas. I conducted an eighteen-week teaching experiment with two children, ages six and seven. I developed a new dynamic geometry environment called Configure that I used in tandem with clinical interviews in each of the episodes of the experiment to elicit these children’s non-metric conceptions and subsequently support their development. I found that these children developed significant and authentic forms of geometric reasoning. It is these findings, which I refer to as qualitative geometry, that have implications for the teaching of geometry and for research into students’ mathematical reasoning. / text

No description available.

<p>During my time as a student of education I have learnt that it is my responsibility, as a teacher, to adjust the ways in which I teach to the needs, abilities, experiences, and thoughts of each individual child. What I have not yet gained much knowledge on is how to go about finding the children’s thoughts.</p><p>In this thesis I investigate the interview as a method of finding out how sixth graders think about their mathematics education. Four children were interviewed. In addition to these inter-views, as a means of giving a broader perspective to and a greater understanding of the chil-dren’s answers, one math lesson was filmed and the math teacher was interview on two sepa-rate occasions.</p><p>What I found was that a number of factors seemed to influence the children’s thoughts and answers, and that their answers were most likely not always a mirror of their thoughts. From this follows that we, as teachers, must be careful and not assume that we know about a child’s thoughts when, in fact, what we know is what the child chooses to communicate about his or her thoughts. I also found that the children seemed unaccustomed to speaking about mathe-matics in the way that I wanted them to. One reason for this seemed to be the way in which their teacher organized the lessons.</p>

Abstract This study is concerned with the ways mathematical understanding emerges when mathematical phenomena are encountered through digital pedagogical media, the spreadsheet, in particular. Central to this, was an examination of the affordances digital technologies offer, and how the affordances associated with investigating mathematical tasks in the spreadsheet environment, shaped the learning trajectories of the participants. Two categories of participating students were involved, ten-year-old primary school pupils, and pre-service teachers. An eclectic approach to data collection, including qualitative and quantitative methods, was initially undertaken, but as my research perspective evolved, a moderate hermeneutic frame emerged as the most productive way in which to examine the research questions. A hermeneutic process transformed the research methodology, as well as the manner in which the data were interpreted. The initial analysis and evolving methodology not only informed this transition to a moderate hermeneutic lens, they were constitutive of the ongoing research perspectives and their associated interpretations. The data, and some that was subsequently collected, were then reconsidered from this modified position. The findings indicated that engaging mathematical tasks through the pedagogical medium of the spreadsheet, influenced the nature of the investigative process in particular ways. As a consequence, the interpretations of the interactions, and the understandings this evoked, also differed. The students created and made connections between alternative models of the situations, while the visual, tabular structuring of the environment, in conjunction with its propensity to instantly manage large amounts of output accurately, facilitated their observation of patterns. They frequently investigated the visual nature of these patterns, and used visual referents in their interpretations and explanations. It also allowed them to pose and test their informal conjectures and generalisations in non-threatening circumstances, to reset investigative sub-goals easily, hence fostering risk taking in their approach. At times, the learning trajectory evolved in unexpected ways, and the data illustrated various alternative ways in which unexpected, visual output stimulated discussion and extended the boundaries of, or reorganised, their interaction and mathematical thinking. An examination of the visual perturbations, and other elements of learning as hermeneutic processes also revealed alternative understandings and explanations. Viewing the data and the research process through hermeneutic filters enhanced the connectivity between the emergence of individual mathematical understanding, and the cultural formation of mathematics. It permitted consideration of the ways this process influences the evolution of mathematics education research. While interpretive approaches are inevitably imbued with the researcher perspective in the analysis of what gets noticed, the research gave fresh insights into the ways learning emerges through digital pedagogical media, and the potential of this engagement to change the nature of mathematics education.

