updated 24 February 2015

Mathematics on the chess-board, by Prof. Sava Grozdev, DSc - Bulgarian Academy of Sciences, VUZF University
Many combinatorial problems are connected with the chess-board. Some of them will be discussed during the workshop together with different strategies, coloring and coordinate methods included. Students of all ages, teachers and fans of mathematics are welcome. 

Games in Mathematics Education, by Prof. Jarmila Novotná - Charles University in Prague, Faculty of Education
In the workshop, practical examples of content, game-like activities adapted for mathematics education will be presented. After a brief theoretical introduction all participants will be involved in playing the mathematical games. The modifications suitable for various domains of school mathematics will be proposed and discussed.

MATHSTORIES - Storytelling and Maths, by Anna Christodoulou, Science Communicator, ICCS-NTUA, Institute of Communication and Computer Systems, National Technical University of Athens

What does maths have in common with storytelling? Much more than one would imagine! They both involve abstract thought and there are many territories and thinking patterns they share. When telling a story, you follow a sequence of events, similar to when you solve a maths problem. Solving a maths problem is reflected in predicting the next steps or even the end of a story. Cause and effect relationships are found both in tales and in equations. 

In addition, maths is full of stories itself! The history of mathematics, from Euclid to Bernard Russell is fascinating; so why not discover some of the most impressing mathematical concepts through the story of their own creators?

In this workshop addressed to students between 10 and 16 years old we will travel from Ceryne to Alexandria, measuring the circumference of Earth, we will investigate basic storytelling principles and we will create on the spot our own unique mathematical stories, mixing quests with questions, dragons with fractions and heroes with zeroes!

No square is negative, by Prof. Sava Grozdev, DSc - Bulgarian Academy of Sciences, VUZF University
The simplest inequality in algebra is the following one: x≥ 0, where equality holds if and only if x = 0. Some applications of it will be discussed during the workshop. Problems for 7-th grade level will be proposed.

Repunits, by Prof. Sava Grozdev, DSc - Bulgarian Academy of Sciences, VUZF University
Repunits are the numbers that contain only the digit 1 in their writing, namely numbers of the form 111…1. Several problems with repunits will be discussed during the workshop, including the following one: Find all quadratic polynomials with integer coefficients that transform repunits into repunits. Unsolved problems will be listed too. The workshop is suitable for 8-th grade students and above. 
SER Chessboard, by prof. Nikos Lygeros, University of Lyon
The chessboard Sierpinski-Einstein-Rosen is a conception which offers to chess and to mathematical thought, the ability to manage a space with two dimensions but with a multiplicity of times due to the central obstacle and simultaneously the hyper move which the blue squares allow. This way and because of the addition of the pieces while the rest of the chess rules are kept the same, we have a game not only more complex but also more creative in terms of studies and the mat. The chessboard SER is ideal for all those who know how to overcome difficult obstacles.
Some games are numbers and the nim-sum, by Andreas Demetriou, MSc., Cyprus Mathematical Society, The Grammar School Nicosia, Cyprus
This workshop will explore the mathematical analysis of two player games without chance moves. In particular, we begin with general background in Combinatorial Game theory by referring to the two different types of games, partisans and impartial. Then we survey with backwards induction the independent components of the game in order to extract information of the game as whole. While this probably won’t make you a better chess player, the workshop will give you a better insight into the structure of combinatorial games. Exercises will be assigned to all participants that will be involved in playing the mathematical games.
Counting around like a clock, by Tomasz Szemberg, Pedagogical University of Cracow

This workshop is suitable for students in grade 7 and higher. I will introduce congruences (i.e. counting modulo a given prime), explain how they come up in the real world and how they can and are used in mathematics. The expected learning effect is that the students will be able to perform basic calculations on division rest classes (no such terminology will be used). There will be a hand out to be worked on during the workshop and containing some after workshop problems.

Geometry of the finite plane, by Anna Ochel, Gimnazjum im. Jana Matejki w Zabierzowie
This workshop is suitable for students in grade 7 and higher. I will introduce the concept of a finite geometry and illustrate it with the example of the plane consisting of 9 points. The students will recognize in particular lines in the finite plane, will compute their intersection points and will be able to do further experiments on their own.
Around the Sylvester-Gallai problem, by Beata Strycharz-Szemberg, Technical University of Cracow

This workshop is suitable for students in grade 7 and higher. Configurations of lines are a classical topic of study in geometry ever since the times of Pappus. I will introduce several nice configurations and explain the celebrated theorem of Sylvester proved by Gallai. Then the students will be asked parallel questions about lines in finite plane (mod 3 and mod 5). They will be encouraged to work on some problems also after the workshop.

