Describes a covariational, rather than correspondence, approach to functions that emphasizes rate of change. Proposes three ways of understanding rate of change in relation to exponential functions. (Contains 41 references.) (Author/MKR)

The knowledge and mental processes called on in mathematics can be used to improve composition. Three desirable requirements of an analogy to be used in teaching writing are that it should bridge the art of writing and science, should be readily accessible to the mind of the average student, and should allow the student to employ an architectural…

An empirical analysis of the relationship between science reasoning skills and the amount of information acquired during science learning as predicted by a neuromathematical model of information processing is presented. Subjects were 93 adolescents (mean age of 15.4 years old) with a IQ range of 91-142. (Author/JN)

Working in groups of three, seventh-grade students were video taped solving an applied mathematical problem. Audio tapes were made of each group discussing their session. Analysis focused on the first stage of Noddings (1984) model of problem solving for school mathematics: Creation of a representation. Some factors identified as impeding…

Criticizes the current method of formalization in Italian schools and the use of tools of the mathematical method. Proposes a general three-stage formalization method which can used for physical quantities, the particular significance of certain quantities, and the description and interpretation of phenomena. (TW)

In multiple-choice items the response probability on an item may be viewed as the result of two distinct latent processes--a cognitive process to solve the problem, and another random process that leads to the choice of a certain alternative (the process of giving the actual response). An incomplete latent class model is formulated that describes…

Research was conducted investigating properties of skill in learning, in the domain of elementary algebra. Thinking-aloud protocols indicate that early knowledge of the subjects studied was fragmentary, rather than involving systematically flawed procedures. Computational models, developed to simulate observed errors, focused on the role of…

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…

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…