This report presents findings from a randomized control trial designed to inform the decisions of policymakers who are considering using online courses to provide access to Algebra I in grade 8. It focuses on students judged by their schools to be ready to take Algebra I in grade 8 but who attend schools that do not offer the course. The study…

The central purpose of this research was to assess student learning outcomes in the Algebra I credit recovery course offered at traditional schools in Louisiana and the Algebra I credit recovery course offered online by the Louisiana Virtual School (LVS). It was also conducted to assess the associations of gender, grade level, and socio-economic…

In this paper we demonstrate that "lesson study" may be adapted from its primary use as a professional development strategy for use as a research strategy, especially to identify principles of good lesson design. We report on a project undertaken in two Australian secondary schools where lesson study research was used to investigate the…

This causal-comparative study evaluated a 30-week chess instructional program implemented within special education math classes for students in the sixth, seventh, and eighth grades in a suburban middle school located in the southwestern United States. An analysis of covariance (ANCOVA) was utilized to compare the adjusted means for the comparison…

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4-8 (aged 9-14). In this paper, we assert that students' development of algebraic…

This paper describes student response, as indicated by an anonymous questionnaire, given by the author to her remedial algebra students at a community college that is part of a large East Coast open-admissions university. The course in question is aimed at the university-wide exit mathematics test necessary to graduation and college-level…

Given the importance of algebra, middle school mathematics teachers have a responsibility to help students transition from understanding arithmetic to understanding the algebra that will be necessary for success in high school. One method of transition involves introducing algebraic concepts in concrete ways using meaningful contexts. The series…

Two methods are presented for counting small "essentially different" sudoku puzzles using elementary group theory: one method (due to Jarvis and Russell) uses Burnside's counting formula, while the other employs an invariant property of sudoku puzzles. Ideas are included for incorporating this material into an introductory abstract algebra course.…

Lindsay E. Carlton has taught mathematics to students at different grades, with different ability levels. Now, the young educator's state wants to recognize her ability to work with one group in particular: 8th graders enrolled in introductory algebra. Carlton is one of many math educators across Arkansas who plan to acquire a new, unusual state…

In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

This causal-comparative study investigates the differences in the End of Course Examination Program (EOCEP) test scores of ninth grade students in English I and Algebra I/Math for the technologies, as influenced by schedules used in South Carolina public high schools during the 2005-2006 academic year. Framing this study is the previous…

Student transition from arithmetical understandings to algebraic reasoning is recognised as an important but complex process. An essential element of the transition is the development of a rich understanding of variables. Drawing on findings from a classroom-based study, this paper outlines the instructional tasks and pedagogical actions a teacher…

This qualitative research study involving 128 students in grades 4-6 was conducted to develop a framework for characterizing upper primary school students' algebraic thinking. Four levels of algebraic thinking were identified from student responses to tasks involving patterns and open number sentences. Level 1 students failed to understand the…

Vectors and vector addition are difficult concepts for many introductory physics students and traditional instruction does not usually sufficiently address these difficulties. Vectors play a major role in most topics in introductory physics and without a complete understanding of them many students are unable to make sense of the physics topics…

Linton Waters and Jayne Kranat ran a session on the Nuffield "Applying Mathematical Processes" (AMP) activities at BCME7 in Manchester in April this year. These 1-2 hour activities are revamps of some of the Graded Assessment in Mathematics (GAIM) resources, developed in the 1980s, and are freely available via the Nuffield website and…