Reactions to John Monaghan's "Computer Algebra, Instrumentation and the Anthropological Approach" focus on a variety of issues related to the ergonomic approach (instrumentation) and anthropological approach to mathematical activity and practice. These include uses of the term technique; several possibilities for integration of the two approaches;…

The authors of this paper examine the use of formative assessment as a tool to assist teachers of mathematics to become more mindful developers of curricula. They focus on instructional design that is based on careful examination of student answers to questions. Empirical studies have shown the effectiveness of formative assessment for students,…

Student enrollment in K-12 online learning programs showed a tenfold expansion in the years between 2002 and 2005. Despite increased implementation to fulfill critical local needs, there is very little evidence-based research available to inform education leaders' decisions relating to these initiatives. To address the important question of…

A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…

The author introduces some basic dynamic programming techniques, using examples, with the help of the computer algebra system "Maple". The emphasis is on building confidence and intuition for the solution of dynamic problems in economics. To integrate the material better, the same examples are used to introduce different techniques. One covers the…

Geometric pattern tasks can be a useful tool for developing students' capacities to reason algebraically and in helping establish classroom norms and practices at the beginning of the school year. In this article, the authors consider the mathematical and social purposes that pattern tasks can serve by examining one middle school's…

The "I CAN Learn[R] Pre-Algebra" and "Algebra" computerized curricula are designed to cover mathematics and problem-solving skills for ethnically diverse, inner-city students in grades 6-12. The curricula are designed to equip students with the skills they need to meet district, state, and national math objectives through an…

The purpose of this study was to construct and evaluate an instrument for determining student preparedness in College Algebra. A 73-item instrument covering prerequisite arithmetic and high school Algebra knowledge for College Algebra was constructed. The instrument was pilot-tested on a freshman population of 595 students. Results of reliability…

The purpose of this study is to identify factors that influence students' performance in the intermediate algebra classes at the college by analyzing parameters such as test scores, grades, attitude towards mathematics, time lapse between subsequent courses, placement, and teaching practices. This study will investigate the correlation of several…

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

This study investigates algebraic reasoning and self-regulation skills among elementary school teachers who participated in a professional development program either with IMPROVE metacognitive questioning (PD + Meta) or with no metacognitive guidance (PD). Sixty-four Israeli teachers participated in a 3-year program designed to enhance…

Student assessment is an integral component of classroom instruction. Assessment is intended to help teachers identify what students are able to do and what content and skills students must develop further. State tests play an important role in guiding instruction. However, for some students, the tests may lead to inaccurate conclusions about…

As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared. "The Misplaced Math Student: Lost in Eighth Grade Algebra," scheduled for release by the Brookings Institution…

This article examines findings on student perceptions of individual interventions based on the principles of universal design for learning (UDL). The examination includes a comparison of the reported perceptions of mainstreamed students with high incidence disabilities (i.e., learning disabilities, behavioral disorders, or other health impairments…

This article focuses on the ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the "Painted Cube" problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways…