A secretary has "n" letters and "n" addressed envelopes. Instead of matching each letter with the corresponding envelope, she inserts the letters in a random manner. What are the chances that every letter will be in the wrong envelope? In this article, the author presents a solution to this problem and discusses possible ways of placing the…

Teachers can use geometric patterns to promote students' understanding of functional relationships. In this article, the authors first look at a problem-solving process that supports the use of figural reasoning to explore and interpret geometric pattern tasks and generalize function rules. Second, the authors discuss a framework for…

The purpose of this research was to investigate student conceptions of the topic of asymptotes of rational functions and to understand the connections that students developed between the closely related notions of asymptotes, continuity, and limits. The participants of the study were university students taking Calculus 2 and were mostly freshmen. …

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic…

Introduction: This study aimed to investigate the errors made by 265 Form 2 male students in simplifying algebraic expressions. Method: A total of 265 Form 2 (Grade 7) male students were selected for this study. 10 high, medium and low ability students in each group were selected for the interviews. 40 items were administered to the respondents to…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…

In my experiences, students with Developmental Disability (DD) are routinely excluded from Algebra and other high-level mathematics courses. People with DD do not have the opportunity to learn Algebra, which may support the understanding and provide purpose for learning money and budgeting skills that, perhaps, could help them avoid financial…

Mathematics, in general, and algebra courses, in particular, have been categorized as "gatekeepers" for higher education, better jobs, and even citizenship. For many low-income and working adults, community college is the institution where they choose to develop their mathematics understanding so they can pursue their dreams.…

This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking…

This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…

There is a common opinion that mathematics is difficult for persons with Down syndrome, because of a weakness in numeracy and in abstract thinking. Since 1996, some single case studies have suggested that new opportunities in mathematics are possible for these students: some of them learned algebra and also learned to use equations in…

Graphing calculators facilitate learners' ability to build cognitive links between mathematical representations by providing quick access to multiple representations. This exploratory study investigated the effects of technology-enhanced instruction on student achievement, perceptions of technology use during instruction, problem-solving success,…

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian…