Publications

2025

Geometrické hrátky s Klokánkem. (Czech)
Martina Uhlířová 

The article is dedicated to problems from an international mathematical contest, the Mathematical Kangaroo. In particular, tasks from the „Klokánek“ cathegory (internationally called Ecolier), which is designed for 4. and 5. grade of primary school. The goal of this article is to introduce primary education teachers to an inspirative set of problems targeted at developing geometric imagination of children. All problems were taken over from competition cathegory „Klokánek“ from the last 10 years (2010–2019).
Učitel Matematiky (Vol. 29, Nr. 3, pp. 129-145)
Link to the article

Mistakes in solutions by primary school pupils in selected problems of mathematical kangaroo competition.
Eva Nováková 

IATED Academy. (EDULEARN25 Proceedings.)

SUCCESS OF AI MATH SOLVER TOOL IN SOLVING NON-STANDARD MATHEMATICS COMPETITION PROBLEMS
Marko Stanković, Aleksandar Milenković, Marina Svičević, Nemanja Vučićević 

Artificial intelligence is increasingly transforming how students learn, including their approach to mathematics and problem-solving, by offering additional support and assistance—a trend that continues to attract research interest. One line of research focuses on helping students prepare for math competitions by solving more complex mathematical problems. In addition to regular national math competitions, which allow students to progress to international mathematical Olympiads, there are also competitions aimed at popularizing mathematics and developing logical thinking in students. One such competition is the international Kangaroo competition. In this paper, we examine the performance of the AI Math Solver, available on the Interactive Mathematics platform, in solving tasks from the 2024 Kangaroo competition. The selected tasks targeted three student categories: 3rd and 4th grade elementary, 7th and 8th grade elementary, and 3rd and 4th grade high school students. The problems were uploaded as images (screenshots) in both Serbian and English, since visual elements frequently appear in the problem formulations and answer choices in the Kangaroo competition. The results are presented in two sections: a qualitative analysis of selected problems that illustrate common patterns and errors, and a quantitative analysis that summarizes the tool’s overall performance. Out of a total of 84 tasks, in both Serbian and English, the solver correctly answered 24, corresponding to a success rate of just under 30% in both languages. Furthermore, some tasks solved in Serbian were not solved in English, and vice versa. Additionally, differences were observed in the distribution of correct answers across tasks of varying difficulty levels.
Facta Universitatis
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Evaluating the Success of AI Tools in Supporting Student Performance in Mathematical Kangaroo Competition
Marina Svičević, Aleksandar Milenković, Nemanja Vučićević, Marko Stanković 

This study explores the potential of generative artificial intelligence (AI) tools in supporting students preparing for mathematical competitions, focusing on the Mathematical Kangaroo competition in the context of the Serbian-speaking region. The research analyzed tools such as ChatGPT-free, ChatGPT-paid, AI Math Solver, Math Mentor, and o1-preview, assessing their accuracy and efficiency in solving tasks of varying difficulty levels and domains (algebra, geometry, logic, and numbers), as well as different formats (text and image-based). Testing included tasks in both Serbian and English, allowing for the evaluation of language barriers in tool performance. The results indicate that tools perform better with text-based task formats, with o1-preview standing out for its exceptionally high accuracy in this format. All tools achieve the highest precision in numbers and algebra, while results are significantly lower in geometry and logic, highlighting challenges in processing visual information and logical reasoning. The conclusions of this study emphasize the importance of generative AI in improving mathematics education but highlight the need for further development of tools that can better handle visual tasks, support local languages, and be more specialized in solving mathematical problems in general.
Computer Applications in Engineering Education
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Kangaroo Mathematics Competition: A Successful International Cooperation Activity
Caceres Luis, Colon Omar 

The Kangaroo Without Borders Association is an international organization with members from over 100 countries. Its main mission is to organize the international competition “Kangaroo Mathematics Competition” whose primary goal is the popularization of mathematics. The competition is held for students from primary to secondary school at 6 levels. Delegates from the countries that make up the association meet once a year to select the problems for the exams. These are chosen from a database of hundreds of problems, created in advance by the members themselves. The association is managed by a Board of Directors that takes care of the administrative part, supporting the member countries and managing the entry of new countries.
The structure of the association and the competition is presented, as well as examples of problems from the different levels offered in the competition. Several million students from over 100 countries participate in this competition, making it the largest international mathematics competition in the world.
The Association's fundamental goal of contributing to the popularization of mathematics through an activity focused on problem solving and critical thinking has become highly relevant today. Teaching mathematics has always been a challenge for educators due to the characteristics of learning this discipline, which requires, for example, knowing certain skills and concepts in order to understand deeper concepts. In other words, it requires step-by-step knowledge, where one step depends on the previous ones. The kangaroo mathematics competition presents a methodology that strongly contributes to learning mathematics and, above all, to fostering a love for this science. The problems posed in this competition are very special; games, situations, drawings, etc. are used so that the problems are not routine and are very attractive.
This model of international cooperation is a success that directly impacts several million students and hundreds of teachers around the world. In addition, other collaborative projects in mathematics education have been created through the association between teachers from the association's member countries. We present metrics that show the impact of this project on the school mathematics community.
Proceedings EDULEARN 25 (pp. 2096)

