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• Levels of students' understanding on infinity

  317-337

  Markku S. Hannula

  Erkki Pehkonen

  Hanna Maijala

  Riitta Soro

  Views:

  24

  Here we report some results of a two-year study for grades 5-6 and 7-8 (during the academic years 2001-03). The study included a quantitative survey for approximately 150 Finnish mathematics classes out of which 10 classes were selected to a longitudinal part of the study. Additionally, 40 students from these classes participated also a qualitative study. This paper will focus on students' understanding of infinity and the development of that understanding. The results show that most of the students did not have a proper view of infinity but that the share of able students grew, as the students got older.

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

  25-43

  Maija Ahtee

  Erkki Pehkonen

  Anu Laine

  Liisa Näveri

  Markku S. Hannula

  Pirjo Tikkanen

  Views:

  37

  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.

• Evaluating admission procedures for teacher education in Finland

  231-243

  Raimo Kaasila

  Markku S. Hannula

  Anu Laine

  Erkki Pehkonen

  Views:

  34

  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.