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This diploma thesis deals with the introduction of equations in an eight-year Grammar school during distance learning. This thesis focuses on action research in the context of distance learning in the first year of the eight-year Grammar school. It consists of a series of lessons focusing on equations that I have taught at OPENGATE Grammar School. This thesis aims to monitor my progress in the field of didactics. The thesis is divided into two main parts - theoretical and practical. The theoretical part itself is further divided into five chapters: Definition of key terms, Closing and re-opening of schools in the Czech Republic with a comparison with other countries of the European Union, Specifics of online teaching, theory of linear equations, analysis of textbooks. The practical part builds a priori on analyses of a continuous reflection. The practical part expands on the theoretical by the creation of scenarios. The description of scenarios is accompanied by a continual reflection and a posteriori reflection. The conclusion presents the key points of the reflection. The analysis and the reflection are put into the context of the linear equation curriculum analysis presented in a selected series of textbooks both at the primary and lower secondary school levels. The practical part was realized...

This thesis focuses on to word problems and elementary school pupils. Research on mathematical word problems suggests that differences in success are not only due to different levels of pupils' cognitive abilities but that their motivation plays a role, too. Therefore, in this study, I focused on the context of word problem as a potential source of situational interest, which may affect the quality of pupils' cognitive function in the short term or permanently. I used my participation in a broader quantitatively oriented research on variables influencing the difficulty of word problems and using its methodology, I investigated the influence of different types of contexts on pupils' success in solving the problems. The examined aspect of context was attractiveness - the question was whether pupils would be more successful in solving word problems with elements of fairy tale, science fiction or humour than in similar problems with the same structure but with a neutral context. Pupils of the 3rd to 6th grades of primary school (n = 2 092) were divided into two groups of a comparable ability and each was presented with one of the variants - attractive or neutral. To evaluate the results quantitatively, the Item Response Theory was used allowed us to determine the difficulty of the problem depending on...

The diploma thesis focuses on generalization tasks. Its aim is to gain insight into the solving strategies that pupils use and to determine whether the chosen approach depends on the acquired knowledge about the variable. The work is divided into theoretical and research part. The theoretical chapter contains three parts. The first is devoted to letters in mathematics and generalization problems as one of the ways of introducing a variable. The next part presents the results of Czech pupils in the international comparative research TIMSS in the problems on generalisation. The last part is devoted to curricular documents and the analysis of selected textbooks in terms of the occurrence of generalization problems. More attention was devoted to the only textbook series which includes generalization tasks. The research part is the core of the work. Its aim is to describe the solution strategies of selected pupils. Four tasks were the basis of the research. They were selected by the author from various research sources and graded according to their difficulty. Pupils who had already encountered the term variable were the target group as well as pupils for whom it was a new term. Eight pupils participated in the research. They were interviewed about their solutions of the assigned tasks. Next, the...

The diploma with the help of algebraic tiles thesis focuses on teaching expressions with variables in the eighth grade in middle school. It is divided into theoretical and experimental parts. A particular chapter is devoted to an analysis of selected textbooks. First of all, the aim of this thesis was to analyse mathematics textbooks from the perspective the algebraic expressions. Some knowledge acquired thanks to the textbook analysis was used for my own educational experiment, whose preparation, realisation and assessment were the second objective of this thesis. The theoretical part provides a look at expressions with variables in curricular documents. Thereafter the pillars of teaching algebraic expressions are presented. This part is completed by the classification of errors made by students in relation to the topic. An analysis of selected textbooks follows the theoretical part. The core of this thesis is the experimental part, where teaching is based on constructivist principles. The preparation of the course explains the manipulation of the algebra tiles used during the lessons. After the teaching experiments, we may conclude that the application of algebra tiles helps students get into the environment of algebraic expressions, improves the understanding of the rules of manipulations with...

The diploma thesis deals with CLIL teaching at primary school with a focus on pupils with special educational needs, specifically pupils with learning disabilities and pupils from socially disadvantaged backgrounds. The work aims to compare the work of ordinary pupils in CLIL classes with the work of pupils with special educational needs and to find out whether it is suitable for pupils with special educational needs. The theoretical part deals with CLIL teaching in general with a focus on teaching primary school pupils and briefly characterises some special educational needs. The practical part contains preparations for lessons and their reflections, an analysis of student work and evaluation of the pupils' satisfaction with content and language integrated learning questionnaire. At the end of the thesis, proposals for the modification of educational materials for pupils with special educational needs are attached. The research showed that CLIL teaching has no negative impact on the sample of pupils from socially disadvantaged backgrounds, but at the same time did not confirm, but also refute, the possibility of applying CLIL teaching to students with specific learning disabilities.

