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…

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument.…

Recent scores on state tests show that middle grades students have made some progress in meeting their state's academic standards over the last half-decade. Yet a closer look at state standards indicates that too many Southern Regional Education Board (SREB) states have set them too low. Quite a few states have taken steps to improve their…

The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently…

Mathematics teaching and learning are inherently complex practices, and reports suggest that American teachers are not as successful at teaching mathematics as the authors might hope. In this article, the authors explore how a seemingly ubiquitous new technology--the personal audio/video player--just might help teachers improve mathematics…

This paper describes a high school project where the mathematics teaching and learning software M@th Desktop (MD) based on the Computer Algebra System Mathematica was used for symbolical and numerical calculations and for visualisation. The mathematics teaching and learning software M@th Desktop 2.0 (MD) contains the modules Basics including tools…

"Algebra for everyone" has been a popular reform, though not commonly implemented and not fully evaluated. Through investigation, one might be able to determine whether courses deemed equivalent to a traditional college preparatory algebra course provide an equitable understanding of algebra concepts and skills, while controlling for…

A long-awaited federal study of reading and math software found no significant differences in standardized-test scores between students who used the technology in their classrooms and those who used other methods. The study compared classes overseen by teachers who used the technology-based products with those of other teachers who used different…

This paper examines the conflict in interest between teaching experiments and professional learning when they are combined in a research project. The study reported in this paper is the fourth year of a five year longitudinal study on the introduction of early algebraic concepts. The ten teacher participants are from five state primary schools in…

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…