Fostering Teachers’ Mathematical Competence in Problem Solving

The problem of a growing shortage of qualified mathematics teachers, which is emerging in many countries today, is also quite acute in Latvia. Moreover, there are only few students in Latvia who want to study mathematics at a serious level and become mathematics teachers. A shortage of students and teachers is one of the reasons for the decline in the quality of mathematics teaching. Teaching and learning mathematics is impossible without understanding and problem solving, which, as noted by the famous mathematician Paul Halmos, is ‘the heart of mathematics’. It is a well-known idea that by developing problem-solving skills, we learn not only how to tackle mathematical problems, but also how to logically work our way through any problems we may face. Unfortunately, this idea does little to contribute to a successful tackling of the teacher shortage, which is not a mathematics problem for which somebody can find a quick and easy solution. This article offers some research topics that may be useful for teachers working with their gifted pupils; deals with a non-trivial problem of constructing magic polygons on a triangular lattice, which is recommended as a research topic for teachers to encourage them and their students to better master different solution strategies and so-called big ideas in mathematics; the article also gives some insights into mathematics teacher training education in Latvia.