This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.

The subject matter presented in this article can be used in the classroom to enrich the learning experience of students taking a course that includes a unit on combinatorics, such as discrete mathematics, graph theory, or probability. In order to provide such students with the background needed to appreciate the significance of the generalization…

Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

This comment attempts to identify different "semiotic perspectives" proposed by the authors of this special issue according to the problems they discuss. These problems can be distinguished as problems concerning the representation of mathematical knowledge, the definition and objectivity of meaning, epistemological questions of learning and…

This article describes how third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children's responses to them are provided.

Teaching teachers to become observers and inquirers into mathematics will help change how they teach math to students. Essential to all professional development in mathematics is the idea that making sense of mathematics is key to learning. Just as learning to read calls for bringing meaning to the printed page, learning math calls for bringing…

The Country Data Project was developed for eighth-grade students of Milwaukee public schools to make them understand the importance of numbers by making them interpret the full descriptions of people of various countries by analyzing the numbers summarizing the population distribution of the respective country. The results prove that the project…

"Progress in Mathematics[C] 2006" is a new core curriculum for students in kindergarten through grade 6. "Progress in Mathematics[C] 2006" differs substantively from "Progress in Mathematics[C] 2000" in both content and assessment material. "Progress in Mathematics[C] 2006" uses a sequence of systematic…

In this narrative of teacher educator action research, the idea for and the context of the lesson emerged as a result of conversations between Shelly, a mathematics teacher educator, and Lisa, a quilter, about real-life mathematical problems related to Lisa's work as she created the templates for a reproduction quilt. The lesson was used with…

Simultaneous renewal in teacher education is based on the notion that improvement at 1 level requires improvement at all levels and that all stakeholders are responsible for such improvement. The authors discuss the creation and impact of a mathematics team as a vehicle for simultaneous renewal by using the team model for simultaneous renewal for…

This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and…

This nonexperimental, longitudinal field study examines the extent to which variation in observed classroom supports (quality of emotional and instructional interactions and amount of exposure to literacy and math activities) predicts trajectories of achievement in reading and math from 54 months to fifth grade. Growth mixture modeling detected…

This article discusses how math teachers at San Marcos High School turned to an online curriculum and in-class assessments to increase student achievement. Setting aside their 7-year-old textbooks, teachers filled the void largely with an online math curriculum, called Agile Mind, that comes equipped with an array of assessment tools. The idea was…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement…