• IMH Joins Mathematics A-Lympiad
• What Is The Mathematics A-Lympiad?
• A New Approach Towards the Improvement of Educational Systems
• Some Comments on the First Round of A-Lympiad Competition in Isfahan

IMH Joins Mathematics A-Lympiad

Today mathematical modeling is an important approach in different scientific areas. For this very reason this topic has been included in math curriculum in modern schools. Every year some competitions are being organized for different levels of students around the globe. One of these competitions is mathematics A-Lympiad which is being organized in the Netherlands and some other countries. The participating students are 16-18 years old, the two upper secondary levels of high school. The main objectives of this competition are to improve: thinking ability, practicing techniques of mathematical modeling, team cooperation, practicing how to write down scientific processes and findings and finally how to present all that is done. Fortunately under the cooperation agreement between the Freudenthal Institute and IMH, Isfahan Mathematics House is organizing this competition for the first time in Isfahan . To introduce Mathematics A-Lympiad, IMH has organized some educational courses for students as well as for teachers.

What Is The Mathematics A-Lympiad?

“Problem solving” and “mathematical modeling” are important tasks that are being practiced in modern schools. Working on these skills is hardly done since there are not enough appropriate books and materials on the subject and math teachers have difficulty in dealing with this. The Mathematics A-Lympiad is an approach to provide a basis for the development of these skills among students. The process is that in a limitted period of time, the students try to solve an open-ended problem in the real world i.e. a real problem expressed in mathematical language by the students themselves and solved through an appropriate strategy. During the competition all the undertaken steps, strategies and conclusions should be recorded and finally presented through a report.
This competition under its own regulations is organized in two rounds. The preliminary round which takes place at schools and the students, under the supervision of their teachers, compete in teams consisting of 3 or 4 members . The competition takes place on a Friday in November from 9am till 4 pm. The composition of the teams should remain the same for the final round. Sharing responsibilities, analyzing the data and assumptions, taking appropriate strategy and process for the solution and summing up the results in a final report are important evaluation factors in this competition. The quality of each report is graded by the organizing teachers and up to 3 of the best reports from each school are sent for the Mathematics A-Lympiad Committee. The Committee will decide which teams can enter the final round. For the final round which takes place in the Netherlands, 12 teams from the Netherlands and 1 or 2 teams from other participating countries will be invited. The assignment problems for the final round are almost similar to those of the preliminary round, except that they are more difficult and more extensive. The international final round will take place at a central location in the Netherlands from Friday 11:30am till Saturday 14pm in the middle of March. The Mathematics A-Lympiad Committee assesses the reports of the final round. This year for the participating students from the IMH, the final round will take place in Isfahan Mathematics House venue. To introduce this new activity and its perspectives, IMH has organized some educational courses for a group of math teachers, these teachers are supposed to introduce to IMH some of the students who are interested in this activity and meet the requirements for some preparation courses before the preliminary and the final rounds.

Perspectives and Development

The environmental changes and rapid technology development especially in information and communication technology impose crucial effects on all aspects of human life. These changes and developments along with globalization phenomenon bring about some inconveniences for those professional and skillful people who were successful in the earlier traditional world, but not in the present developing world. In the modern progressive world, societies and communities, for their own progression demand individuals with different skills and abilities. As it is said in “Strategic Management” by Fred David quoting from Professor Henderson:

“The astronomical changes in the world have resulted in a world full of complexities, therefore the usual and traditional methods of management fail to succeed. The societies and communities need active, creative, analyzer individuals well equipped with information technology and well-informed of how to use it.”

IQ & EQ Two Fundamental Success Factors

IQ or intelligent quotient is a score measuring the ability of comprehension and reasoning of an individual based on his or her own earlier knowledge. EQ or emotional intelligence quotient is a score measuring the ability of using one’s emotions and knowledge at the same time, in managing problems. EQ is related to such characteristics as intuition, creativity, flexibility and suppleness, social intelligence, personality and so on. IQ is almost intrinsic while EQ is acquisitive and could be attained through proper education. In fact, as the psychologists agree, among the success factors, IQ counts for only about 2o percent and the rest depends on EQ. Therefore 80 percent of success factors of a community could be developed through appropriate education.

