We consider the following hypothesis: whereas, the institutions in charge of the teaching of mathematics for future professional mathematicians (IPM, in short) share a "didactic paradigm" (strongly based on logical arguments), there does not seem to be such a thing in secondary mathematics education. In this work, we analyse the notion…

This article presents a synthesis of existing literature on ethnomodeling and the ways in which it extends mathematical modeling research in mathematics teacher education. We also call on the field to consider ways to connect and value culture and content in teaching mathematics. There have been increasing calls for integration of a culturally…

Functions provide powerful tools for describing change, but research has shown that students find difficulty in using functions to create and interpret models of changing phenomena. In this study, we drew on a models and modeling perspective to design an instructional approach to develop students' abilities to describe and interpret rates of…

This paper presents an alternate perspective for utilizing the action/process/object framework when discussing student conceptions of function. This perspective extends previously used frameworks by incorporating student conceptions that deal with functional properties and situational contexts, but differs in the analysis of the nature of the…

Presented is an example meant to enable students with a scant mathematical education to grasp the meaning of the limit of the binomial distribution. (Author/TG)

A two-year study that attempted to measure patterns of pupil attributions for success and failure in mathematics is reviewed. An attribution pattern variable (ATTPAT) was created to categorize individuals studied into three groups. The first group had an attribution pattern thought to lead to generalized low expectancies for success. Students…

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

A communication model suggests that in almost all cases where dissemination and utilization of knowledge has taken place, one or more of seven general factors can be identified as having been active in aiding the phenomena. The proposed factors are: linkage, structure, capacity, openess, reward, proximity, and synergy. In order to use this model…

A simple teaching model, designed to show rapidly which are the principal factors in population growth and how they are related, is presented. The apparatus described allows students to play several different active roles. (MP)

This paper is an attempt to contribute to the development of guiding principles for mathematics education by taking a frame of reference outside mathematics education itself. Examines the implications of long wave theory for mathematics education. (YP)

Describes and illustrates the structure of different versions of Mobius bands called prismatic rings or twisted prisms. Different forms are mentioned, such as the one bent into circular shapes and the toroidal polyhedrons. (GA)

Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…