Publications
2024
Evaluating Large Vision-and-Language Models on Children’s Mathematical Olympiads
Anoop Cherian, Kuan-Chuan Peng, Suhas Lohit, Joanna Matthiesen, Kevin Smith, Joshua B. Tenenbaum abstract
Recent years have seen a significant progress in the general-purpose problem solving abilities of large vision and language models (LVLMs), such as ChatGPT, Gemini, etc.; some of these breakthroughs even seem to enable AI models to outperform human abilities in varied tasks that demand higher-order cognitive skills. Are the current large AI models indeed capable of generalized problem solving as humans do? A systematic analysis of AI capabilities for joint vision and text reasoning, however, is missing in the current scientific literature. In this paper, we make an effort towards filling this gap, by evaluating state-of-the-art LVLMs on their mathematical and algorithmic reasoning abilities using visuo-linguistic problems from children’s Olympiads. Specifically, we consider problems from the Mathematical Kangaroo (MK) Olympiad, which is a popular international competition targeted at children from grades 1-12, that tests children’s deeper mathematical abilities using puzzles that are appropriately gauged to their age and skills. Using the puzzles from MK, we created a dataset, dubbed SMART-840, consisting of 840 problems from years 2020-2024. With our dataset, we analyze LVLMs power on mathematical reasoning; their responses on our puzzles offer a direct way to compare against that of children. Our results show that modern LVLMs do demonstrate increasingly powerful reasoning skills in solving problems for higher grades, but lack the foundations to correctly answer problems designed for younger children. Further analysis shows that there is no significant correlation between the reasoning capabilities of AI models and that of young children, and their capabilities appear to be based on a different type of reasoning than the cumulative knowledge that underlies children’s mathematics and logic skills.
Link to the article
Link to the article
Číselně-teoretické úlohy v Matematickém klokanovi (Tcheque)
Vladimír Vaněk abstract
The article offers interested readers complete solutions of six themed problems from secondary-school mathematics. We have focused on problems from the field of number theory that have appeared in the international competition "Mathematical Kangaroo". In the final part of the article, a more general solution to the problem of finding the last non-zero digit of the number n! is presented, along with stating a useful formula for its quick determination.
Matematika - fyzika - informatika, Prometheus (Vol.. 33, Nr. 3, pp. 177-185. ISSN 1805-7705)
Link to the article
Matematika - fyzika - informatika, Prometheus (Vol.. 33, Nr. 3, pp. 177-185. ISSN 1805-7705)
Link to the article
2023
Zamyšlení nad pravidly soutěže Matematický klokan (Tcheque)
Karel Pastor abstract
The paper is focused on the rules of the Mathematical Kangaroo competition. A contestant enters the competition with 24 points (in the Ecolier, Benjamin, Cadet, Junior, and Student categories) or 18 points (in the Pre-Ecolier category), with 1 point deducted for each incorrect answer. According to these rules, a contestant who does not show effort to solve the problems can get more points than a student who tries hard to find the correct solutions. The teacher's task is to motivate the students to actively approach the competition and thus develop their logical thinking. The paper could provide a probabilistic background to this task. Among other things, we will show with what probability it is possible to get, for example, 12 points when randomly guessing.
ELEMENTARY MATHEMATICS EDUCATION JOURNAL (Vol 5, Nr. 1, pp. 32-36, ISSN 2694-8133)
Link to the article
ELEMENTARY MATHEMATICS EDUCATION JOURNAL (Vol 5, Nr. 1, pp. 32-36, ISSN 2694-8133)
Link to the article
Matematický klokan pro žáky základních škol II (Tcheque)
David Nocar, Vladimír Vaněk abstract
For those interested the authors offer a series of articles, which are devoted to individual categories of the mathematical competition Mathematical Kangaroo. In this article, you can find full solutions of problems in the category Cadet, which covers the 8th and 9th grades of primary schools and equivalent 3rd and 4th grade of 8-year gymnasiums. We introduce several different solutions to each problem.
Matematika - fyzika - informatika, Prometheus (Vol 32, Nr. 2, pp. 86-98, ISSN 1805-7705)
Link to the article
Matematika - fyzika - informatika, Prometheus (Vol 32, Nr. 2, pp. 86-98, ISSN 1805-7705)
Link to the article
Kangaroo Contest and Math Olympiads Inspire and Challenge Students (Anglais)
Mark Applebaum abstract
The International Group for Mathematical Creativity and Giftedness (Newsletter #20, March 2023, pp. 12-14)
Link to the article
Link to the article
2022
Mathematische Werkzeuge originell einsetzen: Aufgaben des Känguru-Wettbewerbs in der Schule (in German) (Allemand)
Lukas Donner and Alex Unger abstract
Dieser Beitrag beschäftigt sich mit den folgenden Fragen: Was macht den Reiz von Aufgaben des Känguru-Wettbewerbs aus? Liegen selbst anspruchsvolle Wettbewerbsaufgaben nah am Unterricht und können für diesen als Bereicherung genutzt werden? Wie könnte das konkret geschehen?
Mathematik lehren (Vol 235, pp.15-20)
Link to the article
Mathematik lehren (Vol 235, pp.15-20)
Link to the article
Matematický klokan pro žáky základních škol I (Tcheque)
David Nocar, Vladimír Vaněk abstract
The paper contains set of tasks with original solutions, which were used in Kangaroo competition.
Matematika - fyzika - informatika, Prometheus (Vol 31, Nr. 3, pp. 178-188, ISSN 1805-7705)
Link to the article
Matematika - fyzika - informatika, Prometheus (Vol 31, Nr. 3, pp. 178-188, ISSN 1805-7705)
Link to the article
Počítejte s klokanem - Benjamín (Tcheque)
Vladimír Vaněk, David Nocar abstract
The paper contains set of tasks with original solutions, which were used in Kangaroo competition.
Učitel matematiky (Vol 30, Nr. 3, pp. 160-174. ISSN 1210-9037)
Učitel matematiky (Vol 30, Nr. 3, pp. 160-174. ISSN 1210-9037)
30 years of Mathematical Kangaroo
Meike Akveld, Gregor Dolinar abstract
Mathematical Kangaroo, the largest international mathematical competition, celebrates its 30th anniversary. In the first part, the article gives a brief insight into the foundations of the competition and evolution of the Association Kangourou Sans Frontieres, which organizes the competition, and in the second part it focuses on many current challenges and recent developments of the competition and the association.
EMS Digest (Nr. 45)
Link to the article
EMS Digest (Nr. 45)
Link to the article
The impact of mathematics competitions on teachers and their classrooms in Puerto Rico, Switzerland and UK
Meike Akveld, Luis Caceres, David Crawford, Ferney Henao abstract
This article presents the results of a small-scale, comparative study on the perceived impact that having students enter Mathematics competitions has on Mathematics teachers in Puerto Rico, Switzerland and the UK and on their classroom practice. The study surveyed a small number of Mathematics teachers in the three countries who teach in both public and private schools and in both rural and urban regions. The perceived advantages and disadvantages to students from taking part in competitions and to teachers who have students taking part in competitions are discussed and the findings compared across the three countries. The effect that Mathematics competitions have on the identification and development of the mathematical talent of students is considered together with the contribution of these activities to the academic environment of the classroom. For the teachers who did have students taking Mathematics competitions, the limitations of entry and the different methods in which teachers prepare or assist students to prepare for the competitions are compared between countries. Since the study is small in scale, no firm conclusions are drawn but suggestions are made as to where future, larger scale, studies might be carried out to see if the classroom experiences of all could be positively influenced by exposure to Mathematics competitions.
ZDM, Mathematics Education, Springer (Vol.54, Nr.5, pp.941-959)
Link to the article
ZDM, Mathematics Education, Springer (Vol.54, Nr.5, pp.941-959)
Link to the article
The Road from Submission to Perfection
Robert Geretschläger, Lukas Donner abstract
In this article, we address the problem-selection process of the Mathematical Kangaroo, which is an international, popular multiple-choice mathematics competition. We describe the necessary steps starting with problem suggestions and ultimately reaching a finalized national version of the competition. The intention here is to illustrate the dynamics typical to such a selection as well as pointing out the multivariate possibilities of modification of submitted problems. We discuss and reflect these modifications by analyzing various examples of competition problems of recent years.
Mathematics Competitions (Vol.35, Nr.,1, pp.30-48 )
Link to the article
Mathematics Competitions (Vol.35, Nr.,1, pp.30-48 )
Link to the article
Writing and choosing problems for a popular high school mathematics competition
Robert Geretschläger, Lukas Donner abstract
In this paper, we consider the issues involved in creating appropriate problems for a popular mathematics competition, and how such problems differ from problems typically encountered in a classroom. We discuss the differences and similarities in school curricula versus the generally agreed upon topics encountered in international competitions. The question of inspiration for the development of competition problems is dealt with from the standpoint of the problem author, while aspects related to the motivation of the contest participant, objective and subjective problem difficulty and mathematical precision in mathematics competitions are also discussed.
ZDM-Mathematics Education , Springer (Vol. 54, Nr. 5, pp.971-982)
Link to the article
ZDM-Mathematics Education , Springer (Vol. 54, Nr. 5, pp.971-982)
Link to the article
AKSF & Math Kangaroo. The world’s largest international mathematics competition
Meike Akveld, Luis Cáceres abstract
Notices of the AMS (Vol.69, Nr.11, pp.1956-1960)
Link to the article
Link to the article
Matematický klokan pro žáky základních škol I (Tcheque)
David Nocar, Vladimír Vaněk abstract
The paper contains set of tasks with original solutions, which were used in Kangaroo competition.
Matematika - fyzika - informatika, Prometheus (Vol.. 31, Nr. 3, pp. 178-188. ISSN 1805-7705 )
Link to the article
Matematika - fyzika - informatika, Prometheus (Vol.. 31, Nr. 3, pp. 178-188. ISSN 1805-7705 )
Link to the article
2021
Kangaroo on the chessboard as a didactical tool. (Anglais)
Karel Pastor abstract
The level of mathematical literacy can be significantly increased by means of board games as for example chess. Solving mathematical chess problems can develop combinatorial skills of pupils aged 6-11. Mathematical chess problems use chessboard or chess pieces. We will focus on a special piece named kangaroo that was introduced in the competition Mathematical Kangaroo. We will deal, among the others, with the domination problem of kangaroo, the independence problem of kangaroo and the kangaroo tour problem. These problems have been already solved for 4×4 and 6×6 chessboards in the previous papers, so we will be interested in 5×5 chessboard. The reduced chessboard is used because a smaller chessboard seems to be more accessible to pupils aged 6 to 11.
ELEMENTARY MATHEMATICS EDUCATION JOURNAL (Vol 3, Nr. 2, pp. 33-39, ISSN 2694-8133)
Link to the article
ELEMENTARY MATHEMATICS EDUCATION JOURNAL (Vol 3, Nr. 2, pp. 33-39, ISSN 2694-8133)
Link to the article
Which test-wiseness based strategies are used by Austrian winners of the Mathematical Kangaroo?
Lukas Donner, Jakob Kelz, Elisabeth Stipsits and David Stuhlpfarrer abstract
Test-wiseness describes the usage of strategies, which support successful responses on multiple-choice tests, independent of the knowledge of the underlying topic. Due to the construction of the Mathematical Kangaroo, it is suitable for applying testwiseness strategies. The strategies were formulated based on the test-wiseness guiding strategies and merged into a specially developed KATS (KAngaroo-Test-wiseness-Strategies) questionnaire. This questionnaire was presented to the Austrian winners of the Mathematical Kangaroo 2018, grades 3 to 13. The findings from this study provide on the one hand information on preferred strategies (top-ranked strategies), and on the other hand how this particular group prepares for the Mathematical Kangaroo.
Mathematics Competitions (Vol 34, Nr. 1, pp. 88–101)
Link to the article
Mathematics Competitions (Vol 34, Nr. 1, pp. 88–101)
Link to the article
2020
Do children cheat to be honored? A natural experiment on dishonesty in a math competition
Ofer H. Azar, Mark Applebaum abstract
We use data from a children mathematics contest in Israel that involved a first unmonitored online stage at home and a second monitored stage in class, both with the same difficulty level. The performance deterioration from the first to the second stage allows to estimate the dishonesty in the unmonitored first stage (mostly in the form of being helped by the parents or older siblings). We also analyze dishonesty using a set of 3–4 problems that appeared in both tests. Contrary to much of the literature on gender effects in dishonesty, in our data girls were not more honest than boys. The sample consists of children in second to sixth grades, and we find that older children are significantly more honest. A stronger socio-economic level of the city was associated with more cheating. Children from religious schools tended to be more honest than children from secular schools. We also discuss other potential reasons for differences between performance in the two stages, such as pressure and stress, but conclude that they are secondary to the effects of dishonesty.
