A number of studies have found that pupils, both newly arrived and other pupils who speak Swedish as a second language, have difficulties with mathematical tasks that consist of a few or more lines of text. It often seems to be a matter of mainly linguistic problems that are related to word and reading comprehension, that is, understanding and interpretation of formal concepts and words in the second language. Multilingual pupils who have recently migrated to Sweden from their home countries, but also pupils with foreign backgrounds who have lived in Sweden for several years - or in some cases, their entire lives - show lack of recognition in terms of cultural and traditional contexts. This study examines the difficulties and possibilities that were created when eight different multilingual pupils were being presented with text-rich mathematical tasks (word problems), but also focuses on examining the resources used during said process where the pupils read, interpreted and tried to solve given tasks. As the study is based on qualitative research, semi-structured interviews were conducted. The basis of the interviews consists of six word problems with related questions where the students had to think, reason and reflect upon the language being used in the tasks as well as the content, context and mathematical problems presented. The study has a theoretical approach based in both the social semiotics and the Language as Resource-model, of which both have been used to analyze the empirical material obtained from the interviews. In social semiotics, meaning-making is explained as a social practice that is created through interaction with the surrounding social and cultural contexts. While gathering and analyzing material, the so called “semiotic resources” were thus being observed, that is, the resources being used to communicate, interpret and create meaning of, for example, in this case, mathematical word problems. The results indicate that multilingual pupils use a variety of resources such as code-switching, translanguaging, drawing pictures, marking numbers and more while working with word problems. In addition to this, they also utilize the interviewer/teacher as a resource to, for example, read out information to them, explain concepts and words they do not understand et cetera. Multilingual pupils thus create bridges in several dynamic ways to overcome their difficulties and rather turn them into possibilities.

No description available.

The purpose of this study is to visualise the challenges that student teachers face when adapting mathematical tasks to different levels of difficulty. Specifically, the study aims to explore which aspects of mathematics didactic knowledge are expressed through the mathematics tasks. Examination tasks from previous mathematics courses were selected and analyzed based on a qualitative content analysis with the MKT framework, Mathematical Knowledge for Teaching (Ball et al., 2008). The students' adaptations can be described through five different themes: linguistic-, visual-, structural- and mathematical adaptations and mistakes. When the themes were analyzed using the MKT framework, it emerged that the students show different aspects of mathematics didactic knowledge and that there is a need to develop certain aspects further. There is a greater variation in the adaptations when the students simplify the task compared to when they make it more difficult. The result also shows that the students need to be given the opportunity to acquire deeper knowledge about the structure and function of the curriculum in order for this aspect of knowledge to develop further. A large percentage of the students make various mistakes in their adaptations. The mistakes have been linked to the students' mathematical content knowledge. Some of the mistakes indicate that the lack of content knowledge also affects and limits the students' mathematics didactic knowledge. An implication of the result is that teachers in the mathematics courses need to consider and address these aspects in future teaching so that the students are given the opportunity to further develop their content knowledge as well as their mathematics didactic knowledge. / Studiens syfte är att synliggöra vilka utmaningar lärarstudenter möter vid anpassning av matematikuppgifter till olika svårighetsgrader. Specifikt syftar studien till att studera vilka olika matematikdidaktiska kunskaper som uttrycks genom anpassningarna av matematikuppgifterna. Studentinlämningar av en genomförd examinationsuppgift från tidigare matematikkurser har valts ut och analyserats med en kvalitativ innehållsanalys där MKT-ramverket, Mathematical Knowledge for Teaching (Ball m.fl., 2008) utgör den teoretiska ramen. Studiens resultat visar att studenternas anpassningar speglas av fem olika teman: språkliga-, visuella-, strukturella- och matematiska anpassningar samt misstag. När de olika temana analyserades med hjälp av MKT-ramverket, så framkom att studenterna visar olika aspekter av matematikdidaktiska kunskaper och att det finns behov av att utveckla vissa aspekter vidare. Det finns en större variation i anpassningarna när studenterna förenklar uppgiften jämfört med när de försvårar den. Resultatet visar också att studenterna behöver få möjlighet att tillägna sig djupare kunskaper om kursplanens uppbyggnad och funktion för att denna aspekt av kunskap ska utvecklas ytterligare. En stor andel av studenterna gör olika misstag i sina anpassningar. Misstagen  har kopplats till studenternas matematiska ämneskunskaper. Vissa av misstagen indikerar att den bristande ämneskunskapen även påverkar och begränsar studentens matematikdidaktiska kunskaper. En implikation är att undervisande lärarutbildare i matematikkurserna behöver beakta och behandla dessa aspekter i kommande undervisning så att studenter ges möjlighet att vidareutveckla såväl sina ämneskunskaper som sina matematikdidaktiska kunskaper.

