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Cosine and sine theorem at the secondary school
Zenkl, David ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis is concerned with a constructivist approach to the introduction of the cosine and sine theorems at the secondary school. The aim was to develop recommendations for teaching which are based on the idea of motivating teaching cosine and sine theorems. This approach is based on available literature and builds on experience from my own teaching of this topic. By motivating teaching, I mean an approach that is consistent with the principles of constructivism and emphasizes pupils' active learning. Current textbooks for secondary schools were analyzed from a mathematical and didactic point of view. The aim of this analysis is to describe how the topic is elaborated in publications available to teachers, and to get inspiration for my own approach. My own teaching approach was based on the theory of generic models and has been implemented in two classes of the secondary grammar school. Data collected during teaching cosine and sine theorems (video recordings of lessons, field notes from teaching and pupil artifacts) were analyzed in a qualitative way. The thesis describes the teaching in detail, with an emphasis on key phases of the discovery of the two theorems. Pupils' involvement in this process is closely followed. Where teaching did not work as planned, possible reasons are found and...
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Cosine and sine theorem at the secondary school
Zenkl, David ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis is concerned with a constructivist approach to the introduction of the cosine and sine theorems at the secondary school. The aim was to develop recommendations for teaching which are based on the idea of motivating teaching cosine and sine theorems. This approach is based on available literature and builds on experience from my own teaching of this topic. By motivating teaching, I mean an approach that is consistent with the principles of constructivism and emphasizes pupils' active learning. Current textbooks for secondary schools were analyzed from a mathematical and didactic point of view. The aim of this analysis is to describe how the topic is elaborated in publications available to teachers, and to get inspiration for my own approach. My own teaching approach was based on the theory of generic models and has been implemented in two classes of the secondary grammar school. Data collected during teaching cosine and sine theorems (video recordings of lessons, field notes from teaching and pupil artifacts) were analyzed in a qualitative way. The thesis describes the teaching in detail, with an emphasis on key phases of the discovery of the two theorems. Pupils' involvement in this process is closely followed. Where teaching did not work as planned, possible reasons are found and...
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Analysis of mathematical models of bark beetle population dynamics
ZENKL, David
This thesis is concerned with mathematical modeling of bark beetle population dynamics. This thesis is divided into five parts. The first part is concerned with the introduction to the issue of modeling bark beetle population dynamics. The second part summarizes the theory necessary to analyze nonlinear dynamical systems. The third part deals with continuous models of bark beetle population dynamics at the level of a single tree. The main topic here is the study of critical value of beetles necessary to overcome the tree defence as a function of various model parameters. In the fourth part I describe discrete models of bark beetle population dynamics at the level of entire forest and examine the effectivity of different methods of supervision of bark beetle outbreaks. The final chapter expands the results and discusses other difficulties which concern this issue. Mathematically, the main aspect of this work is exploration of the stability of equilibrium points of the system of autonomous first order differential equations and difference equations.
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