Novotná Jarmila

Charles University in Prague | CUNI · Department of Mathematics and Mathematical Education

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...

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. Th...

Máme co do činění s publikací napsanou na pomyslném průniku kurikula a didaktiky. "Otázky zaměřené na cíle a obsahy vzdělávání se zde prostupují s otázkami po vzdělávacích formách a metodách. Kurikulární rozměr publikace je dán ukotvením výkladu do teorie obsahové transformace a také do konkrétních vzdělávacích programů. Didaktický rozměr je zohled...

The paper focuses on the skills of prospective mathematics teachers (PMTs) when planning lessons on primary and secondary school levels. The paper is based on a thematic analysis of PTMs' mathematics lesson plans developed within the frame of undergraduate courses at the Faculty of Education, Charles University in Prague, and Faculty of Mathematics...

A significant distinguishing characteristic of the International Classroom Lexicon Project was the documentation of classroom pedagogical practices of mathematics teachers in the original languages of ten communities. These lexicons provide us with an opportunity to compare identified teacher practices within these communities. In this paper, we ex...

The Learner’s Perspective Study (LPS) offers an extremely rich source of data for analyses of classroom situations. In this paper we focus on events in mathematics classrooms through the lens of the Theory of Didactical Situations in Mathematics, namely, on the situation of institutionalization. During the phase of institutionalization, the teacher...

The article presents a study within the international project named The Social Unit of Learning. This study examines the ways in which students interact with each other when solving an open mathematical problem in small groups (four students a group). Attention is focused on peer feedback, especially on its form and how it affects the process of so...

With the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate empirical results, and make progress as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so th...

The article provides an overview of research focusing on pre- and in-service teacher education, conducted in the Czech Republic by teams of researchers of which the authors were members. It employs the methodology of a qualitative meta-analysis of studies aimed at distinguishing key areas of research and their main results. Twenty-one studies were...

The aim of the paper is to show whether the systems of mathematics teacher education in two countries whose historical development may seem quite similar (the Czech Republic and Hungary were parts of the Habsburg Monarchy, and they were part of the Eastern European communist block) are also very similar, or whether each country follows its own, uni...

The goal of this study is to show a novel way of using large-scale data (N = 6203) to identify pupils’ strategies when solving missing value number equations. It is based on the assumption that wrong numerical results appearing more frequently than would be the case if they were consequences of random guessing can be expected to be underlain by a p...

The Czech Republic is a small highly developed country located in central Europe. Its total area is 78,867 km² and it is the 116th largest country in the world (CIA World Factbook 2016). The country is landlocked, having a common border with Austria, Germany, Poland and Slovakia. It is strategically located astride some of the oldest and most signi...

Education has always played an important role in the history of the region of the current Czech Republic. Five phases of development after 1989 can be differentiated: (a) deconstruction (1990–1991)—characterized by opposition against the current state; (b) partial stabilization (1991–2000)—decision-making based on what needed to be addressed and an...

Kniha Matematická slovní úloha: mezi matematikou, jazykem a psychologií se věnuje jednomu z nejproblematičtějších míst ve výuce matematiky – slovním úlohám. Jedná se unikátní publikaci, která představuje výsledky rozsáhlého výzkumu uskutečněného na Pedagogické fakultě Univerzity Karlovy interdisciplinárním týmem didaktiků matematiky, lingvistů a ps...

The paper describes one problem solving strategy – the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual difficult...

This chapter presents the emergence of research in didactics of mathematics in the former Czechoslovakia and gives a glimpse at its present state. It is done against the background of the history of schooling in the area and with respect to international influences such as the New Math movement. Due to a limited access to international research pri...

The paper investigates how the order of numerical data in word problems on division of a whole into unequal parts affects achievement and reasoning of 14-16-year old pupils. The variable was altered in two word problems, in one of which also the context was changed (psychological variable) and in the latter “if-clause” is or is not used (linguistic...

Research has shown that word problem difficulty is influenced by various linguistic, numerical and general variables, but results in this area are inconsistent. This paper focuses on the question of how the order of numerical data, the context, the position of the unknown transformation, and the length of the statement in an additive word problem,...

This chapter focusses on the diverse theoretical and methodical frameworks that capture the complex relationship between whole number arithmetic (WNA) learning, teaching and assessment. Its aim is to bring these diverse perspectives into conversation. It comprises seven sections. The introduction is followed by a narrative of a Macao primary school...

The goal of the chapter is to explore and discuss teacher education in different parts of the world and to emphasize the commonalities and differences not only in the panellists’ countries, but in a broad perspective. By looking at differences in the parts and processes of different educational systems, we can learn from each other and develop a mo...

