Mathematics Competitions Research Articles

Stress reappraisal during a mathematics competition: testing effects on cardiovascular approach-oriented states and exploring the moderating role of gender

ABSTRACTBackground and objectives: Effects of reappraising stress arousal during an interpersonal competition were tested on physiological functioning and performance. Additionally, the moderating role of gender was explored.Design and method: Participants (N = 279) were randomly assigned to a stress reappraisal, stress-is-debilitating, or a neutral control condition. Reappraisal materials educated participants about the adaptive benefits of stress, whereas stress-is-debilitating materials instructed participants to avoid stress. Control materials did not mention stress. Participants then competed against a gender-matched confederate on a 10-minute math performance task while cardiovascular reactivity was assessed. Participants were instructed to complete math problems as quickly and accurately as they could and were informed that a winner and loser would be determined by the resulting math scores.Results: Reappraising stress arousal led to more adaptive challenge-like cardiovascular responses, but no condition effects were observed on math performance. Exploratory analyses revealed that reappraisal instructions were effective for improving physiological functioning and facilitating performance for men, but women were unaffected by the manipulation.Conclusions: Reappraising stress arousal can improve physiological functioning during interpersonal competitions, but effects may be limited to men. Implications for future research are discussed.

Puzzles as a Didactic Tool for Development of Mathematical Abilities of Junior Schoolchildren in Basic and Additional Mathematical Education

Pedagogical science has always faced the issue of finding effective means for achieving educational results. This problem is especially urgent today, when in the rapidly changing world the tools, which yesterday could be used to support the interest of schoolchildren in study of mathematics and could provide an opportunity for the development of their mathematical abilities, quickly become obsolete. Today it is very important to search for new means that foster the development of students with the help of mathematics and mechanisms for including mathematics in the educational process. Thus, the aim of the article is to analyze puzzles as a didactic tool and study the possibilities of using puzzles in the process of teaching junior schoolchildren mathematics, both in the classroom and extra-curricular activities. The leading method here is the modeling of the methodical training system in general and additional mathematical education of schoolchildren, with the inclusion of a new didactic tool that fosters the students’ interest to the subject, develops individual mathematical abilities: logical thinking, abstraction, combining, operating spatial images, critical thinking, mathematical memory, etc. As a result of the research, the authors have determined the place, features and methodological aspects of the inclusion of puzzles in the process of teaching mathematics in general and additional school education. They can be used in the system of classical and creative math lessons and in extra-curricular activities of students: a mathematical club, a system of mathematical competitions, a mathematical camp, etc. The practical use of this model makes it possible to reduce the lack of tools in teaching for the development of students’ mathematical abilities, which in its turn, makes it possible to speak of purposefully high results in students’ mathematical activities, which is confirmed by the conducted experimental research.

On a Problem of Alaoglu and Erdős

Starting with an elementary problem that appeared in the Putnam mathematics competition, we proceed to discuss some techniques of transcendental number theory and prove the following result. If p, q, r are distinct primes and if c is a real number with the property that pc, qc, rc are integers, then c must be a non-negative integer. The tools used are some linear algebra and complex analysis. The zero-density estimate method discussed here was used by Alan Baker to prove his celebrated theorem on linear forms in logarithms. The question as to whether we can replace three primes by two primes is an open question.

Our duties in talent management in the light of the results of the International Hungarian Mathematics Competition of 2017

The 4th International Hungarian Mathematics Competition held in Transcarpathia, Beregszász between April 28 and May 1, 2017, was organized by the Hungarian Carpathian Hungarian Teachers' Association (KMPSZ) and the Ferenc Rákóczi II. Transcarpathian Hungarian Institute (II. RFKMF). The venue for the competition was the building of the Ferenc Rákóczi II. Transcarpathian Hungarian Institute. 175 students participated in the competition from Hungary, Romania, Serbia, Slovakia and Transcarpathia. In this article, we are going to deal with the problems given in the two rounds to students in grades 5 and 6, and, in the light of expectations and performance, we make some suggestions for a more effective preparation of talented students on after-school lessons.

