Anu Laine

Promoting mathematical thinking in Finnish mathematics education

In this chapter, we outline some of the main characteristics of the mathematics education in the Finnish educational context. In Finland, at both primary and secondary school levels teachers are educated to be autonomous and reflective academic experts.

Promoting Mathematical Thinking

In this article, we outline some of the main characteristics of the mathematics education in the Finnish educational context. In Finland, teachers are educated to be autonomous and reflective academic experts at both primary and secondary school levels. This policy means there is a strong emphasis on teachers’ independence and autonomous responsibility and it also has many consequences for teaching mathematics.

Evaluating admission procedures for teacher education in Finland

In Finland the number of applicants for elementary teacher education is many times greater than the number of accepted persons. In this article we focus on the significance of the entrance examination procedures at three Finnish universities. Our findings imply that the differing admission procedures at the institutions yielded different student profiles. The test component “mathematics-science” used on the entrance examination in Turku was found to be a significant separating factor, but also the applicants’ mathematics achievement in upper secondary school seems to be an applicable criterion for developing admission procedures.

A Comparative Study of Finland and Chile: the Culture-Dependent Significance of the Individual and Interindividual Levels of the Mathematics-Related Affect

Mathematics-related affect is established regarding both individual and interindividual levels. However, the interaction between the levels has not been elaborated. Furthermore, it is known that people may draw either from intrinsic or extrinsic experiences to construct their identities depending on their cultural environment. Thus, affective individual and interindividual levels seem to interact with culture. In this study we focus on the significance of and the interaction between the individual and the interindividual levels of affect. This is done with respect to 2 different types of countries (Finland and Chile) to include cultural effect. We use questionnaire-based data and pupils’ drawings of their mathematics class to find out about their individual and interindividual experiences. By using mixed data, we are not only getting a wider picture of pupils’ affect but we can also avoid the most typical errors made in the cross-cultural comparisons as the pupils’ own voice is strengthened. The main finding in the study is that the 2 affective levels are not congruent and that the incongruence appears differently in different types of cultures.

Developing a method to determine teachers’ and pupils’ activities during a mathematics lesson

Third-graders from nineteen classrooms (N = 316) were asked to draw a picture on a mathematics lesson. Based on these drawings we have developed a data analysing method that allows us to find out how pupils present both their teacher’s and their classmates’ activities in their drawings. Two inventories were formed that contain, respectively, teachers’ and pupils’ activities during a mathematics lesson as seen in the pupils’ drawings. The first inventory contains 14 separate items organized into six groups that contain teacher activities like asking questions and giving feedback on mathematics. Ten of the items are related to teaching and the rest contain items like keeping order in addition to the teacher’s location in the classroom. Respectively, pupils’ activities are organized into five groups that contain altogether 22 items. These contain the activities of a single pupil, and also pupil-teacher and pupil-pupil discussions on mathematics.

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

Firstly, we describe a research project on problem-solving implemented in 2010–2013 in the Department of Teacher Education at the University of Helsinki. But we are especially concentrating on the results of one background study in the project—pupils’ drawings in a mathematics lesson. Pupils’ drawings seem to be a powerful method to gather information from small children. With the aid of drawings, one may investigate different topics in children’s thinking. Here, we focus on pupils’ and teachers’ communication, the emotional atmosphere of the class and the types of work used in class. The drawing studies offer three different channels to pupils’ conceptions in problem-solving.