In this study we explored the effectiveness of individualizing instruction using a system that diagnosed students' knowledge gaps in pre-algebra and provided individualized instruction and practice. One hundred middle school students participated, and received either no instruction or individualized computer-based instruction. Diagnosis of…

A correlated science lesson is characterized as an integrated science lesson in that it may incorporate traditionally integrated activities and use math as a tool. However, a correlated math-science lesson also: (1) has the pertinent math and science objectives aligned with state standards; and (2) teaches parallel science and math ideas equally.…

This paper focuses on blended learning in mathematics I module in elementary calculus, at a University of Technology. A computer laboratory was used to create a learning environment that promoted interactive learning together with traditional teaching. The interactive learning was performed using projects to optimize the discovery and error…

This descriptive study was aimed at looking into how Primary 5 pupils solve pre-algebra problems concerning patterns and unknown quantities. Specifically, objectives of this study were to describe Primary 5 pupils' solution strategies, modes of representations and justifications in: (a) discovering, describing and using numerical and geometrical…

This article describes a joint effort between a mathematics educator and a middle school art teacher who wanted their students to experience first hand how construction works in the real world. It starts with students designing and building scale models for a large inflatable item in which they display their art and extends to building the…

This paper reports on a pilot study that examined the use of a science and technology curriculum based on robotics to increase the achievement scores of youth ages 9-11 in an after school program. The study examined and compared the pretest and posttest scores of youth in the robotics intervention with youth in a control group. The results…

Many people believe that the 1989 National Council for Teachers of Mathematics (NCTM) standards heralded the biggest mathematics reform of the 20th century. Despite all reform efforts, recent studies indicate that mathematics taught in primary and middle school mainly consists of basic arithmetic tasks that use memorization and repetition. Today…

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive…

Mathematical literacy is more than numeracy; it is an individual's capacity to identify and understand the role that mathematics plays in the world and to make well-founded judgments that use and engage mathematics to meet his or her future needs as a constructive, concerned, and reflective citizen (Programme for International Student Assessment…

There is much research that documents what many teachers know, that students struggle with many concepts in probability and statistics. This article presents two sample activities the authors use to help preservice teachers develop ideas about how they can use technology to promote their students' ability to understand mathematics and connect…

A first-year seminar general education course provides a good opportunity to search for mathematical topics associated with the popular culture represented in the course's required films and readings. We discuss mathematical connections to several books, including "Life of Pi" and "The Curious Incident of the Dog in the Night-Time," and to the…

Few would argue that students struggle with understanding and representing functions. There are many theories on why the abstraction of mathematical processes poses such cognitive difficulty, but so far functional programming is most often taught in a manner that discourages the use of visual intuition. The paper, by contrast, describes a…

The paper argues that a relationship between visualization and mathematical problem solving ability exists. Research suggests that visual imagery leads to increased understanding of mathematical concepts at both the primary and secondary levels. Mathematical potential is not necessarily "born." Potential can be created in the least likely students…

This volume has been assembled to show what can be learned about learning from large groups of children's responses to well-constructed assessment questions. The wide range of information gathered through the Basic Skills Testing Program (BSTP) has been divided into chapters that focus either on key aspects of mathematics or the major concerns of…