This study is a longitudinal look at the different mathematics placement profiles of Black students and White students from late elementary school through 8th grade. Results revealed that Black students had reduced odds of being placed in algebra by the time they entered 8th grade even after controlling for performance in mathematics. An important…

This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…

The study aimed to investigate students' conceptions on the notion of absolute value and their abilities in applying the specific notion in routine and non-routine situations. A questionnaire was constructed and administered to 17-year-old students. Data were analysed using the hierarchical clustering of variables and the implicative method, while…

Educational video games provide an opportunity for students to interact with and explore complex representations of academic content and allow for the examination of problem-solving strategies and mistakes that can be difficult to capture in more traditional environments. However, data from such games are notoriously difficult to analyze. This…

This study examines the impact of Learning and Teaching Linear Functions (LTLF) professional development materials on teachers' mathematics understanding and teaching practices, as well as students' resulting algebra proficiency, learning, and achievement. Learning and Teaching Linear Functions are modular, video-based professional development…

This dissertation summarizes a study of the use of online homework with developmental mathematics students at the University of Alaska Fairbanks. To address the problem of high failure rates in developmental mathematics courses this study investigated the relationship between online homework and academic achievement, persistence, and attitude.…

In this article, the authors use the High School Longitudinal Study 2009 (HSLS:09) national database to analyze the relationships between algebra failure, subsequent performance, motivation, and college readiness. Students who failed eighth-grade Algebra I did not differ significantly in mathematics proficiency from those who passed lower-level…

We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…

This article investigates the coconstruction of student identity and engagement in the case of a 9th grader in a project-based algebra classroom that afforded students a great deal of autonomy. The focal student, Terrance, utilized classroom resources to serve both project-related and social functions as he interacted with his peers during…

This article aims to describe a type of formative assessment, MAP Classroom Challenge, which has been introduced in mathematics classrooms in recent years. MAP, or the Mathematics Assessment Project Classroom Challenges (formerly known as Formative Assessment Lessons), are developed by teams of math educators from the Shell Centre for Mathematical…

At two-year public community colleges, the 2011 three-year persistence rate was 23.9%. From 1988 to 2006, between 40% and 60% of all first-time community college students were referred to and enrolled in at least one developmental education course. More students begin college underprepared in mathematics than any other subject area, and only about…

Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential…

The Cantor subset of the unit interval [0, 1) is "large" in cardinality and also "large" algebraically, that is, the smallest subgroup of [0, 1) generated by the Cantor set (using addition mod 1 as the group operation) is the whole of [0, 1). In this paper, we show how to construct Cantor-like sets which are "large" in cardinality but "small"…

The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.