Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning.

TL;DR: Analysis of data collected during a three-week professional development programme organised for middle and high school teachers in Florida identified challenges participants face during workshops and evaluated the difficulty levels of GeoGebra tools.

TL;DR: In this paper, the authors investigate the relationship between students' notion of subsets of Cartesian three-dimensional space and the understanding of graphs of two-variable functions, and find that students' understanding can be related to the structure of their schema for R3 and to their flexibility in the use of different representations.

TL;DR: Some of the ways in which parts of the mathematics curriculum, classroom practice, and student learning may differ from the traditional approach are discussed.

TL;DR: A taxonomy of mathematics education can be found in this paper, where Bloom's Taxonomy of Mathematics Education is used to describe the main issues in mathematics education, including the following: "Actions, Processes, Projects, Schema (APOS) in Mathematics Education."

TL;DR: In this article, the authors discuss the experimental basis of the philosophy of legislation, the theory of necessity, the doctrine of necessity of necessity in public amateurs, secret bureaucrats, and the principle of large numbers.

TL;DR: This book discusses the need for a theory of cognitive evolution as an emergent phenomenon culture as evidence for cognitive structure and the transition from episodic to mimetic culture, which is the missing link in human cognition without language.

TL;DR: In this paper, the essence of the Environmental differences logic of cultured adults and the basis for elementary scientific Individual differences thought are provided, reflecting in their ability to reason adolescents hypothetically and independently on concrete states of affairs, these structures may be represented by reference to Logic combinatorial systems and to 4-groups.

TL;DR: In this article, the authors discuss the development of the number concept from intuition to algorithmizing and rationalizing, from the Algebraic Principle to the Global Organization of Algebra.