Patterns pervade our everyday life and are natural and familiar to children. Exciting new research in the field of Early Algebra describes the development of young children's algebraic thinking through the meaningful study of patterns. This paper contributes to this research by reporting on a case study of two primary schools in South Africa and…

We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…

Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

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…

Within the current test-centered educational reform movement, considerable emphasis is placed on using assessment results to make instructional decisions for individual students. Test scores are used to estimate a student's current level of skill, monitor his or her progress during instruction, and identify whether the student has gained the…

Now entering into its 20th year of data collection, Trends in International Mathematics and Science Study, (TIMSS) is an international assessment of mathematics and science at the fourth and eighth grades. TIMSS 2015 is the most recent in the TIMSS series, which began with the first assessments in 1995 and has continued every four years--1999,…

Twelve linear algebra students were interviewed about the concept of a Solution of a System of Equations. The interviews were analyzed using APOS tools, in particular the ideas of Action, Process, Object and Schema, and Genetic Decomposition. The analysis of the interviews revealed several misconceptions of Solution. The analysis also revealed…

A study of 29 students enrolled in Algebra II in an 8-week summer instructional program for minority students was conducted to reveal the skills that students have in translating among representational forms in mathematics problems where the representational form is varied in the given problem and in the required form of the answer. All students…

A major goal of this paper is to document changes that occurred in developmental mathematics classrooms in the community college setting when the graphing calculator (GC) Texas Instruments (TI)-83 was introduced to students. The six-week intervention was conducted during the section of Intermediate Algebra in the Community College Baltimore County…

This collection of four papers deals with problem solving and the measurement of problem solving. "Climbing Up the Competence Ladder: Some Thoughts on Meaningful Assessment of Problem-Solving Tasks in the Classroom" by K. C. Cheung uses the metaphor of a competence ladder to represent the problem-solving continuum with progressive…

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…