The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant coefficients. The significance of this paper is two-fold. First, it represents an innovative alternative…

Since 1994 when the General Law of Education was issued, educational authorities have been claiming that Colombia has embarked on an "educational revolution" [""La revolucion educativa"" (n.d.). From the Colombian Ministry of Education website: http://www.mineducacion.gov.co. Retrieved 23 Nov 2004] where schools have…

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

We report on implementations of online homework systems at two moderately-sized state universities. These implementations were created with the intention of supporting student engagement outside of the classroom by mimicking the attempt-feedback-reattempt sequence of events which often occurs in a teacher's presence. Evidence is presented which…

Students in this study were enrolled in either an Introductory Algebra or Intermediate Algebra class taught through computer-mediated instruction or lecture. In the first year of the study, students were asked what they believed helped them learn mathematics in the instructional format in which they were enrolled. They were also asked what they…

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of…

In this article we suggest a method of evaluating learner expertise based on assessment of the content of working memory and the extent to which cognitive load has been reduced by knowledge retrieved from long-term memory. The method was tested in an experiment with an elementary algebra tutor using a yoked control design. In the learner-adapted…

Recent research suggests that humans and other animals have sophisticated abilities to extract both statistical dependencies and rule-based regularities from sequences. Most of this research stresses the flexibility and generality of such processes. Here the authors take up an equally important project, namely, to explore the limits of such…

Leaders in professional development have called for more learner-centered professional development opportunities for teachers. These approaches allow teachers to have some choice about the content and pedagogies on which they focus during professional development courses. This paper shares case studies of three participants from InterMath, a …

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level…

Mathematics majors' study of abstract algebra should provide these students with opportunities to connect what they are learning to their prior experiences with algebra in high school. This paper illustrates how such connections can be used to motivate the notion of binary operation and the axioms for a group.

Perimeter and area are important real-world concepts in their own right, and their relationship certainly is no less important. This relationship can be intuitively challenging for both children and adults. In this article, the author explores the relationship between perimeter and area with students from grades 4 to 6. The study of perimeter-area…

This article describes a unit of instruction designed to promote algebraic thinking in second graders. Students examined second- and fourth-grade students' ages and heights on a table and graph and described the patterns that they observed in the data.