Publications

2022

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)
Link to the article

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 )
Link to the article

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

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)
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

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)
Link to the article

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

2019

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

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

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

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

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

2002

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

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

1999

Domesticating the Kangaroo at BRG Keplerstrasse
Robert Geretschläger 

This paper is a personal reflection on the first three years of organizing the Kangaroo Competition at an Austrian school, written at a time when such things were no where near as ubiquitous as they were to become later on.
Mathematics Competitions Journal of the WFNMC (Vol.12 Nr.2, pp42-54)
Link to the article