Finnish elementary teachers' conceptions on problem solving in mathematics teaching

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Tutkiva matematiikan oppiminen peruskoulussa

Jotta koulun matematiikanopetuksessa päästäisiin rutiiniopetuksesta ja kyettäisiin kehittämään myös korkeamman tason ajattelutaitoja, on rakennettava sellaisia oppimisympäristöjä, joissa luovan ajattelun avulla yllettäisiin ymmärtämisen kehittymiseen. Usein opettajatkin ajattelevat, että matematiikassa tarvitaan ensisijaisesti logiikkaa ja ettei luovuudella ole paljonkaan tekemistä matematiikan oppimisen kanssa. Toisaalta jos tarkastelemme matemaatikkoa, joka luo uutta matematiikkaa, emme voi sivuuttaa luovuuden merkitystä hänen toimissaan. ’Avoimien tehtävien’ käyttäminen edistää matematiikanopetuksen kehittämistä tähän suuntaan

Open Tasks in Mathematics: Experiences with one Problem Field

In this paper, the task “Number Triangle” stands for problem fields. The problem field in question is planned by the author to be used in the Finnish comprehensive school. With its aid, our purpose is to show how open teaching acts in practice. The most important in these problem tasks is the way they are presented in teaching: A problem field should be offered to pupils little by little. And the continuation in the problem field depends always on pupils’ answers. The answers of problems are not given here, since they are not as important as pupils’ independent solving of problems. How far the teacher proceeds with the problem field in question depends on answers given by pupils.In this paper, the task “Number Triangle” stands for problem fields. The problem field in question is planned by the author to be used in the Finnish comprehensive school. With its aid, our purpose is to show how open teaching acts in practice. The most important in these problem tasks is the way they are presented in teaching: A problem field should be offered to pupils little by little. And the continuation in the problem field depends always on pupils’ answers. The answers of problems are not given here, since they are not as important as pupils’ independent solving of problems. How far the teacher proceeds with the problem field in question depends on answers given by pupils

Pupils' Drawings as a Research Tool in Mathematical Problem-Solving Lessons

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Open-ended Problems: A Method for an Educational Change

Abstract On the problems encountered with realizing educational change will be discussed. The concept "open-ended problem" with some examples will be deal with. The rest of the talk will describe different possibilities to use openended problems in mathematic class. The purpose of school education in each country is, more or less, to develop independent, self-initiative, critical thinking, motivated and many-sided skilled individuals who will manage in societal settings which they will counter later on in their life. The key question is what kind of school instruction is optimal for this goal

Opettajan toiminnan yhteys kolmasluokkalaisten onnistumiseen ongelmatehtävän ratkaisemisessa

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Learning density of numbers in elementary teacher education

Infinity is an important concept in mathematics, which students find difficult to learn. This paper will report Finnish elementary teacher students’ understanding of density at the beginning of their studies and the development of that understanding during a mathematics methods course. The results show that even quite limited teaching can initiate significant improvement. Moreover, students can make progress even if their initial level of performance is low. Yet, only 60 % of elementary education students reach satisfactory content knowledge and pedagogical content knowledge by the end of the course.Peer reviewe