The first aim of this study was to identify important aspects of mathematical thinking, and to investigate the relationships between the different aspects of mathematical thinking and mathematics achievement. The second aim was to examine possible gender and school location (urban, suburban, and rural) differences related to aspects of mathematical thinking and mathematics achievement. Two assessments were developed that were suitable for students in the Year 11 scientific stream in Jordan. One test was for aspects of mathematical thinking and the other for mathematics achievement, the latter being consistent with typical school achievement tests for these students in Jordan. The researcher chose and developed items to test mathematical thinking and mathematics achievement from the Third International Mathematics and Science Study (TIMSS), the internet, research literature, specialist books in mathematics and his own experience. The data were collected in the 2003-2004 academic year from over 500 Year 11 scientific stream students (both male and female) at 20 randomly selected schools from six directorates in the Irbid Governorate, Jordan. In addition, 13 teachers were individually interviewed, and four groups of students were interviewed in focus groups to obtain information about their opinions and about different methods of thinking in mathematics. The teacher interviews were used to identify consistencies and inconsistencies between the test results and the respondents’ opinions of difficulty and importance. In addition, information was obtained about the classroom time teachers devoted to the different aspects of mathematical thinking and the teaching strategies they employed. Six aspects of mathematical thinking were identified by the study: Generalization, Induction, Deduction, Use of Symbols, Logical thinking and Mathematical proof. Mathematical proof was also the most difficult aspect, while Logical thinking was the least difficult. Female students had significantly higher mean scores than males on three of the six aspects of mathematical thinking and on the total test scores. Students attending suburban schools had significantly higher mean scores than students at urban and rural schools on four aspects, and on the total scores. Using multiple regression analysis, all six aspects were found to be important for mathematics achievement. Mathematical proof and Generalization were the most important aspects, Use of symbols and Logical thinking were next in importance, and Deduction and Induction were the least important aspects. Approximately 70 per cent of the variance in mathematics achievement was explained by the six aspects of mathematical thinking, gender, and school location. There was a high level of consistency between teacher opinions of the relative importance of aspects of mathematical thinking and the test results. However, there were some nconsistencies between the teacher opinions and test results with respect to relative difficulty levels of the six aspects. By clarifying the importance for mathematics achievement of the six aspects of mathematical thinking identified, this study has relevance for the teaching of mathematics to Year 11, scientific stream students in Jordan. / PhD Doctorate

During my time as a student of education I have learnt that it is my responsibility, as a teacher, to adjust the ways in which I teach to the needs, abilities, experiences, and thoughts of each individual child. What I have not yet gained much knowledge on is how to go about finding the children’s thoughts. In this thesis I investigate the interview as a method of finding out how sixth graders think about their mathematics education. Four children were interviewed. In addition to these inter-views, as a means of giving a broader perspective to and a greater understanding of the chil-dren’s answers, one math lesson was filmed and the math teacher was interview on two sepa-rate occasions. What I found was that a number of factors seemed to influence the children’s thoughts and answers, and that their answers were most likely not always a mirror of their thoughts. From this follows that we, as teachers, must be careful and not assume that we know about a child’s thoughts when, in fact, what we know is what the child chooses to communicate about his or her thoughts. I also found that the children seemed unaccustomed to speaking about mathe-matics in the way that I wanted them to. One reason for this seemed to be the way in which their teacher organized the lessons.

The aim of this qualitative study is to explore and describe the mathematical thinking skills that students require for a first level programming subject that forms part of the National Diploma in Information Communication Technology (ICT) at a University of Technology (UoT). Mathematics is an entry requirement for many tertiary programmes, including ICT courses, unfortunately the poor quality of schooling in South Africa limits learners' access to higher education. From the literature it is evident that students lack fluency in fundamental mathematical and problem-solving skills when they enter higher education. In this study, the concept of programming thinking skills is explored, described and linked to mathematical thinking skills. An instrument (Mathematical and Programming Thinking Skills Matrix for the Analysis of Programming Assessment) has been developed and used to analyse examination papers of a first-year programming subject (at TUT) in order to identify mathematical skills as these appear in programming assessments. Semi-structures interviews were conducted with first-year programming lecturers, examiners and moderators. The literature as well and the results of the analysed data indicated and confirmed that mathematical thinking skills are extremely important when learning to program. The results of the study indicate a strong relationship between mathematical thinking skills and programming thinking skills. The outcome of this study is therefore a set of mathematical thinking skills that needs to be developed when compiling a mathematics curriculum for first level programming students studying towards a National Diploma in ICT. / Dissertation (MEd)--University of Pretoria, 2016. / Science, Mathematics and Technology Education / MEd / Unrestricted