Grygorіj Oleksіjovych Gruzintsev: the man, the mathematician, the philosopher

In this article, we report on Researching Mathematics Leader Learning (RMLL), a project designed to support leaders in learning how to facilitate robust opportunities for teachers’ mathematical learning. Our two-phase research design allowed us to construct a set of videocase seminars, enact the seminar design with leaders, analyze these data, refine our seminar design, and implement a second set of seminars with a new group of leaders. We drew on the noticing literature to examine leaders’ pedagogical reasoning as they discussed videocases of professional development. In this article, we demonstrate how changes in our framework for leader development and the resulting changes in the prompts and tasks shaped leader noticing in three ways: (a) accounting for the mathematical work of the facilitator and teachers in the videocase; (b) linking the mathematical work to goals for teacher learning; and (c) reasoning around the facilitator’s work in advancing those learning goals. Analysis indicates that in Phase II, leader discussions were more focused on the mathematical and pedagogical work needed to advance teacher learning. Based on our research and development work with over 70 leaders, we offer a set of design principles for leader professional development.

The article, dedicated to prelate Aleksandras Dambrauskas (pseudonym: Adomas Jakstas, 1860-1938), a Lithuanian encyclopaedist, Honorary Doctor of Mathematics, summarizes the researcher’s mathematical works and highlights his merits to the development of the science of mathematics in Lithuania. Most frequently his activities are associated with theology, philosophy, literature and politics. However, it is rarely mentioned that it was actually mathematics which led A. Jakstas’ search to be true and beautiful in philosophy, literature and theology. Firstly, he stands out as a reviewer of the fundamentals of geometry and trigonometry in the development of the science of mathematics in Lithuania. The mathematical works that were written by the prelate fall into three groups. The first group includes the original works covering the field of fundamentals of trigonometry and geometry. The second group embraces popularising and informative articles and booklets, and the third group unites school textbooks on mathematics. A. Jakstas manifested himself as a supporter of mathematics. The prelate was interested in problems which could be practically applied in everyday life or were based on all the generally accepted laws of the Universe. The major part of the mathematical works by the prelate was devoted to school mathematics. Observing the dawn of Lithuanian sciences, A. Dambrauskas’ significant contribution to mathematics in Lithuania is acknowledged. Reading the mathematical works by the prelate, his ability to fill them with humanist philosophy is admired. A. Dambrauskas is a perfect example for all the mathematicians, and his mathematical works occupy an honourable place in the history of mathematics in Lithuania. This article is dedicated to A. Jakstas-Dambrauskas, an outstanding Lithuanian personality, who left indelible marks in the Lithuanian culture and education. The latter merits are usually enthroned, whereas the prelate’s mathematical works are often neglected. In this article, the author returns to the mathematical contribution of A. Dambrauskas, supplementing his presentation delivered in Lithuania in 2011 with new sources, and aims to familiarise readers with this exceptional personality in English. To achieve the established goal not only already published but also archived materials stored in the Office of the Central State Archive of Lithuania and the Manuscripts Department of Vilnius University Library will be used. The research employs the methods characteristic of research work in humanities: text analysis, interpretation and historical description. Moreover, the criterion of objectivity and the principle of historicism are followed to revive the atmosphere of the end of the 19th century to the beginning of the 20th century.

One of the most important tasks of education is to develop research skills aimed at the students' research activity in the study process. Involving students in research activities will enable them to learn to invent, understand and learn new knowledge, to argue their thoughts, to make decisions, to develop their interests and to realize opportunities. The theoretical basis of the study is the learning cognitive and constructivist approach. The topicality of the article relates to the transformations to be made in the education system, as the education system in Latvia and its content have to change. The aim of the article is to raise the issue of the goals of the productive activity of the mathematical school subject and the development of research skills, so that the pupil can transfer the knowledge and skills acquired creatively to solving problem situations of related subjects. The questionnaire of teachers and pupils with open questions, as well as research work in mathematics by students, are used in the article for obtaining data. Data analysis is a case study analysis method.

THIS is the first of a post-war series of mathematical tables published for the British Association, in response to the ever-growing demand arising from research work in mathematics and physics. British Association for the Advancement of Science Mathematical Tables. Part-Volume A : Legendre Polynomials. Prepared by the Committee for the Calculation of Mathematical Tables. Pp. A42. (Cambridge : At the University Press, 1946.) 8s. 6d. net.

