While a significant amount of research has been devoted to exploring why university students struggle applying logic, limited work can be found on how students actually make sense of the notational and structural components used in association with logic. We adapt the theoretical framework of unitizing and reification, which have been effectively…

Conceptual understanding is a major aim of mathematics education, and concept map has been used in non-mathematics research to uncover the relations among concepts held by students. This article presents the results of using concept map to assess conceptual understanding of basic algebraic concepts held by a group of 48 grade 8 Chinese students.…

Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…

Students at a large urban community college enrolled in seven classes of an experimental remedial algebra programme, which integrated study skills instruction and collaborative problem solving. A control group of seven classes was taught in a traditional lecture format without study skills instruction. Student performance in the course was…

This article reports on an exploratory study designed to investigate the reasoning behind algebraists' selection of examples. Variation theory provided a lens to analyze their collections of examples. Our findings include the classes of examples of groups and rings that algebraists believe to be most pedagogically useful. Chief among their…

This research uses two measures of poverty, as well as mobility and selected education variables to study how their relationships vary across 543 Missouri high school districts. Using Missouri and U.S. Census American Community Survey (ACS) data, local R[superscript 2]'s from geographically weighted regressions are spatially mapped to demonstrate…

In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…

The notion of linearity is perhaps the most fundamental idea in algebraic thinking. It sets the transition to functions and culminates with the instantaneous rate of change in calculus. Despite its simplicity, this concept poses complexities to a considerable number of first semester college algebra students. The purpose of this observational…

In this paper, we analyze individual semi-clinical interviews conducted with one kindergarten and one first-grade student. We build on prior research to offer evidence, via excerpts from these interviews, that children as young as kindergarten have a powerful, intuitive sense of generality and indeed naturally draw upon it to reason through…

The quantitative correlational study evaluates and identifies patterns of teacher use of technology in instruction. The study involved evaluating the scores on the South Carolina End-of-Course (EOC) Algebra 1 test to explore trends and relationships between teachers' reported technology use and student achievement. Educators may be interested in…

In the 2014-2015 school year, Eastside Memorial High School implemented a High-Dosage Tutoring (HDT) Program that served approximately 156 Algebra I students. This report summarizes student outcomes, tutor, teacher, and student perceptions, and program logistics.

This quasi-treatment study, using a non-equivalent group design, explored how a set of animations related to various concepts in algebra impacted students' ability to learn as measured by changes in quiz and test scores. The concepts that were investigated were addition and subtraction of rational expressions, solving equations involving rational…

A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive…

This review protocol guides the review of research that informs the What Works Clearinghouse (WWC) "Assisting Students Struggling with Mathematics: Intervention in the Elementary and Middle School Grades" practice guide. The mathematics intervention practice guide will be an update of the original practice guide, "Assisting Students…

Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class…