Journal of Economic Behavior & Organization (Vol.169, pp 143-157)
Link to the article
Journal of Economic Behavior & Organization (Vol.169, pp 143-157)
Link to the article
The Math Kangaroo Competition
Meike Akveld, Luis Caceres, Jose Nieto, Rafael Sanchez abstract
In this paper we briefly explain what Math Kangaroo is. This is followed by a representative sample of Kangaroo questions, varying over all ages and all areas of mathematics that are covered by this competition. The paper concludes with the analysis of some statistical data and suggestions about how Math Kangaroo and this type of questions may be used in Math Clubs.
Espacio Matemático (Vol.1, Nr.2, pp.74-91)
Link to the article
Espacio Matemático (Vol.1, Nr.2, pp.74-91)
Link to the article
Math Kangaroo
Meike Akveld, Luis Caceres, Robert Geretschläger abstract
In this paper we will outline the history of the mathematical competition Kangaroo, describe the structure of the organisation behind it and in particular show a sample of past questions to give a flavour of what this competition is about. It should be underlined that Math Kangaroo is a popularising maths competition which is organised on a non-profit basis.
Mathematics Competitions Journal of the WFNMC (Vol.33, Nr.2, pp. 48-66)
Link to the article
Mathematics Competitions Journal of the WFNMC (Vol.33, Nr.2, pp. 48-66)
Link to the article
Analysis of items from the Mathematical Kangaroo from two perspectives
Lukas Andritsch [Lukas Donner], Evita Hauke [ Evita Lerchenberger] and Jacob Kelz abstract
Items of the Austrian version of the Mathematical Kangaroo 2018 are analyzed with respect to their construction as well as their solution. This is done based on general test-wiseness strategies, promising problem-solving approaches and the study of certain distractors.
Engaging young students in mathematics through competitions - World perspectives and practices. World Scientific (Vol. II, pp. 117-136)
Engaging young students in mathematics through competitions - World perspectives and practices. World Scientific (Vol. II, pp. 117-136)
2019
Girls' performance in the Kangaroo Contest
Mark Applebaum, Roza Leikin abstract
The issue of attracting girls to mathematics has captured our attention when we were analyzing data from the final stage of the Kangaroo mathematics contest in Israel. With general finding showing boys having better results, further analysis of differences across Grades 2-6 indicates that in some grades the gap is smaller than in others. For instance, only insignificant differences were found in Grades 3- 4 for all difficulty levels. Furthermore, on some tasks, the girls' performance was better than the boys'. In this respect, continuous investigation is needed to examine possible factors that make it happen. Furthermore, qualitative data could be collected and analyzed about young students’ thinking when solving different tasks to uncover other possible hidden factors that influence mathematical performance by girls in Kangaroo contest.
Proceedings of the 11th International MCG Conference (pp 87-94)
Link to the article
Proceedings of the 11th International MCG Conference (pp 87-94)
Link to the article
Gender Issues in Solving Problems in the Kangaroo Contest
Mark Applebaum abstract
The issue of attracting girls to mathematics has captured our attention when we were analyzing data from the final stage of the Kangaroo mathematics contest in Israel. With general finding showing boys having better results, further analysis of differences across Grades 2-6 indicates that in some grades the gap is smaller than in others. For instance, only insignificant differences were found in Grade 4 for all difficulty levels. Furthermore, on some tasks, across all five grades, the girls' performance was better than the boys'. In this respect, continuous investigation is needed to ascertain whether a certain trend exists and if so, what might be the possible factors that make it happen. Furthermore, qualitative data could be collected and analyzed about young students’ thinking when solving different tasks to uncover other possible hidden factors.
Mediterranean Journal for Research in Mathematics Education (Vol.16, pp 19-31)
Link to the article
Mediterranean Journal for Research in Mathematics Education (Vol.16, pp 19-31)
Link to the article
2018
České stopy v Matematickém klokanovi (Tcheque)
Vladimír Vaněk, Pavel Calábek,David Nocar abstract
The article offers readers an insight into the origins and history of one of the most important worldwide mathematical competitions, one chapter is devoted to the history and organization of the Czech Mathematical Kangaroo. The most crucial part of the text introduces a few tasks, which Czech authors enriched competition problem sets with.
