The handling of mistakes in the mathematics classroom is an area in which only little research is done so far. In mathematics education there are, in fact, several investigations about students' mistakes from a diagnostic perspective, but hardly any studies on the question how teachers react in concrete mathematics lessons. In this article…

In this paper we focus on the role of signs in students' perceptive processes underpinning the generalization of numeric-geometric patterns. Based on a videotaped Grade 9 classroom group activity undertaken by three students and framed by a cultural-semiotic theoretical perspective, we carry out a microgenetic analysis of an elementary form of…

This is a qualitative study of 22 9th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues…

The increased use of group work in teaching and learning has seen an increased need for knowledge about assessment of group work. This report considers exploratory research where the SOLO Taxonomy, previously used to analyse the quality of individual responses, is applied to group responses. The responses were created as part of an activity…

This pilot study determined some typical cognitive-motivational profiles of Finnish lower secondary students dealing with fractions and decimal numbers. Forty seven students from grades 7-9 participated in a number concept test, where also the motivational aspects, such as self-efficacy, certainty and tolerance were measured. Four distinctively…

The aim of this research is to advance understanding of how mathematical knowledge functions in the proving in geometry. We focus on the rules whose mobilization is due rather to the mathematical knowledge at stake than to the proof. We observed students who are asked to solve construction problem and proving problem. The problems require to…

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

This study is a part of an ongoing research that attempts to explain the relationship between the teachers' instructional practices and students' learning in the context of functions. In this paper we report a case that shows significant differences between the achievements of two classes irrespective of the students' background training, the…

This paper presents the design and some results of a series of teaching experiments. The design was created to develop a model for everyday math lessons, that describes the conditions which foster or hinder the construction of new mathematical meanings. The development process includes the students' epistemic processes, their social interactions,…

Starting from a situated cognition perspective, this paper reports on the activity of 9th grade students who are interpreting the shape of a graph arising from the motion of a bouncing ball. In an unfamiliar context, informed by previous knowledge of similar experiments, the obstacle of understanding why the graph does not start from the origin is…

Equity and computer use for secondary mathematics learning was the focus of a three year study. In 2003, a survey was administered to a large sample of grade 7-10 students. Some of the survey items were aimed at determining home access to and ownership of computers, and students' attitudes to mathematics, computers, and computer use for…

Findings from a survey administered to large numbers of grade 7-10 students are presented in this paper. The focus is on the students' attitudes towards the use of computers for the learning of mathematics. Background information was also gathered which allowed the students' responses to be analysed by a range of equity factors--gender, ethnicity,…

The strengths and weaknesses of using ethnographic research to investigate equity in a study of a grade 9 class that used a dynamic geometry program with laptop computers will be presented. It will be argued that research approaches that involve "windows on practice" provide understanding of not only who is advantaged and disadvantaged in…

In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…

This paper explores the role of organising data in representing numerical data in an organised way--a skill which does not come naturally to most students. Grade 6 children were given a series of lessons on organising data and then representing the data graphically. It was found that after instruction, more students were able to reorganise the…