We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…

The major results of this dissertation are theorems to the effect that certain classes of relational structures are not axiomatizable by universal sentences. Some of the particular classes considered are theories of measurement in the sense of the Scott-Suppes definition while others are theories of measurement according to a natural…

The approaches taken to psychological research are discussed. Studies are classified as axiomatic, classical, stochastic or statistical, or structural. The mathematical models used in each type of study are discussed. (SD)

The approximate nature of measurement is stressed, with examples given of elementary school mathematics problems which confuse reality with its mathematical model. Examples relating measurement to mathematical structure are given. (DT)

Addresses the role that so-called emergent models can play in the process of constituting formal mathematics. Describes how the use of these models became more explicated over time and developed into the notion of emergent models. Uses the design of instructional sequence for flexible mental strategies for addition and subtraction as an example…

Article gives three plans for learning stations on mathematics dealing with measurements. Exercises deal with weight, length, and comparative measurements. (GB)

A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

Discusses how the International System (SI) abbreviations for numerical factors designated as prefixes may be treated in quantity calculus as free-standing algebraic symbols. Illustrative examples are also presented. (HM)

Describes a classroom project involving the construction of a holiday mobile. Necessary supplies include a lightweight hanger, construction paper, string, scissors, protractors, compasses, and rulers. Concepts involved in the construction of the project include illustrating a chord, radius, diameter, shapes, metric measuring, circumference, area,…

Describes the process of mathematical modeling, an extensive teacher's guide, and a student modeling activity to improve the efficiency of soft-drink packaging. (KHR)

The primary objectives of this paper are pedagogical: to provide a reliable semi-subjective transformation procedure that might be used without difficulty by beginning students in factor analysis; to clarify and extend the existing knowledge of oblique transformations in general; and to provide a brief but meaningful explication of the general…

A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive…

Explains that primitive living structures furnish real-world problems that are solvable using mathematics and computer-modeling techniques. (KHR)

Discusses the parallels between Klein's position at the forefront of a movement to reform mathematics education and that of the National Council of Teachers of Mathematics' (NCTM) Standards. Draws a picture of Klein as an important historical figure who saw equal importance in studying pure mathematics, applying mathematics, and teaching…

Presents three teaching ideas: (1) a scoring rubric to assess students' ability to communicate attempts at solving homework problems; (2) a three-part measurement activity using trigonometry, maps, and compasses to locate hidden treasure; and (3) a demonstration of the effects of numerical coefficients on graphs of quadratic functions. (MDH)