Didactic Phenomena Research Articles

Knowledge of Sets: a Didactic Phenomenon

This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and in-service teachers. The paper considers interpretations of the results under various theoretical frameworks and argues that these interpretations can be synthesized around the anthropological theory of the didactic. The paper ends with implications for what is taught under the name ‘mathematics’.

Szkoła Szymona Askenazego - przypadek Janusza Iwaszkiewicza (1879-1944)

Szymon Askenazy’s School – the case of Janusz Iwaszkiewicz (1879-1944) Keywords: University of Lviv, schools of history, Szymon Askenazy, Janusz Iwaszkiewicz. The article refers to the school of researchers of recent history established at the turn of the 19th and the 20th centuries at the University of Lviv by Szymon Askenazy. Thanks to handwritten memories of Janusz Iwaszkiewicz, one of the first students of the modern history researcher from Lviv, it was possible to specify existing knowledge about the subject of a didactic phenomenon of Askenazy’s private seminar in Lviv. The starting point was a photograph from 1903 depicting a group of six seminarians, among whom there was Iwaszkiewicz, and their master. The circumstances in which the photograph was taken have not been known until now. Thanks to an analysis of the memories, we have got to know not only about the individual fate of one of the students who was awarded a habilitation in 1924 in Cracow and became a full professor at the Stefan Batory University in 1938, but also, we have got to know about Askenazy’s anonymous seminarians and relationships between representatives of the school and scholars from Warsaw and Cracow. However, most importantly, we have gained insight into the process of its formation, thanks to which it has been easier to assess relationships between the master and his students.

This cannot be the result! The didactic phenomenon ‘the age of the earth’

ABSTRACT In the frame of national Italian standardized assessments in mathematics, a didactic phenomenon has been observed concerning students’ behaviour when answering an item: students are inclined towards not accepting an output which is not clearly recognizable with something distinct from the starting inputs. The observed effect seems to originate from the teacher-student relationship and could be described as a typical didactic contract situation but it also affects the general relationship between the student and mathematics. Adopting a mixed-method apparatus including large-scale assessments results, questionnaires and interviews, we can describe several behavioural features related to the observed phenomenon. In particular, we show how it is present in different grades and in pupils of different abilities. We consider the ‘ruling principle’ as a connecting concept for the different constructs used here to analyse this phenomenon, i.e. an organizational or normative criterion that shapes the action of the student facing a mathematical task.

Fidelidad en el uso de app para la resolución de ecuaciones diferenciales

This report shows the results of using Computational Algebraic Applications (CAA) for mobile devices, intended as aid in college courses of Ordinary Differential Equations (ODE). The main purpose was for students to gain skills in such software so they could proficiently solve ODEs as well as to provide graphics from the solutions obtained. From the “fidelity” concept of the software, several applications were analyzed and evaluated such as: Differential Equations, Wolfram, Desmos, Photomath, among others. The given results proved than those applications were the most useful. With those results, a Didactic Situation was created in which students interacted with the app to solve equations and to graph results. The results shows some deficiencies in the interface evolution of the app that was used, this cause significant didactic phenomena.

ЗАСТОСУВАННЯ “TELL ME MORE” У ПРОЦЕСІ ФОРМУВАННЯ ГУМАНІТАРНОЇ КОМПЕТЕНТНОСТІ СТУДЕНТІВ

The article studies the specifics of the information and communication technologies in the educational process. The effectiveness of leveraging information and communication technologies in teaching English by means of a pedagogical experiment is substantiated and practically verified. The initial level of students’ humanitarian competency at the ascertaining stage of the pedagogical experiment has been determined. The structural-functional components of humanitarian competency are specified: motivational-self-actualizational, knowledge-content, activity-procedural and reflexive-correctional. The system of diagnostic methods of the studied didactic phenomenon has been developed. The detailed analysis of diagnostic information on the levels of humanitarian competency development and the criteria for the individual strategies effectiveness has been conducted. The authors have determined a number of difficulties such as lack of students’ motivation and skills for independent-cognitive activities. On the basis of analyzing and summarizing the collected diagnostic information the program of the forming stage of the pedagogical experiment supported by information and communication technologies as a means of intensifying students’ independent-cognitive activities has been elaborated. The most well-known computer assisted language learning latforms and programs have been examined. The choice of the "Tell me more" interactive compurer-based program as the didactic mechanism for providing constructive influences is substantiated. The implementation of the program in the educational process with further definition of students’ humanitarian competency levels at the control stage of the pedagogical experiment is described. The results of the experimental and control groups as well as formulated conclusions about the effectiveness of information and communication technologies in teaching English in the context of students’ humanitarian competency development have been researched and compared.

