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Introduction
Skills and Expertise
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January 1994 - present
Charles University in Prague, Faculty of Education
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- Professor (Associate)
Publications
Publications (88)
Acknowledgments We would like to thank Kristýna Nižňanská, David Zenkl and Pavel Sovič for collecting the interview data and help with their analysis. We thank Adrian Simpson for his help with the statistical analysis. Finally, we would like to thank the students who took part in the study for giving up their time to engage with our project. Ethics...
ABSTRAKT Profesní vidění jako schopnost identifikovat ve viděném podstatné jevy, připisovat jim význam a uvažovat nad nimi v souladu s dostupným poznáním je důležitá součást profesního rozvoje učitele, neboť učitelovo vnímání situací ve výuce ovlivňuje jeho rozhodování a jednání, a má tak vliv i na kvalitu výuky. Studie zkoumá, jaký vliv na rozvoj...
The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able gr...
Cílem přehledové studie je podat přehled o výzkumech zkoumajících účinnost intervencí, v nichž je prostřednictvím zlepšování čtení s porozuměním (a to na podkladu zadání slovních úloh) usilováno o zlepšení dovednosti řešit slovní úlohy. Studie je založena na předpokladu, že u slovních úloh, které jsou příkladem vysoce komplexního učiva, může úroveň...
Word problem solving is an important part of school mathematics, yet pupils often fail
in it. In this case study, we investigated whether an introduction of the block model
approach would help two 4th-grade pupils in Kosovo to solve word problems. Think-aloud interviews were conducted, and their transcripts were analyzed in a qualitative
way. Th...
Tato teoretická studie se zabývá tématem definování funkční jazykové gramotnosti pro jazyk mateřský (první). Důvody jsou následující: (1) Téma gramotností je v současné době aktuální a dochází k propracovávání celé řady definic pro různorodé gramotnosti více či méně vázané k tradičním obsahům školního kurikula. (2) Definice funkční jazykové gramotn...
![Figure 2. Three dimensions of a teacher's professionalism [72] and its...](publication/353022165/figure/fig1/AS:1042620809768961@1625591580198/Three-dimensions-of-a-teachers-professionalism-72-and-its-projection-in-the-analyzed_Q320.jpg)
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...
Research has uncovered a semantic cue effect for short inconsistent word problems; the presence of functionally related objects makes them easier for pupils than the presence of categorically related ones. This study builds on this result by investigating other types of problems. Variants of problems differing in a semantic cue were solved by equal...
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 book deals with developing the concept of professional vision (noticing and knowledge-based reasoning) among future primary and secondary school teachers of Biology, Mathematics, English as a foreign language, Art, and Social Studies. Researching the use of video interventions during teacher-training programmes, the authors show that short-term...
Článek se zabývá povrchovými strategiemi řešení slovních úloh, tedy takovými, které nejsou založeny na matematické struktuře úlohy, ale jen na jejích povrchových rysech. Snahou je popsat různé příčiny, které mohou k používání těchto strategií žáky vést, včetně didaktických. Pozornost je věnována vlivu použitých čísel a tzv. signálních slov v zadání...
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...
Kniha se zabývá tzv. kritickými místy matematiky základní školy, tedy oblastmi, v nichž žáci často a opakovaně selhávají. Jinými slovy jde o oblasti, které žáci nezvládnou na takové úrovni, aby se jejich matematická gramotnost produktivně rozvíjela a aby mohla být tvořivě užívána v každodenním životě i v následném studiu. Knihu otevírá teoretická k...
The study is part of action research aiming at the description of concept development in mathematics. Building on socio-constructivist theories of learning, we pursue the question "How do pupils get to know that shapes which do not appear congruent can have the same area, by building on one another's knowledge in a classroom situation?". A qualitat...
Practice-based programmes involving teachers cooperating in professional communities have been shown to develop their professional knowledge and teaching. The chapter concentrates on the blend of two such approaches, namely a video-based course and Lesson Study. While video-based courses are based on joint reflection on the teaching of others and/o...
This chapter is positioned within research on noticing and knowledge-based reasoning of prospective mathematics teachers. It deals with the following research question: What are the differences in the development of noticing and reasoning skills of prospective mathematics teachers during their participation in the same video-based intervention? In...
