Abstract: The article analyses the composition and structure of the motivationally oriented methodological system of teaching mathematics (purpose, content, methods, forms, and means of teaching), viewed through the prism of the student as the subject of the learning process. Particular attention is paid to the problem of methods of teaching mathematics, which are represented in the form of an ordered triad of attributes corresponding to the selected characteristics. A systematic analysis of possible options and their methodological interpretation enriched existing ideas about known methods and technologies of training, and significantly expanded their nomenclature by including previously unstudied combinations of characteristics. In addition, examples outlined in this article illustrate the possibilities of enhancing the motivational capacity of a particular method or technology in the real learning practice of teaching mathematics through more free goal-setting and varying the conditions of the problem situations. The authors recommend the implementation of different strategies according to their characteristics in teaching and learning mathematics in secondary schools.
Abstract: The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.
Abstract: Teaching of mathematics to engineering students is an
open ended problem in education. The main goal of mathematics
learning for engineering students is the ability of applying a wide
range of mathematical techniques and skills in their engineering
classes and later in their professional work. Most of the
undergraduate engineering students and faculties feels that no efforts
and attempts are made to demonstrate the applicability of various
topics of mathematics that are taught thus making mathematics
unavoidable for some engineering faculty and their students. The lack
of understanding of concepts in engineering mathematics may hinder
the understanding of other concepts or even subjects. However, for
most undergraduate engineering students, mathematics is one of the
most difficult courses in their field of study. Most of the engineering students never understood mathematics or
they never liked it because it was too abstract for them and they could
never relate to it. A right balance of application and concept based
teaching can only fulfill the objectives of teaching mathematics to
engineering students. It will surely improve and enhance their
problem solving and creative thinking skills. In this paper, some practical (informal) ways of making
mathematics-teaching application based for the engineering students
is discussed. An attempt is made to understand the present state of
teaching mathematics in engineering colleges. The weaknesses and
strengths of the current teaching approach are elaborated. Some of
the causes of unpopularity of mathematics subject are analyzed and a
few pragmatic suggestions have been made. Faculty in mathematics
courses should spend more time discussing the applications as well as
the conceptual underpinnings rather than focus solely on strategies
and techniques to solve problems. They should also introduce more
‘word’ problems as these problems are commonly encountered in
engineering courses. Overspecialization in engineering education
should not occur at the expense of (or by diluting) mathematics and
basic sciences. The role of engineering education is to provide the
fundamental (basic) knowledge and to teach the students simple
methodology of self-learning and self-development. All these issues
would be better addressed if mathematics and engineering faculty
join hands together to plan and design the learning experiences for
the students who take their classes. When faculties stop competing
against each other and start competing against the situation, they will
perform better. Without creating any administrative hassles these
suggestions can be used by any young inexperienced faculty of
mathematics to inspire engineering students to learn engineering
mathematics effectively.
Abstract: This paper covers the present situation and problem of experimental teaching of mathematics specialty in recent years, puts
forward and demonstrates experimental teaching methods for different
education. From the aspects of content and experimental teaching
approach, uses as an example the course “Experiment for Program
Designing & Algorithmic Language" and discusses teaching practice
and laboratory course work. In addition a series of successful methods
and measures are introduced in experimental teaching.