Strengthened Logical Thinking Through Cooperative Strategies for Primary Level Students with Math Talent
Caceres Luis, Alcala Natalia 

Mathematically gifted children tend to excel at solving math problems individually; however, when teamwork is structured appropriately, it allows them to enhance their skills and significantly improve their performance in math olympiads. This study presents the application of specific cooperative learning strategies in a group of elementary-level math gifted children in Puerto Rico, with the aim of improving their performance in questions related to logical thinking. To do so, a methodology based on group cohesion activities, the cooperative structure “Think, Share and Solve” and the “Rotating Sheet” technique were implemented. The group scores in phases I and II of the Puerto Rico Math Olympiad were analyzed, comparing them with the results obtained in phase III of that same Olympiad, after the implementation of the strategy. The findings show significant improvements in student performance, which supports the effectiveness of cooperative learning in strengthening logical thinking in high-performing math students.
Proceedings EDULEARN 25 (pp. 1079)

2024

Číselně-teoretické úlohy v Matematickém klokanovi (Czech)
Vladimír Vaněk 

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

Beyond Tradition: Fostering Creative Thinking Through NonStandard Problems and Mathematics Competitions (English)
Mark Applebaum and Michael Lambrou 

After a brief introduction to the value of Mathematics and the approach adopted in classical times, we discuss issues related to the benefits of teaching Mathematics via attractive, non-standard problems. The necessity of creative thinking skills in the 21st Century and its value to society is highlighted, aligning with the aims of STEM and PISA. We argue that non-standard but elegant problems, ranging from tractable to challenging, are useful tools for developing creative thinking. We then focus on the Kangaroo Mathematical Contest, presenting examples of Kangaroo tasks and discussing how they support the development of creative thinking. Suggestions for improving mathematical curricula and teaching perspectives are summarized.
Mediterranean Journal for Research in Mathematics Education (Vol. 20, pp.5-22)

Relating Theory and Practice in Mathematics Education: A Historical Overview
Nerida Ellerton, Florence Mihaela Singer  

Three instances of "theories" in mathematics education are offered and discussed, and the question is raised whether theory, or practice, should be the main driving force in mathematics education settings. That is to say, with issues associated with intended, implemented, and attained curricula in mathematics education, should theory arise out of practice or should the reverse be true. Three main cases are introduced to aid the discussion. The first case presents an overview of the historical development of the Hindu-Arabic numeration system and its applications in mathematics education; the second case summarizes the "cyphering tradition," as it gradually came to control school mathematics in many nations during the period 1200-1900. The third case draws attention to how developments in theories associated with neuroscience are being linked to mathematics education. An issue which arises is whether teachers follow theories consciously.
Fourth International Handbook of Mathematics Education (pp. 211-243)

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 

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

Analyzing Proficiency and Growth: A Study of Mat Competitions in Elementary School Students in Puerto Rico
Caceres Luis, Arauz Junior 

WFNMC Journal (V 37, N1, 27-44)

Metodología de Enseñanza en Espiral en Competencias de Matemáticas
Caceres Luis, Reyes Victor 

Invited Contributions: XIII CIEMAC, (book chapter, Rioja University)

Mathematics Competitions by Teams (COMATEQ): An opportunity to compete Internationally
Caceres Luis, Colón Omar 

Proceedings of INTED

2023

Zamyšlení nad pravidly soutěže Matematický klokan (Czech)
Karel Pastor  

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

Matematický klokan pro žáky základních škol II (Czech)
David Nocar, Vladimír Vaněk 

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

Kangaroo Contest and Math Olympiads Inspire and Challenge Students (English)
Mark Applebaum 

The International Group for Mathematical Creativity and Giftedness (Newsletter #20, March 2023, pp. 12-14)
Link to the article

Uluslararasi Kanguru Matematik Yarismasi Turkiye Sorularinin Temel Matematiksel Beceriler Acisindan Incelenmesi
Nejla Deveci 

M.S. Thesis

What are the problems like in the world’s largest international mathematical Olympiad?
Caceres Luis, Colon Omar 

Proceedings of INTED (pp. 7580)

How do Mathematics Teachers in Puerto Rico Perceive the Mathematics Competitions?
Caceres Luis, Henao Ferney 

Proceedings of INTED (pp. 8481)

Comentarios sobre la Formación del Pensamiento Geométrico con soporte Tecnológico: Logros y Desafíos
Falk María, Caceres Luis 

Espacio Matemático (Vol 4, Nr. 1)

Mathematics Olympiads Curriculum for Primary School in Ibero-America
Caceres Luis, Rodriguez Ariana, Alvarado Lizbeth 

Journal of the WFNMC (Vol 36, No1, pp 13-24)