The presented paper focuses on encouraging creativity in mathematics lessons in heterogeneous mathematics classrooms. It is an extended version of a paper presented at ICME 2016 in Hamburg. It describes teaching experiments conducted within the frame of the project M³EaL: Multiculturalism, Migration, Mathematics Education and Language (526333-LLP-1...

Příspěvek popisuje experiment, který byl součástí dlouhodobého výzkumu Rozvíjení kultury řešení matematických problémů ve školské praxi. Experiment byl proveden na vzorku celkem 584 respondentů ve věku 11–17 let a mapuje vývoj ve volbě řešitelských strategií matematických úloh u různých věkových skupin žáků. Žákům 6. a 8. ročníku základní školy, I....

The article investigates what strategies pupils use when solving two missing value word problems with the same mathematical model but different contexts. Both are examples of direct proportional problems. The sample consists of 238 Grade 8 pupils and 175 Grade 9 pupils. Their written solutions were analysed in terms of their correctness and strateg...

The biggest STEM intersection between Chemistry and Mathematics lies in chemical calculations. Despite calculations in elementary and secondary school Chemistry are mostly based on elementary mathematic principles and they are also a part of word problems in Mathematics lessons, students usually struggle with them. In some schools, the calculations...

The paper focuses on the use of projects in STEM education. The paper first introduces inquiry-based learning and project-based education. Then the authors present a detailed classification of projects in school education. This classification comes out of classification of projects in general and of characteristics of STEM. Four main areas are iden...

The article reports the results of a longitudinal research study conducted in three mathematics classes in Czech schools with 62 pupils aged 12–18 years. The pupils were exposed to the use of selected heuristic strategies in mathematical problem solving for a period of 16 months. This was done through solving problems where the solution was the mos...

Heterogeneity of classrooms is one of the most significant changes in many school systems. Differences in cultures and languages make the math teaching-learning process harder than it is. That is why attention should be paid to the specifics of teaching mathematics in these circumstances.

The paper presents a qualitative research study conducted with pre-service teachers of mathematics. The study is based on questionnaires given to future teachers of mathematics who enrolled in the course of teaching mathematics through Content and Language Integrated Learning (CLIL), i.e. teaching mathematics in English to non-native speakers) and...

The paper presents results of a teaching experiment conducted on a primary school in Prague in a 3rd grade. In the period of 6 months a teaching experiment of teaching mathematics in English to non-native speakers was conducted and analysed to answer the question whether mathematics in Content and Language Integrated Learning (CLIL) is possible on...

The paper is a sequel to the article (Novotná et al., 2014), where the authors present the results of a 4-month experiment whose main aim was to change pupils’ culture of problem solving by using heuristic strategies suitable for problem solving in mathematics education. (Novotná et al., 2014) focused on strategies Analogy, Guess – check – revise,...

The paper describes a heuristic strategy for problem solving called Introduction of an auxiliary element. The strategy is described and illustrated on several problems. Moreover, the paper presents conclusions of an experiment in which pupils were exposed to solving of problems using the strategy Introduction of an auxiliary element for the period...

The chapter focuses on off-line communication using (not only) mobile devices where absence of direct communication increases the risk of misunderstanding and loss of time. Two principles that can lower this danger, the principle of charity and the principle of scaffolding, are presented first separately, and then in mutual relationship. The aim of...

Kapitola popisuje historii a současný stav výzkumu v didaktice matematiky v České republice. Jsou shrnuty významné mezníky v historii tohoto vědního oboru v mezinárodním prostoru a jejich vliv na národní výzkum. Pozornost je věnována zejména metodologii výzkumu v didaktice matematiky a některým současným vlivným teoriím (např. teorii didaktických s...

The paper describes one of the ways of developing pupils’ creative approach to problem solving. The described experiment is a part of a longitudinal research focusing on improvement of culture of problem solving by pupils. It deals with solving of problems using the following heuristic strategies: Analogy, Guess – check – revise, Systematic experim...

In the paper, Culture of Solving Problems - a tool for evaluating pupil problem solving in mathematics - is presented and analyzed. The Culture of Problem Solving consists of four components: Intelligence, Creativity, Reading texts with comprehension (tested by psychological tests), and Ability to use the existing knowledge (tested by solution of a...

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 multi...

Van Ameron (2002, p. 3) stated that “Algebra is known to be a major stumbling block in school mathematics, both in the past and present. Historical studies on the developments of algebra education in the twentieth century show that the algebra studied in secondary school has not changed much over the years”. Sutherland (2000) presented a comparativ...