Achievement in large-scale national numeracy assessment: An ecological study of motivation and student, home, and school predictors.

With the rise of large-scale academic assessment programs around the world, there is a need to better understand the factors predicting students’ achievement in these assessment exercises. This investigation into national numeracy assessment drew on ecological and transactional conceptualizing involving student, student/home, and school factors. Student factors comprised mathematics ability, gender, and year group. Student/home factors comprised mathematics tutoring, mathematics competition participation, computer support for mathematics, and practice mathematics tests. School factors included school-average mathematics ability, school-average practice mathematics tests and competition participation, and socioeducational status. These educational ecology factors were modeled as predictors of mathematics motivation. In turn, educational ecology factors and mathematics motivation were modeled as predictors of numeracy achievement. Data were drawn from N = 12,736 Australian elementary (Years 3 and 5) and secondary (Years 7 and 9) school students from 231 schools participating in a national numeracy assessment exercise. Multilevel structural equation modeling revealed that student and student/home factors (Level 1) and school factors (Level 2) explained significant variance in student- and school-level mathematics motivation. In turn, these factors explained significant variance in student- and school-level numeracy achievement. Findings hold implications for the nature, breadth, and depth of efforts aimed at improving mathematics motivation and numeracy achievement in large-scale assessment programs. (PsycINFO Database Record (c) 2018 APA, all rights reserved)

К 70-летию профессора Александра Павловича Солдатова

18 января 2018 г. исполнилось 70 лет доктору физико-математических наук, профессору, заслуженному деятелю науки Российской Федерации Александру Павловичу Солдатову. В настоящей заметке приводятся сведения из научной биографии этого крупного ученого, который хорошо известен в России и за рубежом. Представлены сведения о его вкладе в развитие математики в области дифференциальных уравнений с частными производными и их приложений.

The influence of students’ participation in STEM competitions on their interest in STEM careers

ABSTRACTPre-college student participation in science fairs, robotics competitions, computing contests and other science, technology, engineering, and mathematics (STEM) competitions increases every year in the United States. This is despite the fact that little is known about the relationship between STEM competition participation and career interest in STEM. Through logistic regressions, this study addresses three main research questions: Controlling for student background variables and prior STEM career interest, does participating in a STEM competition increase the likelihood of STEM career interest at the end of high school? Does the field of competition (robotics, engineering, science fair, information technology) a student participates in influence the sub-discipline of STEM career interest? And, what is the relationship between the number of competitions participated in and the probability of interest in a STEM career? The study uses data from the ‘Outreach Programs and Science Career Intentions’ survey (N = 15,847), a large-scale sample of university students enrolled in mandatory English courses. Our data reveal three results of interest. First, students who participate in STEM competitions are more likely to express interest in a STEM-related career at the end of high school than are students who do not participate, even when students’ prior career interest in STEM is controlled for. Second, the relationship between competition participation and interest in a STEM career appears to be domain specific. Third, the impact of competition participation on pursuit of a STEM career is three times stronger when students compete in more than one competition. These findings suggest that competitions are an effective way to foster career interest in specific STEM careers.

Mathematics and engineering in real life through mathematical competitions

ABSTRACTWe bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Mathematical contests as seen by participants

Motivation to take part in mathematical competitions and sources of information concerning the competitions is analysed on a basis of a questionnaire presented to a group of students.

IMPROVING MATHEMATICAL COMPETENCE IN PRIMARY SCHOOL TO ENABLE SKILL TRANSFERS IN NEW SITUATIONS

Mathematical competence is one of the basic competences defined in the EU. Results of international studies in recent years show that the percentage of pupils in Latvia with high level (5.,6.) of mathematical competence has decreased from 8% (PISA, 2012) to 5,2% (PISA, 2015). Observations of mathematical lessons show that individualization of studies is not a popular everyday feature, nonstandard problems are rarely used in the work with primary school pupils. Sustainable education can not be envisioned without creative thinking necessary for solving various nonstandard problems. Mathematical competitions also require creative applications of knowledge. The goal of this study was to analyze problems of Latvian mathematical contests for grades 4-6 of the last 3 years according to categories of mathematical content. The most important cognitive and metacognitive strategies necessary for their solution are shown. It is important to turn attention of teachers to much wider inclusion of contest problems into study process of primary school. It will enable to individualize studies and stimulate skill transfer to new situations for gifted pupils. The authors encourage teachers to use nonstandard (contest) problems as an indivisualization tool which will give opportunity for pupils to master knowledge and skill transfer. It will provide regular training of mind and positive emotions for pupils who are bored with solving standard problems.