2022

Mathematische Werkzeuge originell einsetzen: Aufgaben des Känguru-Wettbewerbs in der Schule (in German) (German)
Lukas Donner and Alex Unger 

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

Matematický klokan pro žáky základních škol I (Czech)
David Nocar, Vladimír Vaněk 

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

30 years of Mathematical Kangaroo
Meike Akveld, Gregor Dolinar 

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)
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The impact of mathematics competitions on teachers and their classrooms in Puerto Rico, Switzerland and UK
Meike Akveld, Luis Caceres, David Crawford, Ferney Henao 

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)
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The Road from Submission to Perfection
Robert Geretschläger, Lukas Donner 

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 )
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Writing and choosing problems for a popular high school mathematics competition
Robert Geretschläger, Lukas Donner 

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

AKSF & Math Kangaroo. The world’s largest international mathematics competition
Meike Akveld, Luis Cáceres 

Notices of the AMS (Vol.69, Nr.11, pp.1956-1960)
Link to the article

Matematický klokan pro žáky základních škol I (Czech)
David Nocar, Vladimír Vaněk 

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

Počítejte s klokanem - Benjamín (Czech)
Vladimír Vaněk, David Nocar 

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)

Playing on patterns: is it a case of analogical transfer?
Florence Mihaela Singer, Cristian Voica 

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns, namely, numerical, discrete geometric, and continuous geometric. We found that the mechanisms involved in analogical transfer for continuing sequential patterns are based on two complementary cognitive processes: decoding and adapting. In addition, at a basic level of processing, students activate one of the operational tools of shape recognition or counting, and based on it, they find a surface analogy that leads them to use isometric transformations or one-dimensional development for continuing the given pattern. At a more complex level of processing, students activate both shape recognition and counting and are thus able to apply a filter of processing that uncovers a deep-structure analogy, which allows cognitive framing of the problem and leads to coherent 2D developments within the understood conceptual frame. At a more advanced level of processing, students can use a refined filter not only to uncover a deep-structure analogy but also to use an external language to verbalize that analogy, and consequently, to find 2D developments that trigger changes in cognitive framing, showing that pattern generation is a creative activity. Teaching and learning implications are discussed.
ZDM Mathematics Education (54(1), p.211–229)
Link to the article

2021

Kangaroo on the chessboard as a didactical tool. (English)
Karel Pastor 

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

Which test-wiseness based strategies are used by Austrian winners of the Mathematical Kangaroo?
Lukas Donner, Jakob Kelz, Elisabeth Stipsits and David Stuhlpfarrer 

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

2020

Do children cheat to be honored? A natural experiment on dishonesty in a math competition
Ofer H. Azar, Mark Applebaum 

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)
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The Math Kangaroo Competition
Meike Akveld, Luis Caceres, Jose Nieto, Rafael Sanchez 

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

Math Kangaroo
Meike Akveld, Luis Caceres, Robert Geretschläger 

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

Analysis of items from the Mathematical Kangaroo from two perspectives
Lukas Andritsch [Lukas Donner], Evita Hauke [ Evita Lerchenberger] and Jacob Kelz 

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)

How are motivation and self-efficacy interacting in problem-solving and problem-posing?
Cristian Voica, Florence Mihaela Singer, Emil Stan 

Affects are intuitively accepted as having a role in the key stages that determine success in problem-solving (PS) and problem-posing (PP). Two disjoint groups of prospective mathematics teachers with similar background and competences have been exposed to PS and PP activities, respectively, and they had to describe their affective states during these activities. The students’ reports have been analyzed from the perspective of epistemic affects, motivation, and self-efficacy. While in the PS context, several students expressed reluctance to report emotional feelings or frustrations over failing to find a solution for the given problems, in the PP context, a phenomenon of adaptation to one’s own cognitive possibilities appeared and the posed problems created a state of comfort/ enjoyment in students. PP conveyed a sense of autonomy and control to a greater extent than PS. It seems that intrinsic motivation is influenced by factors that are different in PP vs PS tasks, with an effect on perceived self-efficacy. The PP activity instilled a robust sense of coping efficacy, which made the students perceive their work as successful, to a large extent. In PS, the initially perceived self-efficacy triggered motivation to persevere with the solving, while in PP, the initial motivation generated by a novel task evolved into students’ perceptions of self-efficacy and confidence in one’s own capabilities. The conclusions of this study can help prospective teachers to use emotions in teaching for understanding, anticipating, and dealing with students’ ideas about mathematics and mathematical thinking and, finally, for improving students’ self-esteem and self-confidence, with an effect in more successful results.
Educational Studies in Mathematics (105/3, 487-517)
Link to the article

2019

Girls' performance in the Kangaroo Contest
Mark Applebaum, Roza Leikin 

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

Gender Issues in Solving Problems in the Kangaroo Contest
Mark Applebaum 

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

2018

České stopy v Matematickém klokanovi (Czech)
Vladimír Vaněk, Pavel Calábek,David Nocar  

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

Úspěšnost žáků na počátku sekundárního vzdělávání při řešení geometrických úloh ze soutěže Matematický klokan (Czech)
David Nocar, Tomáš Zdráhal 

