This article aims to problematize the role of programming in mathematics education. Problematizing involves acknowledging a deeper complexity in the understanding of programming than originally perceived and questioning its assumed value in mathematics education. This approach entails identifying its underlying paradigmatic assumptions in relation…

This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

In this article, the authors begin by considering symbolic literacy in mathematics. Next, they examine the origins of misuse of the equals sign by primary and junior secondary students, where "=" has taken on an operational meaning. They explain that in algebra, students need both the operational and relational meanings of the equals…

The Organization for Economic Cooperation and Development [OECD] is a global policy organization that includes the United States and about half of the Western Europe countries. It administers international comparison tests, called Programme for International Student Assessment (PISA), for 15 year-old students in Mathematics and other subjects. I…

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive…

Accurate and accessible expressions for the probability of having a matching birthday are obtained by using Stirling's formula and Taylor series. For interest, the results are applied to the planets of our solar system.

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

Teaching mathematics in real-word contexts is a strategy to make math relevant for undergraduate students. However, very little research exists on students' methods of integrating contextual and mathematical knowledge through writing. This study uses an interdisciplinary writing assignment to investigate the relationship between students' written…

This paper focuses on using technology to support mathematics instruction. Technologies such as computers and calculators are widely used in the teaching of mathematics. The educators advocate the use of these tools to reduce tiresome computations and tasks so that class time can be more effectively used for learning mathematics. The purpose of…

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…