Experience sharing: Mathematical Contest in Modelling (MCM)

In January 2016, Coventry University’s sigma Mathematics Support Centre (MSC) funded three students for MCM, a multi-day mathematics competition held annually in the USA. This is organised by the Consortium for Mathematics and Its Applications (COMAP) and sponsored by the Mathematical Association of America (MAA), the Society of Industrial and Applied Mathematics (SIAM) and the Institute for Operations Research and the Management Sciences (INFORMS). In this article the team leader and advisor reflect on their experience.

Structure and Maintenance of a Mathematical Creative Lesson as a Mean of Pupils’ Meta-Subject Results Achievement

The purpose of the research is to study and change the structure of a mathematical lesson to improve quality of pupils’ mathematical training and design mechanisms of inclusion the systems of open type tasks in educational process considering specifics of pupils’ creative personality development. The leading method is modeling of a mathematical creative lesson. The structure of it contains such stages, as motivation, psychological relief, intellectual warm-up and resume, besides traditional substantial sections. More than 700 pupils from 5-9 grades of comprehensive school took part in the experiment, which has been carrying out for the last three years. The result of the research is the author’s idea of using separate open type tasks, and the system of open type tasks, which consider psychological, physiological, motivational and cognitive features of pupils, promote development of their creative component for meta-subject results achievement. The practical use of the structure of a mathematical creative lesson and the systems of open type tasks shows pupils creative results and progress in mathematical training, expressed by best marks on the subject and at mathematical competitions of various levels. It proves the quality improvement of mathematical education among pupils trained by the offered technique.

Does Society Need IMO Medalists?

With a title that sounds provocative but with no intention to embarrass the organizers and participants of the event of IMO (International Mathematical Olympiad) this article should be seen as the sharing of some thoughts on this activity, or more generally on mathematical competitions, by a teacher of mathematics who had once helped in the coaching of the first Hong Kong Team to take part in the 29th IMO held in Canberra in 1988 and in the coordination work of the 35th IMO held in Hong Kong in 1994. The author tries to look at the issue in its educational context and more broadly in its sociocultural context.

Seventy-Five Years of the Putnam Mathematical Competition

We review the 75-year history of the world's foremost college-level mathematics competition. Evidence is provided to support the assertion that exceptional performance in premier secondary-school-level and college-level mathematics competitions correlates well with an exceptional research career in mathematics.

Do Schools Matter for High Math Achievement? Evidence from the American Mathematics Competitions

This paper uses data from the American Mathematics Competitions to examine the rates at which different high schools produce high-achieving math students. There are large differences in the frequency with which students from seemingly similar schools reach high achievement levels. The distribution of unexplained school effects includes a thick tail of schools that produce many more high-achieving students than is typical. Several additional analyses suggest that the differences are not primarily due to unobserved differences in student characteristics. The differences are persistent across time, suggesting that differences in the effectiveness of educational programs are not primarily due to direct peer effects. (JEL H75, I21, I24, I28, R23)

Validity and Diagnostic Attributes of a Mathematics Olympiad for Junior High School Contestants