Much research on teachers’ professional vision examines development through video interventions. Evidence suggests they change focus towards specifics, subject matter and students and away from the evaluation. This study was designed to examine whether there was a discernible difference between viewing pre-service teachers’ own videos or general vi...
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...
A key requirement of successful initial teacher education is the development of professional vision, which includes shifting attention to features of the situation relevant to the specialized goals of teaching. Existing research hints at the value of targeted video-based courses in the development of professional vision, but often raises questions...
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,...
Abstrakt: Profesní vidění je důležitým spojníkem mezi profesním věděním a profesním jednáním. Článek představuje výsledky výzkumu profesního vidění studentů učitelství jednak pro 2. a 3. stupeň a jednak pro 1. stupeň ZŠ, a to na počátku studia obecné didaktiky i didaktik oborových. Pomocí analýzy písemných refl exí (n = 211) na videu zhlédnuté vyuč...
Measurement in geometry belongs among key areas of school mathematics, however, pupils make serious mistakes when solving problems on measurement and hold misconception. The article focuses on possible links between lower secondary pupils’ (n = 870) success in solving non-measurement and in calculations tasks on area and volume and on their problem...
The aim of the paper is to shed more light on noticing skills and reasoning of 94 student teachers of biology, English and mathematics. Their written reflections about a lesson were divided into units and coded for comments on expert 'important moments'. Just before entering teaching, students did not demonstrate good noticing skills. The English l...
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...
Abstrakt: Cílem článku je uvést do českého prostoru tzv. lesson study jako specifickou formu dalšího vzdělávání učitelů založenou na spolupráci učitelů při zkvalitňování výuky prostřednictvím plánování, realizace a vyhodnocení experimentální hodiny. Lesson study má společné rysy s akčním výzkumem a souvisí s pojmy kvalifikovaná reflexe a rozvíjejíc...
The aim of this paper is to a) shed light on the nature of student teachers' noticing of mathematics specific phenomena as observed in a video recorded lesson and to b) compare this nature for student teachers at the beginning of their master studies at the university and those at its end. Our study is based on a thorough examination of student tea...
Kniha přináší výsledky výzkumu dosažené v rámci projektu GAČR Kritická místa matematiky základní školy v letech 2012–2014. Jedním z cílů projektu bylo shromáždit a analyzovat žákovské postupy při řešení úloh z tzv. kritických oblastí v matematice základní školy. Jde o oblasti, v nichž žáci často a opakovaně selhávají, jinak řečeno, které nezvládnou...
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 goal of the empirical study is to describe critical areas of primary mathematics as can be found from the Czech Grade 8 pupils’ results in TIMSS 2007 and to identify possible causes of their difficulty for pupils. In the first part, a research background is briefly given – international comparative research in mathematics and possibilities of t...
In 2013, the Faculty of Education, Charles University in Prague, was awarded a grant project FRVŠ whose main goal was to build and upgrade current technological facilities for the use of modern informational and communicational technologies in the education of future mathematics and elementary teachers. The new facilities have been used in several...
The article concerns pupils’ strategies for a geometric problem effectively solvable without calculations. The problem was solved by 125 pupils (aged 12 – 17) whose work was analysed using techniques of grounded theory. Three types of solving steps were identified: geometric in theoretical space, geometric in spatio-graphic space, calculation. Spat...
The study concerns a mathematical game Tandemat based on the Activity game. The research questions are: What are the benefits and limits of Tandemat for the development of pupils’ mathematical knowledge? What knowledge does the game bring to the teacher? Does the game have any benefits outside the field of mathematics? A qualitative analysis of exp...
This book Critical places of primary mathematics through the eyes of teachers presents the results of research that was conducted under a GACR project in the years 2011 to 2013. The aim of the research was to collect and analyze teachers‘ experience with regards to so called critical places in primary and lower secondary school mathematics. These p...
The aim of this paper is to a) shed light on the nature of student
teachers’ noticing of mathematics specific phenomena as observed in a video recorded lesson and to b) compare this nature for student teachers at the beginning of their master studies at the university and those at its end. Our study is based on a thorough examination of student tea...
