This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

In this personal essay, I explain how my use of visual modelling has the capacity to broaden constructionism in five important ways. (1) It introduces new techniques for students to describe and document, in a personal way, what they are actually doing in modelling. (2) It introduces the big ideas of mathematical modelling and computational…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

As the authors are proponents for engineering education that is done well, they have provided an explanation of truss design using the Method of Joints that combines the application of practical hands-on learning with sound mathematical and scientific theory. The Method of Joints will allow students to design trusses to meet specified criteria…

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

Integrating the disciplines of mathematics and science is one way to place the calculations of volume and surface area into a real life context. The authors present an activity for middle-school students that aims to promote their learning of these key concepts in a personally meaningful way, whilst also developing inquiry and problem solving…

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

Optimizing the dimensions of a soda can is a classic problem that is frequently posed to freshman calculus students. However, if we only minimize the surface area subject to a fixed volume, the result is a can with a square edge-on profile, and this differs significantly from actual cans. By considering a more realistic model for the can that…

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

Our paper describes a solution we found to a still existing need to develop mathematical modeling courses for undergraduate biology majors. Some challenges of such courses are: (i) relatively limited exposure of biology students to higher-level mathematical and computational concepts; (ii) availability of texts that can give a flavor of how…

This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…