The article is devoted to the problem of organizing independent work in mathematics for future primary school teachers. This problem is actualized today – in the period of education reform and Ukraine’s accession to the Bologna Process. Among the priority areas of pedagogical search is the problem of organizing the students’ independent work on the basis of personally-oriented and activity-based approaches using innovative teaching technologies. The development of important job-related qualities of a future teacher is to update and creatively apply theoretical knowledge, to form independency as a trait of character, in the approximation of educational activity to the future profession. The optimum use of all types of independent work, compliance with the conditions of its implementation, the functional preparation of the teacher and the student are the necessary conditions for its organization. Independent work of students in mathematics is one of the most important types of formation of subject and key competences, formation of a professiogram of future primary school teachers. The effectiveness of this process depends on the teacher’s ability to organize it correctly and optimally (clearly formulated tasks for students, availability of appropriate methodological support, timely consultations, discussion of results, an analysis of completed work, etc.).Today, within the framework of independent work in mathematics for students of the specialty “Elementary education” it is important to draw up an individual plan of study of the student (syllabus), which is at the same time a means of informing the student about the necessary amount of independent mastering of discipline. This ensures the organization of systematic independent work of students in mathematics during the semester. The syllabus, in particular, states the purpose and objectives of the course – to acquaint students with the basic concepts and methods of mathematics necessary for a thorough mastering of the entire course of mathematics, and the methods of teaching mathematics for the successful learning and education of younger students; to prepare students for the practical application of the acquired knowledge in their practical activities and for independent study of those sections of mathematics that may be required additionally in the practical and research work of future teachers.

This response to Ted and Michael points out that we are unified in considering mathematics to be central in the work of mathematicians, mathematics educators, and mathematics education researchers. However, there are distinctions between the fields of pure mathematics research, the teaching and learning of mathematics, and research in mathematics education, and unless these differences are honored it is possible for researchers to talk past one another. The case of Swedish mathematics education research is examined to exemplify the distinctions. Another distinction is that between “training” and “education”. To further characterize mathematics education research, submission of manuscripts to Educational Studies in Mathematics is explored. Values and aesthetics in various relevant fields are touched upon. Finally, an example is given of the mutual enhancement that exists when mathematicians and mathematics education researchers work together in university mathematics departments.KeywordsDistinct fieldsPure mathematics researchMathematics educationMathematics education researchSwedenTrainingResearch manuscript submissionsAestheticsMutual enhancement

Ramanujan was born in 1887 in Erode in South India. Although he was only 32 years old at the time of his death, he was so genius that he ranked as a world class mathematician. He was a self taught mathematician and failed to gain a degree. In 1916, in England, Cambridge University granted him a Bachelor of Science degree on the basis of his research work. Here, we shall throw light on some of his mathematical works which is related to his work in the area of partition function, number theory, elliptic functions, Landau Ramanujan Constant etc.

The four classic conjectures of mathematics presented here are still open. They appear together with trains of thought that lead to them and relevant partial results. This material shows how strongly problems of mathematical Olympiads in general, and the Colorado Mathematical Olympiad in particular, are interwoven with the forefront of mathematics, and influence each other. These conjectures are “classic” because they are easy to understand and hard to prove or disprove. They are accessible to young high school and college mathematicians and allow students to commence research and creative work in mathematics.

When the Econometric Society was founded in 1930 to promote mathematical and statistical work in economics, its constitution echoed a new view of what it meant to be scientific:

Literary positivism? Scientific theories and methods in the work of sainte-beuve (1804-1869) and wilhelm scherer (1841-1886) This paper compares the research and critical work of Charles-Augustin Sainte-Beuve and Wilhelm Scherer, two of the most important representatives of ‘literary positivism’ in France and the Germanophone countries in the nineteenth century. It argues that although Sainte- Beuve and Scherer shared a research interest in deterministic biography, their work is too rich and too varied to lump it together under the commonly assigned label of ‘positivism’. Sainte- Beuve’s descriptive comparative literary criticism was meant to establish a database of human character types and thereby lay the groundwork for a future science of morals. Scherer, on the other hand, was mainly interested elaborating inductive hypotheses on the causal determination of individual life and literary history by various social and physiological factors. The paper elicits the different scientific sources of knowledge that Sainte-Beuve and Scherer drew upon. While Sainte-Beuve’s classification of character types is strongly in - formed by his reception of the comparative natural sciences, especially late eighteenth/early nineteenth century botany and zoology, Scherer’s research is in many respects conceived as a humanistic equivalent to the empirical inductive research model of German physical reductionism. Finally, the paper elucidates the specific political contexts to which Sainte-Beuve and Scherer reacted in their research.

The greater part of Newton's original work in mathematics and science was first expressed in the form of university lectures. This is true of his researches in geometrical and experimental optics, of his discoveries in theoretical and celestial mechanics, and of his investigations in algebra and some other parts of mathematics. He never lectured upon calculus, no doubt believing that this topic was far beyond the reach of his student auditors; and he did not lecture either upon his chemical, alchemical, biblical and historical studies, not only for the reason that they lay far outside the scope of his professorship. The details of Newton's lecturing are formally known to us from the manuscripts of his optical lectures (in two versions), of the Arithmetica universalism and of the De motu corporum which he submitted to the University Library in accordance with the statutes of his professorship – or nearly so! These statutes, indeed, required the Lucasian Professor of Mathematics to deliver upwards of twenty lectures in each academic year, neatly written copies of ten of them to be deposited with the vice-chancellor in the following year. But although these statutes had been drawn up only in 1663, when the professorship was founded by Henry Lucas, their provisions were at once disobeyed. While his predecessor, Isaac Barrow, had probably lectured in two terms of each year, Newton went to the Schools in one only, half an hour being reckoned a near enough approach to the statutory ‘about one hour’.