The article focuses on a one-to-one computing initiative in the Czech Republic in which netbooks were implemented in the teaching of mathematics in three primary schools. The teachers got didactic support from the publishing house which publishes e-textbooks but otherwise were expected to use their professional knowledge for the implementation of n...
The article presents a part of research which deals with a certain type of geometric problems, i.e., problems effectively solvable without algebraic calculations, for which we have observed pupils' preference to (often lengthy) algebraic solutions over (often quick) geometric ones. In particular, we study the pupils' solving strategies, hints which...
The poster will concern the persistence of the conceptions of what is mathematics and what it means to learn mathematics which the pupils bring from their elementary classes to the lower secondary school. A case study of one class of pupils is presented while the data ("stories") were taken from the teacher's written self-reflections of lessons.
Kniha představuje případové studie, jejichž cílem bylo nabídnout pohled na procesy implementace kurikulární reformy na gymnáziích v jednotlivých oborech školního vzdělávání. Byly realizovány případové studie v předmětech Český jazyk a literatura, Anglický jazyk, Matematika, Chemie, Zeměpis, Tělesná výchova, Výtvarná výchova a Etická výchova.
Publikace pojednává o využití videa v učitelském vzdělávání na pozadí konceptu reflektivní praxe. Autoři vycházejí z analýzy vztahu mezi učitelovým jednáním a myšlením a představují teoretická východiska i konkrétní formy podpory profesního rozvoje učitelů (supervize, mentoring, koučování, akční výzkumu a hospitace). V publikaci jsou prezentovány v...
Videos of real lessons are increasingly used in the education of pre- and in-service mathematics teachers, both in the Czech Republic and abroad, mostly to bridge the gap between theory and practice. They have become a part of my mathematics education course at the Faculty, too. The article presents examples of activities from the course in which v...
Článek se zabývá schopností všímat si („ability to notice“), která zahrnuje identifikaci dídaktícko-matematíckých jevů a jejích interpretaci, a která je chápána jako součást didaktických znalostí obsahu. Je popsán výzkum se 119 účastníky, studenty učitelství a učiteli matematiky, kteří vyplňovali dotazník týkající se šesti videoukázek z hodin matem...
The article focuses on the way modern technologies are used in the education of mathematics, biology and chemistry. Namely, it deals with a multimedia classroom (dataprojector, PC, visualiser, audio, interactive board) and a 'laptop mobile classroom' (laptops with software such as Mathematica, Statistica, Cabri Geometry II plus, Cabri 3D etc.). Som...
The teaching of mathematics is a very complex process. One of the problems a teacher has to solve on a daily basis is to decide on the way he/she is going to present mathematics to students. Is there one 'perfect' way? The article focuses on concrete examples of teaching the same subject matter in several different ways. Each one is described and i...
The article describes a geometric context, the so called Trileg mini-geometry which can be used to introduce some deep mathematical ideas (such as the axiomatisation of geometry, the introduction of coordinates, non-solubility of some problems in synthetic geometry, models, etc) to secondary school and university students. Each idea arises naturall...
Existuje řada učitelů, kteří by rádi vylepšovali své výukové strategie, ale zjišťují, že to není vůbec jednoduché. Vyžaduje to zkušenosti s novými výukovými metodami, odlišné matematické úlohy i jiný způsob práce od jejich žáků. Materiál, který přináší tato kniha, by tento úkol měl učitelům ulehčit.
Kniha obsahuje pět kapitol: Pravidelné mnohoúhel...
Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions
to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit
pedagogical intention that students will use their understanding of particular examples of an algeb...
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...
The teachers-as-researchers movement or action research has become very popular recently, among others, for its potential to connect practice and research. However, a review of relevant literature did not provide much help for developing a methodology of such research. In this paper, we will explore collaborative action research between a practicin...
Within the large range of potential theoretical perspectives on fractions, this paper considers one particular interpretation: fractions' duality as process and object. By considering the number-fractionbar-number composite symbol as simultaneously representing division and rational, some process-object theories imply that fraction-as-process and f...
