This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…

The ability to flexibly solve problems is considered an important outcome for school mathematics and is the focus of this paper. The paper describes the impact of a three-week summer course for students who struggle with algebra. During the course, students regularly compared and contrasted worked examples of algebra problems in order to promote…

"Cognitive" technology tools have been described as "technologies that help transcend the limitation of the mind... in thinking, learning and problem solving activities" (Pea 1985, p. 168). These tools also respond to a user's commands and make mathematical actions more overtly apparent (Zbiek et al. 2007). By definition, these cognitive…

To help struggling seniors with the expectations of a high school precalculus course, their lack of confidence, and the "new" intimidation they feel in the classroom, the teacher discusses additional study skills necessary for performing well in the mathematics classroom. The author compares studying mathematics to the practice necessary to…

Research has shown that affordances of computers may be exploited in the design of mathematical tasks so as to provide interesting and challenging activities. At the same time, opportunities for learning mathematics may be constrained if the design of the task is not appropriate. A tool which allows teachers, researchers and task designers to…

The content standards reform movement and the accountability movement that have occurred over the past 10 to 20 years have received much attention among educational professionals and the general public. The federal government legislated accountability measures with the implementation of the No Child Left Behind Act of 2000. The Pennsylvania…

This article justifies classifying the TI-Nspire CAS Touchpad as a mobile device for grades 8-16 mathematics classrooms equipped with a Navigator system. The 2010 Horizon Report: K-12 indicates virtually every secondary school aged child has some sort of mobile device. Yet, many school policies ban the use of mobile devices, preventing students…

Typical middle and high school math curricula are template based, meaning the use of standardized methods to solve mathematical problems as examples on which to base other problem solving. Template based math instruction may help a student to pass tests; however, it is an insufficient way to develop mathematical thinking. Mathematicians are…

Background: Trigonometry is an area of mathematics that students believe to be particularly difficult and abstract compared with the other subjects of mathematics. Trigonometry is often introduced early in year 8 with most textbooks traditionally starting with naming sides of right-angled triangles. Students need to see and understand why their…

Adam, an 11th grader, was identified as gifted and accepted into a two week summer enrichment program. He signed up for "Geometry with Flash Programming." He had no prior programming experience but had a strong and healthy self-image as mathematics student. Although Adam had a positive attitude toward mathematics and saw himself as a successful…

Often the differences students see in science and mathematics classrooms are in perspective, approach, or application. Understanding those differences can help teachers to present a unified picture of mathematics and science to their students. In this article, the science teacher is given a glimpse of the treatment of topics shared by both…

This article presents a case study of one pre-service secondary school mathematics (PSSM) teacher taken from a larger study within an English-speaking Caribbean context. The major goal of the larger study was to investigate the experiences and perceptions of the PSSM teachers as they explored the graphing calculator and mathematics software in…

Learning about the area formulas provides many opportunities for students even at the beginning of junior secondary school to experience mathematical deduction. For example, in easy cases, students can put two triangles together to make a rectangle, and so deduce that the area of a triangle is half the area of a corresponding rectangle. They can…

This article presents practical perspectives on mathematics teacher change through results of collaborative research with two mathematics secondary school teachers in order to improve the teaching and learning of mathematics in Rwanda. The 2006 national mathematics curriculum reform stresses pedagogies that enhance problem-solving, critical…

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers' shoulders. This paper focuses on one secondary school teacher's reactions to students' suggested proofs and justifications in elementary number theory. To determine…