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

Enhancing Creative Capacities in Mathematically-Promising Students. Challenges and Limits.
Florence Mihaela Singer 

The links between research in mathematics education, psychology of creativity and research in gifted education started to gain more attention in the last decade, from researchers and the large public as well. The paper is intended to provide a concise survey of these links, with a focus on: frameworks for studying students’ creativity and giftedness in mathematics; domain specificity of creativity; some characteristics of mathematical creativity resulting from its specificity; relationships between mathematical giftedness and creativity from a mind-and-brain perspective; relationships between creativity, giftedness and social inclusion; underlying connections between mathematical creativity and innovation, creativity and metacognition, creativity, giftedness and expertise; and the teaching of mathematically-promising students with a focus on structuring their mathematical competencies. The paper offers also brief reviews of the chapters included in the book, stressing on the benefits of an integrated approach of creativity and giftedness in mathematics education.
F.M. Singer (Ed.) Mathematical Creativity and Mathematical Giftedness (pp. 1-23)
Link to the article

2017

Spatial Abilities as a Predictor to Success in the Kangaroo Contest
Mark Applebaum 

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

Cognitive styles in posing geometry problems: implications for assessment of mathematical creativity.
Florence Mihaela Singer, Cristian Voica, Ildiko Pelczer 

While a wide range of approaches and tools have been used to study children’s creativity in school contexts, less emphasis has been placed on revealing students’ creativity at the university level. The present paper is focused on defining a tool that provides information about the mathematical creativity of prospective mathematics teachers in problem-posing situations. To characterize individual differences, a method to determine the geometry-problem-posing cognitive style of a student was developed. This method consists of analysing the student’s products (i.e., the posed problems) based on three criteria. The first of these is concerned with the validity of the student’s proposals, and two bi-polar criteria detect the student’s personal manner in the heuristics of addressing the task: Geometric Nature (GN) of the posed problems(characterized by two opposite features: qualitative versus metric), and Conceptual Dispersion (CD) of the posed problems (characterized by two opposite features: structured versus entropic). Our data converge on the fact that cognitive flexibility – a basic indicator of creativity – inversely correlates with a style that has dominance in metric GN and structured CD, showing that the detected cognitive style may be a good predictor of students’ mathematical creativity.
ZDM Mathematics Education (49(1), p37–52)
Link to the article

2015

How difficult is a problem? Handling multi-layered information conveyed in a variety of codes.
Florence Mihaela Singer, Cristian Voica, Ligia Sarivan 

We use statistical data to identify the problems that appear to be difficult with students in a problem-solving contest counting 9,580 participants from grades 2 and 3. Our analysis considers the level of complexity of the reading and problem-solving processes, as well as the diversity of the forms the information is conveyed by. We found the students’ inability to control a variety of information displays, with impact in problem solving. These results bring about a relevant starting point for further training in problem posing and solving within real-life contexts.
Procedia - Social and Behavioral Sciences (203, 192–198)

When Communication Tasks Become Tools to Enhance Learning. 

Effective communication in the classroom is a key element for learning, yet when and how future teachers should acquire such competence is not clear. In this article we explore students-prospective teachers’ written productions of a set of instructions in a learning situation. Through three emblematic cases we illustrate how a communication task focused on a partner selected by the student reveal snot only the student's domain-specific knowledge, but also a mental frame induced by an assumed paradigm, which is both constrained by the student's knowledge level, and purpose oriented by the need of successful social interaction.
Procedia-Social and Behavioral Sciences (187, 503-508)

2014

Dynamic Thinking and Static Thinking in Problem Solving: Do they Explain Different Patterns of Students’ Answers?
Ildiko Pelczer, Florence Mihaela Singer, Cristian Voica 

We look at dynamic thinking and static thinking in relation to mathematical problem solving. We examine the distribution of answers chosen by large samples of students to multiple-choice problems. Our empirical data suggest that static thinking activated by students in problem solving is likely to be responsible for a certain pattern of students’ responses, which is characterized by a uniform distribution among the choices. This finding has implications for curriculum development, as well as for the teaching practice in school.
Procedia – Social and Behavioral Sciences, Special issue (: EPC – TKS 2013, Vol. 128, April 2014, 217–222)

2013

A problem-solving conceptual framework and its implications in designing problem-posing tasks. (English)
Florence Mihaela Singer, Cristian Voica 

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that allow different levels of description of the initial wording. Within these transformations, the passage between successive phases of the problem-solving process determines four operational categories: decoding (transposing the text into more explicit relations among the data and the operating schemes, induced by the constraints of the problem), representing (transposing the problem via a generated mental model), processing (identifying an associated mathematical model based on the mental configurations suggested by the problem and own mathematical competence), and implementing (applying identified mathematical techniques to the particular situation of the problem, with the purpose of drafting a conventional solution). The study of this framework in action offers insights for more effective teaching and can be used in problem posing and problem analysis in order to devise questions more relevant for deep learning.
Educational Studies in Mathematics (83(1), 9-26)
Link to the article