Didactic Contract as a Key to Interpreting Gender Differences in Maths

Research, at both national and international levels, has started to focus on the gender gap regarding student performances in technological/scientific topics. Fervent ideological and epistemological debates have sprung up, particularly concerning the differences in mathematics test results between males and females (with males outshining females in most countries). In this paper, we analyse some questions taken from the INVALSI mathematics tests administered at varying educational stages; emergent didactic phenomena are investigated via one of the key concepts of mathematics education, the didactic contract. From a quantitative analysis, based on the percentage of answers given and Rasch Model results, it is possible to identify the presence of significant gender differences between the performances which can be traced back to the effects of the didactic contract. Furthermore, study of the features which accompany these gender gaps in the case studies allows us to investigate the gender gap in mathematics via a new interpretative method which also takes into account student ability levels.

Training Platform: The Network of Best Language Teaching Practices Sharing

The article represents an innovative model of accumulation and promotion of best practices of foreign language teaching in the system of lifelong learning. It gives the idea about the nature, status, and features of language teaching practices as a new didactic phenomenon. The author describes the functions and justifies the role of a training platform as a form of exchange of best practices of teaching foreign languages. The research provides the analysis of positive aspects of training platforms as special forms of cooperation between teachers in the sphere of teaching foreign languages with the purpose of sharing best practices. Alongside with that the paper lists the unrealized potential of the platforms, the implementation of which will improve the quality of foreign language teaching within LLL.

Principles of students’ independent work organization and requirements to its realization

The notion of independent work as didactic phenomenon is analyzed. Its main principles of organization (students’ performance, individualization of learning, affordability of educational material, strictness of tasks, visualization, systematicity and succession in the formation of independent work skills, consciousness and independence of learning etc) are elucidated and requirements to its realization are given

Contexts and functions of music in the Orbis sensualium pictus textbook by John Amos Comenius

The present study deals with the content-related and thematic, as well as visual and semantic, contexts in which musical motifs, and words and notions with a musical meaning, are placed in the Orbis sensualium pictus textbook of John Amos Comenius. They can be found in several places in the textbook in both its textual and pictorial components. They are used for a broad demarcation of the fields in which music is presented as a philosophical and aesthetic, didactic, communication, ethical and theological phenomenon. In this way, music is presented to the children of the seventeenth century through the Orbis sensualium pictus not only in the form of its specific object or event, in its metaphorical or symbolical meaning but, first of all, as a phenomenon present in the various fields of spiritual and everyday life. The reader becomes acquainted with music in its various functions, with its form, practical utilisation, relation to other fields of art and science, its position within philosophical concepts, its ethical dimension, aesthetic values, spiritual as well as transcendental essence. The purpose of the present study is to explore the essence, present the origins, genesis, sources for inspiration and objectives of the textual as well as the pictorial form of the music syllabus in this pictorial textbook, most widely used in the European context, and, at the same time, to point out the juxtapositions, links, functions and contexts into which music is placed throughout its contents.

Developing mathematics teacher knowledge: the paradidactic infrastructure of “open lesson” in Japan

In this paper, we first present a theoretical approach to study mathematics teacher knowledge and the conditions for developing it, which is firmly rooted in a systemic approach to didactic phenomena at large, namely the anthropological theory of the didactic. Then, a case of open lesson is presented and analysed, using this theoretical approach, to show how the format of open lesson contributes to the construction and diffusion of didactic knowledge in the community of mathematics teachers in Japan. The basic idea of this format is that teachers from other schools are invited to observe a class taught by a teacher then participate in a discussion session with him on the details of the lesson. For the case study, we analyse the lesson plan prepared for an open lesson, the observed lesson and the teachers’ discussion. As a result, an open lesson session has been described as a specific form of post-didactic practice related directly to an actual observed lesson, and aiming specifically at elaborating the theoretical aspects of teacher’s didactic practice in the lesson and beyond it.

The onto-semiotic approach to research in mathematics education

In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.

Mastering by the teacher of the instrumental genesis in CAS environments: necessity of intrumental orchestrations

In this article, we study didactic phenomena identified in integration experiments within our classes, CAS (implemented in calculators). From this study, we show the interest of an instrumental approach to understand the influence of tools on the mathematical approach and on the building of student's knowledge: through a process—instrumental genesis—a calculator becomes a mathematical work tool; this process depends on the tool's constraints and potentialities, on students' knowledge, and on the class' work situations. To analyze the differentiation of instrumental genesis, we then have taken interest in students' behaviour and we propose a method enabling us to constitute a typology of extreme behaviour in environments of symbolic calculators. To take the variety of these genesis into account, the professor needs a particular organization of space and time of the study in the class. We suggest the notion of instrumental orchestration to name this organization. We demonstrate how this notion gives a better definition of the objectives, the configurations and the exploitation modes of different arrangements which aim at constituting coherent instrument systems for each student and for the class.