Logic and the school mathematics

In the Introduction to the Monograph, the standards set for developing logical thinking of pupils set by the key documents for regulating the activities of the secondary school are discussed upon. In the Chapter One of the Monograph, the general knowledge in formal logic needed for a mathematics teacher is provided. Theoretical statements are illustrated with mathematical examples. In the Chapter Two of the Monograph, the methodics of formation of mathematical concepts at school along with types of mathematical definitions and applying of classification in school mathematics are discussed upon. In the Chapter Three of the Monograph, applying of non-syllogistic considerations, such as induction, analogy, formation of hypotheses to formation of mathematical images as well as the role of analysis, synthesis, intuition, fantasy in mathematics teaching process are analyzed. The Chapter Four analyzes mathematical statements. It described in details the concept of theorem and the types of theorems. The Chapter Five reviews applying the key regulations of logic in teaching the school mathematics. The considerably large Chapter Six analyzes the place of syllogisms and proofs in teaching mathematics. In the Chapter Seven, an application of logic mathematical theory in solution of tasks is discussed upon. The large Chapter Eight analyzes the urgent problems of mathematical education, such as didactics of mathematics, hodegetics and psychology of mathematical education, putting a particular stress on the problems of developing logical thinking of pupils.In the Chapter Nine, the materials on the attempts of teachers to develop logical thinking of pupils in the process of teaching mathematics collected by the author while observing mathematical lessons at primary and higher classes of Lithuanian schools are provided. The results of interviewing teachers of primary schools and mathematics teachers processed using methods of mathematical statistics are discussed upon as well. In the Chapter Ten, the statistically processed analysis of the results of observing cadets of General Jonas Žemaitis Military academy of Lithuania in the period between the years 2000 and 2006, while the author was their lecturer of logic and integrated its statements with the mathematical skills of the cadets acquired at the secondary school. In the Conclusions, it is stressed that there are no considerable imperfections in development of logical thinking skills of pupils in the process of teaching mathematics; the introduction of state examinations in mathematics should be assessed positively and methodic assistance to teachers of primary school is good. A concern about insufficient methodic assistance to mathematics teachers of higher forms and feminization of Lithuanian school is expressed