Problem-Posing Research in Mathematics Education: New Questions and Directions.
Florence Mihaela Singer, Nerida Ellerton, Jinfa Cai  

As an introduction to the special issue on problem posing, the paper presents a brief overview of the research done on this topic in mathematics education. Starting from this overview, the authors acknowledge important issues that need to be taken into account in the developing field of problem posing and identify new directions of research, some of which are addressed by the collection of the papers included in this volume.
Educational Studies in Mathematics (83(1), 1-7)

Cognitive Framing: A case in Problem Posing. Procedia – Social and Behavioral Sciences
Ildiko Pelczer, Florence Mihaela Singer, Cristian Voica 

We analyse a student's creative expression in problem-posing situations. The findings suggest that a small but significant difference in creative behaviour at an interval of one year (from 11 to 12 years old) indicates a passage from cognitive variety to small incremental changes, under the constraints of a strong cognitive frame. We found a specialization of the student's creative behaviour in the direction of specific mathematical creativity, a process accompanied by the weakening of the ability to engage spontaneously in intuitive explorations. This conclusion may nuance the phenomenon known in the literature as the 4th grade slump in creative thinking.
Procedia – Social and Behavioral Sciences, Special issue (Vol 78, 13 May 2013, 195–199)

2012

Suchen nach der schönsten Aufgabe – Wie entstehen mathematische Wettbewerbe (in German)
Robert Geretschläger 

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

Boosting the Young Learners' Creativity: Representational Change as a Tool to Promote Individual Talents (Plenary lecture)
Florence Mihaela Singer 

This review highlights the importance of representational change (RC) for effective and creative learning. The RC capability has been deduced from three types of observations that concern respectively: children’s innate propensities, their cognitive endowment for recursive processes, and their spontaneous bridging ability. The introduction of RC as part of the teaching-learning design essentially means, on the one hand, to center the didactical approach on representation as a powerful tool in mathematics learning, and on the other hand, to bring milestone-concepts early in school learning, in an informal way, in order to stimulate a natural construal of abstraction during cognitive development. Within the teaching for RC, together with the target concept, a variety of (procedural) representations and ways to move from one representation to another are internalized, and thus, RC becomes a trustful tool for dealing creatively with problems in various domains and cross domains.
7th International Group for Mathematical Creativity and Giftedness (MCG) International Conference Proceedings (p.3-26)

2011

Between algebra and geometry: the dual nature of the number line
Ildiko Pelczer, Florence Mihaela Singer, Cristian Voica 

We analyze the statistical distribution of the answers given by 2nd to 10th graders to a set of number line problems. To structure our analysis of students’ misconceptions, we identified three clusters of problems related to the number line. Our analysis shows that neglecting one of the main features of the number line can be a potential cause for misconceptions. By further exploring the students’ mistakes, we found that children ignore either the geometric or the algebraic nature of the number line, making inappropriate decisions within the problem context. The errors in the problems treated within this paper originate from lack of understanding of the dual nature of the number line and are persistent over time.
Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education (376-385)

2010

O jedné zajímavé úloze z Matematického klokana (Czech)
Filip Švrček, Vladimír Vaněk 

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 )

In Search of Structures: How Does the Mind Explore Infinity?
Florence Mihaela Singer, Cristian Voica 

When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g-structures), arithmetic (a-structures), fractal-type (f-structures), and density-type (d-structures). Students select different problem-solving strategies depending on the structure they recognize within the problem domain. They naturally search for structures in challenging learning contexts. This tendency to search for structure might be a characteristic of human cognition and a necessary condition for human knowledge development. For example, specific fractal structures are intrinsic to concepts such as the numerical system that have been developed by humans over a long period of time. When these structures are emphasized within teaching, they can facilitate the deep understanding of several basic concepts, in mathematics and beyond.
Mind, Brain and Education (4(2), p. 81-93)

Children’s Cognitive Constructions: From Random Trials to Structures
Florence Mihaela Singer 

This chapter focuses on a specific type of the child's mental activity: processing structures. The practice of structuring starts in the first years of the child's life, while she/he explores the environment within categorical learning, and it extends along cognitive development through the organization of spontaneous and aggregate structures. The dynamic infrastructure of mind—an inborn system of operational clusters—activates mechanisms that make possible the specialization-modularization of the cognitive system. Within these processes, trial-error procedures are shortcut through trial-error-organize iterative constructions. The implications of this view refer to a teaching process that meets the cognitive needs of children. Dynamic structural learning (DSL) is based on two dimensions: developing dynamic conceptual structures within the curriculum, and organizing the teaching practice in a way that generates dynamic structures of thinking. The impact of this conceptual framework concerns to what extent DSL might be used on a large scale. Previous experiments show that the DSL tasks are relatively easy generalized in school practice, at least at the level of primary education.
Advances in Sociology Research (vol. 6, pp: 1-35)

2009

Co se do Matematického klokana nedostalo (Czech)
Vladimír Vaněk 

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)

Soutěž Matematický klokan - zdroj zajímavých inspirací nejen pro učitele primární školy
Bohumil Novák 

Banská Bystrica : Univerzita Mateja Bela (pp. 142-149, ISBN 978-80-8083-742-6 )

Problem posing in mathematics learning: establishing a theoretical base for research.
Singer, F. M., Ellerton, N., Silver, E.A., Cai, J., Pelczer, I., Imaoka, M., Voica, C.  