Estimation competence is assumed to be a relevant skill that needs to be addressed in the mathematics classroom (Sowder, 1992; Bright, 1976). However, little is known about cross-country differences in primary school students’ length estimation competence and what impact different opportunities to learn in the different educational contexts have on this competence. Taking into account an extensive analysis of 202estimation situations, Heinze et al. (2018) proposed a model that holds 72 estimation situations as a basis for assessing length estimation competence. Based on this model, a test on length estimation competence was developed and used in 43 German and Taiwanese classes. In total, 903 third and fourth grade students fulfilled the length estimation tasks. The test on students’ length estimation competence proved to be partially measurement invariant. Cross-country comparison revealed that Taiwanese students outperform the German students in length estimation Estimation competence is assumed to be a relevant skill that needs to be addressed in the mathematics classroom (Sowder, 1992; Bright, 1976). However, little is known about cross-country differences in primary school students’ length estimation competence and what impact different opportunities to learn in the different educational contexts have on this competence. Taking into account an extensive analysis of estimation situations, Heinze et al. (2018) proposed a model that holds 72 estimation situations as a basis for assessing length estimation competence. Based on this model, a test on length estimation competence was developed and used in 43 German and Taiwanese classes. In total, 903 third and fourth grade students fulfilled the length estimation tasks. The test on students’ length estimation competence proved to be partially measurement invariant. Cross-country comparison revealed that Taiwanese students outperform the German students in length estimation.

Title: Pupil's personality and solving problems of school Mathematics by heuristic strategies Author: Mgr. Markéta Škutová Supervisor: prof. RNDr. Jarmila Novotná, CSc This thesis deals with the relationship between the type of pupil's personality in the dimension of information reception and their ways of solving problems of school Mathematics with the use of heuristic strategies at the lower secondary education of basic school and in the corresponding years of grammar schools. The theoretical part summarizes the knowledge of heuristic strategies in the teaching of mathematics at the lower secondary education of basic school and their application on examples. Furthermore, the theoretical basis of type theory and its use in education is explained. In the practical part the results of the typological questionnaire are presented and an extensive qualitative analysis of the student's problem solving is offered. The resulting findings are supported by concrete examples of students' solutions. In this diploma thesis, there is evidence that the intuitive pupils use the heuristic strategies of problem solving more often than the sensory pupils and are more successful in solving non-traditional tasks. Keywords: heuristic strategies, MBTI, type theory, problem solving

Reading comprehension as a prerequisite for successful strategy of word problems solving in mathematics DISSERTATION Mgr. Alena Sigmundová ABSTRACT The dissertation describes the results of an interdisciplinary research study examining the linguistic aspects of word problems in mathematics and the connection between comprehension of the text of word problems and the success of their solution. In the introduction the research is set into the framework of theoretical bases: the term word problem in mathematics and the concept of reading comprehension, including factors influencing the understanding of the text are characterized and the results of previous research studies are described. Subsequently the work presents a methodology, course and results of testing of pupils in three pilot studies and in the main survey and the conclusions from the semi-structured interviews. The research is based on the linguistic analysis of 18 word problems with low solution success, taken from international research surveys PISA 2012 and TIMSS 2007, as well as on the level of comprehension of the text of these tasks in the 8th and 9th grade primary schools, modifying selected language phenomena and detecting the effect of these reformulations. 773 pupils from 13 elementary schools participated in the research. The study...

This diploma thesis deals with Content and Language Integrated Learning (CLIL). The term stands for a teaching method used in the non-language classes that has a content-oriented and lingual goal. CLIL has been incorporated into the learning process as one of the instruments that leads to improving language learning in Europe. The aim of my thesis was to prepare, realize and evaluate a twomonth long process of using CLIL in lessons of Math for lower secondary pupils. In the experiment I surveyed the impact of the connection between Math and English language on pupils' motivation and Math knowledge. The experimental lessons were focused on the topics of ratio, direct and inverse proportion. The main method used in the thesis was action research. Other applied methods were quantitative methods (questionnaires) and qualitative methods (interview and mediated observation). Parts of the thesis include preparations of seven CLIL lessons accompanied by methodical description and worksheets. These materials were used in lessons during the experiment. The experiment showed and proved the procedure of successful CLIL method implementation to the lessons of Math. The implementation did not have a negative impact on pupils' motivation, knowledge and activity on the lesson's.

The diploma thesis focuses on learning Maths through French language using the CLIL method at a secondary vocational school. The acronym CLIL (Content and Language Integrated Learning), EMILE (Enseignement de Matières par Intégration d'une Langue Etrangère) or e.g. AICL (Apprentissage Intégré d'un Contenu et d'une Langue) refers to integrated learning of a content-based subject through an additional language. There are always two aims of such tuition. The first aim is the content goal (e.g. to gain particular specialized knowledge or skill in mathematics); the second aim is the language goal (e.g. to learn essential vocabulary and sentence structures in order to lead a discussion concerning the solution of a quadratic equation in the French language). Based on a literary research, analysis of educational CLIL materials, and especially in connection with theoretical grounds of the method (constructivism, problem-solving, critical thinking, active and communicative approach) there was established a study plan focusing on the topic of quadratic equations. The experimental tuition was put into practice with the 1st year students of a secondary school, where the French language is taught as the second foreign language. The main objective, apart from the tuition itself and its analysis, was to assess the...

