The cognitive significance of the body has become one of the major topics in current psychology. However, it is our contention that claims about the embodied nature of thinking must come to terms with the problem of the relationship between the body as a locus for the constitution of students' subjective mathematical meanings and the historical…

Within the large range of potential theoretical perspectives on fractions, this paper considers one particular interpretation: fractions' duality as process and object. By considering the number-fractionbar-number composite symbol as simultaneously representing division and rational, some process-object theories imply that fraction-as-process and…

The paper considers a teaching experiment carried out with secondary school students (9th grade), who face modelling tasks to approach some basic concepts of algebra and early calculus. The focus is on an embodied analysis of students' cognitive processes. The analysis highlights the use of metaphors as a means of sharing knowledge. (Contains 2…

This paper describes how a researcher developed task and four different data collection instruments provide evidence for the identification of various affordances of a technology-rich teaching and learning environment (TRTLE) that were perceived and/or enacted by Year 9 students in their solution of a linear function task utilising a graphing…

This paper explores levels of perceived parental influence on mathematics learning among over 700 students in China and Australia. Students in China had stronger perceived parental influences than students in Australia, and while students in China, Chinese speaking students in Australia, and other language speaking students in Australia…

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…