Det finns flera faktorer som påverkar elevers prestation inom matematik, bland annat elevers matematiska självkänsla. Denna pilotstudie utvecklar och diskuterar ett verktyg för att undersöka hur väl matematiklärare uppfattar sina elevers matematiska självkänsla. Frågeställningen som avsågs att försöka besvaras var följande: Hur väl stämmer matematiklärares uppfattningar om sina elevers matematiska självkänsla överens med elevens matematiska självkänsla?  Genom att granska elev-lärarsvarskombinationer undersöktes hur väl individuella elevers matematiska självkänsla uppfattades av sin matematiklärare. Resultatet påvisar att lärare summativt överskattar elevers matematiska självkänsla. Nollhypotesgranskning visar ej på någon tydlig trend då hälften av de undersökta elev-lärarsvarskombinationerna styrker nollhypotesen och hälften motsäger nollhypotesen. / There are several factors which affect students' performance in mathematics, including the students’ mathematical self-esteem. This pilot study tests a tool to examine mathematics teachers' perception of their students’ mathematical self esteem. The research question that was intended to be answered was the following:  How well do mathematics teachers' perceptions of their students' mathematical self-esteem agree with the students mathematical self-esteem?  By examining student-teacher response combinations through a null hypothesis, it was investigated how well individual students' mathematical self-esteem was perceived by their mathematics teacher. The results show that teachers summatively overestimate students' mathematical self-esteem. Null hypothesis review does not show any clear trend since half of the student-teacher response combinations examined confirmed the null hypothesis and half rejects the null hypothesis.

For an education system to function effectively it is important that its planning functions are executed effectively and efficiently. Among others this implies that the system must know what the teacher supply and demand is and how it will change in time. If the teacher supply and demand is known it could result in sound intervention strategies being developed and implemented. Education planners will be able to plan for the number of bursaries to be awarded and in which subject fields; it will be known how many foreign teachers to employ and for which subjects. This is the basic rationale that underpins this study. This study explored the problem of teacher demand and supply in the Further Education and Training (FET) phase (Grades 10 to 12) in South Africa and offers a critical analysis of strategies adopted by Provincial Education Departments in an endeavour to diminish the demand for teachers, specifically for Mathematics and Science, in rural and poor schools. Initially the study involved a secondary data analysis to extrapolate the demand and supply of teachers in Mathematics and Science over the next ten years. The first key finding of the study was that the data needed for such an analysis does not exist in any reliable form that would facilitate the development of such a projection. What the study had to rely on was anecdotal evidence that suggests that a shortage of Mathematics and Science teachers does exist and that posts are often filled by unqualified and under-qualified staff. In the second phase of the research in which the study explored the effectiveness of strategies developed to address the shortage of Mathematics and Science teachers, a qualitative research approach was adopted within a descriptive interpretive design. The views and opinions of human resource managers responsible for post provisioning in schools were explored through in-depth interviews to understand the types of strategy adopted by the provinces, their potential to alleviate the problem of Mathematics and Science teacher shortage in Grades 10 to 12, their success, challenges and factors internal to the Department of Education that may deter Provincial Education Departments from achieving their objectives. The findings revealed that Provincial Education Departments (PEDs) do take heed of strategies developed by the national Department of Basic Education (DBE). However implementation is far removed from the original intention and no significant impact results. Although the reasons are not always obvious from this study, a few important aspects did emerge. First, the strategy developed may not be popular with a particular province - employing foreign teachers is a case in point. Secondly, focusing on just a number of schools to improve their results (e.g. as with the Dinaledi schools) may meet with resistance from educators and teachers’ unions. Thirdly, creating bursaries for initial teacher education in certain key areas can only be successful if the number of teachers in need is known. Finally, even the best strategies are doomed if post provisioning and appointment of staff are dealt with by different stakeholders. Based on the findings, it is recommended that both the DBE and PEDs ensure that quality education management information is collected and maintained. Information that is reliable and accurate will inform planning and key decisions to ensure that the supply of teachers is based on a specific need. As such, deficiencies in skills that are in short supply such as Science and Mathematics can be averted and better opportunities can be created for new teacher graduates. While an improved performance of learners in these subjects is requisite for related study fields at universities, the Dinaledi schools must be adequately supported and such a model applied to other schools. The employment of foreign teachers on short-term contracts does not create stability in schools, therefore, their employment must be standardised. Significantly, retention in rural and poor schools is a problem since they struggle to attract quality teachers; for that reason teacher incentives are indispensable. Making a declaration for unqualified and under-qualified teachers to acquire professional teaching qualifications and subsequently discontinue such appointments, will raise the standard of teaching and learning in schools. Rather, databases of unemployed qualified teachers could be maintained and such information made accessible to school principals. In the absence of reliable data that can indicate teacher qualification and specialisation versus subject taught, the extent to which Mathematics and Science are taught by unqualified and under-qualified teachers as well as out-of-specialisation teaching, is not known. However, poor pass rates in these subjects at the exit point of the schooling system (Grade 12) attest to the lack of appropriately skilled teacher workforce. Therefore, if Mathematics and Science specialisation is required, then strategies being implemented by the DBE and PEDs must have a clear purpose to address this shortage. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Education Management and Policy Studies / PhD / Unrestricted

