This article serves as an overview of activities and selected assessment findings of a three-year research study titled, Closing the Mathematics Achievement Gap of Native American Students Identified as Learning Disabled Project (CMAG Project). Methods used were problem-based, consistent with those of Cognitively Guided Instruction, and culturally…

Can prospective elementary teachers "unlearn" harmful algorithms used with fractions as they are invited to develop fraction number sense? This study examined the development of prospective elementary teachers' fraction number sense during an intermediate (grades 5-8) mathematics methods course. During this course, participants' were involved in a…

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…

This paper focuses on the first session of a professional development course revolving around the topic of mathematical statements and their appropriate proving methods. It analyzes the interactive development of the teachers' knowledge by focusing on the relation between the mathematical statements, the instructor, and the teachers. Different…

In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on pre-kindergarten and kindergarten students' ability to rote count, read two-digit numerals, model two-digit numbers, and identify the…

Multicriteria analysis constitutes a way to model decision processes, which allow the decision maker to assess the possible implications each course of action may entail. A multicriteria problem is chosen from the Programme for International Student Assessment 2003 Report and then extended to include questions involving a choice of preferences and…

This study qualitatively explored teachers' responses to doubling errors (e.g., 3/4 x 2 = 6/8) that typically reflect students' difficulties in understanding the "rule" for finding equivalent fractions (e.g., 3/4 x 2/2 = 6/8). Although all teachers claimed to teach for understanding in interviews, their responses varied in terms of effectiveness…

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…

Mathematical discussion allows for students to reflect upon math concepts and understand such concepts at a deeper level. This process of reflection requires a certain amount of internalization on the part of the student. This internalization is facilitated by meeting the needs of autonomy, competence, and relatedness as advocated by…

The central role that tasks play in student learning has become clearer in the last decade. As a result of calls for a structured design process, task design has become one of the main fields of investigation in mathematics education. Here, we propose five design considerations (deciding on the mathematical content, choosing the context, deciding…

Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…

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…

Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research…

This study identifies the kinds of problems teachers pose when they are asked to (a) generate problems from given information and (b) create new problems from ones given to them. To investigate teachers' problem posting, preservice and inservice teachers completed background questionnaires and four problem-posing instruments. Based on previous…