Research in math education in Latvia

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

2. 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”.

3. 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.

4. 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.

5. 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.

6. 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

7. 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

8. 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

9. 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.

10. Thank you for attention!