Research in math education in Latvia Dace Bonka, Agnis Andžāns University of Latvia

Didactics of mathematics – subbranch of mathematics In Latvia didactics of mathematics is considered as a part of mathematics (accordingly to the structure of science) Didactics of mathematics is included into one of 12 branches of mathematics: “Modern elementary mathematics and didactic of mathematics”.

Modern elementary mathematics Modern elementary mathematics was first in the world recognized as an official subbranch of science in 1995 by the decision of Latvian Concil of Science. Since then, similar decisions have been made also in other countries; also didactics of physics, didactics of informatics etc. are included into corresponding branches of science in Latvia. This reflects the strong opinion that the inner logic of the scientific discipline has the dominant role in developing its didactics.

Modern elementary mathematics Elementary mathematics consists of:  1) the methods of reasoning recognized by a broad mathematical society as natural, not depending on any specific branch of mathematics and widely used in different parts of it,  2) the problems that can be solved by means of such methods.

Modern elementary mathematics Many new areas of mathematics, especially in the discrete and algorithmic parts of it, are still today exploring elementary methods as the main tool. The movement of mathematical contests, has made an important service to elementary mathematics  the system of math competitions created a large and constant demand for original problems on various levels of difficulty  school curricula couldn’t settle the situation, and the organizers of the competitions turned to their own research fields where they found rich and still unexhausted possibilities.

Modern elementary mathematics One of important results that originated from the “olympiad mathematics” was the identification of the so called general combinatorial methods  mean value method  invariant method  extremal element method  interpretation method

Directions of research: modern elementary mathematics and mathematical competitions  the research in these areas is concentrated in the University of Latvia and has gained high international reputation Main research areas and results  Līga Ramāna: Method of invariants (2004)  Dace Bonka: The interpretation method in elementary mathematics and mathematical competitions for the elementary school age students (2008)  Ingrīda Veilande: Mean value method  Aija Cunska: Method of mathematical induction and ICT in math education  Andrejs Cibulis: polyomino and elementary methods for solving extremum problems

Directions of research: didactics of mathematics Main problem: How to go out of crisis in math education? Research areas: New didactical approach in teaching mathematics New textbooks ICT Main research topics and results  Ilze France: Teaching of geometry in the basic school (Grade 7-9) (2005)  Gunta Lāce: Teaching of elements of combinatorics in the basic school and training of math teachers  research in the general math education for junior students - mainly carried out at the University of Latvia and the Liepāja University. Prof. Jānis Mencis (sen.) is an undoubted and internationally recognized leader here

Directions of research research in higher education possibilities and impact of ICT on teaching mathematics Research in these two areas is carried out in many institutions (University of Latvia, Liepāja University, Daugavpils University, Latvian Agricultural University etc.) Historically, research in the history of mathematics in Latvia is closely tied with research in didactics.

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