Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

The Center for Improved Engineering and Science Education (CIESE) at Stevens Institute of Technology helps mathematics teachers to integrate and implement engaging and innovative collaborative lessons into their curriculum for illustrating complex mathematics concepts. CIESE has developed online projects that incorporate complex mathematics…

In this article, the author discusses the combined artistry of third, fourth, and fifth graders as they illuminate a formerly dark corner of their school's entry plaza with a sparkling mosaic mural. The students worked in small groups to form the letters of the alphabet on 12" x 15" (30.5 x 38 cm) panels of cement board decorated with flat-backed…

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence--implicit, construction, similarity,…

The authors measure math skills with a broader set of explanatory variables than have been used in previous studies. To identify what math skills are important for student success in introductory microeconomics, they examine (1) the student's score on the mathematics portion of the ACT Assessment Test, (2) whether the student has taken calculus,…

This paper presents an assessment tool which can be used during the first weeks of calculus to measure students' visual thinking skills. We have developed and applied this instrument in classes for the last three years, tabulating results and interviewing students on a regular basis. We discuss our findings and provide hints to using the…

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…

The mathematical reasons that we cannot divide by zero are not easy for most students to understand; in fact, even those students who have more than just a basic understanding of algebraic concepts still have difficulty. This is most problematic for college students who are prospective teachers since they need to develop a deep understanding of…

While mathematics instruction for very young children needs to be age-appropriate in format and content, it also needs to prepare children conceptually for the kinds of mathematics learning that will be expected of them in future years. This perspective, informed by the work of Russian psychologists and educators on a measurement-based approach to…

National Numeracy Strategy (NNS) guidance appears to characterise mathematical language as a set of specialist words with unambiguous definitions, yet analysis of the classroom transcript suggests that at least some mathematical concepts cannot be captured by such definitions. This paper explores the notion of definition within mathematics,…

Extending B. L. Fredrickson's (1998) broaden-and-build theory of positive emotions and M. Losada's (1999) nonlinear dynamics model of team performance, the authors predict that a ratio of positive to negative affect at or above 2.9 will characterize individuals in flourishing mental health. Participants (N=188) completed an initial survey to…

Computer-based mathematical cognitive tools (MCTs) are a category of external aids intended to support and enhance learning and cognitive processes of learners. MCTs often contain interactive visual mathematical representations (VMRs), where VMRs are graphical representations that encode properties and relationships of mathematical concepts. In…

This paper critically examines the discrepancies among the pre-requisite fractional concepts assumed by a curricular unit on operations with fractions, the teacher's assumptions about those concepts and a particular student's understanding of fractions. The paper focuses on the case of one student (Tim) in the teacher's 6th grade class who was…

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…

This study investigated how understanding of the equal sign changes as a function of experience in mathematics and variations in context. Students with different levels of mathematics experience (elementary school, seventh grade, undergraduate, and graduate) were randomly assigned to view the equal sign in one of three contexts: (a) equal sign…