Mathematics Competitions Research Articles

Evaluation of the Mathematical Processes in the Practices of Teaching and Learning in Childhood Education

The contemporary orientations, about mathematical education, indicate the need to favour the acquisition of mathematical competitions from the first ages. It is exposed, besides the fact that in these ages the numerical knowledge is key for other mathematical learnings, and there is emphasized the importance of the mathematical processes to achieve thus a better performance in the daily life. With the intention of analysing the practices of education of the number of the teachers of the first ages (4-8 years), and to investigate on the presence of the mathematical processes, an instrument has been designed by specific indicators that allow to analyse the presence (or not) of these processes in the above mentioned practices. The instrument of analysis includes five categories that represent five mathematical processes proposed by the National Council of Teachers of Mathematics (NCTM, 2000): resolution of problems, reasoning and test, communication, connections and representation. For each of the categories there contribute seven indicators of evaluation, elaborated from the contributions realized by the NCTM (2000), Alsina (2011) and the Departament d’Enseyament de la Generalitat de Catalunya (2013). The analysis of the information is going to allow to describe, first, the strengths and weaknesses in the practices of education learning of the mathematical processes; and secondly, relevant information is going to be obtained to return it to the teachers, to discuss and to give them specific support in relation to the necessary knowledge for the pedagogy of the notion of number in childhood.

A CASE STUDY OF AN EXPERT PROBLEM POSER FOR MATHEMATICS COMPETITIONS

This paper is concerned with organizational principles of a pool of familiar problems of expert problem posers and the ways by which they are utilized for creating new problems. The presented case of Leo is part of a multiple-case study with expert problem posers for mathematics competitions. We present and inductively analyze the data collected in a reflective interview and in a clinical task-based interview with Leo. In the first interview, Leo was asked to share with us the stories behind some problems posed by him in the past. In the second interview, he was asked to pose a new competition problem in a thinking-aloud mode. We found that Leo’s pool of familiar problems is organized in classes according to certain nesting ideas. Furthermore, these nesting ideas serve him in posing problems that, ideally, are perceived by Leo as novel and surprising not only to potential solvers, but also to himself. Because of the lack of empirical research on experts in mathematical problem posing, the findings are discussed in light of research on experts in problem solving and on novices in mathematical problem posing.

Engaging learners in cybersecurity careers

Educators and sponsors endorse competitions as a strong, positive influence on career choice. However, empirical studies of cybersecurity competitions are lacking, and evidence from computer science and mathematics competitions has been mixed. Here we report initial results from an ongoing study of the National Cyber League to provide a glimpse of the role of competitions in fostering cybersecurity career engagement. Preliminary results suggest that cyber competitions attract experienced individuals who will remain in the profession for the long-term, but future research is needed to understand how cyber competitions may engage women and those new to the field.

The Romanian Mathematics and Informatics Education

Aims: The main aim of this report is to set forth a survey of the Romanian Mathematics and Informatics Education at the present time. We emphasize some of the recent, specific and significant Romanian methods concerning the teaching and learning of Mathematics and Informatics, starting from pre-school and primary level to the university mathematics and informatics education, the role of national and international mathematical competitions, the education of mathematics and informatics teachers, the formation of researchers in mathematics and informatics, their contributions and perspectives, the mathematics and informatics education in society and culture, the technologies in mathematics and the future of computers in education, links between research and practice, and developments in both these fields. Our considerations show, in a concise manner, the significant details regarding the current Romanian Mathematics and Informatics Education and the corresponding scientific studies. Conclusion: In Romania, mathematics and informatics are taught, learned and applied by interand trans-disciplinary related applications, honoring both pupils and the teachers, aiming and succeeding at properly synchronizing the traditional forms of education and the Original Research Article British Journal of Education, Society & Behavioural Science, 4(2): 226-240, 2014 227 international ones, in particular those corresponding to the forms existing in the European Community, following the new Law of Education and starting from the pre-education given in the family.

一位国小教师资优数学课程的创意教学设计与实施

本研究旨在探讨一位国小专家教师如何设计与实施资优数学课程与教学。以教学观察、访谈和文件等方式来进行一学期的数据搜集，结果发现个案教师设计多样化、生活性与高认知的数学问题，透过主题式探索与讨论的教学实施，以培养学生的数学思考、推理、沟通、连结与表征等能力，并引导学生进行探索性的独立研究。个案教师资优数学课程的设计与实施，是根据她个人的教学理念、先备经验和兴趣，在没有特定教学进度的压力和家长的支持下，她依据资优课程的目标、学生的需求和喜好，来进行数学课程的设计与实施，也因此引发学生探索数学的兴趣，并将学生探索的结果参加数学科展竞赛，获得良好的成绩表现。 The purpose of this study was to investigate how an expert elementary teacher designed and implemented gifted mathematics curriculum and teaching. Teaching observation, interviews and document were used to collect data for one semester, and the results indicated that mathematics problems the teacher designed were diverse, life-related, and classified as high cognitive problems. Exploration and discussion were used to solve the problems in order to foster students’ abilities on mathematical thinking, reasoning, communication, connection and representation, and guide students to conduct independent study for getting more exploration. Mathematics curriculum design and implementation of the teacher was based on her personal teaching ideas, prior experiences and interests, and in the context of parents’ support and without pressure from specific teaching progression, she integrated the objectives of gifted curriculum, students’ needs and interests into the design and implementation of the mathematics curriculum. Thus, her teaching evoked students’ interest to explore mathematics further. The teacher also used the results of students’ exploration to attend mathematics competition in elementary level, and got a good grade and performance.

Influences of Formal Schooling on International Mathematical Olympiad Winners From Korea

Interviews with five former International Mathematical Olympiad winners were analyzed to determine how various aspects of their schooling influenced their academic development and ability. The influential factors include school administrations, teachers, peers, and participation in mathematics competitions and clubs. Participation in mathematics clubs was found to be most influential on their academic development in mathematics because of the peer interaction. Teacher influences were identified as both positive and negative because some encouraged their students’ achievement and talents, whereas others were not focused on the students’ interests or developmental needs. The school system or administration was a positive influence when flexibility allowed younger students to participate in competitions. Educators are urged to recognize various influences identified through this study.

Adilet Imambekov

Adilet Imambekov

Impact of the Assessment of Tenth-Formers’ Achievements in Mathematics on Learning Motivation


 The enhancement of the attractiveness of the subject of mathematics has currently become a topical problem of education policy. The conducted secondary analysis of the data of national survey (2008) has shown that learners take interest in mathematics, are motivated to learn mathematics and believe that mathematics contributes to learning other subjects, as it is related to their everyday life and prospective professional career.
 The secondary comparative analysis of the data of national survey (2006 and 2008) reveals that the assessment of tenth-formers’ achievements (the teacher’s attitude towards learners’ achievements and success) affect learning motivation. Statistically significant correlation coefficient shows that learners appreciate receiving fair assessment, and they understand how to accomplish tasks in order to receive good evaluation from the teacher; the teacher praises learners for their achievements and helps when they experience some difficulties. Hence, the willingness of learners to study mathematics is determined by both the assessment of achievements and mutual understanding of teachers and learners.
 Having conducted secondary data analysis of 2008 survey on the learners’ inclination to learn mathematics and the teacher’s influence in enhancing learning motivation, it appears that the strongest statistical correlation is between the activities related to teachers’ professional readiness – the teacher should be able to raise learners’ interest in the taught subject; is able to explain difficult things; encourages to participate in mathematical competitions and Olympiads. The strongest correlation defines the teacher’s professional competency (excellent knowledge of the subject and ability to explain difficult things).

Proof and Problem Solving at University Level

Abstract: This paper will be concerned with undergraduate and graduate students' problem solving as they encounter it in attempting to prove theorems, mainly to satisfy their professors in their courses, but also as they conduct original research for theses and dissertations. We take Schoenfeld's (1985) view of problem, namely, a mathematical task is a problem for an individual if that person does not already know a method of solution for that task. Thus, a given task may be a problem for one individual, who does not already know a solution method for that task, or it may be an exercise for an individual who already knows a procedure or an algorithm for solving that task.Keywords: Hungary, mathematics education, mathematics competition, Olympiads, international comparative mathematics education, problem solving, creativity, mathematically talented students.A Continuum of Tasks from Very Routine to Very Non-routineWhile what is a problem depends on what a solver knows, it is possible for most mathematics teachers to judge what is difficult for most students in a given class. Thus, we see mathematical tasks for a given class, such as a calculus class, on a continuum from those that are very routine to those that are genuinely difficult problems (Seiden, Seiden, Hauk, & Mason, 2000). At one end, there are very routine problems which mimic sample worked problems found in textbooks or lectures, except for minor changes in wording, notation, coefficients, constants, or functions that are incidental to the way the problems are solved. Such problems are often referred to as exercises (and might not be considered to be problems at all in the problem-solving literature).The vast majority of exercises in calculus textbooks are of this nature. Lithner (2004) distinguished three possible solution strategies for typical calculus textbook exercises: identification of similarities (IS), local plausible reasoning (LPR), and global plausible reasoning (GPR). In IS, one identifies surface features of the exercise and looks for a similar textbook situation - an example, a rule, a definition, a theorem. Without consideration of intrinsic mathematical properties, one simply copies the procedure of that situation. In LPR, one identifies a slightly similar textbook situation, but one in which a few local parts may differ. The solution strategy is to copy as much as possible from that similar situation, modifying local steps as needed. In GPR, the strategy is mainly based on analyzing and considering intrinsic mathematical properties of the exercise, and using these, a solution is constructed and supported by plausible reasoning. Lithner selected a textbook used in Sweden [Adams' Calculus: A Complete Course (5th ed.), Addison-Wesley], and worked through and classified solution strategies for 598 single-variable calculus exercises. He found 85% IS, 8% LPR, and 7% GPR. Furthermore, he concluded that "it is possible in about 70% of the exercises to base the solution not only on searching for similar situations, but on searching only the solved examples."Moving toward the middle of the continuum, there are moderately routine problems which, although not exactly like sample worked problems, can be solved by well-practiced methods, for example, ordinary related rates or change of variable integration problems in a calculus course.1 Moving further along the continuum, there are moderately non-routine problems, which are not very similar to problems that students have seen before and require known facts or skills to be combined in a slightly novel way, but are "straightforward" in not requiring, for example, the consideration of multiple sub-problems or novel insights. This is the type of problem we used on the non-routine test in our three studies of undergraduate students' calculus problem solving. One of those problems was: Find values of a and b so that the line 2x+3y=a is tangent to the graph of f (x) = bx2 at the point where x=3. …

Foundations for success in mathematical competitions: A study of best praxis in lower secondary schools in Norway

The purpose of this study is to investigate the following questions: What factors leads to success in mathematics, and how can these success factors and qualities be described? Will the teacher's education and pedagogical praxis have an impact on good learning results? We report results from a case-control association study on among high achievement classes in mathematics in Norway. The data were collected from matched pairs of schools, paired on the basis of location and socioeconomic status. The questionnaire was first distributed to teachers in 38 Norwegian secondary schools at grade 9, which have had repeated success in the annual KappAbel competition in mathematics. Subsequently, 38 teachers at schools without success were contacted, and answered the same questionnaire. The main findings of the study are the following: The formal academic competence of the teacher is the best predictor for good results. Moreover, the pedagogical profile is reason oriented, where students are challenged to evaluate and substantiate their arguments, and spreadsheet is used for exploration and computation.

Competitions to Support STEM

To prosper in the global economy, each nation must focus on growing its next generation of scientists, engineers, and entrepreneurs. Success will require exciting many more young students about science and mathematics. When appropriately organized and directed, science and engineering competitions can provide a lifelong appreciation of, interest in, and enjoyment of science and engineering activities in much the same way that involvement in sports competitions provides a lifetime enjoyment of sporting events. In February, the second-ever White House Science Fair celebrated the student winners of a broad range of science, technology, engineering, and mathematics (STEM) competitions from across the United States. And this year will see monetary and scholarship prizes awarded to students by longstanding prestigious competitions that include the Intel Science Talent Search; the Siemens Competition in Math, Science and Technology; the Google Science Fair; the FIRST Robotics Competition; and the Toshiba/National Science Teachers Association ExploraVision competition, among others. But these competitions require financial support in much the same way that extracurricular sports and Olympic teams do. More private industries, large and small, are needed to support STEM education by sponsoring such competitions.

Mathematical Competitions in Hungary: Promoting a Tradition of Excellence & Creativity

Abstract: Hungary has long been known for its outstanding production of mathematical talent. Extracurricular programs such as camps and competitions form a strong foundation within Hungarian tradition. New types of competitions in recent years include team competitions, multiple choice competitions, and some exclusively for students who are not in a special mathematics class. This study explores some of recent developments in Hungarian mathematics competitions and potential implications these changes have for very competition-driven system that currently exists. The founding of so many new competitions reflects a possible shift in focus and purpose of competitions away from a strictly talent-search model to a more inclusive enrichment approach. However, it is clear that in Hungary, tradition itself remains a strong motivating factor and continues to stimulate development of mathematically talented students. The involvement of mathematical community in identification and education of young talents helps perpetuate these traditions.Keywords: Hungary, mathematics education, mathematics competition, Olympiads, international comparative mathematics education, problem solving, creativity, mathematically talented students.(ProQuest: ... denotes formulae omitted.)IntroductionWorld-renowned for its system of special schools for mathematically talented students, Hungary also has a long tradition of extracurricular programs in mathematics. Extracurricular activities play an important role in overall education of mathematically talented students (Koichu & Andzans, 2009). Some of longeststanding extracurricular mathematics activities in Hungary can be traced back to 1890s and efforts of Lorand Eotvos (Weischenberg, 1984). The Bolyai Society continues to coordinate many of traditional extracurricular programs established at end of 19th century, including journal KoMaL and Eotvos Competition (now called Kurschak Competition), along with several new competitions and programs for mathematically talented students. This article focuses on mathematical competitions in Hungary and reviews recent developments, new competitions, and modifications to traditional offerings over past twenty years.MethodsThis article is an excerpt from a larger study on changes in Hungarian mathematics education system for mathematically talented students over past twenty years (Connelly, 2010). During study a series of in-depth interviews were conducted with current Hungarian secondary school teachers, mathematicians, professors, and other educators. Interviews were conducted by researcher in Budapest, Hungary, with aid of a native-Hungarian-speaking research assistant when necessary. Commentary on history, purpose, and impact of mathematics competitions was gathered through interviews with competition directors, organizing committee members, journal editors, and past participants. The interviewees will be referred to as respondents A-U in remainder of article.Historical background information was gathered from sources such as ministry of education publications, mathematical and pedagogical professional journals, and earlier dissertations in field. Information on competition structures and rules was obtained primarily from each competition's official website and contest documentation. Example problems from a variety of Hungarian mathematics competitions are presentedthroughout. For larger compilations of Hungarian competition problems published in English, see Berzsenyi & Olah, 1999; Kurschak, 1963; Liu, 2001; and Szekely, 1995.Traditional CompetitionsOne of most famous Hungarian mathematics competitions, Eotvos Competition, is considered the first mathematical Olympiad of modern world (Koichu & Andzans, 2009, p. 287). Founded in 1894, it was designed for students who had just graduated from secondary school; competition consisted of three questions based on mathematics of secondary school curriculum. …

Heterogeneity in High Math Achievement Across Schools: Evidence from the American Mathematics Competition

This paper explores differences in the frequency with which students from different schools reach high levels of math achievement. Data from the American Mathematics Competitions is used to produce counts of high-scoring students from more than two thousand public, coeducational, non-magnet, non-charter U.S. high schools. High-achieving students are found to be very far from evenly distributed. There are strong demographic predictors of high achievement. There are also large differences among seemingly similar schools. The unobserved heterogeneity across schools includes a thick tail of schools that produce many more high-achieving students than the average school. Gender-related differences and other breakdowns are also discussed.

