Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Algebra is often described as the gateway to higher mathematics (Carpenter, Franke, & Levi, 2003; Kaput, 2008; Kaput & Blanton, 2001; Mason, 2008). Unfortunately, many students do not navigate this gateway successfully. Kaput (2008) and Mason (2008) suggested that this is due in part to the abrupt switch from arithmetic to algebra that…

Data from a cough challenge study are displayed with dot charts to demonstrate the importance of graphs in understanding data, principles of graph construction and visual perception. The data are available for use in the classroom.

Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

This article explores the use of children's photography as a method for conducting mathematics education research with young children. Collected as part of a study focusing on the experiences with measurement children have at the start of schooling, the photographs presented here were taken by children aged five and six years, from two Australian…

Research has shown that students should be given the opportunity to explore mathematical concepts by building on their knowledge and focusing on mathematical reasoning. When students represent ideas, make conjectures, collaborate with others, and give explanations and arguments, they are using mathematical reasoning (NCTM 2000). Certain teaching…

Teachers are continually confronted with meeting the needs of all students and preparing them to be successful on state end-of-course assessments while changing or evolving to be more of a facilitator of student-centered. Lessons are to be relevant for the students, engaging them so they are active participants in their learning. However, many…

Parents can positively impact children's learning of mathematics. To productively engage families in the learning process, teachers must support such interpersonal relationships. The author describes the investigative work of a group of teacher candidates as they sought to attain such understanding. Eighteen preservice teachers, who were…

Background: Robot-math is a term used to describe mathematics instruction centered on engineering, particularly robotics. This type of instruction seeks first to make the mathematics skills useful for robotics-centered challenges, and then to help students extend (transfer) those skills. A robot-math intervention was designed to target the…

There is a body of research around the uptake of digital technologies in secondary schools, and a growing body of research specifically designed to investigate the use of one-to-one laptop programs. However this research focused on the initial uptake of the digital technology or initial implementation of a one-to-one (1:1) laptop policy. Given the…

This paper describes a program of research aimed at better understanding mathematics conceptual learning. Rather than studying the products of learning (conceptual steps), it focuses on the process (mechanism) of students' learning -- learning that occurs through their mathematical activity in the context of a sequence of mathematical tasks.…

In this note, we introduce M-bonomial coefficients or (M-bonacci binomial coefficients). These are similar to the binomial and the Fibonomial (or Fibonacci-binomial) coefficients and can be displayed in a triangle similar to Pascal's triangle from which some identities become obvious.

As an experienced educator of some 25 years, the author can appreciate the flexibility that emergent curriculum affords. The author has been able to integrate her background in fine art and love for storytelling easily into her day-to-day work. But sometimes projects take off in unexpected directions and when an exploration of boxes evolved into…

Every two years in the United States, districts in each state elect representatives to the U.S. House of Representatives. The district boundaries are not permanent; rather, they are redrawn every ten years in a process known as redistricting. Mathematics is useful in understanding this important and often contentious process. Redistricting is a…

This book provides targeted mathematics instruction for every child. This book combines formative assessment with practical activities to differentiate the elementary classroom. The formative assessments include student work samples at varying levels. The authors: (1) Illustrate the distinction between a "traditional" assessment and an "enhanced"…