Search

In this article, the authors share a European perspective on teaching linear equations in Finland, Flanders, and Hungary. They begin with an assertion that it is through observation, in its broadest sense, and opportunities for participation, that people assimilate themselves into the culture in which they are raised. They discuss three approaches to mathematics teaching and reflect on the one characteristic common to these approaches. They compare that commonality with what they have seen in other European countries. This interesting commonality is that trainees have always begun their formal treatment with arithmetic equations; equations with the unknown on one side that they know their students can solve mentally.

In this article, the authors compare texts, times, technologies, and trails in mathematics lessons in five European countries (Flanders, England, Finland, Hungary and Spain). They start by discussing the provision and use of textbooks. After this they discuss lesson lengths and their impact on learners. They consider the extent of technology integration in project classrooms and close with a brief look at the ways in which teachers trail the content of their lessons. (Contains 2 tables and 2 notes.)

Finnish students' success on all three content domains of each of the four cycles of the OECD's Programme for International Student Assessment (PISA) has created much international interest. It has also prompted Finnish academics to offer systemic explanations typically linked to the structural qualities of Finnish schooling and teacher education. Less well-known has been the modest mathematics performance of Finnish grade 8 students on the two Trends in International Mathematics and Science Study (TIMSS) in which Finland has participated, which, when compared with its PISA successes, has created something of an enigma. In this paper, we attempt to shed light on this enigma through analyses of Finnish mathematics classroom practice that draw on two extant data sets-interviews with Finnish teacher educators and video-recordings of sequences of lessons taught on standard topics. Due to the international interest in Finnish PISA success, the analyses focus primarily on the resonance between classroom practice and the mathematical literacy component of the PISA assessment framework. The analyses indicate that Finnish mathematics didactics are more likely to explain the modest TIMSS achievements than PISA successes and allude to several factors thought to be unique to the Finns, which, unrelated to mathematics teaching practices, may be contributory to the repeated Finnish PISA successes. Some implications for policy-borrowing are discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived equations-related problems. The analyses showed all four sequences passing through four phases that we have called definition, activation, exposition and consolidation. However, within each phase were similarities and differences. For example, all three constructed their exposition around algebraic equations and, in so doing, addressed concerns relating to students’ procedural perspectives on the equals sign. All three teachers invoked the balance as an embodiment for teaching solution strategies to algebraic equations, confident that the failure of intuitive strategies necessitated a didactical intervention. Major differences lay in the extent to which the balance was sustained and teachers’ variable use of realistic word problems. [Copyright &y& Elsevier]