As biological and socio-cultural beings, humans are encouraged and aspire to "see" not only what comes "within sight," but also what is not possible to see. Visualization is described as offering a method of seeing the unseen. These ideas are organized into sections that focus on seeing the unseen in data, seeing the unseen in…

This paper focuses on some cognitive and didactical phenomena that feature processes and products of pupils in grades 7-12 who learned mathematical proof within technological environments. The main issues in the analysis of students' performances consist of metaphors, deictics, mental times, narratives, functions of dragging, abductions, and…

Argues that the organization of cognitive structures for technical domains can be visualized as a network of connected thinkable models. Describes a taxonomy of models that has been developed and discusses the issue of how representations relate to human modes of perception and action. Contains 25 references. (DDR)

Interest in mathematics learning that focuses on understanding, mathematical reasoning, and meaning-making underscores the need to develop ways of analyzing classrooms that foster certain types of learning. The goal of this paper is to show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic…

This book explores what makes mathematics possible as well as what makes mathematics difficult. Included is a discussion of the definition of mathematics, mathematics in language, the meaning of numbers, calculating and measuring, notation, numbers in space, and the best ways to learn mathematics. Historical information and practical examples are…

This paper examines students' mathematics learning in a social context as two versions of an instructional sequence designed to facilitate students' development of a conceptual foundation for place-value numeration are enacted in two third grade classrooms. The same instructional sequence is used in each classroom with the regular classroom…