Success Factors in the Modern World

As has been noted by one of the experts in the 17th Study of International Commission of Mathematics Instruction, some of the characteristics of successful people in the modern world are:

•  Positive thinking
•  Effort and Sense of responsibility
•  Good communication and cooperation skills
•  Sense of research and study
•  Critical thinking
•  Creativity
•  Flexibility and suppleness
•  Self-confidence in confronting new problems
•  Time and activity management
•  Providing documentation

The Conventional Education Systems

As you can see, all the factors mentioned above are related to EQ abilities, and could be achieved through appropriate training. Unfortunately in conventional education systems these skills are generally ignored. The students have to learn some prescribed materials in a limited period of time and give them back in a traditional, systematic exam. No time and space for creativity and self management. The students work and compete as individuals with no sense of cooperation and helping others. The IQ faculty is well supported whilst trainable faculties are being ignored.

Modern Educational Systems

Summing up, in modern educational policies which are being practiced in modern schools, latest educational strategies are defined as follows:

I. Self accessed: That is, along with his/her own group, every student has access to a supply of different resources such as books, papers, cds, internet and so on which have been selected by himself/herself.
II. Self paced: That is the student learns subject materials according to his/her own ability and aptitude and is involved nor in competitive situations, neither in topics out of his/her capability.
III. Within their own groups, students are allowed to be involved in the topics that they are more interested in, and not forcing themselves to get deep into subjects that they do not like. Confining students to a closed, prescribed education system is avoided.

Therefore an educational system with the above characteristics, if well organized and well performed, develops such skills as: effective studying, time and activity management and likewise the spirit of cooperation and comradeship. Furthermore, it discovers students with different skills and abilities and provides an opportunity for the progression of every individual within his/her own interests.

A Glance at High School Mathematics

Professor Peter Taylor the head of Australian Mathematics Foundation and the director of Mathematics Olympiad for 15 years, says:

“Often we overlook the fact what we are teaching students is ‘how to think’ … It is time to address this issue various aspects of enriching mathematics education to graduate students who are well equipped to encounter real issues”.

In fact, one who does not possess thinking ability and a critical mind, is not capable of confronting personal and social problems reasonably in the real life. As Professor Taylor points out “We must provide students with those topics in mathematics that are concrete and challenge the mind in the real life”.

A-Lympiad

Mathematics A-Lympiad has some special characteristics which deserve noting; in the following we take a look at some of these features:

•  This competition is between groups of students and not individuals.
•  The questions are real problems that are posed by societies, industries, companies, research centers or even a public problem.
•  To solve the problem, a mathematical model is presented by the students then a special idea follows for discussion.
•  These ideas might be different and have problems; possibly none of them can solve the problem completely.
•  In general the assumptions are too long and it may happen that one solution does not use all the assumptions.
•  The solutions are not short and generally need critical argumentations; this improves writing ability and the ways of how to organize findings and thoughts in a text. The reasoning ability is also improved, since every claim must be supported by evidences.
•  Some questions only require effective reading of the assumptions followed by self management, reasoning and then analytic details of the hypothesis in a final report.

Let’s have a critical look at A-Lympiad competition and former traditional competitions like Tournament of Towns and Olympiad, considering the success factors mentioned at the beginning of this article.

1. In competitions like Olympiad, we often confront with problems that never happen in the real life. This, moreover, prevents the motivation of thinking.
2. Since in A-Lympiad competition, the questions are real problems, the students enjoy challenging to solve them.
3. The fact that questions are real problems brings about a sense of responsibility towards society and makes students to look for a solution, wherever they encounter inconveniences, which in turn keeps their minds active.
4. The contexts of questions are long, and within each group, the students are required to read problem effectively in a reasonable time period. This develops the effective and cooperative reading skill, furthermore they practice self management, reasoning and analyzing the given presumptions, to find appropriate ideas for solution. All these activities develop creativity, critical thinking and mind activeness.
5. Since the problems cover a variety of topics, a more extensive variety of ideas for solution are presented by students, each one from a different aspect which makes students to develop a multi aspect mind.
6. Every individual can put forward his own idea and defend it in his own group and makes improvements if criticized, in this way team work skills such as good behavior and communication, respecting others’ views, ways of argumentation and reasoning, methods of analyzing, critics and suggestions and finally being fair with others are developed.
7. The fact that this competition evaluates a great deal the writing skill and documentation methods, encourages students to practice their inscription ability in writing down what they have in mind.