In recent years, problem posing has received more attention in the mathematics education community – both as a means of instruction (to engage students in learning important concepts and skills and to enhance their problem-solving competence) and as an object of instruction (to develop students’ proficiency in posing mathematics problems). experience with mathematical problem posing can promote engagement in authentic mathematical activities. for example, problem-posing activities can allow students to encounter many problems, methods and solutions, and promote students’ creativity – a disposition to look for new problems, alternative methods, and novel solutions. many studies have detected positive effects on students' problem-solving achievement and/or their attitudes towards mathematics when problem posing has been systematically incorporated into mathematics instruction. some scholars have recognized that problem posing is an important part of mathematical activity, yet research on problem posing has not yet become a major focus in mainstream mathematics education research. thus, the field would benefit from an effort to systematize the theoretical curriculum and pedagogical foundations for and the empirical findings accumulated to date in problem-posing research. Our working session will engage participants in discussion on the following topics: 1. Problem posing as an integral component of school mathematics. 2. Contrasting the cognitive components of problem posing and problem solving in mathematical thinking. 3. Problem posing and discourse in mathematics classrooms. 4. Problem posing processes and how these relate to creativity. Coordinators of the working session will also engage participants in making specific plans for proposing a special issue of educational studies in mathematics and for planning the structure and chapters of a book on problem posing.
Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (vol 1, pp.299)

The Dynamic Infrastructure of Mind - a Hypothesis and Some of its Applications
Florence Mihaela Singer 

A mechanism underlying the computational properties of the cognitive architecture is construed based on a minimal list of operational clusters. This general processing mechanism constitutes the dynamic infrastructure of mind (DIM). DIM consists in categories of mental operations foundational for learning that contain inborn components called inner operations, which are self-developing in the interaction mind-environment. Within the DIM paradigm, the input cognitive systems are not domain specific or core-knowledge specific, they are operational specific and capable of further developments that become domain specific while experiencing the environment. Arguments for this construal come from three sources: literature review, data collected through classroom observations, and a four-year experimental study of teaching and learning mathematics in primary grades. The outcomes of that experiment led to a methodology of learning based on activating the operational infrastructure of mind, which enhances students' flexibility of thinking and predicts the capacity to solve creatively a variety of problems.
New Ideas in Psychology (27(1), 48–74)

2008

O úlohách ze soutěže Matematický klokan. (Czech)
Bohumil Novák 

Acta Universitatis Palackianae Olomucensis, Mathematica (Vol 2008, pp. 191-196, ISSN 0862-9765)

Between perception and intuition: thinking about infinity
Florence Mihaela Singer, Cristian Voica 

Based on an empirical study, we explore children’s primary and secondary perceptions on infinity. When discussing infinity, children seem to highlight three categories of primary perceptions: processional, topological, and spiritual. Based on their processional perception, children see the set of natural numbers as being infinite and endow Q with a discrete structure by making transfers from N to Q. In a continuous context, children are more likely to mobilize a topological perception. Evidence for a secondary perception of N arises from students’ propensities to develop infinite sequences of natural numbers, and from their ability to prove that N is infinite. Children’s perceptions on infinity change along the school years. In general, the perceptual dominance moves from sequential (processional) to topological across development. However, we found that around 11–13 years old, processional and topological perceptions interfere with each other, while before and after this age they seem to coexist and collaborate, one or the other being specifically activated by the nature of different tasks.
The Journal of Mathematical Behavior (27, pp. 188-205)

Teaching and learning cycles in a constructivist approach to instruction.
Florence Mihaela Singer, Hedy Moscovici 

This study attempts to analyze and synthesize the knowledge collected in the area of conceptual models used in teaching and learning during inquiry-based projects, and to propose a new frame for organizing the classroom interactions within a constructivist approach. The IMSTRA model consists in three general phases: Immersion, Structuring, Applying, each with two sub-phases that highlight specific roles for the teacher and the students. Two case studies, one for mathematics in grade 9 and another for science in grade 3, show how the model can be implemented in school, making inquiry realistic in regular classes. Beyond its initial purpose, the IMSTRA model proved to be a powerful tool in curriculum development, being used in producing mathematics textbooks, as well as in developing teaching courses for a long-distance teacher-training program.
Teaching and Teacher Education (Vol. 24/6 pp 1613-1634)

2007

Beyond Conceptual Change: Using Representations to Integrate Domain-Specific Structural Models in Learning Mathematics.
Florence Mihaela Singer 

