This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

Data science is emerging as a field that is revolutionizing science and industries alike. Work across nearly all domains is becoming more data driven, affecting both the jobs that are available and the skills that are required. As more data and ways of analyzing them become available, more aspects of the economy, society, and daily life will…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

Discusses students' exploration of a particular rational function in the context of people waiting in line for service. The concepts of domain, range, and asymptotes are also developed in that context as is the effect of changes in input variables on function outputs. (Author/NB)

In this workshop, we will continue to reflect on a models and modeling perspective to understand how students and teachers learn and reason about real life situations encountered in a mathematics and science classroom. We will discuss the idea of a model as a conceptual system that is expressed by using external representational media, and that is…

Investigates issues of mathematics instruction of problems in blocks. Discusses the best way to construct mathematical problems with connections to one another as parts of a coherent whole and how to reflect on the types of connections that can arise between them. (Author/KHR)

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

Suggestions are provided for activities involving the construction of mathematical models to solve "real-life" problems. (SD)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

A programing language called DYNAMO, developed especially for writing simulation models, is promoted. Details of six, self-teaching curriculum packages recently developed for simulation-oriented instruction are provided. (MP)

Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

Graph theory is presented as a tool to instruct high school mathematics students. A variety of real world problems can be modeled which help students recognize the importance and difficulty of applying mathematics. (MP)

The similarity between two apparently dissimilar problems is explored. Pascal's triangle is involved. (SD)