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This paper presents a study of lesson plans created by pre-service mathematics teachers (PMTs) from two universities (Faculty of Education, Charles University in Prague, and Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava) in the course Didactics of Mathematics. The collaboration of the two research teams brought new perspectives on several questions that were come across in one or the other group of PMTs. The focus of the study was on lesson plans since the lesson plan is one of the significant parts of mathematics teacher education. The studied issues were the PMTs' willingness to implement digital technologies (DT) in their lesson plans and the changes in their lesson plans that could be linked to the COVID-19 pandemic. For data processing, a mixed research design was used. In the qualitative part of the research, the thematic analysis resulted in identification of several codes related to the hybrid mode of teaching. In the quantitative part, Statistical Implicative Analysis (C.H.I.C) was applied. Relations inside the groups of PMTs and among them are presented and discussed in the paper by interpreting the results from the implicative trees and graphs. We concluded that (i) PMTs from our sample are, to a limited extent, prepared for using DT in their teaching, (ii) PMTs used DT in their teaching mainly for testing and feedback collection, (iii) PMTs in our sample focused on the content and the choice of software (or application, applet, etc.) when preparing a lesson plan. Besides that, we found (by using C.H.I.C.) that not all codes identified in thematic analysis were connected to the others. The findings are of interest to teacher educators in general, researchers interested in teachers' lesson planning, and in-service teachers in general. In this paper we focus on PMTs' lesson plans. We plan to do a similar analysis of in-service teachers' lesson plans in order to gain a deeper insight into the role of experience in the studied domain. [ABSTRACT FROM AUTHOR]

The paper presents the partial results of a research study conducted within the project AI Assistant for Pupils and Teachers. The university, non-profit sector and organization established by the Ministry of Education are cooperating on this project. The aim of the project is to prepare an AI assistant for communication with teachers and pupils. The output of the project should be a system that communicates with pupils and teachers. AI assistant will offer them appropriate teaching materials based on their needs. The system will use not only pre-prepared materials (which is the case presented in this paper), but will be able to independently search and evaluate materials in open databases. We primarily focus on supporting the teaching and learning of mathematics and Czech language. In this paper, we focus on one of the partial researches. The aim of this research was to prepare and experimentally test the possibility of using a series of pre-prepared math problems of an increasing difficulty for individual (partly pupil-managed) practice of algebraic expressions. The topic of algebraic expressions was chosen because it is relatively well-structured and is therefore suitable for this method of processing. At the same time, and this is very important, the topics include the so-called critical topics, i.e. topics that cause problems for pupils and where pupils very often seek help. The topic of algebraic expressions is divided into several subchapters, each of which contains about ten steps, consisting of three tasks, one of basic, one of standard and one of higher difficulty, and supporting materials for mastering them. The pupil can decide what difficulty of the task they want to solve and what supporting materials they want to use. The developed application is available to pupils online in the web environment as well as in the form of an app for the mobile phone. The application has already been published and is in a test regime. [ABSTRACT FROM AUTHOR]

In many European countries, mathematics teachers feel the need for teaching materials being aware of and sensitive to the multicultural background of their classrooms (Favilli, 2015). A number of studies show that such materials should follow certain inclusive criteria (Favilli, 2013; Novotná, Ulovec & Moraová, 2020): Fostering tolerance, inducing interest, value diversity, emphasize cooperative learning, make use of different cultural backgrounds, use a variety of contexts and names from multiple cultures, avoid cultural stereotypes etc. Based on these criteria, the authors, in an international collaboration project, have developed a few exemplary teaching units (Novotná & Ulovec, 2020), as well as a number of teaching unit concepts specifically designed for multicultural classrooms (Novotná, Ulovec & Moraová, 2020). In this paper, we demonstrate how -- based on one of these concepts -- teachers in the field can create their own fully-developed mathematical teaching units for their multicultural classrooms, making use of ICT tools and thereby following the recommendations of Ebenhofer, M. & Knierzinger, A. (2007). We use the concept of "How (seemingly) simple things can be very different (and difficult) in other places and cultures" to develop two teaching units: First, a teaching unit using Dynamic Geometry Software to analyse parabolas, and second, a teaching unit using CAS to analyse the relation between air pressure and the boiling point of water. These examples can then serve as guidelines for teachers on how to develop teaching units for other mathematical topics and different cultural backgrounds. [ABSTRACT FROM AUTHOR]

