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…

Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

The National Council of Teachers of Mathematics (NCTM) is committed to strengthening relations between research and practice and to the development of a coherent knowledge base that is usable in practice. The need to work toward connection and coherence is not unique to the field of mathematics education. Fields such as medicine, software…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…