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Use of selected geometry problems from the world of finance in upper secondary mathematics education
Kocourková, Zuzana ; Novotná, Jarmila (advisor) ; Tůmová, Veronika (referee)
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...
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Pupils' problem solving strategies at lower and upper secondary level
Hoffmann, Jan ; Novotná, Jarmila (advisor) ; Tůmová, Veronika (referee)
THESIS Pupils' problem solving strategies at lower and upper secondary level ABSTRACT Thesis Pupils' problem solving strategies at lower and upper secondary level deals with pupils' strategies of solving mathematical problems that we can observe at primary and secondary school. The theoretical part summarizes basic concepts in the field of mathematical problems and pupils' strategies. The main aim of the experimental part of the thesis is finding new knowledge from this field at the second level of Czech education. I focused primarily on tasks involving data, addiction and statistics, including the concept of a mathematical function that is deeply linked to these educational contents. In the experimental part, there are selected tasks, expected or discovered strategies, statistics of chosen strategies and the success of the solutions and strategies found, in some cases even the transcription of pupils' errors. Keywords Problem, word problem, assignment, strategy, error, analysis, success rate, solving problems.
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Symmetric and asymmetric context of word problems and its influence on the success of pupils' and on the types of their mistakes
Matějková, Klára ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
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...
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Using mathematical calculations to solve problems in sciences
Gáborová, Andrea ; Novotná, Jarmila (advisor) ; Jančařík, Antonín (referee)
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.
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Error in teaching mathematics at elementary schools
Krpálková, Romana ; Novotná, Jarmila (advisor) ; Pilous, Derek (referee)
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
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Use of mathematical knowledge in chemical calculations
Schwarzbacher Zeman, Tomáš ; Novotná, Jarmila (advisor) ; Mošna, František (referee)
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.
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Understanding the part to whole relationship within primary school pupils of the sixth to ninth grade
Sojková, Tereza ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee)
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...
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Strategies of solving problems focusing on area of plane figures in elementary school
Patočková, Věra ; Novotná, Jarmila (advisor) ; Tůmová, Veronika (referee)
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
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Use of didactical games in teaching mathematics at the lower secondary level
Svobodová, Veronika ; Novotná, Jarmila (advisor) ; Jančařík, Antonín (referee)
This thesis entitled "Use of didactical games in teaching mathematics at the lower secondary level" deals with the use of educational games in math classes at secondary schools. This work is composed of two main parts, theoretical and practical. The theoretical part introduces the concepts of the game, didactic game, math games. More specifically focus on the modification of the board game Monopoly. The practical part is devoted to quantitative research, which determines what is the attitude of mathematics teachers of lower secondary school teaching to the use of games in education, as well as focus on the views and experiences of students with didactic game. Also, the work compares the written test of the curriculum for the class that graduated mathematical hour with the inclusion of educational games monopolies and class that this teaching not undergone.
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