Mathematics teachers feel the necessity for concrete teaching materials, which reflect the needs of their students in terms of different linguistic and cultural backgrounds (Favilli, 2015). A number of studies (e.g. Hastedt, 2016; Secada, 1992) show that these students encounter even more difficulties than their native classmates in acquiring fundamental mathematical skills. It is recommended that appropriate teaching materials for multicultural classrooms should follow certain inclusive criteria (Favilli, 2013; Novotná, Ulovec & Moraová, 2020): Fostering tolerance, inducing interest, value diversity, emphasize cooperative learning, make use of different cultural backgrounds, use a variety of contexts and names from multiple cultures, avoid cultural stereotypes etc. To take into consideration the different learning levels and learning styles of students, it is also recommended that such materials make use of ICT (Bartolini Bussi et al., 2004; Ebenhofer & Knierzinger, 2007). The paper shows how the recommendation to respect inclusive criteria, the recommendation to use ICT, and the recommendation to have concrete suggestions for classroom use, can be fulfilled, by giving two examples demonstrating the use of ICT in teaching mathematics to multicultural students. In the first one, we show how a classical multicultural teaching unit can be enhanced by using ICT. The second example demonstrates how an ICT product - a learning software that has been designed specifically for migrant students - can be used to produce a concrete teaching unit for multicultural classrooms. These examples show how the use of ICT - appropriately applied and eventually combined with already existing materials - can support mathematics teachers in their needs for teaching materials suitable for multicultural classrooms. [ABSTRACT FROM AUTHOR]

The paper focuses on good questions as originally developed by Clarke, Sullivan and their team for primary mathematics education. In accordance to their work, we understand a good question as an open question that asks for more than recollection of known facts. It has several answers that can all be accepted. When answering it, pupils learn something new and the teacher learns something about their pupils from their answers. Most publications focusing on good questions focus on their use in face-to-face teaching of mathematics. The use of good questions in the e-learning environment has not been studied yet. There are obvious differences between face-to-face and e-learning environments. The work in e-learning offers the access to resources, more time to think about possible answers etc. But are open questions used in the e-learning practice? If yes, to which extent? In the paper, an analysis of good questions from mathematics and natural sciences, developed for home schooling at the elementary school ZŠ Březová is presented. The e-learning materials of the 6th and 9th grades (309 pieces in total) were examined. We found 87 good questions in the materials. Usually, however, the educational potential of using good questions was not exploited. The analysis of good questions in the materials resulted in dividing them into categories. The categories are presented with examples, enabling the reader to grasp the specificities of the categories better. Based on the research findings, the e-learning environment at the monitored school will be adjusted. [ABSTRACT FROM AUTHOR]

The paper addresses the important topic of implementation of ICT into mathematics education. Use of ICT in mathematics education on primary and secondary school levels and in pre-service teacher education is a very up-to-date topic. Implementation of ICT into mathematics teaching and learning should never be purposeless. It should be an 'added value' to learning activities. In the paper, one additional principle for selecting suitable activities with a solid potential for teaching are added to those already published. These principles follow from the use of new ICT tools. In the article, the new set of principles is illustrated. Examples of good practice are contrasted with the so called "for show" implementation of ICT in lessons of mathematics. The topic discussed in the article is relevant especially for teacher education. [ABSTRACT FROM AUTHOR]

The goal of the paper is to show the specifics of technology-supported mathematics education, both using computer technology in classical school environment and in an e-learning course. The survey is conducted within the frame of the international Lexicon Project: Analysing pedagogical naming systems from different cultures to reconceptualise classroom practice and advance educational theory. In the research study the authors work with the Czech Lexicon (i.e. a lexicon of terms in Czech with their equivalents in English) that was designed for description of any general lesson of mathematics. The question the authors ask is which moments in a technology-supported mathematics lesson cannot be described using terms from the Lexicon. Detection of these moments show which aspects of a technology-supported mathematics lessons are unique and specific and need to be paid additional attention to in lesson planning, when conducting the lesson and in teacher training. The methodology used for detection of these moments was analogical to methodology of creation of the original, general Lexicon. The analyzed material consisted of three video recordings of mathematics lessons from the Lexicon set of recordings where technological devices were used at least in a part of the lesson and field notes from preparation, conduction and observation of an e-learning mathematics set of activities (considered as one lesson). When supplementing the Czech Lexicon, the authors used open axial coding. The entries that the original Lexicon did not contain or did not use them explicitly for description of computer-supported mathematical education can be divided into the following two groups: Terms that are used in the original Lexicon and refer to use of technological devices in a mathematical lesson regardless of whether the lesson uses e-learning or ICT in "traditional" lesson; terms that are specific for technologysupported mathematics lessons with attention paid to specifics of e-learning. The newly included terms are divided into the following categories: Used technological device, Time span, Activity in a lesson, Way of use, User, Use of results. The authors show that the newly included terms do not ask for major revisions of the original Lexicon and can be integrated into the already existing categories of the Lexicon. [ABSTRACT FROM AUTHOR]