This thesis focuses on the teaching of mathematics using the CLIL method. The topic is Venn diagrams and learning how to solve problems using these diagrams. The language chosen for the CLIL method is English. First, the CLIL method is described, and later I introduce sets and Venn diagrams. The aim of the thesis is to prepare and implement two lessons using the CLIL method in English, and two lessons in Czech, followed by preparing a test in both languages for a third lesson. The thesis was realized by conducting a teaching experiment, which took place in two classes of multi- year grammar school (in the Quintas - the first year of secondary school). I have compiled and tested four worksheets - two with Czech tasks, two with English tasks, a presentation for the lesson using the CLIL method, and tests for both language versions. Both the tasks and solutions are part of the thesis. Before the preparation of the thesis, the following two research questions were identified: 1. What needs to be taken into consideration when preparing for the Venn diagrams lesson using the CLIL method, and what needs to be added to this lesson compared to the Czech lesson? 2. At what success rate will pupils learn using the CLIL method in English and pupils using Czech, with regard to equation building and answers to...

The thesis is aimed on the mathematical knowledge and skills development in leisure time activities. The theoretical part of the thesis is dedicated to leisure time, pedagogy of leisure time, out-of-school education - its content, functions and requirements for realization of out-of-school education. This part of the thesis is also dedicated to the motivation and its use in leisure time activities and development of mathematical knowledge in leisure activities. Based on this information and on my own experience, I worked out and introduced the prin- ciples for preparing leisure time activities developing mathematical knowledge and skills. Following is a compilation of leisure time activities that develop knowledge and skills in geometry, arithmetic, algebra, logical thinking, or geometric imagination. The compilation contains activities suitable for relaxing, recreational and hobby activities. The practical part includes a case study of the Textile Applications activity, which deals with consolidation and development of knowledge in axial symmetry within the leisure time sewing ring. The case study verified if participants in this activity developed knowledge in axial symmetry, if the activity respects the requirements for out-of-school education and if it improves belief in the applicability of...

This diploma thesis deals with the teaching of mathematics in Italian language in the bilingual Italian-Czech section of Grammar School Ústavní in Prague, the Czech Republic, where I have been teaching since 2012. The main aim of this work is to analyse and systematize the positives and negatives of the bilingual teaching of mathematics in this environment. The most important problems and challenges, a teacher has to deal with while teaching mathematics in Italian, the language different from pupils' mother tongue, are introduced in this work. All the used and illustrating examples are based on my own practical training of an Italian Math teacher and are taken within one school year. Moreover, these examples are supported by my own problem solving options. The thesis also contains reflections about results of the bilingual teaching of mathematics both in mathematical and linguistic terms. Theoretical part deals with a general description of bilingualism, bilingual teaching of mathematics, and bilingual Grammar School Ústavní. Practical part describes not only the main differences between curriculums, textbooks, and mathematical assessments in Italy and the Czech Republic but also the course of school year 2016/2017 in classes 3.C and 4.C. The description is based on both the analysis of lessons of...

1 Solving strategies of word problems depending on the context topicality ABSTRACT The thesis deals with word problems solvable by linear equations. The aim of the work is to show if the context, on which the word problem depends, influences how pupils participating in the research solve it and verify if word problem phrasing and modern language usage help pupils solve the word problem. It is accomplished by assigning pupils a set of varied word problems and assessing their solutions. More results were gained by assessing questionnaires related to the context of the word problems being calculated. The second aim of the thesis is to explain various definitions of word problems, putting the term into the context of school mathematics and a brief summary of the historical development of mathematics focusing on word problems. The work consists of three parts. In the first part, problems and word problems are defined and it is shown how word problems are included in the Framework educational programme. Word problems are put into historical context. The second part shows the conception of motion word problems, word problems on joint work and word problems on dividing a whole into parts in the present-day mathematical textbooks in the second stage of elementary schools and in the lower classes of secondary grammar...

The aim of the diploma theses is to find out if the study in a form of an e-learning course is more beneficial to the student than the isolated study text. To find the benefits, the research among nineth grade students from two different schools was done. A study text called Functions for the nineth grade was prepared together with a collection of solved and unsolved problems. Based on this text an e-learning course called Functions for the nineth grade was prepared. The e-learning course was placed on the website linked http://funkcepro9r.maweb.eu/. For the communication of the students and the tutor of the course, for the completion of the compulsory tasks and for the carrying out the study agenda, the modul iTřída on the web link itrida.dumy.cz was selected. Both forms of the study materials were tested by the nineth grade students on two selected schools. The efectivity of both of the forms was tested by the written test. The evaluation of the both forms was done by the electronic questionnaire. According to the results of the written test, the students which used the isolated study text were more succesful than the students studying the e-learning course. The results of the questionnaire verified that the study text was more acceptable for the students. The e-learning course did not suit the...

Content and language integrated learning (CLIL) is a dual focused educational approach in which an additional language is used for the learning and teaching of both language and a non- linguistic subject or its part. While there are numerous forms of CLIL implementation, it is possible to define universal pedagogical principles for CLIL teaching and planning. This research presents a content analysis of 56 lesson plans for a CLIL lesson of financial mathematics/literacy. The aim of this research was to establish whether these lesson plans reflected the CLIL pedagogical principles, to establish what features the respondents saw as key features to a CLIL lesson plan, and whether/how the lesson plans corresponded to the respondents' theoretical proclamations. Our research investigated also the differences in lesson plans by these two sub-groups. An original lesson plan analysis tool (LPAT) was created for this research. It was used as a basis for a quantitative survey and as a framework in content analysis of the lesson plans. The tool identified eight key features of a CLIL lesson plan. The respondent combined approximately five of the key features with other features of the LPAT both in the survey and in the lesson plans. Both the survey and the analysis show that the respondents did not identify...

