A goal of this study was to examine elementary preservice teachers' (PSTs) ability to contextualize and decontextualize fraction subtraction by asking them to write word problems to represent fraction subtraction expressions and to choose prewritten word problems to support given fraction subtraction expressions. Three themes emerged from the…

The perception of what a teacher says s/he does in the classroom may or may not match the reality of their actual teaching practice. This case study considers one second-grade teacher's instructional methods and pedagogical decisions when teaching number sense and her perception of what informed her teaching practice. This teacher supported…

The purpose of this study was to explore middle grade mathematics students' uses of scaffolding and its effectiveness in helping students solve non-routine problems. Students were given two different types of scaffolds to support their learning of sixth grade geometry concepts. First, students solved a math task by using a four square graphic…

As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate…

Decision making during instruction that is responsive to children's mathematical thinking is examined reflexively by the researcher in the context of teaching second graders. Focus is on exploring how the research base on learning informs teaching decisions that are oriented to building on children's sound conceptions. The development of…

During an informal, after-school, math program, a group of middle school students worked collaboratively on open-ended problems. The students co-constructed arguments, provided justifications for their solutions, and engaged in mathematical reasoning. This paper describes the specific teacher moves that promoted this phenomenon. The findings of…

One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of…

This mixed methods study describes the effects of a "minute contextual experience" on students' ability to solve a realistic assessment problem involving scale drawings and proportional reasoning. Minute contextual experience (MCE) is defined to be a brief encounter with a context in which aspects of the context are explored openly.…

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…

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 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 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…