The diploma thesis is aimed at reeducation of mechanical knowledge in the area of fractions. Since every student has different needs and pace in his/her process of gaining knowledge, the reeducation is set into their private supplementary tutoring lessons. In the theoretical part, the basic concepts (how is the private supplementary tutoring understood in this thesis, which students are taken into consideration, and what is mechanical knowledge) are explained based on Czech and foreign literary sources, subsequently, the constructivist way of teaching, which is suitable for the reeducation of mechanical knowledge, is described. The second part of this thesis is constituted by the practical implementation of the theoretical findings into three case studies. Three students were diagnosed with mechanical knowledge in the area of fractions. Subsequently, their knowledge was being reeducated during their private supplementary tutoring lessons. The process of reeducation of each student is described in detail, moreover, a kind of manual describing what should not be avoided when dealing with this topic is included. KEY WORDS mechanical knowledge, reeducation, private supplementary tutoring, fractions 5

The goal of this thesis is to outline the situation of private supplementary tutoring in the first years of primary school in the Czech Republic, as this topic has not been investigated properly so far. A questionnaire for young pupil's parents was chosen as an appropriate method to collect the data needed. Although the research sample was not large, the research has brought valuable information about the children who have supplementary tutoring, about the reasons they (their parents) have for it, and also the tutors chosen to teach the pupils. The thesis builds on foreign sources and compares the situation in the Czech Republic with the situation in other countries in the world. Despite its limited extent this work could be used as a first groundwork for subsequent more extensive research in this field.

The dissertation thesis deals with the shadow education phenomenon, which has yet not been explored in the Czech context. In the international literature, the term shadow education entails various forms and types of paid private supplementary tutoring. The dissertation provides a diagnostic-analytical inquiry on taking paid private tutoring lessons and preparatory courses for university entrance examinations by students of upper-secondary schools in programmes concluded with maturita examination in Prague and Moravian-Silesian Region. Its objectives are: 1) to describe the chosen types of private supplementary tutoring at upper secondary level of education concluded with maturita examination (scale, subjects, intensity, organisational forms, providers etc.), 2) to analyse the contextual factors underlying the demand for these types of private supplementary tutoring. The research employed multi-phase mixed-method research design with priority given to quantitative data. Three research methods were used: 1) quantitative content analysis of the internet mediated notice board for private tutoring lessons, 2) the quantitative questionnaire survey research of randomly chosen students studying in academic and technical track upper-secondary schools in Prague and Moravian-Silesian Region (n=1265), 3)...

I det svenska undervisningslandskapet har extraundervisning, från både privata och offentliga aktörer, under senaste decenniet fått en mer och mer betydelsefull och naturlig plats. Där både ideella och vinstdrivande organisationer under de senaste årtionden erhållit statliga subventioner eller bidrag. Det blir därför viktigt att skapa en förståelse för vilken typ av matematikundervisning som ges av dessa organisationer. Av särskilt intresse för denna studie är de ideella organisationerna, och dess volontärer, som erbjuder kostnadsfri undervisning i form av räknestugor i matematik för elever från gymnasieskolan. Tidigare forskning om de svenska ideella räknestugornas undervisning och dess volontärer lyser med sin frånvaro. Syftet med detta arbete är att skapa förståelse för verksamheten inom de ideella räknestugorna, dess volontärer och vilken matematikundervisning som där ges. För att undersöka volontärernas undervisning så genomfördes dels intervjuer med volontärerna, om deras föreställning om matematik som ämne och om matematikundervisning, dels observationer av volontärernas undervisning inom räknestugans verksamhet. Analys och tolkning av observationer och intervjuer tar utgångspunkt i tidigare forskning om lärares föreställning om matematik, lärande och dess undervisning. De intervjuade och observerade volontärerna gav en samstämmig bild, där föreställningen av matematik som kom till uttryck i intervjuer stämde väl överens med vad som observerades i undervisning. Av den tidigare forskningens tre föreställningar av matematiken gav de intervjuade och observerade volontärerna uttryck för två av de tre föreställningarna. Matematik som verktyg var ett förhållningssätt som uttrycktes av samtliga volontärer i både intervju och undervisning. Perspektivet matematik som problemlösning uttrycktes inte av någon av volontärerna i undervisning, och hade en tämligen tillbakaskjuten roll i den föreställning om matematik som uttrycktes i intervjuer. Slutsatsen är att utifrån vilka föreställningar av matematik som synliggörs inom undervisning kan räknestugor medföra vissa begränsningar sedda som undervisningsform, då den observerade undervisningen primärt gav uttryck för en föreställning om matematik som verktyg. Medan de platonska synsätten förekom till viss del och föreställningen av matematik som problemlösning ej kom till utryck i undervisningen. / In the Swedish educational landscape, supplementary tutoring, from both private and public organizations, has in the last decade gained a more and more significant and natural place. Where both non-profit and for-profit organizations have received government subsidies or grants in recent decades. It is therefore of important to gather an understanding of the type of mathematics education provided by these organizations. Of particular interest for this study are the non-profit organizations, and its volunteers, offering free tutoring in mathematics for student in the upper secondary school.Previous research on the non-profit supplementary tutoring in Sweden, and its volunteers, is lacking. The purpose of this work is to create an understanding of the activities in the non-profit supplementary tutoring, its volunteers and the mathematics teaching that is there provided. In order to investigate the volunteer’s educational practice, both interviews with the volunteers regarding their beliefs about mathematics as a school subject and their beliefs about mathematical education where conducted, and also on observations of the volunteer’s educational practice where done. Analysis and interpretation of observations and interviews are based on previous research about teachers’ beliefs of mathematics, learning and its teaching. The volunteers gave a coherent picture, where the beliefs of mathematics expressed in interviews was in agreement with what was observed in teaching practice. Of the previous research’s three beliefs of mathematics, the interviewed and observed volunteers, expressed two of the three beliefs. The Instrumentalists beliefs, mathematics as a tool, was expressed by all volunteers in both interview and teaching. The perspective of mathematics as problem solving was not expressed by any of the volunteers in their tutoring practice, and was almost invisible in the beliefs of mathematics expressed in interviews. The conclusion is that, from the beliefs of mathematics expressed in tutoring practice, the supplementary tutoring can be seen to have certain limitations as a form of education, since the observed practice primarily expressed the belief of mathematics as a tool. The platonic perspective appeared to some extent and the notion of mathematics as problem solving was not expressed in teaching.