The paper uses digital fabrication as a learning environment to demonstrate the importance of conceptual understanding of one-variable inequalities. These inequalities are hidden within two-variable inequalities used to construct geometric shapes the borders of which are the graphs of basic functions from the secondary mathematics curriculum. As…

The goal of this study is to explore and characterize the effects of using a dynamic graphing utility (DGU) on conceptual understanding and attitudes toward mathematics, measured by the responses of college algebra students to an attitude survey and concepts assessment. Two sections of college algebra taught by the primary researcher are included…

For many the phrase "teaching math online" evokes a vision of teaching and learning that is not based in physical classrooms. Perhaps teachers and students are even interacting asynchronously. In math classrooms in the United States, the increasing availability of devices (e.g. laptops, Chromebooks™, smartphones, and tablets) and…

In this paper we describe the design and implementation of a technology-active introductory first year university mathematics course. The design principles underpinning the course are presented. The results of the implementation show some areas where the technology-active approach has proven of value, as well as improvements that can be made for…

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…

Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results.…

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

There are opposing views about calculator use in school mathematics. This paper reports on a study that investigated the arithmetic proficiency of mathematics 1 university students and the effects of calculator usage at school level on their proficiency. The study followed a descriptive survey design involving the use of questionnaire and data…

An iPad® can be used to teach students to graph parabolas with ease and grasp vocabulary quickly. Parabolas come to life for students in this easily implemented activity described in this article. Teachers can use this tool in a fun and interactive way to not only address these graphing and vocabulary concepts but also introduce and explore…

Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students'…

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…

The purpose of this study was to determine if there was a significant difference in scores on the Mississippi Algebra I SATP2 when one group was allowed to use programs and the other group was not allowed to use programs on TI-84 calculators. An additional purpose of the study was also to determine if there was a significant difference in the…

Inclusion and differentiation--hallmarks of the current educational system--require a paradigm shift in the way that educators run their classrooms. This article enumerates the need for techno-kinesthetic, visually based activities and offers an example of a calculator-based programming activity that addresses that need. After discussing the use…

This paper explores the potential of mobile devices to support novel forms of mathematics classroom activity. In particular, I consider two salient aspects of contemporary practice with mobiles--networking/communication, and picture taking--and explore technology designs that might exploit their potential for supporting related forms of…

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…