Abstract: The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.
Abstract: The paper compares the treatment of fractions in a
typical undergraduate college curriculum and in abstract algebra
textbooks. It stresses that the main difference is that the
undergraduate curriculum treats equivalent fractions as equal, and
this treatment eventually leads to paradoxes and impairs the students-
ability to perceive ratios, proportions, radicals and rational exponents
adequately. The paper suggests a simplified version of rigorous
theory of fractions suitable for regular college curriculum.