The paper focuses on collaborative activities used in one form of distance learning, the so called home-schooling. As shown by several authors, collaborative activities play an important role in face-to-face education, regardless of their form. In the here presented study the focus is on collaborative activities used in online teaching and learning. The authors analyse what type of collaboration particular activities support and look at their advantages, disadvantages as well as their limits. Attention is also paid to their potential to get home-schoolers more involved in collaborative activities. The results were obtained through analysis of several online lessons and from interviews with a small number of pupils. [ABSTRACT FROM AUTHOR]

The proposed paper focuses on the issue of developing and supplementing teaching mathematics in linguistically and culturally heterogeneous classrooms using computers and multimedia. The issue of how to support teachers who face the reality of having to teach in a setting where the mother tongue of some learners is not the language of instruction has recently attracted a lot of attention due to the fact that EU countries have to face an increasing flood of migrants. The authors ask if and how the use of computer technologies and multimedia might help in preparation and individualization of teaching materials suitable for use in linguistically and culturally heterogeneous environment, i.e. when both teachers and learners have to cope with a situation when language and culture may be an obstacle to learning and teaching mathematics. The authors demonstrate that meaningful and appropriate use of computer technologies and multimedia may significantly support preparation of teaching materials and their use in lessons. The authors discuss different uses of ICT proposed in the different teaching units developed by members of the project team M3EaL - Multiculturalism, Migration, Mathematics Education and actually used in piloting in 6 European countries (France, Italy, Austria, Norway, Greece, the Czech Republic). They discuss their potential for development of both mathematical competence and communication skills in the language of instruction. The paper also shows the potential of ICT as the source of materials that can supplement traditional printed materials that do not reflect the specific needs of migrant pupils. Examples of concrete didactical units are shown and discussed. The developed materials illustrate the rich potential of the use of computers and multimedia materials both by teachers and pupils. Each of the developed units was piloted by three project partners. Each of the piloting teachers adapted the proposed material to meet the conditions of their own classroom. And it was the process of adapting and piloting the materials that showed the rich variety of possible uses of ICT both while planning and while conducting the lessons. The experience of implementation of these units into lessons also confirm the enormous motivational potential of the prepared teaching units. [ABSTRACT FROM AUTHOR]

The main goal of the presented paper is to show how electronic teaching materials can be designed in such a way that they support pupils' creativity and culture of problem solving. It focuses on e-textbooks, e-manuals and materials for the teachers who use ICT in their classrooms. The paper also focuses on the extent to which the potential of multimedia teaching materials is made use of in practice and on the possible modifications whose result will be turning these materials into materials that develop pupils' creativity and independence. The paper builds on two areas: on the concept of "pupils' culture of problem solving" as it used in the research project GAČR Development of culture of problem solving in mathematics in Czech schools and on those properties of multimedia teaching materials that make them a suitable tool for development of pupils' creativity and culture of solving problems. Teaching materials have impact not only on the selection of concepts and types of tasks but also on the selection of solving strategies a teacher introduces, or possibly encourages or recommends to their pupils. Multimedia teaching materials have an immense potential in support of development of pupils' creativity. The author demonstrates on three examples how electronic teaching materials can, if their potential is used well, enhance pupils' creativity. In Example 1, an analysis of few pages selected from a Czech multimedia teaching material that fails to support pupils' culture of problem solving is followed by a demonstration of possible modifications of the material that change it from a mere conversion of a printed text into electronic form into a material which makes use of the potential of multimedia teaching resources fully. Examples 2 and 3 illustrate the possible use of electronic materials as scaffolding in situations when routine calculations are too long (Example 2) or when fast access to a missing piece of information is needed. The results presented in the paper have significant consequences for pre- and in-service teacher training. [ABSTRACT FROM AUTHOR]

A preface to the book "Proceedings of the European Conference on e-Learning" is presented.