The topic of the thesis is the use of selected tasks, which I created in my bachelor thesis, in the mathematics teaching at grammar schools. These are problematic word problems from geometry curriculum with financial themes. The aim of the thesis is to find out the role of the word problems in pupils' motivation in teaching. The theoretical part describes the issue of motivation and pupil motivation for learning. I also deal with problem of word problems, their definition and typology. The practical part is focused on experiment with aim to find out the use of selected tasks in the mathe- matics teaching at grammar school. In the experiment, I primarily examined whether the tasks motivated pupils , how successful they were in solving and the influence of financial themes in selected tasks on the pupil's emotional state or his success in solving the task. I processed statistical data quantitatively and qualitatively. To collect statistical data, I used a questionnaire and observation. The evaluation of the experiment includes statistics on pupils' motivation to solve the tasks and pupils' success in solving the task. According to research results, pupils were motivated by the tasks. The difficulty of the tasks is proportional to the level of mathe- matical abilities of pupils at grammar school. The...

This thesis Pupils' problem solving strategies at lower and upper secondary level brings a focus on the issue outlined by the name. At the same time, it focuses on pupils' strategies to solve problems that are closely related to information literacy. At first I define basic terms for the area of word problems. Consecutively I focus on the theoretical knowledge from the area of problem solving strategies themselves. The content of the experimental part of the thesis is the survey of pupils' solutions of eight selected tasks, by which I was looking for an answer of the three basic questions of this thesis. My experiment is divided into two branches. The first branch of the experiment took place at the lower level of the multi-year grammar schools. The second branch of the experiment took place at the higher grade of the multi-year grammar schools and, to a small extent, at the secondary school. The theoretical part contains views of various authors on issue of problems and word problems. I present and compare these individual approaches. The result is the demarcation of the terms needed for the experimental part of the work. The main aim of the experimental part of the thesis is to find the answers of three basic questions of this thesis, where I was using data from lower and higher grades of...

The purpose of this thesis is to give account of experimental teaching of a CLIL, namely in combination with blended learning at the second level of elementary school. The starting point was a reflection on how to relieve the overloaded of schedule of lessons devoted to non-linguistic subjects, in which many teachers now struggle with time to manage to teach all that is needed. To answer the question as to how pupils of an eighth grade of primary school, would respond to a new type of lessons in an unusual form, I tried to perform a teaching experiment in which the pupils went through a hard CLIL programme driven by blended learning. The available resources on this issue have been elaborated in the form of the theoretical part, which forms the first part of this work. It deals with CLIL, e- lerarning and blended learning. The second part consists of the preparation of the research and the third part is devoted to its implementation. The research consisted of three hours of full-time teaching enriched by blocks of e-learning support. During the preparation and implementation of the project, I tried to find sources of motivation that would encourage pupils to spend their extra-maths learning time. I collected the data for the subsequent analysis by participating and mediated observation, using...

This work deals with word problems from natural sciences whose main mathematical apparatus are circle, sphere and their parts. The work is divided into three main parts - part about word problems, part about used mathematical apparatus in word problems and part containing verbal tasks from sciences. The first part defines the word problems and describes how to solve the problems. The second part contains the mathematical apparatus used in the word problems in part three. The third part is a collection of verbal tasks from the sciences, divided into the taskes solved at primary and secondary schools. The individual vocabulary is presented as a necessary theoretical basis of sciences. In the third part, I created most of the vocabulary myself.

The theme of the diploma work are pupil's strategies of solving selected problems focusing on area of plane figures. The theoretical part includes definitions of basic ideas - problem, area, problems of area, solving problems, solving strategies. Plane figures are classified into particular school classes. Every plane figure is presented by examples of types of the problems, which are most common in elementary schools. The practical part of the work begins with the preparation of an experiment, where the objektive of the experiment is introduced, selection of problems for this experiment, description of tested group and the way of getting data. Follows the description of realization of the experiment. It contains three problems of the area of plane figures which were solved by pupils of the eighth and the ninth class. Supposed strategies, expected mistakes and analysis of pupil's solutions are presented. Expected and obtained solving strategies are compared for every problems. The result of the experiment is summarised in the conclusion. Keywords: problem, area, problems of area, solving problems, solving strategies, heuristic strategy

A basic summary of the most common types of chemical calculations for primary and high schools and their connection with the mathematical knowledge is mapped in this work. The work is divided into three main parts - the chemical calculations at primary schools, part of chemical calculations at high schools and part mapping tasks that contain chemical calculations in chemical competitions for pupils of primary and high schools. The first two parts contain the necessary theory in mathematics and chemistry, including chemical formulas which are used. The first two parts also contain a few typical examples for better understanding of the topic. The last part shows the application of knowledge of chemical calculations in competitions for pupils.