Keeping in mind the facts just mentioned , IMH believes that this competition by reinforcing effective components of students’ success in this complicated modern world helps them to develop their understanding and reasoning.

A New Approach Towards the Improvement of Educational Systems

Success Factors in the Modern World and Training Systems

Introduction

The environmental changes and rapid technology development, especially in communication and information technology impose crucial effects on all aspects of human life. These changes and developments along with globalization phenomenon bring about some inconveniences for those professional and skillful people who were successful in the earlier traditional world, but not in the present developing world. In the modern progressive world, societies and communities, for their own progression demand individuals with different skills and abilities.

In this article, we are trying to present some principles on the success factors in the modern world according to the standards given by UNESCO. We also take a look at the world educational systemsand their contexts, especially mathematical topics in textbooks as well as mathematical competitions. Full Text

Some Comments on the First Round of A-Lympiad Competition in Isfahan

The Primary Round of the 19th Mathematics A-Lympiad Competition in Isfahan
Due to Isfahan Mathematics House (IMH) educational activities, Isfahan joined the 19th mathematics A-Lympiad competition held in the Netherlands. Led by Isfahan Mathematics House, the primary round of this contest took place in Nov 2007. This is a survey report on this exam provided by Rahmati, Shiravi and Behrouz.
The Problem in Brief
In this challenge, the students are asked to compute the efficiency and the work produced by an employee, taking into consideration the following two issues:

1. Increasing working hours reduces the efficiency of each employee.
2. Rest breaks during working days increases significantly the efficiency of the employees .

Finally, the students are asked to offer two well-organized and suitable working programs for both the employee and the employer.
Mathematical Goals of the Problem
In general, this question is designed to illustrate the advantages of using a graph or diagram and its related concepts, in expressing and solving problems. Therefore all the assumptions are presented through a graph so that in the first step, the students make an effort to read and manipulate it. Then the students themselves pursue such concepts as the area under a graph, the slope of a graph and the extension of a graph in the regions where it is not defined. The concepts of limit and approximation are also looked upon in this problem.
A Survey Report on the Results of this Challenge
The following facts were observed in students’ answer sheets:

1. Students have many errors in computation, although the calculations are easy; for example almost all the teams made mistakes in converting minutes into hours and addition.

2. Most of the teams had difficulty in reading information from the graphs; e.g. instead of taking into account the work efficiency during a specific hour, they took into consideration the efficiency at the end of that particular hour.

Few teams could express the working programs by correct diagrams; for example to show the efficiency after the break they have jumped to the beginning of the diagram or else they forgot to take into consideration the resting hour.
Many teams have regarded linear diagrams as nonlinear ones.

In the educational system the application of a diagram in expressing and solving problems is not looked upon adequately; this concept is taught only in theory. That is why the students are not convinced to use it.

3. It seems than nobody pays attention to the remarks mentioned at the beginning of the exam.

4. Many teams ignored to create a common language at the beginning of their discussions.

In the educational system the students are not trained to express mathematical solutions reasonably and logically, finding an answer is more evaluated than understanding and reasoning.

5. None of the groups calculated the gross efficiency; merely the net labor was computed.

6. In many answer sheets there are errors raised from not understanding the question properly. It seems that the students have difficulty in reading and understanding the assumptions.

7. Although writing ability is not practiced in the educational system sufficiently, the students could express their own ideas in a clear and reasonable manner.

I. In this exam, a part of the time is assigned for writing style, whereas in other competitions, this is not the case.

II. In other math competitions, the reasoning is abstract, while in this one the reasoning is based on the common sense.

8. Some teams have offered special programs which represent a concrete perspective; e.g. one team suggests different working hours for different week days by taking into account the fact that employees have more energy at the beginning of the week. Some others made a division between married and unmarried employees.

9. Some groups have answered some parts correctly without any computation, based on a sense of intuition which is risky and not permissible.

10. An interesting point was that some groups used such concepts as limit and integration which they have not studied yet.

In the end, asking the students’ opinions about a more effective participation in the future, they mentioned the following remarks:

1. They asked for the best selected answers to the previous competitions.
2. Starting preparation trainings in middle school and not in high school.
3. Their ability in reading and writing should be improved through appropriate training.
4. Providing optimization discussions on different correct answers for one question.
5. Performing similar exams regularly.