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for promoting representational change across cognitive development. I provide an example of an integrated structural model that highlights the underlying cognitive structures that connect numbers, mathematical operations, and functions. The model emphasizes dynamic multiple representations that students can internalize within the number line and which lead to developing a dynamic mental structure. In teaching practice, the model focuses on a counting task format, which integrates a variety of activities, specifically addressing motor, visual, and verbal skills, as well as various types of learning transfer.
Mind, Brain, and Education (1(2), pp. 84-97)

2006

Das Känguru der Mathematik - Einige Gedanken zum Österreichischen Ergebnis 2005 (in German)
Robert Geretschläger 

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

2004

Jak na tom jsme.
Josef Molnár 

Makos 2003/Praha: Univerzita Karlova (pp. 38-41, ISBN 80-7290-156-7)

Models, complexity and abstraction – how do they relate in school practice?
Florence Mihaela Singer 

Do we need models in explaining the outer world and the self? What types of models might be helpful in school to explain both complexity and abstraction? What level of representation is appropriate? What dimensions of training should be focused on in constructing an inquiry-based learning? How could these dimensions be reflected in developing students’ competencies? Analysing the dual relationship between complexity and abstraction, the study proposes some strategies to enhance learning in a model-building environment.
Applications and Modelling in Mathematics Education, Dortmund: ICMI Study (14, p. 255-260)

Modeling both complexity and abstraction: A Paradox? The dynamic structural learning: from theory to practice
Florence Mihaela Singer 

Do we need models in explaining the outer world and the self? What types of models might be helpful in school to explain both complexity and abstraction? What level of representation is appropriate? What dimensions of training should be focused on in constructing an inquiry-based learning? How could these dimensions be reflected in developing students’ competencies? Analysing the dual relationship between complexity and abstraction, the study proposes some strategies to enhance learning in a model-building environment.
Proceedings, Copenhagen, Denmark: IMFUFA

2002

Ke strategiím řešení úloh soutěže Matematický klokan. (Czech)
Josef Molnár, P. Voglová 

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 

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

2001

Klokan v Česku (Czech)
Tomáš Zdráhal, Petr Rys 

Ústí nad Labem: Univerzita J. E. Purkyně (pp. 4-7. ISBN 80-7044-376-6)

Internationaler Wettbewerb Känguru der Mathematik (in German)
Robert Geretschläger, Michael Hofer 

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

1998

Matematická soutěž Klokan 1997.
Tomáš Zdráhal 

Acta Universitatis Purkianae/Univerzita J. E. Purkyně (pp. 87-93, ISBN 80-7044-186-0)

2024

Mathe mit dem Känguru 6 - Die schönsten Aufgaben von 2020 bis 2024 (German)
Alexander Unger, Meike Akveld, Robert Geretschläger 

Hanser Verlag (978-3-446-48183-1)

Canguro matemático 2024. (Spanish)
Alarcón Díaz, E.M.; Barrientos Fernández,F.; Haro Laguardia, F.; Martín Álvarez, P.A.; Pérez Rojo, M.A. y Rodríguez Taboada, J 

Federación Española de Sociedades de Profesores de Matemáticas. (ISBN: 978-84-122154-3-4)

2023

Canguro matemático 2023 (Spanish)
Haro Laguardia, F.; Martín Álvarez, P.A.; Pérez Rojo, M.A. y Rodríguez Taboada, J.A.  

Federación Española de Sociedades de Profesores de Matemáticas. (ISBN: 978-84-122154-2-7)

2021

Easy Problems for Smart People. Playing Math with Kangaroo (English)
Florence Mihaela Singer 

Based on a long experience in problem posing and solving, the author gathers into this book a selection of problems addressing middle school, distributed in 8 chapters: numbers and operations on numbers, plane geometry, space geometry, algebraic computation, logic and sets, patterns and functions, measurement, and data processing. Many of these problems are related to the International Kangaroo Competition.
Bucharest: Sigma (ISBN: 978-606-727-379-3)
Link to the article

2019

Mathe mit dem Känguru 5 - Die schönsten Aufgaben von 2015 bis 2019 (German)
Alexander Unger, Monika Noack, Robert Geretschläger, Meike Akveld 

Hanser Verlag (978-3-446-45655-6)

2018

Mathematical Creativity and Mathematical Giftedness: Enhancing Creative Capacities in Mathematically Promising Students (English)
Florence Mihaela Singer 

This book discusses the relationships between mathematical creativity and mathematical giftedness. It gathers the results of a literature review comprising all papers addressing mathematical creativity and giftedness presented at the International Congress on Mathematical Education (ICME) conferences since 2000. How can mathematical creativity contribute to children’s balanced development? What are the characteristics of mathematical giftedness in early ages? What about these characteristics at university level? What teaching strategies can enhance creative learning? How can young children’s mathematical promise be preserved and cultivated, preparing them for a variety of professions? These are some of the questions addressed by this book.
Springer Nature (ISBN: 978-3-319-73155-1; 978-3-319-73156-8)
Link to the article

