The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Minimal guidance or maximal independence? How can teachers achieve that complex balance when teaching mathematics? In this pre-and post-test quasi-experimental research study, the authors explored the above broad questions in Grade 10 Financial Mathematics following guided discovery and mathematical modelling principles. Fifty-four (54) Grade 10…

Metamodeling ideas move beyond using a model to solve a problem to consider the nature and purpose of a model, such as reasoning about a model's empirical basis and understanding why and how a model might change or be replaced. Given that chemistry relies heavily on the use of models to describe particulate-level phenomena, developing…

Hypovolemic and orthostatic challenge can be simulated in humans by the application of lower body negative pressure (LBNP), because this perturbation leads to peripheral blood pooling and, consequently, central hypovolemia. The classic paper by Foux and colleagues clearly shows the effects of orthostasis simulated by LBNP on fluid shifts and…

As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

Invention and Productive Failure activities ask students to generate methods that capture the important properties of some given data (e.g., uncertainty) before being taught the expert solution. Invention and Productive Failure activities are a class of scientific inquiry activities in that students create, implement, and evaluate mathematical…

The author presents a method of producing a scatter diagram of data on two variables with Pearson product moment correlation of .50; he also provides a proof that the method will work for any number of data pairs. (SD)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)

A sophomore-level course in applications of mathematics was designed to introduce students to the diversity of situations in which mathematical models are used. The course precedes the study of the calculus, and is composed of a sequence of modules. A problem-solving approach is used. (SD)

An approach is illustrated that introduces selected models of addition and subtraction to students who have previously learned a model for either operation. (JT)

A series of simple games can be analyzed inductively to determine strategies. Students explore possibilities, hypothesize solutions, prove their solutions correct, and then generalize to more complex games. (SD)

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (SD)

In this report, the theoretical background and procedures for a study of concept learning are discussed. Several definitions of the term "concept" are analyzed, and the relations among concepts, chains of concepts, and hierarchies of concepts are explored. Conceptual learning is discussed from several points of view, and axiom systems for the…

In this volume, the results of a study of concept learning are presented. (The background for the study, and descriptions of the treatments--rote reception, rote discovery, conceptual reception, and conceptual discovery--are provided in Part 1.) Several hypotheses concerning the effectiveness of these treatments in learning concepts and on the…