This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…

In an age when reform is based on standards and instruction is based on research, this article gives practical advice for how mathematics teachers can analyze errors in student problems to create interventions that aid not only the individual's development, but the entire class's as well. By learning how to correct mathematics…

The aim of this study is to evaluate sixth-grade Turkish students' spatial visualization ability and to determine the strategies that students employ and the mistakes that they make while solving the problems requiring spatial reasoning. Therefore, the study examined the following achievements: visualizing different view images of…

Previous research has documented schemes and operations that undergird students' understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students' ways of operating on a whole-class scale. In this…

In this article, we present a case study of six Singaporean elementary school teachers working in a Lesson Study team that prepared them for problem solving instruction. The Lesson Study process included preparing, observing, and critiquing mathematics lessons in the context of solving fractions tasks. By conducting Lesson Study, we anticipated…

The transition from learner to teacher of mathematics is often a difficult one for prospective elementary teachers to negotiate. Learning to teach necessitates the opportunity to practice the discourse of teacher of mathematics. The undergraduate mathematics content classroom provides a setting for prospective teachers to practice the discourse of…

This paper describes a development and evaluation process used to create teacher education materials that help prepare middle and secondary mathematics teachers to teach data analysis and probability concepts with technology tools. One aspect of statistical reasoning needed for teaching is the ability to coordinate understandings of center and…

Undergraduate preservice teachers face many challenges implementing inquiry pedagogy in mathematics lessons. This study provides a step-by-step case analysis of an undergraduate preservice teacher's actions and responses while teaching an inquiry lesson during a summer math camp for grade 3-6 students conducted at a university. Stumbling blocks…

In this article I report on a study of the cognitive tools that research mathematicians employ when developing deep understandings of abstract mathematical definitions. I arrived at several conclusions about this process: Examples play a predominant role in understanding definitions. Equivalent reformulations of definitions enrich understanding.…

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…

Tasks regularly completed by elementary teachers reveal the mathematical nature of their work. However, preservice teachers demonstrate a lack of depth of mathematical thought. This study investigated the criteria preservice teachers intuitively used to evaluate algorithms. The intent was to use that knowledge as a foundation for modeling…

The use of technology to create multiple representations of a concept has become one of the significant instructional environments that the National Council of Teachers of Mathematics (2000) suggests strongly for mathematics teachers to consider. One example of this type of environment is educational software with linked multiple representations.…

This paper articulates a perspective on learning to discuss ways in which students develop personal sense and negotiate meaning in a middle school algebra context. Building on a sociocultural perspective that incorporates mental objects, learning is described as a mutually dependent process involving personal sense making and the public…

In a secondary school mathematics teaching methods course, a research team engaged 22 preservice secondary teachers (PSTs) in designing and posing tasks to algebra students through weekly letter writing. The goal of the tasks was for PSTs to elicit responses that would indicate student engagement in the mathematical processes described by NCTM…

This article discusses how a teacher can prepare the terrain for students to understand what it means to define a figure. Drawing on writings from mathematicians and mathematics educators on the role of definitions in mathematics, the authors argue that students develop a greater appreciation for the conciseness of a mathematical definition if…