Short preface of the e-book
The team preparing the e-book within the frames of the DynaMat project is not homogeneous - it is composed by mathematics educators and pure mathematicians who are lacking long experience in didactics but have strong interests in mathematics education at different levels. This specifics seems to be very important since synergy between science and science education research (with emphasis on mathematics in our case) faces the challenges of the increased use of inquiry-based learning. Together with the expected positive impact the project team was ready to face a number of challenges.
Starting from the main objectives of the DynaMat project and following the same positive spirit of fruitful collaboration we tried to create different didactic units in such a way that- The problems considered in the didactic units would have as an initial point models and events from the surrounding world
- The arguments in the units would have a reasonable mathematics content supporting the preparation of pre - and in - service teachers in mathematics
- All different arguments could be unified by creative ideas in posing and solving problems in the context of math education at different levels
Furthermore, the e-book is intended as a basic resource for the professional development of broad spectrum of teachers (pre-service and in-service alike) for a natural integration of specialized dynamic software in the classes in mathematics, science, IT and art. Thus, variety of the modules in terms of software, age groups and subject area has been intentionally sought.
The e-book contains materials based on the use of dynamic geometry software as a suitable platform for explorations of conjectures and hypotheses of the users, thus stimulating teachers and students alike to enter the skin of working mathematicians.
The book itself has a dynamical nature, since the authors have been improving the content taking into account the feedback from previous e-courses based on it.
Teachers and motivated students can use the e-book as a catalog of ideas - a good math model or example for further work on a specific problem. A possible hint for your choice is the file with the subject index - the corresponding didactic scenario could be used as starting point in the study of the problem. Of course the starting point depends on the concrete curriculum followed by the school. Therefore the next key point is how to adapt the scenario to the specific target audience - here the experience and the creativity of the teacher are essential. After a relevant introduction of a unit, it could be enriched and further developed by tasks, problems, and project ideas, following the examples proposed in it.
It is true that there is no royal road to mathematics, but the project team hopes that your journey with the DynaMat e - book will be pleasant and dynamic!
E-Book
The initial plan for the E-Book with materials has to include:
a) Examples showing how the use of ICT can develop further the visualization process,
b) Examples of simulations of real or hypothetical processes, so that appropriate math models are constructed and will be further improved to aid the learner,
c) Instructions and tips on how to use ICT to improve the simulation and modeling skills together with creativity of pupils.
General description of the E-Book
The team preparing the e - book is not homogeneous and it is composed by specialists in didactics of Mathematics as well as pure mathematicians without long experience in didactics. This particular point seems to become very useful since real interaction between different fields can give very positive impact on the whole work (but can provoke also negative results also!). There were no particular restrictive schemes imposed at the beginning of the work.
Starting from the main objectives of the Dynamat project and following the same positive spirit of fruitful collaboration we tried to create different didactic units in such a way that
1) The arguments in the didactic units had as an initial point models and events from the surrounding world
2) The arguments in the units have reasonable math contents supporting the preparation of future and in service teachers in Mathematics
3) We tried to unify all different arguments by using creative and attractive new ideas in posing, solving math problems and teaching math
The e-book itself also has a dynamical state, since we tried to improve the content taking into account the feedback from the preliminary e-course based on the e-book and after this from the e - course.
On one hand, teachers and motivated students can use the book in order to choose a good math model or example for further work on concrete argument. One possible hint to make this choice is to use the file with subject index. Once the argument is chosen it is nice to use the corresponding didactic unit/units as starting point in the study of the problem. We do not pretend to have a well prepared introduction in the subject, since the starting point depends on the concrete curricula followed in the school. Therefore the next key point is the decision of the teacher materials from the book can really be adapted in the class work. This difficulty requires a good and clear introduction of the students in the subject. Once this is done one can use the unit to develop further tasks, following the examples proposed in the book.
Technical hints to use the book
Since there are different arguments treated in the e-book and there is a variety of materials, a simple search engine is included. In this way the reader will have the possibility to connect some of different didactic materials according to the level of students and specific target group. For example one can introducing some of the key words: art, calculus, complex numbers, curves, dynamical systems, extremal problems in geometry, fractals games, geometry in reality, GPS, linear algebra, loci, modeling, polygons, statistics and probability. Once the key word is chosen one realize such a connections between different materials, having the list of all materials associated with the given key word. Some additional didactic materials and outputs ( developed during or after the preparation of the e – book and the corresponding courses) can be found in the section Outcomes (other outputs and results of the project different from the e – book).
Content of the e-book
Here below is the content of the e-book (titles of didactic materials together with different translations indicated with corresponding national flag. |