Matematika - fyzika - informatika, Prometheus (Vol 27, Nr.5, pp. 334-346ISSN 1210-1761)
Link to the article
Matematika - fyzika - informatika, Prometheus (Vol 27, Nr.5, pp. 334-346ISSN 1210-1761)
Link to the article
Úspěšnost žáků na počátku sekundárního vzdělávání při řešení geometrických úloh ze soutěže Matematický klokan (Tcheque)
David Nocar, Tomáš Zdráhal abstract
The article deals with the geometrical problems from the Math Kangaroo Contest and its solutions by pupils after completing primary school. The focus on geometric tasks is mainly due to this that this part of mathematics is for pupils in elementary schools more demanding and therefore less popular. Tasks from the Math Kangaroo Contest were used because it's a task other than the conventional type of problems in mathematics textbooks for elementary schools. Tasks from this contest could be for pupils more interesting, more attractive and it could inspire them for this part of mathematics. Tests were prepared from selected geometric tasks and so modified form of the Math Kangaroo Contest was realized at the elementary school Horka nad Moravou. Participating 6th grade elementary school correspond to the Benjamin category of the Math Kangaroo Contest. The 6th grade were chosen in order to verify the pupils' ability to solve geometric problems after primary school just before continuing with another lesson from the geometry at secondary (lower secondary) school. Interesting could be a comparison of the results in classes with differently realized teaching. Mentioned school is the only school in Olomouc region where, in addition to regular teaching method, the Montessori teaching method is also being realized at primary school.
Magister : refexe primárního a preprimárního vzdělávání ve výzkumu , VUP (Vol 2018, Nr. 2, pp. 16-29, ISSN 1805-7152 )
Link to the article
Magister : refexe primárního a preprimárního vzdělávání ve výzkumu , VUP (Vol 2018, Nr. 2, pp. 16-29, ISSN 1805-7152 )
Link to the article
2017
Spatial Abilities as a Predictor to Success in the Kangaroo Contest
Mark Applebaum abstract
In the few years since the Kangaroo Contest arrived in Israel, we have discovered that all the winners in grades 2-6 succeeded in spatial abilities (SA)-oriented tasks. In this study, we investigate a potential relationship between spatial abilities and mathematical performance (focusing on non-standard problems) in mathematically-motivated students (MMS) who participated in the Kangaroo Contest. We also sought to ascertain whether the correlation between scores of SA tasks and the rest [of the] non-standard problems (RNSP) in the contest is age-dependent. A strong correlation between SA tasks and mathematical performance, together with well-known malleable spatial abilities can lead us to the conclusion that the development of spatial abilities in early childhood is necessary as a predictor of later mathematics achievement. This issue is important for students at all levels and especially for MMS, some of whom will later become mathematically promising students
Journal of Mathematics and System Science (Vol.7, pp.154-163)
Link to the article
Journal of Mathematics and System Science (Vol.7, pp.154-163)
Link to the article
2012
Suchen nach der schönsten Aufgabe – Wie entstehen mathematische Wettbewerbe (in German)
Robert Geretschläger abstract
Die meisten Teilnehmer und Teilnehmerinnen an mathematischen Wettbewerben machen sich wohl kaum darüber Gedanken, wie die Aufgaben für den jeweiligen Wettbewerb ausgesucht werden. Man erwartet einfach, dass die Aufgaben korrekt, fachlich packend, lösbar und möglichst originell sein sollen. Die Prozesse, die zur Aufgabenauswahl führen, sind aber komplex und interessant, mit vielen inhaltlichen und organisatorischen Aspekten, an die man normalerweise nur denkt, wenn man selbst daran beteiligt ist.
Anhand der Beispiele der Internationalen Mathematikolympiade und des Känguru der Mathematik möchte ich im Folgenden einen Einblick in die Hintergründe der Auswahlprozesse derartiger Wettbewerbe geben, und auf einige relevante Fragen dazu eingehen. Wie werden Aufgaben für die Wettbewerbe entwickelt und wer schlägt sie vor? Wie werden sie ausgewählt, welche scheiden aus? Wie weit wird der Zusammenhang zu Lehrplänen und zum Schulalltag berücksichtigt? Welche Rolle spielt fachliche und fachdidaktische Forschung bei der Aufgabenauswahl?
Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft (ÖMG) (Heft 44, pp. 17-25)
Link to the article
Anhand der Beispiele der Internationalen Mathematikolympiade und des Känguru der Mathematik möchte ich im Folgenden einen Einblick in die Hintergründe der Auswahlprozesse derartiger Wettbewerbe geben, und auf einige relevante Fragen dazu eingehen. Wie werden Aufgaben für die Wettbewerbe entwickelt und wer schlägt sie vor? Wie werden sie ausgewählt, welche scheiden aus? Wie weit wird der Zusammenhang zu Lehrplänen und zum Schulalltag berücksichtigt? Welche Rolle spielt fachliche und fachdidaktische Forschung bei der Aufgabenauswahl?
Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft (ÖMG) (Heft 44, pp. 17-25)
Link to the article
2010
O jedné zajímavé úloze z Matematického klokana (Tcheque)
Filip Švrček, Vladimír Vaněk abstract
In the article is presented very interesting problem about measrures of two squares which are inscribed in to right angle triangel.
Matematika - fyzika - informatika (Vol 20, Nr. 3, pp. 136-143, ISSN 1210-1761 )
Matematika - fyzika - informatika (Vol 20, Nr. 3, pp. 136-143, ISSN 1210-1761 )
2009
Co se do Matematického klokana nedostalo (Tcheque)
Vladimír Vaněk abstract
The paper solves interesting tasks of mathematical competition Kangoroo which are not published.
Ani jeden matematický talent nazmar/Hradec Králové: Univerzita Karlova (pp. 155-164, ISBN 978-80-7290-417-4, proceedings paper)
Ani jeden matematický talent nazmar/Hradec Králové: Univerzita Karlova (pp. 155-164, ISBN 978-80-7290-417-4, proceedings paper)
2006
Das Känguru der Mathematik - Einige Gedanken zum Österreichischen Ergebnis 2005 (in German)
Robert Geretschläger abstract
In dieser Arbeit werden einige Rückschlüsse auf den Schwierigkeitsgrad der Aufgaben des Känguru der Mathematik in Österreich im Jahr 2005 vorgestellt. Zu diesem Zweck wurden die statistischen Daten des Wettbewerbs herangezogen und einer kurzen Interpretation unterworfen. Die Arbeit ist eine Zusammenfassung eines Vortrags, der vom Autor beim 16. Internationalen Kongress der ÖMG und Jahrestagung der DMV in Klagenfurt/Österreich im September 2005 gehalten wurde.
Fokus Didaktik, Edith Schneider (Hrsg.) (Profil Verlag, München, Wien, ISBN 3-89019-598-9, pp. 133-138)
Link to the article
Fokus Didaktik, Edith Schneider (Hrsg.) (Profil Verlag, München, Wien, ISBN 3-89019-598-9, pp. 133-138)
Link to the article
2002
Ke strategiím řešení úloh soutěže Matematický klokan. (Tcheque)
Josef Molnár, P. Voglová abstract
Olomouc: Univerzita Palackého (Makos 2002, pp. 33-39. ISBN 80-244-0549-0, proceedings paper)
Raumgeometrische Aufgaben im internationalen Wettbewerb Känguru der Mathematik (in German)
Robert Geretschläger, Michael Hofer abstract
In dieser Arbeit werden 15 Aufgaben aus dem Känguru der Mathematik mit raumgeometrischem Inhalt aus dem Jahr 2001 vorgestellt.
Informationsblatt für darstellende Geometrie (IBDG) (Jg.21, Heft 1, pp. 4-5)
Link to the article
Informationsblatt für darstellende Geometrie (IBDG) (Jg.21, Heft 1, pp. 4-5)
Link to the article
2001
Internationaler Wettbewerb Känguru der Mathematik (in German)
Robert Geretschläger, Michael Hofer abstract
In dieser Arbeit wird der Wettbewerb Känguru der Mathematik vorgestellt. Einige exemplarische Aufgaben aus dem Wettbewerb werden dabei, zusammen mit einer Erklärung der Organisationsstruktur in Österreich und seinem internationalen Kontext, angegeben.