This master thesis deals with middle school pupils and their comprehension of Part-whole theory within the area of Mathematics. The theory section is divided into five parts. The first part presents sets of knowledge and skills of lower-secondary school pupils that are essential for completing a particular time period in selected thematic areas of mathematics at primary schools. In the second part, individual stages and mechanisms of cognitive processes needed in Mathematics are determined, and the third part focuses on teaching methods of Mathematics. Among the issues mentioned in this part are for example the difference between formal and informal knowledge or transmissive and constructivist way of teaching. Lastly, the fourth and fifth parts specify various expressions of wholes and their parts. The research part of this paper provides an analysis of interviews with certain teachers that are employing different teaching methods, testing applied on their pupils and also an analysis of the textbooks that are being used by these teachers. The other part of the thesis is the evaluation of the interviews with the selected teachers, what gives us the information about the relationship of the teachers to particular didactic approaches, and the evaluation of the tests taken by pupils including standard...

The theoretical part deals with approaches to teaching, especially constructivistic, instructivistic and transmissive approach. The goal of this part is to compare the approaches and evaluate them considering the permanency of knowledge and active engagement of students. Simultaneously it aims at evaluating the approaches from the point of their of the mechanical knowledge. The charter dealing with inquiry based mathematics education is focused on teaching related to constructivistic approach. The next chapter describes tool called concept cartoons, which can be used as a mean to research. The theoretical part is focused on the topic of fraction, especially fraction interpretation and models and fraction representation. The second part of the thesis describes a survey realized at basic school. I narrowed the problem to fraction interpretation and representation according to survey of student's work. The next part of research is based on this analysis. Trying to accomplish the aims and find the answers to questions of the survey I chose strategy inspired by action research, because the main goal of the research was to improve and enhance my teaching knowledge and skills. The survey was processed qualitatively. The making of the thesis helped me make it clear, why the topic of fractions is so...

The diploma thesis deals with the position of error in the teaching of mathematics in the awareness of pupils and teachers. It also focuses on the responses of pupils and teachers to errors. Main attention is paid to mathematical errors. The thesis consists of two parts, theoretical and practical. The theoretical part contains an overview of selected error views. It contains a look at the development and changes of views on the concept of "error", the different concepts of error classification and pedagogical and psychological views on the term "error". The practical part is based on the research carried out at the 2nd level of two primary schools in Prague and Neratovice. Pupils filled in a questionnaire and a guided interview was conducted with teachers. KEYWORDS work with error, error classification, causes of errors, learning without errors, learning with error

The thesis deals with the connection between the way the mathematical word problems are formulated and their being understood correctly by the pupils. The main focus is on the semantic cues present in the assignment of the word problem. The thesis can be divided into two parts. The first part, which provides the theoretical framework for the whole thesis, contains the definition of a word problem. The phases of word problems solving and the possible classification of word problems are mentioned. More attention is paid to the problems with translation cues; new concepts of asymmetric context and symmetric context, called semantic cues, are introduced. An overview of several related research studies from abroad follows. The core of the thesis lies in its second part, containing a study that examines whether the pupils would be more successful in solving problems with asymmetric contexts than in solving problems with symmetric contexts. The influence had been examined on two types of problems and four age categories of pupils and students. The research was carried out through the short tests and it was attended by the total of 503 pupils of selected elementary schools and grammar schools in Prague and students of the Faculty of Education of Charles University. A higher success rate for the asymmetric...

Title: Working with numerical and algebraic expressions in the compulsory education Author: Bc. Lenka Pantůčková Department: Department of Mathametics and Mathematical Education Supervisor: Prof. RNDr. Jarmila Novotná, CSc. This Diploma Thesis deals with numerical and algebraic expressions in elementary school. The theoretical part deals with the framework educational programme for elementary education and grammar schools. It further mentions the propaedeutic of algebraic expressions at the first and second levels. It also introduces the most frequent mistakes done in calculating algebraic expressions. Meanings for the variable are stated as well. The last pre-chapter of the theoretical part is focused on statistics, which is further used for the experiment result evaluation. The experimental part first states the aims and methods of the research. Selected elementary schools taking part in the experiment are further introduced. An analysis of mathematics text books for the eighth grade (mainly chapters concerning the algebraic expressions), the selected schools use in their lessons, is also carried out. The experimental part also introduces the test presented to 128 pupils. Further pre-chapters are devoted to hypotheses and expected mistakes in single subtasks. In the conclusion of the experimental...

The drop-out rate among students attending vocational training institutions is higher than for other forms of education at the same entry level (in Denmark, but also generally in Europe). A recent Danish reform has aided students, who enter the first part of the basic program directly from primary school. However, there remains a high risk for older students, who do not come directly from primary school; and there is a risk of becoming ‘school-weary’ (in its broadest understanding) in the periods between school and company practice. This paper introduces experiences with students own digital multimedia and video productions in Vocational Educational Training (VET). These video productions focused on the subjects of their future profession, and increased students’ motivation and experience of professional pride. Through a semistructured literature review, the paper then argues for a research agenda focusing on video productions in combination with digital storytelling, followed by a presentation of the digital storytelling features. The paper concludes with a suggestion to initiate research in what is identified as Personal Digital Video (PDV) Stories within longitudinal settings, while students are at school and in practical placements with companies. This may increase students’ social engagement and interest in the subject matter, together with greater awareness of professional identity, which could help decrease drop-out rates for vocational training.

