This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

In this article, the authors explore the reasons why some mathematical functions are referred to as odd, and others as even. They start by recalling the definitions of both functions. Simply stated, the value of an even function is the same for a number and its opposite, whereas the value of an odd function changes for the opposite number when the…

Kinesthetic learning, one of the VAK learning styles, is now also being adapted by different gaming consoles and platforms. This paper presents Salapiggy, a two-part kinesthetic educational Sifteo game that has both a tutorial on money and sorting game. It is localized in the Philippines and uses Filipino as the User Interface Language and the…

These days, multiplying two numbers together is a breeze. One just enters the two numbers into one's calculator, press a button, and there is the answer! It never used to be this easy. Generations of students struggled with tables of logarithms, and thought it was a miracle when the slide rule first appeared. In this article, the author discusses…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This guide is linked to a science curriculum and was designed for use by those involved with early childhood education. The goal of this document is to enable caregivers and teachers to use the curriculum in a more varied, stimulating, and developmentally appropriate way. Topics discussed include student attitudes toward mathematics, parent…

This middle school mathematics unit is organized around themes relating to sports activities in the Boston (Massachusetts) region and has a content focus on decimals and percents. The activities follow a story line which features a sports reporter (the student) and his/her assignments and adventures. Each activity begins with a headline, defines a…

This guide describes 20 learning activities that can be used with elementary school students on the topic of probability and statistics. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in…

This guide is designed to help classroom teachers implement the Alabama Course of Study: Mathematics K-12. It is inclusive also of the objectives tested by the Stanford Achievement Tests and the Alabama Basic Competency Tests. One characteristic of the curriculum guide is that it clearly states what students should learn in each grade level. These…

This guide describes 47 number and numeration learning activities that can be used with elementary school students. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in developing further…