2016

Research On and Activities For Mathematically Gifted Students. (English)
Florence Mihaela Singer; Linda Sheffield, Viktor Freiman, Mathias Brandl  

The aim of this Topical Survey is to give a brief overview of the current state of research on and activities for mathematically gifted students around the world, being of interest to educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. The focal topics include empirical, theoretical and methodological issues related to the following themes: Nature of Mathematical Giftedness; Mathematical Promise in Students of Various Ages; Pedagogy and Programs that contribute to the development of mathematical talent, gifts and passion; and Teacher Education. Current and historical research and suggestions for new research paths are included in each category.
Springer Nature (ISBN 978-3-319-39449-7; ISBN 978-3-319-39450-3)
Link to the article

2015

Mathematical Problem Posing: From Research to Effective Practice (English)
Florence Mihaela Singer, Nerida Ellerton, Jinfa Cai  

The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.
Springer (ISBN: 978-1-4614-6257-6)
Link to the article

2014

Mathe mit dem Känguru 4 - Die schönsten Aufgaben von 2012 bis 2014 (German)
Monika Noack, Alexander Unger, Robert Geretschläger, Hansjürg Stocker 

Hanser Verlag (978-3-446-44259-7)

2011

Mathe mit dem Känguru 3 - Die schönsten Aufgaben von 2009 bis 2011 (German)
Monika Noack, Alexander Unger, Robert Geretschläger, Hansjürg Stocker 

Hanser Verlag (978-3-446-42820-1)

2010

Mathe mit dem Känguru für die Grundschule (German)
Monika Noack, Robert Geretschläger, Hansjürg Stocker 

Bildungsverlag Lemberger (978-3-85221-027-8)

2008

Mathe mit dem Känguru 2 - Die schönsten Aufgaben von 2006 bis 2008 (German)
Monika Noack, Robert Geretschläger, Hansjürg Stocker 

Hanser Verlag ( 978-3-446-41647-5)

2007

Počítejte s klokanem - Junior (2000-2004) (Czech)
Radek Horenský, Petr Rys, Jaroslav Zhouf, Josef Molnár 

Prodos, Olomouc (63 pages, 978-80-7230-179-9)

Počítejte s Klokanem "Kadet" (Czech)
Jitka Hodaňová, Vladimír Vaněk, Radek Horenský 

Prodos, Olomouc (62 pages, ISBN 978-80-7230-178-2)

Počítejte s Klokanem - STUDENT. (Czech)
Pavel Calábek, Jaroslav Švrček 

Prodos, Olomouc (64 pages, ISBN 978-80-7230-180-5)

Počítejte s Klokanem - Benjamín. (Czech)
Martina Uhlířová 

Prodos, Olomouc (47 pages, ISBN 978-80-7230-177-5 )

2006

Mathe mit dem Känguru 1 - Die schönsten Aufgaben von 1995 bis 2005 (German)
Monika Noack, Robert Geretschläger, Hansjürg Stocker 

Hanser Verlag (978-3-446-40713-8)

2005

Matematický klokan 2005 (Czech)
Bohumil Novák, Josef Molnár, Dita Navrátilová, Pavel Calábek, David Nocar 

Olomouc: Univerzita Palackého (64 pages, ISBN 80-244-1178-4)

2004

Matematický klokan 2003 (Czech)
Josef Molnár, Bohumil Novák, Dita Navrátilová, Pavel Calábek 

Olomouc: Univerzita Palackého (52 pages, ISBN 80-244-0808-2)

2003

Matematický klokan 2002 (Czech)
Josef Molnár 

VUP Olomouc (48 pages, ISBN 80-244-0548-2)

2001

Matematický klokan 2001 (Czech)
Josef Molnár, Milan Kopecký, Pavel Calábek, Dita Navrátilová 

Olomouc: Jednota českých matematiků a fyziků (48 pages, ISBN 80-7015-816-6)

Počítejte s Klokanem - Student. (Czech)
Pavel Calábek, Jaroslav Švrček, Tomáš Zdráhal, Josef Molnár 

Prodos, Olomouc (64 pages, ISBN 80-7230-097-0)

Počítejte s Klokanem - Junior (Czech)
Radek Horenský, Petr Rys, Josef Molnár, Jaroslav Zhouf 

Prodos, Olomouc (64 pages, ISBN 80-7230-096-2.)

2000

Počítejte s Klokanem, Kategorie Benjamín. (Czech)
Bronislava Růžičková, Milan Kopecký, Josef Molnár 

Prodos, Olomouc (92 pages, ISBN 80-7230-068-7)

Počítejte s Klokanem - kategorie Klokánek. (Czech)
Bohumil Novák, Josef Molnár, Anna Stopenová, Martina Uhlířová 

Prodos, Olomouc (64 pages, ISBN 80-7230-058-X)

Počítejte s Klokanem kategorie "Kadet (1995-1999) (Czech)
Petr Emanovský, Jitka Hodaňová, Radek Horenský, Josef Molnár 

Prodos, Olomouc (65 pages, ISBN 80-7230-077-6)