The idea of the child “creator” is historically associated with its activity and with “construction” of connaissances and savoirs2. These ideas developed within pedagogical streams, namely in active pedagogy, and their boom was brought about with the emergence of constructivism especially with Piaget. In fact, Piaget’s theory triggered a fundamenta...

The paper presents one of the possible perspectives on what can be called "good" questions in teaching. This perspective view is based on the definition of "good" questions in Sullivan and Lilburn (2010) and extends it to natural sciences and problems based on interdisciplinary relations. The presented activities are anchored in the Theory of Didac...

The main research subject of this study is a teacher. Our goal is to contribute to changes in teacher training in the direction of developing their motivation and creative potential, so that creative personalities of students could be subsequently developed. We chose the methodological concept of a natural developing experiment, in which we study t...

One of the manifestations of learning is the student’s ability to come up with original solutions to new problems. This ability is one of the criteria by which the teacher may assess whether the student has grasped the taught mathematics. Obviously, a teacher can never teach the ability to invent new solutions (at least not directly): he/she can as...

The paper presents results of research focusing on cultural and gender aspects of mathematics textbooks and on culture of problem solving. Word problems as they are presented in Czech textbooks of mathematics tend to involve many stereotypes and the images of female and male worlds and roles in these assignments are often defined very rigorously an...

Introduction of computers to mathematics education is a worldwide trend touching all levels and types of schools. Although development of ICT is rapid and first-class, its introduction to schools often faces many difficulties. Teachers and their training play a significant role in this process. The aim of this paper is to show some aspects that mak...

Giving students the space to actively participate in the introduction of new knowledge through their own independent discovery is one of the demands of pedagogical theory and curricular documents. For example, Czech official pedagogical documents demand that pupils develop their problem solving competence by “making use of the acquired knowledge to...

This chapter addresses, from various perspectives, issues associated with teacher education and its development. Several categories of mathematics educators are characterized and their development and roles in the teaching/learning processes are summarized. Cooperation between teachers and researchers as well as the concept of teachers as researche...

This Working Session [WS] is a follow up of WS5 on the same topic at the PME 35 conference (Goos, Chapman, Brown, & Novotna, 2011). WS5 built on Discussion Group 4 of PME 34, facilitated by the same team. The Discussion Group explored a range of theoretical perspectives on the learning and development of university-based mathematics teacher educato...

The aim of this paper is to show how analysis of mathematical textbooks can contribute to the effort of uncovering the roots of common biases and prejudices in the society, for example the stereotypical gender roles. The authors build on the fact that the world of word problem assignments and expository narrative of school textbooks of mathematics...

One of the goals of teaching mathematics is to commu- nicate the purpose and nature of mathematical proof. Jahnke (2008) pointed out that, in everyday thinking, the domain of objects to which a general statement refers is not completely and definitely determined. Thus the very notion of a “universally valid statement” is not as obvi- ous as it...

It can be often observed that some school students can use taught knowledge in new contexts, while others although familiar with the taught algorithms are not able to apply their knowledge in new contexts. The chapter starts from this observation. The main focus is consideration of these inter-personal differences as an effect of the teachers’ dida...

This article presents the results of an investigation carried out across 20+ country-regions under the auspices of ICMI Study 15 into the structures, approaches and general characteristics of the mathematics preparation and development of teachers. We use a global framework provided by the larger research literature on teacher education to contextu...

Teacher education programmes at tertiary educational institutions traditionally comprise three key strands–disciplinary studies, educational studies, and teaching practice (Comiti & Ball, 1996). The aim of these strands is to develop an integrated competence in student teachers and is often referred to as teacher knowledge. Winsløw and Durrand-Guer...

From a system as well as from an institutional perspective, the education of teachers is dependent on the occurrence of a number of interconnected events which are in turn closely related with the life cycle of teachers’ careers: entry to teacher education signals the beginning of teachers’ careers, and it comes accompanied by recruitment and selec...

The teacher’s task is to enable his or her students to develop their individually different processes of knowledge building and meaning construction as well as positive attitudes (De Corte, 2000). It is a common belief that mathematics is a difficult subject. Therefore, in order to help learners succeed it is of the utmost importance that the teach...

Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense components...

This document contains the third volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Ead and Kou: (1) Explor...

Building on some research on structure sense in school algebra, this contribution focuses on structure sense in university algebra, namely on students' understanding of algebraic operations and their properties. Two basic stages of this understanding are distinguished and described in detail. Some examples are given on student teachers' insufficien...

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education confe...