Department of Curriculum Studies and Education Management / MEDCS

Syftet med denna studie är att undersöka lärarnas upplevelse av elevers missuppfattningar vid inlärning av bråk och sannolikhet samt om det är möjligt att minska missuppfattandet med hjälp av kategorisering av dessa. Genom att fråga matematiklärare om de upplever att eleverna de undervisar ofta har missuppfattningar och om samma missuppfattningar är återkommande, kan vi få en bild av vilka delar av de matematiska begreppen som kan uppfattas svåra av eleverna. De missuppfattningar som tenderar att återkomma kan komma att behöva mer fokus på förklaring. Studien genomfördes genom en surveyundersökning i enkätform som publicerades i grupper som samlar matematiklärare på sociala medier, samt skickades till matematiklärare via mail. Det resulterade i 41 enkätsvar som analyserades genom beskrivande statistik i kombination med en induktiv innehållsanalys. Studien visar att orsaken till att missuppfattningar kopplade till matematiska begrepp kan bero på ett för stort fokus på procedurinriktad undervisning i de tidigare skolåren. Detta upplever lärarna medför att eleverna inte har tillräcklig begreppsförståelse när de börjar på gymnasiet. Det vanligaste åtgärdsförslaget är kopplat till undervisningsstrategier med mer sociokulturella inslag i undervisningen. De allra flesta av studiens deltagare upplever att begreppsförståelse är viktigt och utgör en förutsättning för att klara av både problemlösning och mer avancerad matematik. För att skapa förståelse för matematiska begrepp är det nyttigt för lärare att känna till vanliga missuppfattningar. Kategorisering av missuppfattningar kan därför vara till nytta för lärarna i undervisningen, som ett stöd i lektionsplanering och som ett pedagogiskt verktyg för att utveckla elevernas matematiska kunskaper. / The purpose of this study is to investigate the teachers' experience of students' misconceptions when learning fractions and probability, and whether it is possible to reduce misconceptions by categorizing them. By asking mathematics teachers if they feel that the students they teach often have misconceptions and if the same misconceptions are repeated, we can get a picture of which parts of the mathematical concepts may be perceived as difficult by the students. The misconceptions that tend to recur may need more focus on explanation. The study was carried out through a survey in questionnaire form that was published in groups that bring together mathematics teachers on social media and was also sent to mathematics teachers via email. This resulted in 41 survey responses that were analysed through descriptive statistics in combination with an inductive content analysis. The study shows that the reason for misconceptions connected to mathematical concepts may be due to too much focus on procedure-oriented teaching in the earlier school years. The teachers feel that this means that the students do not have sufficient conceptual understanding when they start high school. The most common proposed measure is linked to teaching strategies with more socio-cultural elements in the teaching. The vast majority of the study's participants feel that conceptual understanding is important and constitutes an essentiality for being able to cope with both problem solving and mathematics at more advanced levels. In order to create an understanding of mathematical concepts, it is useful for teachers to know about common misconceptions. Categorization of misconceptions can therefore be useful for teachers in teaching, as a support in lesson planning and as a pedagogical tool to develop students' mathematical knowledge.

