This article addresses an important problem of graphing quantitative data: should one include zero on the scale showing magnitude? Based on a real time series example, the problem is discussed and some recommendations are proposed.

Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key "stumbling blocks" for students as they attempt to make this transition? How do differences in faculty expectations for students…

This article presents a study done in an elementary mathematics methods course that focused on the transition of novice teachers' epistemological stances: former elementary student, university student, and teacher stances. In order to help them develop the teacher stance, we designed a three-phase activity, where two phases took place inside…

Linear board games have shown great promise as tools to teach whole number concepts (Ramani & Siegler, 2008), but little is known about their utility for supporting negative integer concepts. This study sought to extend the use of linear board games to teach integer concepts. Forty-eight first graders (ages 6-7) counted along an integer board…

In this paper, we explore an approach to understanding how multimodality works in a community of practice. Using a social learning framework, we show how a community of practice, involving a pair of high school students, engaged in perceptual, bodily, and imaginary experiences while discussing about calculus concepts in a dynamic geometry…

Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study…

The purpose of this study was to examine children's musical and mathematical behaviors as they participated in an interdisciplinary pre-K curriculum. Research questions were: 1. What connections--if any--do young children make between music learning and mathematics learning? 2. Is there a relationship between young children's emergent rhythm…

Research shows that children of different backgrounds and cultures learn and perform differently in mathematics despite similar intelligence levels and mathematics instruction (Alvarez & Bali, 2004). Ethnomathematics strives to explore and explain such phenomena in terms of the complex role culture plays in one's background experiences and…

As highlighted by the National Math Panel Report (2008), consistent results from laboratory studies have demonstrated that interleaving worked examples with problems to solve improves learning for novices. The purpose of this work is to create materials and tests that can be used flexibly in classrooms and which employ worked examples interleaved…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

This article describes a project that focuses on numeracy in secondary school mathematics. During the course of the project a teacher had the chance to develop and trial new tasks and styles of teaching and learning numeracy. She became increasingly comfortable with using more extended tasks for learning mathematics. However, she believes that it…

In underscoring the affective elements of mathematics experience, we work with contemporary readings of the work of Spinoza on the politics of affect, to understand what is included in the cognitive repertoire of the Subject. We draw on those resources to tell a pedagogical tale about the relation between cognition and affect in settings of…

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

Developmentally, middle school students progress from being concrete thinkers and learners to abstract thinkers. Traditional middle school mathematics instruction introduces a curriculum that is intuitive and taught within a natural trajectory of the content. However, with this traditional approach, students may miss out on being exposed to…

Values education is crucial since it is one of the factors to reach success in education in broader sense and in mathematics education in particular sense. It is also important for educating next generations of societies. However, previous research showed that expected importance for values education was not given in Mathematics courses. In a few…