A two-phase cultivation system was developed which will enable studies of streptomycete differentiation by molecular biological and global techniques such as transcriptomics and proteomics. The system is based on a solid phase formed by glass beads corresponding to particles in soil, clay, or sand natural habitats of streptomycetes. The beads are i...

This paper is a part of a longitudinal study focusing on qualitative aspects of learning in a foreign language in the development of cognitive processes in mathematics. The aim of the paper is to present a more complex analysis of textbook-based obstacles to communication. These obstacles originate in the process of vocabulary and grammar acquisiti...

In the paper I focus on the following aspects: grasping word problem assignments levels of understanding and students’ solution strategies and their relation to their understanding of the solved word problems. This is a part of broader research project aimed at the following questions: What is going on between the posing of a word problem and the s...

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Our aim in this paper is toidentify factors affecting problem solvingstrategies in the case of a multiplicativecomparative situation, involving threeunknown quantities whose sum is known, andin which comparison relations between twopairs of the quantities are given. Wepropose a model of the complexity of a wordproblem about such situation. The mode...

Changes in synthesis and abundance of proteins associated with chlortetracycline (CTC) production in Streptomyces aureofaciens were investigated by two-dimensional polyacrylamide gel electrophoresis of proteins pulse-labelled in vivo with L-[35S]methionine. Eleven individual protein spots were selected as being related to formation of the antibioti...

The lincomycin-production gene cluster of the industrial overproduction strain Streptomyces lincolnensis 78-11 has been sequenced (Peschke et al. 1995) and twenty-seven putative open reading frames with biosynthetic or regulatory functions (lmb genes) identified. Two distinct hypothetical genes, lmbI and lmbH, were found downstream of the lmbJ gene...

In our research presented in the paper we concentrate on the influence of elements of symbolic algebraic description in the word problem assignments on grasping processes and mathematisation of problem structures. We also monitor the different interpretations of letters in student's solving processes -the variable and the unknown. Prior students' e...

Bromouridine-triphosphate is commonly used for in situ immunocytochemical labeling of newly synthesized RNA in living cells. While extranucleolar transcripts do not require special conditions for visualization, special treatment prior to fixation (e.g. incubation with alpha-amanitine) is necessary for immunofluorescence detection of bromouridine-la...

Content and language integrated learning (CLIL) refers to teaching of non-linguistic subjects (e.g. mathematics) through an additional language (L2). When using L2 to understand and learn a non-linguistic subject, a wide range of cognitive processes are activated. In our paper we will concentrate on two items related to CLIL in mathematics educatio...

The teaching of mathematics in the Czech Republic has traditionally been of an 'instructive' nature. This teaching strategy has alienated most students in mathematics because they have been expected to use the skills they have learnt without understanding the underlying concepts. They have not been able to appreciate the usefulness of mathematics n...

The genes lmbA,B1,B2 in the lincomycin A production gene cluster of Streptomyces lincolnensis were shown to form a common transcription unit with the promoter located directly upstream of lmbA. The proteins LmbB1 (mol. mass, 18 kDa) and LmbB2 (mol. mass 34 kDa), when over-produced together in Escherichia coli, brought about enzyme activities for th...

1. vyd. Ilustrace Jan Smolík

The first valine dehydrogenase of S. aureofaciens had been described (Vancurová, I., Vancura, A., Volc, J., Neuzil, J., Flieger, M., Basarová, G. and Bĕhal, V. (1988) J. Bacteriol. 170, 5192-5196). In the present work, a second valine dehydrogenase was detected and purified by hydrophobic and fast protein liquid chromatographies. The enzyme has a r...

Cell protein profiles of submerged cultures of Streptomyces aureofaciens cultivated in the absence or presence of 12 microM benzyl thiocyanate (BT) were analyzed by one-dimensional SDS polyacrylamide gel electrophoresis. Substantial increase in the intensity of the 13, 35, 37, 60, and 100 kDa protein bands was observed in cultures treated with BT....

Thermosensitive submerged endospores formed by Streptomyces globisporus 0234 and its natural variant A resembled those of thermoresistant actinomycetes not only in their morphology ultrastructure, but also in the content of dipicolinic acid. The production of endospores containing this substance is unusual in Streptomyces while other features of th...

An asporogenous spontaneous mutant of Streptomyces aureofaciens named ASR1 was selected on streptomycin gradient plates. The mutant is very stable and differs in ultrastructure and morphology, it is prototrophic but it lost the ability to grow well on soybean extract medium and produces one-tenth tetracyclines of the parent. The ASR1 mutant has a 3...