The article considers the issue of the formation of research competencies of future fire and techno sphere safety engineers in the process of teaching mathematical disciplines. It is proposed to organize the research activities of cadets, taking into account the principles of practice-oriented teaching. The methodological basis of the research is based on the key provisions of a practice-oriented approach to teaching mathematics, modern methods of scientific and pedagogical research, requirements for the level of development of research competencies among future rescue engineers. The structure of the research activity of cadets in the process of teaching mathematics is presented in the form of four components: motivational, cognitive, activity-based, reflexive. The characteristics of each component from the point of view of practice-oriented learning are given. The types of research activities that contribute to the formation of research competencies of cadets of fire-technical specialties in teaching mathematics are indicated, the goal and educational tasks of performing each type of activity. Requirements for the subject matter, the content of term papers and research work in teaching mathematics to future fire safety engineers are formulated. The examples of assignments for the course work in the discipline "Probability theory and mathematical statistics" are given. A fragment of tasks for research work in higher mathematics for cadets of the specified specialties is presented. The specifics of assessing the level of formation of cadets' readiness for research activities in the study of disciplines of mathematical training cycle are indicated. Incentive and operational criteria are dominant. Based on the results obtained, the goal of the practice-oriented research activity of cadets of fire-technical specialties in the process of teaching mathematics was formulated. The conditions that favor the formation of practice-oriented research competencies of a fire and techno sphere safety engineer in the study of mathematical disciplines are indicated.

The processes of transformation of political and socio-economic systems taking place in the world in the last decade are pushing countries to search for new approaches from the point of view of public policy in the field of public-private partnership. Over time, there is an increasing need to expand the mechanisms of interaction between the state and the private sector in partnerships in order to meet the needs of society. Through the formation of a strategic partnership between the state and the private sector, the Republic of Kazakhstan can form a system of economic order and relations that ensure and guarantee the future of the country. The Republic of Kazakhstan gained independence and modernized all spheres of society in accordance with the requirements of the democratic regime. The transformation of the economic sphere in accordance with the system of market relations has become the basis for the formation and development of private entrepreneurship. At the same time, the spheres of ensuring the needs of society are schools, kindergarten, healthcare, services, infrastructure, agriculture, tourism, etc. With the support of the state through the private sector, they were carried out based on world experience. The activities of public-private partnerships in economically developed countries have been established and are developing in the world. The private sector in each country should function as a political system that allows its activities to work in order to meet the interests of both parties in order to ensure the potential of society. That is, on the liberal principle that an open society under a democratic regime gives freedom to all forms of ownership, the way opens up in the state to a partnership of private and public property, one of the most important sectors of the economy. The article considers, first of all, the theoretical justification of this problem when studying the problems of public-private partnership, providing ways and mechanisms to solve it. That is, analyzing the theory on which the research work is based, relying on general scientific methods, operationalizing the theory, analysis of analogical theories, their classification, methods of induction, and deduction, clarifying the theory, and describing the methodology of this problem. Consequently, a scientific theory is determined and verified by methods.

In this article, the concept of first instance court decisions in civil cases and their types have been analyzed. In particular, the concept and types of court decisions, the scientific and theoretical views of legal scholars in this area were studied. The first instance court decisions, its peculiarities, the requirements to them have scientifically and theoretically been examined. Some items have been revealed in the final part of the court decision as well as a comparative analysis of the foreign countries’ experience in this regard, and suggestions and recommendations for improving the national civil procedural legislation have been discussed in the article. The work also analyzes the concept, objectives and specific procedural features of external proceedings, foreign experience in external proceedings, and comments that do not necessarily need to improve national procedural management. In addition, in this research work, the concept of court rulings and their classification have been studied in scientific theory. The scientific views of legal scholars were analyzed and the criteria for classifying court rulings were indicated. As another document of the first instance court, the court order and its significance, its role in court decisions, comparative analysis of civil procedural legislation of foreign countries, judicial practice, court statistics were also studied and examined.

This article is based on my research in the field of semiotics, a field in which I have been involved for over 25 years. Throughout that time, I felt that my work was situated on the boundary between semiotics and philosophy. Recently, I concluded that all semiotic activity related to scientific research is part of epistemology, in that it deals with certain aspects of the acquisition of knowledge. Semiotic activity is a significant part of all scientific research. Along with observation and experimentation, it is included to varying degrees in all stages of the scientific process. Scientists rely on signs throughout their research work, from the time they plan a project through the summarizing of their conclusions. Every branch of science develops its own sign-system or systems. The development process is one of constant and continuous innovation, because the system of signs used by a science must grow and develop along with the science itself. My research has led me to conclude that sign-systems evolve in predictable patterns, gradually becoming more abstract by incorporating increasingly abstract symbols. If we can identify these patterns, we may be able to determine the stage of maturity of a given scientific theory at a particular time. The essays in this article are one of the first attempts to begin identifying and characterizing these patterns.