This research seeks to investigate the influence of lesson study on preservice secondary mathematics teachers' view of self as mathematics expert. The study acknowledges the commonly held belief that prospective mathematics teachers have that they know and understand secondary mathematics. The purpose in engaging the preservice teachers in lesson study is to dislodge this belief. In particular, this research report focuses on one preservice teacher and her experiences during lesson study. Using the data collected, the researcher reports on the baseline beliefs that the preservice teacher held toward her knowledge of secondary mathematics, her mathematical experiences during the actual lesson study phase of the research and the final status of her beliefs in relation to her secondary mathematics understanding. After assessing the preservice teacher's beliefs, the report focuses on the moves the preservice teacher makes to protect her identity as a knower of mathematics. The report details how the researcher probed the subject's views through a follow-up interview. The researcher discovered during the follow-up interview that the subject was finally able to admit her lack of mathematical knowledge and her desire to not be seen as 'dumb' in front of the interviewer. The implications of the study suggest that teacher educators should be sensitive to preservice secondary teachers' perceptions of their mathematical knowledge and teacher educators should watch for the moves preservice teachers make to shift conversation away from mathematics topics.

<p>  </p> <p>Radian angle measure is central to learning trigonometry, with researchers providing evidence that a coherent understanding of radian contributes to a coherent understanding of trigonometric and inverse trigonometric functions. However, there are few opportunities for students to engage with curricular situations that involve radian angle measure. The purpose of this dissertation is to explore and provide insights into preservice mathematics teachers’ (PMTs’) conceptions of radian angle measure using three curricular situations. The first chapter reviews the relevant literature, which reported that PMTs’ conceptions of radian angle measure involve angles measured in terms of π, in relation to degrees, and in relation to the unit circle. In chapter two, I explored PMTs’ conceptions of radian angle measure using textbook representations. Seven PMTs participated in a think-aloud semi-structured interviews, where they defined radian angle measure from six textbook diagrams of radian, including a diagram of the unit circle. In chapter three, building on literature that reported that PMTs’ conceptions of radian angle measure involve relating radian to degrees, I explored how PMTs conceptualize this relationship. Five PMTs participated in semi-structured interviews, where they described radian angle measure given the angle measure in degrees. In chapter four, I explored the PMTs’ conceptions of radian angle measure given a novel context. Four PMTs participated in semi-structured virtual interviews, where they engaged with a digital activity that involves radian angle measure in the context of light reflection. Some of the dissertation’s findings align with previous research, where PMTs’ conceptualized radian angle measure in relation to the unit circle. However, this dissertation provides empirical evidence of why the PMTs refer to the unit circle. The PMTs acknowledged knowing the unit circle from memorization, but also explained that the purpose for using the unit circle is efficiency. At the same time, the PMTs acknowledged limitations in the unit circle and in their conceptions of it. Overall findings from the dissertation demonstrate the complexity of PMTs’ conceptions of radian angle measure. The PMTs’ conceptions were reported as concept definitions, ways of thinking, and spatial ways of thinking. The PMTs demonstrated flexibility with reasoning about radian angle measure using foundational conceptions in learning higher mathematics topics (e.g., proportional reasoning concepts, spatial ways of thinking). By positioning the PMTs as knowers and thinkers with valuable insights to provide, I was able to uncover and report a collection of conceptions that were demonstrated by PMTs when a curricular situation involved radian angle measure. The findings from this dissertation extend existing research that explored conceptions of angle measure and radian angle measure by reporting PMTs’ conceptions of radian angle measure given three different curricular situations. While there is still much that needs to be investigated about complexities in PMTs’ conceptions of radian angle measure, this dissertation represents one step toward providing insights about those complexities. </p>