Why does mathematics in school matter?, by Andreas Skotinos, Cyprus Mathematical Society and Thales Foundation

Quite a number of people, both in the school context as well as in the wider community,  cannot see the extent and value of mathematics as a Human Activity  with a very broad range of  consequences and uses for the majority of us.  Instead they just feel that

“Maths beyond simple and applied arithmetic is needed only by specialists. Ramming it down pupils' throats in case they may one day need it is like making us all know how to fly a plane  that we might become pilots. Maths is a 'skill to a purpose', and we would ponder the purpose before overselling the skill."

In view of such conceptions the proposed workshop aims at discussions and exchange of views in order to identify a set of causes and facts explaining the value of Mathematics, the extent they should be taught in schools, what elements of them should be taught and to produce some recommendations concerning their place and role in the school curriculum.

ORIGAMI –metamorphose of plane paper into geometry solid, by Natalija Budinski, Primary and secondary school “Petro Kuzmjak”

The workshop goal is to develop mathematical and aesthetical students’ skills trough origami activities. Students learn through discovery and during that process they rely on use of economically acceptable materials. Workshop covers wide range of geometry lessons, such as:

  • Mathematical definition of geometrical solids, area and volume
  • Regular and irregular polyhedrons, convexity and concavity
  • Construction of third root, Pascal triangle

Students use origami to investigate underlying mathematic concepts. The main focus is on mathematics, but it could be use as a reference for art, history, geography and culture. Also workshop tends to raise awareness about importance of mathematics in everyday life through different activities outside of school. More about origami activities you can find on www.math4all4math.blogspot.com.

The role of counter: Examples in overcoming errors in Mathematics, by Prof Athanasios Gagatsis, University of Cyprus

To prove a statement, we cannot test all cases, but should use some method of proof. However, to reject a claim, we only need to find a single example that contradicts the claim. In this case, the example we use is called a counterexample.  Counter-example is “an example that reverses a given statement (conjecture, hypothesis, proposition or rule)”. A counter-example does not meet all the conditions and restrictions of problems. However, examples are those that do fulfill the conditions and restrictions of problems.

The use of counter-examples enriches and improves the usual way of teaching and their use can have much better educational results. Apart from this, they can be used as a very effective criterion for measuring the degree of students’ understanding of mathematical concepts.  Another function of counter-examples is that they can be used to modify an original definition, an initial statement. Many times statements are expressed as conjectures without giving all the conditions and restrictions, so that they apply only to simple and routine cases.  In this way, the counter-examples discovered, modify the original statement by adding conditions and restrictions, so that there are exceptions for cases which are not applicable.

Finding suitable examples and counter-examples, proves to be a difficult task, since they contain an element of uncertainty and freedom of choices. It is undeniable that counter-examples have played a large role in the development of mathematics. The various statements that are taught today are the final product formed through a process containing conjectures and counter-examples. In fact, the conjecture, its testing by a trial and error method, counter-examples and ultimately its proof, is inherent in the history of mathematics. Nevertheless, students are taught only the result of this long course, as something given and true.

A framework for teaching that includes the conjecture, the examples and the counter examples, changes the way students approach mathematical statements since they are required to think, judge and infer in order to reply. With the introduction of statements that may or may not be applied, students are forced to think about each statement separately and not to follow procedures that have been previously learned. They will have to make sense of the statement to prove, or to reject it. Thus, not using counter-examples in the teaching of mathematics deprives the teacher a powerful teaching tool for deeper conceptual understanding of mathematical concepts.

In relation to the above, in this talk emphasis will be given at presenting common students’ mathematical errors from primary education until the end of secondary education and how we can deal with these errors through providing proper counter-examples. These examples of students’ misconceptions are extracted from different mathematical concepts. For each error that will be presented a counterexample will be also provided and discussed. 


European Mathematical Society
Mathematical Society of South Eastern Europe (MASSEE)
Hellenic Mathematical Society