We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…

In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

Abstraction is a key adaptive mechanism of human cognition and an essential process in the personal construction of mathematical knowledge. Based on the notion of abstraction, this paper aims to conceptualise a framework for analysing textbooks. First, I search for the meaning of abstraction from a constructive-empirical and a dialectic…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Presents an exploratory study with expert university students to determine how students could reseal the rupture and restore a sense of unity between the figural and conceptual components of conic sections. Suggests certain tools of semiotic mediation which could be introduced to enable students to achieve the conceptual oversight that is possibly…

Describes the different types of reasoning in scientific research activity. Outlines three different but complementary ways to integrate history into the presentation of science. Considers and illustrates the close historical relationship between mathematics and physics. (Contains 50 references.) (ASK)

The origins of the emphasis on formal proof are discussed as well as more recent views. Factors in acceptance of a proof and the social process of acceptance by mathematicians are included. The impact of formal proof on the curriculum and implications for teaching are given. (DC)

Compared and contrasted are the concepts intuition and logic. The ideas of conceptual thought and algorithmic thought are discussed in terms of the world as a labyrinth, intuition and time, and the structure of knowledge. (KR)