To make mathematics more significant for the beneficiaries, the problem studied in this thesis is to investigate how to connect mathematical daily practices with educational contexts. The overarching aim is to investigate how to contextualise school mathematics within Rwandan cultural mathematics practices. The content of the thesis reports on the characteristics of mathematical organisations in three workplace settings (taxi driving, house construction and restaurant management) which in turn serve as source for the design of contextualised mathematical activities for student teachers in a teacher education programme. Three levels of mathematical practices are described: (1) mathematical practices that are performed by workers within their respective workplaces, (2) mathematical practices that are performed by student teachers while solving and posing contextualised mathematical tasks for secondary school students, (3) mathematical practices that are carried out by secondary school students. Data gathered from individual and group interviews, transcripts of group discussions and students’ written reports of mathematical work were analysed from the perspective of both activity theory and anthropological theory of didactics. Findings from workplace settings revealed that mathematical organisations performed by workers are characterised by techniques which are functional to the problem at hand, the cultural constraints and the educational background of the workers. As long as they are pragmatic towards the goals of the activity no further justification of the techniques used is needed, resulting in a mathematical organisation with undeveloped know-why (logos). On the contrary, at university and secondary school settings, students justified the used techniques throughout the related taught content of the subject mathematics. Also from each category of mathematical practice, it is shown that while connecting workplaces and educational settings the didactic transposition process was much influenced by the institutional conditions and constraints. / För att göra matematiken betydelsefull för avnämarna är problemområdet som studeras i denna avhandling hur den matematik som finns i samhället kan överbryggas till en undervisningskontext. Syftet med avhandlingen är att undersöka hur man kan kontextualisera skolmatematik i kulturella praktiker i Rwanda. I avhandlingen belyses först matematisk organisation på tre arbetsplatser – i en taxiverksamhet, hos en byggmästare och hos en restaurangägare. Matematik i dessa verksamheter utgör underlag för att konstruera uppgifter för lärarstudenter inom ämnet matematik som först löser uppgifterna och sedan i sin tur konstruerar uppgifter för elever motsvarande årskurs nio i grundskolan. Uppgifterna konstrueras med utgångspunkt i den information studenterna fått om de tre verksamheterna. Datainsamlingen skedde med hjälp av individuella intervjuer, gruppintervjuer och bandinspelade gruppdiskussioner samt studenters och elevers nedtecknade lösningar på respektive uppgifter. Data analyserades med hjälp av aktivitetsteori och antropologisk didaktisk teori. Resultaten från arbetsplatserna visade att matematisk organisation kännetecknades av tekniker som är funktionella för de problem som behövde lösas, de kulturella villkor som förelåg och deltagarnas utbildningsbakgrund. Så länge som teknikerna ledde till önskade mål för verksamheten fanns inga behov att utveckla tekniken som kännetecknades av en matematisk organisation med outvecklad logos. I kontrast till denna strategi sågs studenter och elever i respektive miljöer redovisa de tekniker som användes och motivera dem i enlighet med vad som krävs inom matematikämnet. Den matematiska transpositionsprocessen som utfördes av deltagarna i de olika miljöerna influerades i hög grad av rådande institutionella villkor och begränsningar.

The thesis on "Critical places at the first stage of primary school in the teaching of mathematics by the Hejný method" focuses on the problematic places of the Hejný method, which make it difficult for teachers and especially their pupils at the first stage of primary schools. In the theoretical part of the thesis, the constructivist and transient educational style teaching of mathematics using the Hejný method are characterized. The critical points in mathematics identified in the project of the Grant Agency of the Czech Republic are also introduced and conceived into a unified structure. The theoretical part also includes an analysis of pupil solutions to mathematical tasks from the 2015 TIMSS international survey. The empirical part deals with the experience and view of primary school teachers in teaching mathematics by the Hejný method. The first research survey finds from future primary school teachers their experience and opinions on this method. The second research survey focuses on the identification of problematic places and roles in the teaching of mathematics by the Hejný method from the point of view of teachers who teach mathematics using the Hejný method at the first stage of primary schools. The questionnaire survey was carried out using the questionnaire method, which identifies...

At the moment, there is a low level of students’ knowledge in natural sciences. The problem is particularly acute in the field of tasks solving. This paper offers actual ways to solve a task by developing a universal technology for solving tasks. This technology will become the basis for training courses aimed at filling students' knowledge gaps and improving their ability to solve tasks. The paper also considers the automation of educational activities of the Network Engineering School. As a result of the work, the current level of schoolchildren’s training was determined and the causes of the problem were identified. The existing methods of solving tasks were analyzed and identified their shortcomings. A universal technology for solving problems using the method of tabular analysis has been developed and its mathematical justification has been given. Compiled methodological manual and published in scientific journals. The business processes of the Network Engineering School were also automated: a distance learning system was introduced into the learning process. The obtained results have already been applied in practice: the developed methodology has become the base of mathematics course at the Network Engineering School, in which classes are already being held. Also, the effectiveness of the methodology was evaluated during a study conducted on the basis of the school Olympiad. In addition, an assessment of the effectiveness of the project on the implementation of a distance learning system was made and it was revealed that the project is profitable. / В настоящий момент наблюдается низкий уровень подготовки школьников по естественно-научным направлениям. Особенно остро ощущается проблема в области решения задач. Данная работа предлагает актуальные пути решения проблемы путем разработки универсальной технологии решения задач. Данная технология станет основой для учебных курсов, направленных восполнить пробелы в знаниях учеников и подтянуть их способности решать задачи. Также в работе рассматривается автоматизация учебной деятельности Сетевой инженерно-технической школы. В результате работы был определен текущий уровень подготовки школьников и определены причины возникновения проблемы. Проанализированы существующие методики решения задач и выявлены их недостатки. Разработана универсальная технология решения задач методом табличного анализа и дано ее математическое обоснование. Составлено методическое пособие и опубликовано в научных изданиях. Также были автоматизированы бизнес-процессы Сетевой инженерно-технической школы: в процесс обучения была внедрена система дистанционного обучения. Полученные результаты уже применены на практике: разработанная методика стала основной курса по математике в Сетевой инженерно-технической школе, по которому уже проводятся занятия. Также эффективность методики была оценена во время исследования, проведенного на базе школьной Олимпиады. А также была произведена оценка эффективности проекта по внедрению системы дистанционного обучения и выявлено, что проект является прибыльным.