1. díl. 2004. 212 s. -- 2. díl. 2004. S. 213-455
In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus)....
The article focuses on the methodology of research within the Prague Seminars of Didactics of Mathematics. Its main characteristics will be identified: the phenomenon of formalism as a research question, models of a cognitive net and their use for diagnosis, re-education and prevention as the main aims, introspection as a research method. Finally,...
The contribution illustrates a constructivist approach to the teaching of geometrical transformations to future mathematics teachers at the Faculty of Education, Charles University in Prague. Traditionally, this subject was presented as a series of logically connected definitions and theorems and students were asked to apply them in problems. A lot...
The paper deals with the education of teachers to be prepared for the demands of the educational reform in our schools. The tool we use, among others, is engaging student-teachers in their own mathematical research thus providing them with experience of 'doing' mathematics. This is hoped to influence their future teaching towards using more investi...
At the Faculty of Education, Charles University, Prague, problem solving represents one of the key subjects in the preparation of future teachers. For four years, the first of a series of problem solving courses has been organised as an individual learning course as the only course during the study. By that we mean that students have no scheduled c...
Much of the existing research relating to students training to teach particularly in Primary schools often shows that they have a weak mathematical background and lack of understanding of the subject. This often results in them disliking and having a fear of the subject and later teaching pupils facts and algorithms to commit to memory and reproduc...
The aim of this article is to look into the concept of good practice in the teaching of mathematics. I will present my idea of good practice through the formulation of seven principles which will guide the teacher's activity in the classroom. Two extensive illustrations of Grade 8 teaching will be presented to illuminate the seven principles. A way...
The ability to notice key features of teaching is seen as part of student teachers' pedagogical content knowledge. The study shows what student teachers focus on when they have no experience of guided observation of lessons either in reality or on video and when they are not directed by the educator. Some preliminary findings from a wider study are...
Článek seznamuje čtenáře s evropskou organizací ERME, která byla založena v roce 1997 s cílem mapovat a do jisté míry koordinovat evropské výzkumy v didaktice matematiky. V této organizaci jsou již od jejího založení aktivní i čeští badatelé. Podrobněji jsou popsány vědecké konference a akce pro mladé badatele, které Společnost organizuje.
Článek se věnuje problematice konstrukce poznatků v matematice žáky, konkrétně mechanizmu individuální a společné konstrukce poznatků na příkladu znovuobjevování Pythagorovy věty v prostředí čtverečkovaného papíru. Teoretické pozadí práce sestává z teorie generických modelů a konstruktivistických přístupů k výuce matematiky, resp. podnětné výuky. B...
Popsáno podle opraveného dotisku z r. 1997
Část. slovenský text
Pod názvem: Katedra matematiky a didaktiky matematiky, Univerzita Karlova v Praze, Pedagogická fakulta
Název z titulní obrazovky Pod názvem: Katedra matematiky a didaktiky matematiky, Univerzita Karlova v Praze, Pedagogicka´ fakulta, Společnost učitelů matematiky JČMF
Projects
Projects (3)
The goal of MaTeK is to provide the DME of Comenius University in Bratislava opportunity to learn from partners, to exchange best practices, and establish extensive networks for excellence. MaTeK will twin DME with Departments of Mathematics and Mathematics Education of the following universities: Charles University in Prague, Czech Republic, University of Palermo, Italy, Norwegian University of Science and Technology in Trondheim, Norway and Middle East Technical University, Turkey.
The goal of the project is to investigate what future teachers notice in a teaching situation and how they reason about it and also how it is possible to influence such noticing. The focus are (future) elementary teachers, biology, mathematics, English and art teachers.
Cílem projektu je identifikovat lingvistické, psychologické a matematické parametry kontextových úloh ovlivňujících jejich obtížnost, popsat změny vlivu těchto parametrů na úspěšnost žáků v průběhu základní školy a vztahy mezi úrovní lingvistické a matematické kompetence u žáků různého věku.
The project aims to identify linguistic, psychological and mathematical parameters of context problems influencing their difficulty, describe those influences on primary school pupils’ success and the relationships between levels of linguistic and mathematical competence at different ages.