Previously defined profiles for using a computer algebra system (CAS) describe prototypical uses of such a tool. When students use a dynamic geometry environment (DGE), however, new opportunities arise for transitions within and beyond the DGE. In this article, CAS profiles are used to explore students' uses of a DGE. Four cases of students, all…

Middle school students who need help understanding how to manipulate math expressions involving the negative sign have demonstrated difficulty learning pre-algebra content that prepares them for higher-level math courses. This study involved a multimedia intervention to improve student negative sign proficiency and math self-efficacy. The…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

This paper reports the factors that three Year 11 mathematics students identified as influencing their choice to use a Computer Algebra System (CAS) for solving selected problems, some of which were expected to be outside their pen-and-paper (p&p) range. In individual interviews, the students were presented with eleven algebra problems and…

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

We propose a framework for improving accuracy, fluency, and retention of basic skills essential for solving problems relevant to STEM introductory courses, and implement the framework for the case of basic vector math skills over several semesters in an introductory physics course. Using an iterative development process, the framework begins with…

Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

The math emporium model was first developed by Virginia Tech in 1999. In the emporium model students use computer-based learning resources, engage in active learning, and work toward mastery of concepts. This approach to teaching and learning mathematics was piloted in a rural STEM high school. The purpose of this experimental study was to compare…

Mathematics educators frequently extol the virtues of inquiry-based instruction to classroom teachers. Although research suggests that inquiry benefits learners by allowing them to make sense of the mathematics they encounter, particularly through discourse with peers, to assume that all (or even most) teachers successfully create and implement…

This article is the result of a comprehensive research study investigating the impact of computer-learning technology as well as the impact of a synergistic teaching approach (Keystone Method) on developmental mathematics classes at the college level. The study focused on mathematics skills of elementary and intermediate algebra students and…

This study attempted to determine the influence of prior knowledge in mathematics of students on learner-interface interactions in a learning-by-teaching intelligent tutoring system. One hundred thirty-nine high school students answered a pretest (i.e., the prior knowledge in mathematics) and a posttest. In between the pretest and posttest, they…

In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch…

This paper examines various cognitive strategies applied while CAS (Computer Algebra System) are used in undergraduate-level engineering mathematics teaching and learning. We posed some questions in relation to such CAS use: What kind of tools can CAS offer to enhance different cognitive strategies of students? How can the use of CAS widen the…

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…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…