Vi lever i ett samhälle där datorer och annan digitalteknik blir allt mer central i vår vardag. Sveriges regering har därför ålagt Skolverket att stärka elevernas digitala kompetens. Som en del av detta införs programmering som ett digitalt verktyg i matematikundervisningen både i grundskolan och på gymnasiet. Det krävs dock i nuläget inga kurser i programmering för att bli en legitimerad matematiklärare. Syftet med undersökningen som presenteras i denna rapport är att undersöka matematiklärares uppfattningar som uppkommit på grund av att Skolverkets revidering av läroplanerna i matematik. Denna revidering innebär att vissa matematikkurser på gymnasiet innefattar att programmering skall användas som problemlösningsverktyg. Underlaget till denna undersökning är en transkribering och tematisering av kvalitativa intervjuer med tio matematiklärare, samt tidigare forskning. Undersökningen fann en viss oro bland lärarna som till stor del handlade om bristande kunskap i programmering samt problematiken med att hinna med att få in ytterligare ett moment i undervisningen. Under intervjuerna framgick det att lärarna var allmänt fundersamma om vilka digitala verktyg de skulle använda för att lösa detta nya krav. En majoritet av lärarna förordade dock Excel och Geogebra. Det framkom ett visst missnöje med att detta nya krav infördes med mycket kort varsel. Många lärare förväntade sig och litade på att läroboksförfattarna skulle komma med en uppdatering av läroböckerna i matematik. En uppdatering som förväntades innefatta programmering och som därmed skulle lösa den nya pedagogiska utmaningen. / Computers and other digital technology are becoming increasingly important in our society. Due to that, the Swedish Government has instructed their National Agency for Education to strengthen the students' digital competence. One outcome of this was that programming become a part of teaching mathematics both in primary and upper secondary school. Programming is not a part of the mandatory studies needed to become a certified mathematics teacher. The purpose of this study is to investigate the ideas, attitudes and ideas of mathematics teachers that have arisen because of the National Agency for Education's revision of the curricula in mathematics. According to this revision of the curricula, students should use programming as a problem-solving tool. The basis for this study is a transcription of qualitative interviews with ten mathematics teachers and an examination of previous research. This study found that there was some concern among the teachers. Most of the concern was about lack of knowledge in programming. The majority of teachers preferred to use Excel and Geogebra as a digital tool to teach programming. Many teachers expressed spontaneously a general dissatisfaction with the impact that calculators already have in mathematics education. There was some dissatisfaction with the introduction of this new requirement at very short notice. Many teachers expected and trusted that the textbook authors would come up with an update of the textbooks in mathematics. An update that would thus solve their new educational challenge.

The aim of this study was to investigate the differentiation practices of mathematics teachers within the framework proposed by Tomlinson (2016). Tomlinson's framework outlines general principles of differentiation and how teachers tailor these to meet students' diverse needs. Previous research suggests that differentiation among teachers is not utilized to the necessary extent. One primary research question was established to guide this study: How do teachers' application of general differentiation principles relate to the practical operationalization of teaching, considering the unique needs and conditions of their students? A qualitative approach was employed, utilizing semi-structured interviews and observations to gather data and analyze teachers' approaches to differentiation. The study involved the participation of four teachers from three different schools. Through coding, thematization, and summarization a deductive thematic analysis was applied to reveal patterns in teachers' practices. The findings revealed that teachers varied in their differentiation practices across different levels of Tomlinson's framework. Some teachers consistently differentiated across all aspects, while others showed moderate to no differentiation. Furthermore, the study highlighted the importance of addressing and integrating students' needs more comprehensively into differentiation practices. Assessment and routine were also found significant for an effective practice differentiation. The study is of relevance for teachers because it has led to conclusions that can show where the area of improvement in differentiation education lies in the Swedish context. Suggestions for further research include exploring the impact of different teaching materials on differentiation practices, and examining specific areas where teachers differentiate more or less frequently.

No description available.

Continuing Professional Development (CPD) of teachers is increasingly becoming a priority in most countries throughout the world. It is widely viewed as the most effective approach to prepare teachers adequately, and to improve their instructional and intervention practices, for when they enter the workforce (Fraser et al 2007). Despite the general acceptance of CPD programmes as essential to the improvement of education, reviews of professional development research constantly point out the ineffectiveness of most of these programmes (see Cohen and Hill, 1998 and 2000). Furthermore, many teachers express dissatisfaction with the professional development opportunities made available to them in schools and insist that the most effective development programmes they have experienced have been self-initiated (National Research Council, 2007). There is a consensus that many CPD programmes have yet to understand professional development from a teacher‘s perspective. This perspective acknowledges what drives teachers to enlist in these programmes and how such programmes can make a difference to them and their classrooms. Therefore, this study seeks to return the emphasis of professional development to the teachers. The study explores the teachers‘ perspectives of CPD in general, the personal meaning of CPD, and its meaning in the context of their work. By interviewing the teachers who were part of the Mpumalanga Secondary Science Initiative (MSSI) project (a seven year science and mathematics professional development intervention), I explore: the teachers‘ opinions of the intervention; its meaning to them and their work; and its impact on their classroom practices and students for the duration of the intervention and beyond. In this study, I explore data from an extensive and longitudinal study of teachers who were part of the CPD programme in greater detail. In discussing my data, I propose that CPD, however well intentioned and executed, is received differently by each teacher as a result of their personal circumstances and investment in the programme. I argue that the greater the unity between the personal circumstances and motivations of the teachers and those of the CPD intervention, the more likely the outcome will be meaningful for the participating teachers. In turn, the ability to sustain the benefits of the intervention will be enhanced. / Further Teacher Education / D.Ed. (Curriculum Studies)