In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…

In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…

This paper reports some recent developments in mathematical computer-aided assessment which employs computer algebra to evaluate students' work using the Internet. Technical and educational issues raised by this use of computer algebra are addressed. Working examples from core calculus and algebra which have been used with first year university…

The purpose of this exploratory study was to investigate the impact of writing during mathematical problem solving. The study involved an analysis of ninth grade algebra students' written and verbal descriptions of their mathematical problem solving processes. Through this comparison, a better understanding of the connection between problem…

Four groups (three engineering students in each group) were videotaped while constructing concept maps in Linear Algebra. There are two aims of this study. The first is to characterize the discourse in the groups by addressing the following research questions: Do the students communicate in an "effective" way? Do the students'…

Using multiple representations in mathematical contexts can enhance mathematical learning. Firstly how students use and conceptualize multiple representations in mathematics should be investigated. Because of this, it was aimed to examine how students use multiple representations in algebra word problems and what are the reasons behind their usage…

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to…

This paper describes writing assignments from a modern algebra course which were used to foster the development of proof-writing skills. Each assignment consists of proofs and mathematical work supposedly written by fictional characters, where the proofs are designed to illustrate common misconceptions, difficult points, and typical writing flaws.…

The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…

This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers.

Trouche's [Third Computer Algebra in Mathematics Education Symposiums, Reims, France, June 2003] presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing…

The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…

This evaluation was designed to compare student achievement scores of students enrolled in Saxon Algebra 1/2 classrooms (intervention group) with students enrolled in Scott-Foresman Mathematics classrooms (comparison group). Crawford and Raia conducted three analyses, but this study report focuses on the strongest analysis of the three and…

When culture is integrated into the mathematics classroom, it improves students' academic achievement, helps move classrooms towards an equitable learning environment, helps students to have positive beliefs about mathematics, and integrates mathematics with other disciplines. Moreover, if you observe today's kids, the use of video games in their…

According to the NCTM reform suggestions, when teachers are orchestrators of student interactions, students adopt a more active role in explaining and learning mathematics. This research, which mapped the nature and role of meaningful mathematical discourse, provides insights into discursive practices that lead to rich mathematical interactions.…