This article proposes an interconnected framework, "Ways of thinking in STEM-based Problem Solving," which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry,…

In this paper the mathematical structures of Bourbaki, the Piagetian developmental structures, and Polya's heuristic structures are compared. (SD)

A theory that there is a correspondence between Piagetian conservation operations and groups of symmetry transformations, and that these symmetry transformations may be used in explaining human problem solving behaviors, is developed in this paper. Current research in artificial intelligence is briefly reviewed, then details of the symmetry…

We explore the nature and consequences of teachers' problem solving through an example of a teacher's mathematical problem solving as it was occasioned by a student's mathematics. This illustration demonstrates the value of an interpretive framework that points to the mathematics of the classroom as a collective. Arising from this exploration is…

The author argues that teaching students to program a computer enhances their logical reasoning, problem solving skills, understanding of models, and ability to examine one's work critically. (SD)

This paper notes three objections to the use of hand-held calculators in schools: they would (1) block reasoning, (2) make individuals machine-dependent, and (3) broaden the gap between developed and underdeveloped nations. Each is addressed, with specific examples used to refute them. The belief is strongly expressed that calculators can aid in…

Mathematical skills and reasoning and their applications are considered as forming one of the basic and essential areas of knowledge and experience that should be available to all Australian children. This collection of essays explaining problem solving in mathematics as an organizing theme for current and future curriculum development is a means…

Abstracts of 36 research reports are provided. The reports were prepared by investigators for presentation at the 55th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education is covered. Nine reports deal with problem solving, eight are concerned with instructional methods, five…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…