The purpose of mathematics competitions, and in our case the South African Mathematics Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest and enthusiasm for mathematics and to identify the most talented mathematical minds. SAMO is organised in two divisions—a junior and a senior division—over three rounds. We analysed the results of the junior second round over seven years, 2006–2012. Based on the literature, a mathematical content framework was developed, dividing the mathematical content into seven broad content areas. In this paper we investigate the face validity, diagnostic attributes and predictive criterion validity of mathematics olympiad question papers over the period by focussing on the frequency of content area occurrence in the different items. We also look at the performance of contestants in the different content areas as a broad diagnosis. Lastly we investigate the item performance, comparing the expected performance by the problem committee of experts setting the question papers and the actual performance of contestants. Topics such as numbers, algebra, patterns and functions, measurement, applications, modelling and logic were used abundantly whereas (quite surprisingly) there were few items on graphs, decimal fractions, spatial logic and vertices and edges of polygons, indicating that the face validity can be improved. Contestants performed best in items on algebra and weakest in items on statistics. The ability of the problem committee to anticipate student item performance varied considerably and was significantly worse in 2012 than in 2006, indicating better predictive criterion validity in 2006.

Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2016 to George Berzsenyi for Distinguished Service to Mathematics

The Mathematical Association of America presented the 2016 Gung and Hu Award for Distinguished Service to Mathematics to Dr. George Berzsenyi for his remarkable career promoting the art of problem solving, creating national and international mathematical talent searches, supporting mathematical competitions, and empowering generations of high school students to pursue their mathematical and scientific passions. George is a native of Hungary and came to the United States as a high school student in 1957 following the end of the Hungarian Revolution of 1956. He completed his education in Texas, including a Ph.D. in mathematics at Texas Christian University. He taught at universities in Texas and Louisiana prior to moving to Indiana to chair the Department of Mathematics at Rose-Hulman Institute of Technology (RHIT), where he is now Professor Emeritus.

Book Review: Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads.

There are many excellent books on plane Euclidean geometry, exploring the subject at various levels. The book under review, which is foreworded by Michael H. Freedman (Fields Medal, 1986), adds yet another facet to this colorful subject. This delightful book presents a collection of problems in plane Euclidean geometry in the spirit of mathematical olympiads, along with their solutions. Additionally, it provides essential theory of plane Euclidean geometry, with proofs of some fundamental theorems. As such, this monograph is an excellent training manual to use in preparation for mathematical competitions and olympiads. Hence, this is a book that belongs in all academic libraries, from high school through graduate level.

Evaluación Diagnóstica en Andalucía: Una investigación del área «competencia matemática»

The present paper is part of the R & D Project SEJ 2007-66967 focused educational competency assessment Learning how to Learn. The main purpose of the study was to analyze the potential of external and diagnostic to estimate the degree of acquisition of these skills assessments.We analyzed tests Diagnostic Evaluation of Andalusia in the area of ‘Mathematics Competition’ (2006-2007 / 2009-2010). The methodology is based on qualitative and quantitative analysis of the various tests based on a matrix categorization capabilities involved, distinguishing between the percentage of current capabilities and the level of difficulty in which they appear.The evolving evidence in Primary and Secondary was similar in both types of tests and levels of difficulty. About the predominant capabilities, ‘application’ and ‘understanding’ are those that are more present, even at a basic level. By contrast, items including ‘argument/communication’ downstream evolved.In light of the results obtained, we value the distance between the concept proposed in DeSeCo (OECD, 2005) and it really seems to evaluate these tests.

Expert Recurrence of Linear Problem Posing

According to Pelczer & Gamboa (2009) the Mathematical problem posing process of the skilled problem posers (teachers, mathematically gifted students) is usually cyclic whilst the novices usually pose problems in a linear way. (Cyclic model means that the skilled problem poser is able to switch between the phases of problem posing, to learn from his/her mistakes, to transform the idea which is not suitable. Linear model is just a simple straight way.)In my study I set expert category. (Expert = professional in problem posing, preparing problems for Mathematical competitions such as Mathematical Olympiad.) With respect to previous statements the hypothesis would be that the experts will show nearly no signs of linear problem posing process. But this is not true – there is some recurrence of linear problem posing in the expert group. The signs of the problem posing process are seemingly the same as in the novices’ case. But the background is different. The expertness lies in the fact that the expert is so experienced that he/she is able to come with an idea that needs no transformations. During the problem posing trajectory the experts usually perform the Final assessment stage. The experts also do not perform multiple Setup stages. (They may return to the Setup stage in order to do Transformations but they usually do not restart their work by the use of totally new Setup.)