This paper investigates the possible influence of attitude on seven Year 11 students' use of a Computer Algebra System (CAS) during a class activity where students could choose to use CAS or pen-and-paper in solving a range of problems. Investigation of anxiety, confidence, liking and usefulness through a survey and interview revealed that these…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

In this paper we analyze and discuss students' performance in a CAS environment related to the simplification of rational expressions. Results indicate that if students have more initial paper-and-pencil techniques, the CAS environment spurs them to deeper theoretical reflections than for students who have fewer techniques. [For the complete…

Determining how to provide good tutoring functions is an important research direction of intelligent tutoring systems. In this study, the authors develop an intelligent tutoring system with good tutoring functions, called "FUDAOWANG." The research domain that FUDAOWANG treats is junior middle school mathematics, which belongs to the objective…

Transfer is typically thought of as requiring individuals to "see" what is the same in the deep structure between a new target problem and a previously encountered source problem, even though the surface features may be dissimilar. We propose that experts can "see" the deep structure by considering the first-order interactions…

Has technology revolutionised the mathematics classroom, or is it still a device waiting to be exploited for the benefit of the learner? There are applets that will enable the user to solve complex equations at the push of a button. So, does this jeopardise other methods, make other methods redundant, or even diminish other methods in the mind of…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

Mathematics textbooks play a critical role in shaping instruction and the ways students and teachers use strategies. Math textbooks are written using language patterns that differ from the narrative patterns many elementary students typically read (Fang & Schleppegrell, 2010; Moje et al., 2012). Mathematical texts rely on a large amount of…

This article investigates the algebraic non-routine problem-solving skills of grade 12 learners of a high-achieving school in northern Namibia. The school was selected on the basis of its outstanding results and sound management style. The study followed a descriptive survey design that involved a written test to examine learners' problem-solving…

Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned…

This article reports on the results of research, the objective of which was to document and analyze the manner in which students relate different representations when solving problems. A total of 20 students attending their first year of university studies took part in the study. In order to design the problem, the underlying information in each…

In this article, the author explores her personal views on mathematics and how she solves problems. She experiences some personal revelations while attending a "Mathsjam". Organised by some of the more prominent names in the popularisation of mathematics, "Mathsjam" was billed as the UK's first Gathering for Gardner, an event…

Many optimization problems can be solved without resorting to calculus. This article develops a new variational method for optimization that relies on inequalities. The method is illustrated by four examples, the last of which provides a completely algebraic solution to the problem of minimizing the time it takes a dog to retrieve a thrown ball,…