The Role of Competitions in a Mathematics Programme

What role do competitions play in a mathematics programme for our students, especially our gifted and talented students? This question is examined from the perspectives of fifteen students (10-13 year olds) identified by their schools as mathematically gifted and talented, their teachers, and their parents. Students participated in variety of different types of mathematics competitions – local, national, and international. There was differential access to the competitions and differing perspectives; students and parents shared similar views about the value of competitions, but there was a difference of opinion among the teachers.

Reply to Drago: Culture and history are important in understanding the low number of women

Drago (1) makes a number of good points about the need to consider historical trends and culture in understanding women's underrepresentation in math-intensive fields. We agree with some of these points and have no position on others. Nevertheless, we want to point out that the main point—that we should consider historical and cultural influences in sex segregation—is something that we have done consistently in our publications on this topic, including this one (2–4). In online SI Text accompanying our article, we reiterated a point we have made in numerous past articles, namely, that sex cannot be considered in isolation from culture or history, and we discussed a number of historical trends. In SI Text, we wrote: “Lest these data be assumed to reflect innate, biological superiority of males, it deserves noting that there is large variance in cross-cultural analyses, with females outperforming males at the right tail in some countries, and the best predictor of international sex differences is the degree to which its citizens exhibit implicit gender-science stereotypes.” This goes well beyond the Asian countries the writer mentions because international trends in the production of top female mathematical talent have shifted from Asian to non-Asian countries over the past few decades several times. For example, among the top 25 female medalists in the 1992–2007 Putnam Mathematical Competition, viewed by many as the top mathematics competition in the world, small Eastern European countries, such as Romania and Bulgaria, supplied a larger number of female medalists than did the United States or Asian countries, despite being less than or equal to 1/15 in size (5, table 1).

A Lottery-like Stock Market

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsDavid BenkoDavid Benko is an assistant professor of mathematics at the University of South Alabama. He has Erdős number two (with multiplicity three) and will represent the American Mathematical Society on the MAA Committee on the American Mathematics Competitions beginning in 2012. email: dbenko@jaguar1.usouthal.edu

Mathematics Taught Me Einstein's Old Cocktail of Inspiration and Perspiration: Mathematically Talented Teenagers as Adults

Abstract Does success in mathematics at school influence educational and career paths? Are talented mathematics students attracted to a mathematics intensive field or are they more likely to turn to other areas? Using purposeful sampling, insight is gained into the lives—after they have left school—of high achievers in the annually conducted Australian Mathematics Competition. Of particular interest are their attitudes to school mathematics and to mathematics more generally, their motivations, career choices, and working habits. When possible, differences and similarities in males' and females' responses are noted. Collectively these data provide constructive glimpses into the immediate and longer term needs and goals of this exceptionally able group.

The Alberta High School Mathematics Competitions 1957–2006: A Canadian Problem Book edited by Andy Liu

The Alberta High School Mathematics Competitions 1957–2006: A Canadian Problem Book edited by Andy Liu

For Your Information: Publications: October 2010

A multitude of mathematics contest books has been published over the years, but this book is a great find for those who cannot get enough of mathematics contest questions. The Alberta High School Math Competitions anniversary volume provides fifty years of questions, both multiple-choice and free-response questions, and their solutions. For serious students who live for world-class mathematics competitions and for the teachers who prepare them for these competitions, this book is a must-have resource. It is divided into five parts: questions from the ancient period (from the 1957–66 contests), questions from the medieval period (from the 1967–83 contests), and questions from the modern period (from the 1983–2006 contests), followed by answers, solutions, contest statistics, and a list of all winners (1983–2006).

The Gender Gap in Secondary School Mathematics at High Achievement Levels: Evidence from the American Mathematics Competitions

This paper uses a new data source, American Mathematics Competitions, to examine the gender gap among high school students at very high achievement levels. The data bring out several new facts. There is a large gender gap that widens dramatically at percentiles above those that can be examined using standard data sources. An analysis of unobserved heterogeneity indicates that there is only moderate variation in the gender gap across schools. The highest achieving girls in the U.S. are concentrated in a very small set of elite schools, suggesting that almost all girls with the ability to reach high math achievement levels are not doing so.