Elements of the ECMI Educational Program in a high school

Since September 2009 the mathematical modeling  experiment is running in the Grammar-School in Rawicz- Sierakowo (Poland)  The project entitled  “Mathematical Modeling as a key to the future – the support of the mathematical education in a grammar-school” is supervised by the ECMI Teaching  Center in the Wroclaw University of Science Technology (WUST). The aim of the venture having the form of pedagogical experiment is understanding by pupils of the role of mathematics in contemporary world  and   in the future the choice of studies in technical universities. The Grammar-School in Rawicz counts all together about  600 pupils from 13 to 16 years old. In present moment in  the school there are three class departments with mathematical modelling (one in each age education group). Each class counts 26 pupils. selected by some recruitment criteria. For the modelling the class is divided into four 6-7 pupils groups. During one semester every group is realizing one modelling project under supervision of a teacher playing the role of instructor. Every group has different project and different instructor. Every semester the pupils composition of modelling group is changed. Every week pupils have one hour obligatory meeting with instructor, but they have free access to the instructor all the time. Pupils exchange ideas concerning the project during their stay in the school and also meet sometimes in the free time.  Problems solving by modelling gives pupils an opportunity to develop their own creativity and to work at teams. Some examples of projects  are below:

• What is cheaper? Chair made of wood or of the recycled  paper.
• Any advices on wastes litter to the town council? How  to reduce wastes litter? When our town will be covered   with the mountain of wastes?
• How to control the frequency of traffic lights in our town to avoid traffic jams?
• How remove the snow from our town streets?
• How to reduce the usage of paper sheets in the school during one year?

The Grammar-School is situated 60 kilometers of Wroclaw.   Frequently pupils together with teachers visit the WUST.  They participate in the student modeling seminars. Moreover from time to time the University professors give talks in the Grammar-School. There also some meetings between pupils and doctoral students

Every year all pupils participating in the modeling activities gave answers for  questions from the special evaluation questionnaire.  Excellent majority of pupils likes to solve problems through mathematical modeling .  Also the majority of asked young people say that the choice of the modeling classes was their best decision at the beginning of education at the high school. Teachers instructors prepare notes with remarks concerning every project. This is a very interesting pedagogical material . The most impressive is, that the groups, which has realized the full three year modeling program, have passed  the final national mathematics exam with the much more better result that   the national average .

It should be emphasized that teachers related to mathematical modeling were prepared for that project since September 2008 (the project has started in September 2009). During one year time they participated at different seminars and modeling activities at the WUST. In August 2009 teachers took part at final presentations of the 23rd ECMI Modeling Week in Wroclaw.  In October 2010 teachers visited the EMS School on Industrial Mathematics in Bedlewo (Poland). During that visit professor Helmut Neunzert gave a special talk to them entitled: “Models for industrial problems: How to find and how to solve them in industry and in education”.

According new governmental rules concerning pupils selection  since 2014  the STEM style education has been introduced at that high school. It means that the modeling groups join pupils having different interest, for example, in maths and biology or even in math and history. For example, one of such a groups  on basis of a historical description calculated parameters for the war machine trebuchet. And even reconstructed it.

The  experiment improves the mathematical vision of the real world by pupils of that high school.