In the Finnish comprehensive schools and also European ones, the teaching of school mathematics and others school sciences is a variation of Initiation-Response-Evaluation model and describes as a Traditional Cyclic Model (TCM). Traditionally, teaching of school mathematics in comprehensive schools is based on behaviorism and it is the reason why teachers choose TCM. Therefore, following of the instructions is a main stream teaching method. Because of the curriculum content teachers presents only illustrative interdisciplinary relations in their own teaching activity. The teaching in school is a result-oriented process and this is the reason to the teacher-centered process.
The teacher-centered process in mathematics can be seen as an efficient way of teaching, even though it has its flaws. It is not a requirement for the curriculum to be coherent since mathematics is split into pieces. Each lesson consists of repetative tasks leading to students having a hard time grasping the whole picture which of course lowers the interest of the subject since is does not become clear why you have to do these calculations. Neither does this approach ensure that students learn to do research and learning on their own, which is exactly what is needed as a part of our modern society. The problem basically is that students only learn to do arithmetical calculations for one lesson and then forgets them since the knowledge never was used in real applications nor used in future chapters. Another problem is that if you cannot combine the set of skills you possess you will never be able to solve complex problems and apply your knowledge on your creative ideas. This is also a necessery set of skills needed to derive proofs in mathematics.
However, research shows that many teachers are eager to introduce new teaching methods towards a more investigating approach, but the structure of existing material and the lack of time to create own material makes it easier to follow the books. The fixed structure of a book can unintentionally guide teachers into a teaching model that can be called the Traditional Cyclic System, where teachers try to get desired answers to questions and where all the laborative work is planned in advance with prepared instructions. References to other subjects in the laborations do not in this form activate students’ interest and understanding of multidisciplinary relations. In order to activate students and encourage them to use their background knowledge another approach is needed. A suitable approach which has been proven to work is the Humanistic and Scientific Inquiry Oriented (HSIO) method, where the teacher takes a different role and is seen as partner in the information gathering – and simultaneously available technology is seen as a natural necessity.
In order to assist and encourage teachers to practice their beliefs and adept a constructivistic approach in the classroom an appropriate curriculum and tools are needed. Teachers must also see technology as a necessity, and this can be acheived by striving for a HSIO approach in the classroom.
Me and Sebastian Laxell belive that we need teachers who use constructivistic methods. But in order to introduce new teaching methods in schools a new curriculum combined with simple tools where teachers easily can modify the material to their liking is needed. A tool that opens up for interdisciplinary collaboration and enables the teacher to focus on methods and pedagogy instead of time consuming and fragmented material. This is why we created “Ma.fi” a book in mathematics for junior-high with a curriculum that follows the constructivistic view of teaching with exploring tasks for students and coherent chapters. The online content of the book opens up for interactivity on a whole new level and enables students to make use of existing technology in a familiar surrounding.
The project was started in 2012 and only after four years of hard work schools in Finland, and even Sweden, have started to use our book and we even won “STV’s teacher award”in 2016 for our creation.