The drop-out rate among students attending vocational training institutions is higher than for other forms of education at the same entry level (in Denmark, but also generally in Europe). A recent Danish reform has aided students, who enter the first part of the basic program directly from primary school. However, there remains a high risk for older students, who do not come directly from primary school; and there is a risk of becoming ‘school-weary’ (in its broadest understanding) in the periods between school and company practice. This paper introduces experiences with students own digital multimedia and video productions in Vocational Educational Training (VET). These video productions focused on the subjects of their future profession, and increased students’ motivation and experience of professional pride. Through a semistructured literature review, the paper then argues for a research agenda focusing on video productions in combination with digital storytelling, followed by a presentation of the digital storytelling features. The paper concludes with a suggestion to initiate research in what is identified as Personal Digital Video (PDV) Stories within longitudinal settings, while students are at school and in practical placements with companies. This may increase students’ social engagement and interest in the subject matter, together with greater awareness of professional identity, which could help decrease drop-out rates for vocational training.

This study informs researchers of educational technology, teachers, teacher associations and moderators or admins of online platforms who are interested in knowledge sharing among teachers within online communities of practice (CoPs). The continuous professional development of teachers is primarily about improving their teaching practice. It includes both formal and informal learning activities to transform attitudes, behaviour, skills and knowledge. Formal knowledge sharing methods like training workshops have failed to deliver the desired on-demand, context-appropriate knowledge. On the other hand, informal knowledge sharing through CoPs can transform teachers by contributing to their immediate context or needs. There are various national and global IT platforms that are designed to enable teachers to participate and share knowledge in a CoP but in many countries, online platforms for the professional development of teachers are relatively new. This systematic literature review reports a qualitative synthesis of literature on in-service teachers’ online CoP participation. It adheres to the five-step literature search and analysis process by Creswell (2012). Seven peer-reviewed articles were included from 603 initial records. Applying an approach inspired by grounded theory (Corbin & Strauss, 1990), themes were identified in each article and then grouped into seven categories as follows: (1) In the online communities of practice, in which activities do teachers engage with one another? (2) What knowledge do teachers share in the online CoP? (3) What motivates teachers to participate and share knowledge in the online CoPs? (4) What are the barriers to teachers’ participation and knowledge sharing in the online CoP? (5) What roles do moderators play in teachers’ online platforms? (6) What are the perceived benefits of teachers’ online CoPs? (7) Which factors should be considered while developing online platforms for teachers?

The paper focuses on collaborative writing in Google Docs and presents a framework for how students can develop methods for collaborations that include human and non-human actors. The paper is based on the large-scale research and development project Students’ Digital Production and Students as Learning Designers (2013–2015), funded by the Danish Ministry of Education. The target groups were primary and lower-secondary schools. The project explored teacher-designed frameworks that involved students’ agency as digital producers of learning objects aimed at peer students. The project demonstrated that digital production facilitates students’ learning processes and qualifies their learning results when executed within a teacher-designed framework that allows for and empowers students’ agency. The overall research design was organised as a mixed methods approach. A sub-study within the large project, which is based on an ethnographic approach, shows that the students develop their own strategies for the online collaborative process, through which they organise the work in different ways when interacting with the technological affordances and material performance of the technology. The sub-study also shows that teachers do not introduce or refer the students to online collaborative strategies, roles or communications. The students’ online collaborative writing is entirely within the students’ domain. On this basis, the paper focuses on how teachers’ awareness and articulation of the students’ online collaborative writing within a framework can qualify students´ methods to collaborate online with the intention to improve their learning results. In relation to this, the paper explores how digital technologies may act as co-participants in collaboration, production and reflection. Moreover, the framework is designed to help teachers to scaffold students’ reflections of their strategies, roles and communications in online collaborative writing processes. The paper focuses on collaborative writing in Google Docs and presents a framework for how students can develop methods for collaborations that include human and non-human actors. The paper is based on the large-scale research and development project Students’ Digital Production and Students as Learning Designers (2013–2015), funded by the Danish Ministry of Education. The target groups were primary and lower-secondary schools. The project explored teacher-designed frameworks that involved students’ agency as digital producers of learning objects aimed at peer students. The project demonstrated that digital production facilitates students’ learning processes and qualifies their learning results when executed within a teacher-designed framework that allows for and empowers students’ agency. The overall research design was organised as a mixed methods approach. A sub-study within the large project, which is based on an ethnographic approach, shows that the students develop their own strategies for the online collaborative process, through which they organise the work in different ways when interacting with the technological affordances and material performance of the technology. The sub-study also shows that teachers do not introduce or refer the students to online collaborative strategies, roles or communications. The students’ online collaborative writing is entirely within the students’ domain. On this basis, the paper focuses on how teachers’ awareness and articulation of the students’ online collaborative writing within a framework can qualify students´ methods to collaborate online with the intention to improve their learning results. In relation to this, the paper explores how digital technologies may act as co-participants in collaboration, production and reflection. Moreover, the framework is designed to help teachers to scaffold students’ reflections of their strategies, roles and communications in online collaborative writing processes.

