Title: Implementation of Challenging Tasks in Mathematics Education Author: PhDr. Lucie Růžičková Department: Department of Mathematics and Mathematics Education Supervisor: RNDr. Alena Kopáčková, Ph.D. ABSTRACT The thesis deals with practical implementation of challenging tasks in mathematics education. The methodology for examining "the fidelity of implementation of mathematical tasks" is being designed to describe whether the task is used according to the original intention of the teacher or according to the intention of its author. This methodology is employed in the analysis of four experiments to examine mathematical tasks and task environments. Then, based on the experience with the analysis, the methodology is adapted to the needs of both the teaching practice and educational research. The main result of the thesis is the creation of the methodology for examining the fidelity of implementation of mathematical tasks which is based on contrasting the descriptions of four general elements of the mathematical task at different phases of its implementation. KEY WORDS: mathematics education, mathematical task, challenging task, implementation of tasks

Several studies show that students with a mother tongue other than Swedish are disadvantaged in the meeting with text rich mathematical tasks. This is especially so when the tasks have a context that is linked to Swedish culture and tradition that is unknown to the students. This study examines how multilingual middle school students respond to text-rich mathematical tasks. More specifically, the study has investigated multilingual students' difficulties and resources in meeting text-rich mathematical tasks.To answer the questions, qualitative interviews were conducted with a total of eight pupils who, on the basis of four text-rich textbook tasks, had to reason and reflect on the content, language and problems of the tasks. The theoretical approach to analyze the empirical material was social semiotics. Social semiotics is about how people communicate, create meaning and interact with the outside world through different social and cultural contexts. In these social and cultural contexts, humans creates so-called resources that are available to interpret, communicate and create meaning.The results of this study indicate that multilingual students encounter linguistic, cultural and contextual difficulties in the mathematical text-rich tasks. Furthermore, the results of this study also show how these multilingual students use different semiotic resources in their encounter with the text-rich mathematical task such as; dynamically thinking through two languages in parallel, pointing at words, pictures and using a mental “number-exchange”, where the students exchange the mathematical numbers, from Swedish to their native language to cognitively calculate the mathematical numbers.

The following study aims to define what an open-ended question in mathematics education is and investigate what the effects are on the learning process. Firstly, conversations were conducted with teachers that are using this approach in their mathematics education. Then systematic searches for relevant scientific articles were conducted in various databases.The result shows that there are three main features of open-ended questions; there may be more than one acceptable answer, it requires a higher level of thinking from the person solving the problem compared to closed questions and both the students and the teacher will learn during the process. Moreover, the result indicates that using open-ended questions has positive effects on student’s engagement, contributes to a positive classroom climate, increases the possibility that all students can be involved in the same teaching activity and makes the students’ knowledge visible for both the student and the teacher.The findings conclude that it requires good planning from the teacher before using this approach in the classroom to enhance the possibilities of the good effects. Furthermore, I discussed what I, as a future teacher, need to think about while using open-ended questions in my classroom. Lastly, I give suggestions on further research about open-ended questions in the early years.

After an intelligence test battery, the sixty right-handed subjects (30 males, 30 females) performed two visual field (VF) reaction time (RT) tasks requiring odd-even judgments concerning the whole numbers 1 through 8. Numbers were presented as words, a right VF left-hemisphere (LH) advantage task, or as bargraphs, a left, VF right-hemisphere (RH) advantage task, the height of the bargraphs indicating the number.

This study describes in-class and home literacy events that occur when students work in groups to create web pages as evidence of learning the academic content that was presented within a fourth grade classroom. The constructivist approach to learning was the underpinning idea examined as well as its connection to technology and group work. Data were collected in a variety of ways to obtain a picture, as comprehensive as possible, of the oral, listening, viewing, and written on-task communication and interactions that occurred. As the in-class and home literacy events emerged, the competencies and strategies that students used while interacting with traditional text were uncovered. These events encompass the strategies that the students used after they encountered the text and had to modify it for one reason or another. These literacy events illustrate how the Internet supports reading and writing in the elementary classroom when it is utilized as a tool for promoting instruction.

Despite the steady rise in online education and increasingly empirical studies on related learning technologies and technology support, there is considerable evidence that the field has not kept the pace with studies related to online education administrators (OEAs). Further investigation was needed into OEAs’ practice of day-to-day administration of their programs. Therefore, this study examined OEAs’ perceptions of their areas of responsibility, tasks to be accomplished and skills and knowledge needed for them to get the job done. A three-round Delphi research technique was employed as a structured group communication method between five participants to answer three research questions. The protocol consisted of anonymous participants using online surveys to respond to several rounds of questioning. The research concluded with a group consensus. The results produced nine functional areas, 12 operational tasks and 14 competencies of skills and knowledge for OEAs. Based on the findings, it was now possible to illustrate an operational management competency model as a resource for the administrator in charge of an online education program. After conclusions were drawn, the study provided recommendations for future research.

Studies have shown that when young EFL (English as a Foreign Language) learners participate in oral collaboration tasks, it may have both positive and negative effects for them. Nearly all of the research done in this area has been carried out on older learners, which makes the information related to younger learners relatively narrow. In the last decade, however, research done with young learners has gradually increased. This has led to elementary school teachers being given a wider range of knowledge regarding oral collaborative tasks and their impact on their students. Through a handful of selected research carried out on young English learners, this study’s aim is to highlight both positive and negative impacts that oral collaboration tasks may have on students in elementary school (K3). All of the research from our selected articles was conducted through observation in the classroom, in which two of them included students’ own perceptions. Different factors can have an influence on oral collaboration tasks, such as patterns of interaction, task content, attitudes and feelings, and the teacher’s role.

Filamentous microfungi play an important role in the environment and they can have either a positive impact on a man, e.g. in a form of medicine or food production, or a negative one, when filamentous microfungi may cause diseases or deteriorate food. Pupils usually start learning about filamentous microfungi in form 6 of a primary school, or they get some tangential information in the first year of an eight-year grammar school. In addition, in most of student's books, microfungi are incorrectly referred to as moulds, which is an unprofessional term. The objective of my thesis is to elaborate two practical tasks for the presence form of study in which pupils find out the difference between unicellular and multicellular fungal organisms, acquaint themselves with the fungal phytoparasite - mildew, take the substrate, make native and coloured mounts which are then observed under the microscope. The other two practical tasks have been elaborated for the distance form of study via exploration tasks, which can be carried out at home conditions. It means creation of a mycological garden and observation what kind of bakery products is more prone to be affected by microfungi. The other elaborated tasks relate to across-the-curriculum use of the filamentous microfungi topic in Maths and Czech, in which some...

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...

京都大学 / 0048 / 新制・課程博士 / 博士(人間･環境学) / 甲第20722号 / 人博第831号 / 新制||人||199(附属図書館) / 29||人博||831(吉田南総合図書館) / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)教授 田地野 彰, 教授 桂山 康司, 准教授 金丸 敏幸, 教授 植松 茂男 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DGAM