Internationale Mathematische Nachrichten (IMN) (Nr.187, pp. 49-56)
Link to the article
Internationale Mathematische Nachrichten (IMN) (Nr.187, pp. 49-56)
Link to the article
2024
Mathe mit dem Känguru 6 - Die schönsten Aufgaben von 2020 bis 2024 (Allemand)
Alexander Unger, Meike Akveld, Robert Geretschläger details
Hanser Verlag (978-3-446-48183-1)
2019
Mathe mit dem Känguru 5 - Die schönsten Aufgaben von 2015 bis 2019 (Allemand)
Alexander Unger, Monika Noack, Robert Geretschläger, Meike Akveld details
Hanser Verlag (978-3-446-45655-6)
2014
Mathe mit dem Känguru 4 - Die schönsten Aufgaben von 2012 bis 2014 (Allemand)
Monika Noack, Alexander Unger, Robert Geretschläger, Hansjürg Stocker details
Hanser Verlag (978-3-446-44259-7)
2011
Mathe mit dem Känguru 3 - Die schönsten Aufgaben von 2009 bis 2011 (Allemand)
Monika Noack, Alexander Unger, Robert Geretschläger, Hansjürg Stocker details
Hanser Verlag (978-3-446-42820-1)
2010
Mathe mit dem Känguru für die Grundschule (Allemand)
Monika Noack, Robert Geretschläger, Hansjürg Stocker details
Bildungsverlag Lemberger (978-3-85221-027-8)
2008
Mathe mit dem Känguru 2 - Die schönsten Aufgaben von 2006 bis 2008 (Allemand)
Monika Noack, Robert Geretschläger, Hansjürg Stocker details
Hanser Verlag ( 978-3-446-41647-5)
2007
Počítejte s klokanem - Junior (2000-2004) (Tcheque)
Radek Horenský, Petr Rys, Jaroslav Zhouf, Josef Molnár details
Prodos, Olomouc (63 pages, 978-80-7230-179-9)
Počítejte s Klokanem "Kadet" (Tcheque)
Jitka Hodaňová, Vladimír Vaněk, Radek Horenský details
Prodos, Olomouc (62 pages, ISBN 978-80-7230-178-2)
Počítejte s Klokanem - STUDENT. (Tcheque)
Pavel Calábek, Jaroslav Švrček details
Prodos, Olomouc (64 pages, ISBN 978-80-7230-180-5)
Počítejte s Klokanem - Benjamín. (Tcheque)
Martina Uhlířová details
Prodos, Olomouc (47 pages, ISBN 978-80-7230-177-5 )
2006
Mathe mit dem Känguru 1 - Die schönsten Aufgaben von 1995 bis 2005 (Allemand)
Monika Noack, Robert Geretschläger, Hansjürg Stocker details
Hanser Verlag (978-3-446-40713-8)
2005
Matematický klokan 2005 (Tcheque)
Bohumil Novák, Josef Molnár, Dita Navrátilová, Pavel Calábek, David Nocar details
Olomouc: Univerzita Palackého (64 pages, ISBN 80-244-1178-4)
2004
Matematický klokan 2003 (Tcheque)
Josef Molnár, Bohumil Novák, Dita Navrátilová, Pavel Calábek details
Olomouc: Univerzita Palackého (52 pages, ISBN 80-244-0808-2)
2003
Matematický klokan 2002 (Tcheque)
Josef Molnár details
VUP Olomouc (48 pages, ISBN 80-244-0548-2)
2001
Matematický klokan 2001 (Tcheque)
Josef Molnár, Milan Kopecký, Pavel Calábek, Dita Navrátilová details
Olomouc: Jednota českých matematiků a fyziků (48 pages, ISBN 80-7015-816-6)
Počítejte s Klokanem - Student. (Tcheque)
Pavel Calábek, Jaroslav Švrček, Tomáš Zdráhal, Josef Molnár details
Prodos, Olomouc (64 pages, ISBN 80-7230-097-0)
Počítejte s Klokanem - Junior (Tcheque)
Radek Horenský, Petr Rys, Josef Molnár, Jaroslav Zhouf details
Prodos, Olomouc (64 pages, ISBN 80-7230-096-2.)
2000
Počítejte s Klokanem, Kategorie Benjamín. (Tcheque)
Bronislava Růžičková, Milan Kopecký, Josef Molnár details
Prodos, Olomouc (92 pages, ISBN 80-7230-068-7)
Počítejte s Klokanem kategorie "Kadet (1995-1999) (Tcheque)
Petr Emanovský, Jitka Hodaňová, Radek Horenský, Josef Molnár details
Prodos, Olomouc (65 pages, ISBN 80-7230-077-6)
Počítejte s Klokanem - kategorie Klokánek. (Tcheque)
Bohumil Novák, Josef Molnár, Anna Stopenová, Martina Uhlířová details
Prodos, Olomouc (64 pages, ISBN 80-7230-058-X)