The purpose of this article is to show how the philosophical theory of inferentialism can be used to understand students' conceptual development in the field of mathematics. Based on the works of philosophers such as Robert Brandom, an epistemological theory in mathematics education is presented that offers the opportunity to trace students'…

This article explains how high-stakes standardised tests are distorting primary school mathematics and failing to promote pupils' cognitive development. It argues for observation and journaling for both formative and summative assessment in order to recover an emphasis on reflective mathematical understanding and problem-solving.

This study gives insights into how Logo-like microworlds can affect cognitive development related to mathematics education of students with math learning difficulties. In particular, we analyse the case of a 15-year-old student with dyslexia and severe dyscalculia. Among the various cognitive aspects involved, here we delve into the development of…

Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Arbitrarily applicable derived relational responding has been argued by relational frame theorists to be a form of operant behavior. The present study examined this idea with 4 female participants, ages 4 to 5 years old, who could not perform a series of problem-solving tasks involving arbitrary more than and less than relations. In a combined…

Describes a student's unique perspective on the algorithm for finding equations of non-vertical lines given one point and the slope. Indicates that students had a better understanding of what they were doing. (KHR)

Many educators may or may not be familiar with the term constructivism, but probably recognize it as something to do with learning. The main tenet of constructivist learning is that people construct their own understanding of the world and in turn, their own knowledge. This ERIC Digest examines the constructivist view of learning and how it…

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…

Examples from some area tasks indicate that misconceptions about linear measurement can be carried over to area measurement; children will occasionally count points rather than length units or area units. (MP)

An example is used to illustrate the four levels: rote, observational, insightful, and formal. (MP)

Different types of understandings are presented as different facets of the development of the mental processes. (MP)

This paper is a reflection of the preparation of the Psychology of Mathematics Education Panel (PME26) that discuss the issue of "learning from learners." What it implies to be a learner is formulated in order to reflect upon the way teachers and/or researchers learn from learners. The idea of conceptualizing the notion of "learning from learners"…