Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

When teaching transformations of functions, teachers typically have students vary the coefficients of equations and examine the resulting changes in the graph. This approach, however, may lead students to memorise rules related to transformations. Students need opportunities to think deeply about transformations beyond superficial observations…

Educational games provide a fun introduction to new material and a review of mathematical algorithms. Specifically, games can be designed to assist students in developing mathematical skills as an incidental consequence of the game-playing process. The programs presented in this article are adaptations of board games or television shows that…

This paper examines experimental and algorithmic contributions of advanced calculators (graphing and computer algebra system, CAS) in teaching the concept of "diagonalization," one of the key topics in Linear Algebra courses taught at the undergraduate level. Specifically, the proposed hypothesis of this study is to assess the effective…

The aim of the study was to investigate the effect of Microsoft Math Tool (graphical calculator) on students' achievement in the linear function. The study employed Quasi-experimental research design (Pre-test Post-test two group designs). A total of ninety-eight (98) students were selected for the study from two different Senior High Schools…

Archimedes, the famous Greek mathematician, lived from 287 BCE until approximately 212 BCE. He thought that the figure of two semi-circles on a straight line enclosed by a larger semi-circle resembled a shoemaker's knife. Archimedes called this figure an "arbelos" since arbelos is the Greek word for a shoemaker's knife. The author describes the…

This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

Learning mathematics is challenging. It requires discipline, logic, precision, perseverance, and accuracy. It can also be fun. When mathematics is set in a context that inspires students to want to solve interesting problems, students will have an intrinsic desire to learn the necessary skills to accomplish a specific goal. The game of Crypto! was…

This article presents a design experiment in which we explore new structures for classroom collaboration supported by a classroom network of handheld graphing calculators. We describe a design for small group investigations of linear functions and present findings from its implementation in three high school algebra classrooms. Our coding of the…

This study was designed to explore secondary mathematics teachers' beliefs about graphing calculators, their practices with the graphing calculators when teaching linear and quadratic functions, and the relationship between the teachers' beliefs and their practices. The study was conducted in two phases. In the first phase, 81 teachers…

Card sorting has the potential to provide opportunities for exploration of a variety of topics and levels. In a card-sorting task, each participant is presented with a set of cards--each of which depicts a relationship--and is asked to sort the cards into categories that make sense to him or her. The concept of function is critical to…

In this culture of instantaneous technology, students are familiar with immediate feedback. To maintain student engagement, it is vital for teachers to create similarly interactive experiences. Student-centered instruction is important in connecting students to key mathematical concepts. If the connection is not obvious, they may be unaware of…

Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…

The purpose of this study was to investigate the nature of preservice mathematics teachers' understanding of inequalities. The design of the study was a multi-case study of secondary mathematics education preservice teachers with a focus on their understanding and the lessons that they plan and implement. Data from individual interviews,…

This study highlights ways in which generative activities may be coupled with network-based technologies in the context of teacher preparation to enhance preservice teachers' cognizance of how their own experience as students provides a blueprint for the learning environments they may need to generate in their future classrooms. In this study, the…