This study examines the research on middle school students' understanding of variables and explores preservice elementary and middle school teachers' knowledge of variables. According to research studies, middle school students have limited understanding of variables. Many studies have examined the performance of middle school students…

This study took a broad view of generalization, exploring how classroom instruction within opportunities of implicit generalization may be related to students' abilities to generalize. From an integrated perspective of generalization and problem solving, we investigated twelve lessons of two middle level teachers based on three pattern-based…

In this qualitative study, we explored how oral interviews can inform instructors about students' understanding of abstract algebra and their ability to construct a proof in this setting. Our findings indicate that some students had a good understanding of the ideas needed for a subgroup proof, but could not write a coherent proof. On the other…

The paper describes a study that examined the impact of two teaching approaches "focus on correctness" and "discuss errors" on secondary students' solutions to algebraic inequalities. Two groups of 10th graders were taught by two experienced teachers, Corry and Era, who followed their different didactical beliefs about the use of errors in…

This study focuses on the types of models created by students during algebraic pattern finding tasks. Attention is also given to the change in models over time. This is an important area of study because a closer look is needed to better understand the models created during mathematical activity, especially in the elementary classroom. It is…

This paper gives results of a study on a Personal Response System (PRS). Three sections of college algebra are compared; one section used PRS and PowerPoint, one used PowerPoint, and one was considered a control. Students were given a pretest and posttest with a retired version of a mathematics ACT test, and all students gained an average of one…

In this paper we consider important factors influencing different curricular approaches to the study of numerically and geometrically defined pattern-type problems in the middle school curriculum. Our analysis involves the consideration of recommendations from national standards documents and their influences on state framework documents…

In this qualitative study, we initiate a discussion as to why instructors should implement numerous assessments into their mathematics courses. We describe the purpose and structure of formative and summative assessments implemented in an undergraduate two-semester sequence of abstract algebra. The evaluations included homework, exams, projects,…

This study investigated the influence of regular structured writing about problem solving on college algebra students' locus of control, flexibility of articulation, and accuracy in responding to written problem tasks. The writing assignments, acronym PSOLVE, provided students a framework for expressing their thoughts about mathematical actions,…