This diploma thesis deals with CLIL which stands for Content and Language Integrated Learning, to be more precise it deals with the integration of Mathematics and English for lower secondary pupils. To realize this method I have chosen the topics of congruent figures in the plane and reflective symmetry. The aim of my thesis was to check whether the chosen topics are suitable for CLIL lessons, whether CLIL method is not an obstacle for the activity of pupils in the lesson or if it does not create any problems with understanding of the subject matter in Mathematics. The theoretical part is focused on describing the CLIL method in general, then I summarize the preparation of the educational experiment and describe the project of the lessons in English and in Czech language. The last part is dedicated to the realization of the experiment with three different groups of pupils of the 6th grade of elementary school. The gained data have been processed on the basis of observation and analysis of the final individual work and the questionnaire. The results of observation and analysis confirm that it is possible to integrate the teaching of Mathematics and foreign language successfully. The thesis includes English and Czech worksheets together with methodology for the topics of congruent figures and...

This paper presents results from eye-tracking studies of audience interaction and knowledge generation in the technology-enhanced health promotion exhibition PULSE at a science centre in Copenhagen, Denmark. The main purpose of the study was to understand what types of knowledge audiences build in health promotion exhibitions designed to include direct physical interaction. The current study is part of the larger PULSE project, which aims to develop innovative health promotion activities that include a science museum exhibition as a key setting. The primary target group is families with children age 6–12. Health promotion technologies are defined here, as technologies designed specifically for the purpose of health promotion, be they educational or focused on physical activities. The study was conducted in late 2015 and comprised eight families with children in 2nd-6th grade visiting the science centre. Eye-tracking glasses and qualitative interviews were used to collect data. Before entering the PULSE exhibition, one adult in each family group and one child in each school group were asked to wear eye-tracking equipment while interacting with various installations. Primarily adult test persons were chosen because wearing the eye-tracking glasses seemed less of an intrusion for adult visitors than for children. The glasses recorded audio, video and gaze point from the test person’s point of view. All members of each group were interviewed briefly following their interaction with the exhibition to understand how they had experienced the exhibition, what they saw as the thematic focus and if they thought they had gained new knowledge from the activities. Results from the project indicated that the participants gained knowledge linked to both health fitness topics and social aspects. Results also showed that the exhibition supported both themes related to discovering new types of physical activity and themes of collaboration and social family activity. This paper presents results from eye-tracking studies of audience interaction and knowledge generation in thetechnology-enhanced health promotion exhibition PULSE at a science centre in Copenhagen, Denmark. The main purpose ofthe study was to understand what types of knowledge audiences build in health promotion exhibitions designed to includedirect physical interaction. The current study is part of the larger PULSE project, which aims to develop innovative healthpromotion activities that include a science museum exhibition as a key setting. The primary target group is families withchildren age 6–12. Health promotion technologies are defined here, as technologies designed specifically for the purpose ofhealth promotion, be they educational or focused on physical activities. The study was conducted in late 2015 and comprisedeight families with children in 2nd-6th grade visiting the science centre. Eye-tracking glasses and qualitative interviews wereused to collect data. Before entering the PULSE exhibition, one adult in each family group and one child in each school groupwere asked to wear eye-tracking equipment while interacting with various installations. Primarily adult test persons werechosen because wearing the eye-tracking glasses seemed less of an intrusion for adult visitors than for children. The glassesrecorded audio, video and gaze point from the test person’s point of view. All members of each group were interviewedbriefly following their interaction with the exhibition to understand how they had experienced the exhibition, what they sawas the thematic focus and if they thought they had gained new knowledge from the activities. Results from the projectindicated that the participants gained knowledge linked to both health fitness topics and social aspects. Results also showedthat the exhibition supported both themes related to discovering new types of physical activity and themes of collaborationand social family activity.

The present paper is an account of a design-based action research study. The research question focused on how to create a pedagogical concept for ICT-supported peer interaction that enabled cross-age students to share experiences and knowledge in relation to internships. Internships in higher education are a natural booster of the elusive concept of professional identity. Students return from internships with a better understanding of what they do, know and areprofessionally. The learning that takes place for the intern remains individual and is only shared with a supervisor. The present study is based on the idea that internship students’ individual learning could be shared with younger peers through online interaction. In the context of a bachelor programme in Northern Denmark, the concept was implemented as discussion forums embedded in the local LMS. In these forums, the students engaged in discussions of professional matters and accounts of daily practices in internships. The analysis of the forum interactions, a survey and a focus group interview revealed that the students perceived the concept as a meaningful activity. The key findings centered on issues regarding: responsibility, relevance and roles. The students felt a strong sense of responsibility toward each other in providing meaningful content and frequent activity and replies to posts, which served as a source of motivation. The question of relevance relates strongly to the timing of the activity, as well as clear expectations and purpose. To the cross-age students, tutor/tutee roles could have provided further direction and purpose of the interaction, but this was not initially part of the concept. This research gave insight into the creation of a pedagogical cross-age concept supported by ICT that could benefitpractitioners and researchers in higher education.

The thesis is dealing with the current state of teaching financial literacy and financial mathematics at high schools. The purpose of this thesis is to sum up information about documents that are source for teaching of financial literacy and to inform about current state of its teaching at high schools. Theoretical part concerns with involving of financial mathematics in framework education programme. This part also shows what subjects are involving financial mathematics. Practical part is dedicated to research, which had been realised at selected high school - Technical high school of food technologies, which follows "Food analysis" and "Environmental ecology" FEP. Level of students in financial mathematics is detected though the questionnaire carried out at the chosen school. Using a questionnaire and test. It compares levels of students, who were educated in financial literacy and financial mathematics, and those who weren't. Powered by TCPDF (www.tcpdf.org)

Title: Pupils' problems when solving problems requiring substitution Abstract: The work focuses on 8th and 9th graders' difficulties and mistakes when solving problems using substitution. The theoretical part defines the used concepts and discusses selected results from international comparative studies and studies focusing on substitution. The main goal of the work is to identify pupils' difficulties and mistakes they make when solving problems using substitution and to discover their origin or cause. To achieve this goal the empirical part begins with an analysis of three sets of textbooks used by pupils involved in this research study. This is followed by a description of conducting and subsequent analysis of fifteen clinical interviews on problems with substitution with 14 to 15 year old pupils (9th graders from elementary schools and 3rd graders from lower secondary grammar schools). In the final part the most common mistakes are summarised and relations to their possible origin in the set of textbooks used looked for. The conclusion is that pupils do not have problems with substitution as such when substituting natural numbers into first power variables. However, this does not hold for substitution of variable in the second power. Pupils have problems when substituting for a variable with a negative...

This thesis is aimed at the transfer of pupils from lower to upper secondary schools from the point of view of teaching mathematics. Three pupils were selected who attended the same lower secondary school and moved to the same upper secondary school. The impact of the change of schools on the girls (from the pedagogical-psychological and mathematical points of view) was measured via questionnaires and mathematical tests. The girls' teachers were given similar questionnaires to see what their views of some characteristics of the girls were. It was found out that the change of schools had mostly negative effects for the pupils. During their first half of the year at the secondary school, their knowledge of algebraic expressions did not improve and their attitude to mathematics got worse, mainly due to the higher demands of the new teacher. It is assumed that this is only a temporary issue and that the girls' attitude to mathematics will improve again when they get used to the new way of teaching. KEYWORDS: Education, transfer, learning, school educational programme, personality, behavior

This thesis Financial Mathematics at lower secondary level focuses on financial mathematics at lower secondary level. The first part consists of two chapters. The first chapter describes financial mathematics and its importance for financial literacy. The second chapter presents research of textbooks in which there is the financial mathematics topic. The second part of the thesis describes pedagogical experiment aimed to determine how a selected group of pupils cope the tasks and problems from financial mathematics. The tasks and problems in this section were posed by the author of the thesis. The evaluation of the experiment is based on students' work samples. The last chapter describes teaching of financial mathematics in two classes at lower secondary level.

This thesis focuses on errors and difficulties that students face when solving problems with algebraic expressions in mathematics at secondary school. Its aim was to describe the factors that affect pupils' achievement while dealing with algebraic expressions, classify them on the basis of a classification of pupils' errors used in mathematics and identify the biggest pupils' difficulties. The thesis consists of theoretical and experimental parts. The theoretical part focuses on the factors that influence the success of pupils in their learning process. I present their summary based on information gained from literature and I complete them with my own teaching experience of mathematics at secondary school. Next I deal with the concept of error, error classification and one of the most important phases of learning process, which is a description of teacher's work with pupil's error (again on the basis of information gained from the literature). The theoretical part ends with definitions of basic concepts from specialized literature on algebraic expressions at the end of the theoretical part. In the experimental part I deal with my own experiment during teaching of mathematics at secondary school, which is based on individual written work of students in the first year of their study and on the...

5 TITLE: A priori analysis as a part of teacher's lesson planning AUTHOR: Mgr. Hana Nováková DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. This thesis focuses on a priori analysis as a part of teacher's lesson planning. The theoretical background consists of the Theory of didactical situations in Mathematics (TDSM). In TDSM, the a priori analysis is seen as one of the teacher's tools that he/she has when planning a lesson. The goal of the thesis is to analyse differences between a priori analysis as described in TDSM and the reality in teacher's practice, to compare lesson plans of experienced teachers with those of students and demonstrate the significance and application of a priori analysis in teacher's and researcher's practice. The thesis consists of three parts, theoretical, experimental and applicational. In the theoretical part, the main concepts of TDSM linked with a priori analysis are explained and the issue of teacher's lesson planning is presented. The experimental part starts with a pre-experiment. Its results contributed to precise the structure of a priori analysis for further use. During the main experiment, the lesson plans of experienced teachers were compared with those of pre-service teachers. The differences and the...