Pattern generalization and a focus on quantities are important aspects of algebraic reasoning. This article describes two different approaches to teaching and learning linear functions for middle school students. One group focused on patterns in number tables, and the other group worked primarily with real-world quantities. This article highlights…

This article analyzes the findings from an 18-section experiment studying the effect of homework-completion tutoring on community college students' remedial mathematics performance. The experiment involved 529 students registered for two remedial math courses: math skills and algebra. For each course, the experiment studied nine sections: three…

As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The PARCC Model Content Frameworks were developed through a…

This study examines the relationship between performance on Utah's English proficiency assessment and English language arts and mathematics content assessments by English language learner students and compares the performance of English language learner and non-English language learner students on the content assessments. Two research questions…

Edited by National Math Panel veteran Russell Gersten with contributions by all of the country's leading researchers on RTI and math, this cutting-edge text blends the existing evidence base with practical guidelines for RTI implementation. Current and future RTI coordinators, curriculum developers, math specialists, and department heads will get…

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

In order to improve the quality of technology instruction, the Career and Technical Education (CTE) Business Department in the Spokane Public School district has aligned its Computer Applications (CA) course to the district's ninth-grade Springboard (Language Arts) curriculum, Algebra I curriculum, and the Culminating Project (senior project)…

In educational practice, a test assembly problem is formulated as a system of inequalities induced by test specifications. Each solution to the system is a test, represented by a 0-1 vector, where each element corresponds to an item included (1) or not included (0) into the test. Therefore, the size of a 0-1 vector equals the number of items "n"…

This article presents situations involving perimeter, area, volume and mass, and the misconceptions often encountered with these measurements. The author suggests possible interventions that teachers can use to correct these misconceptions and help students to better understand these properties.

The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although…

The authors explore the importance of "range" and its relationship to continuously differentiable functions that have inverses when their graphs are reflected about lines other than y = x. Some open questions are posed for the reader. (Contains 5 figures.)

The basic rules of elementary algebra can often appear beyond the grasp of many students. Even though most subjects, including calculus, prove to be more difficult, it is the simple rules of algebra that continue to be the "thorn in the side" of many mathematics students. In this paper we present a result intended to help students achieve a…

We present a derivation for the coordinates of the centre of mass--or centre of gravity--of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the…

This article presents a problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. (Contains 1 figure.)