Studies that consider the displays that students create to organize data are not common in the literature. This article compares fifth through eighth graders' difficulties with the creation of bar graphs using either raw data (Study 1, n = 155) or a provided table (Study 2, n = 152). Data in Study 1 showed statistical differences for the type…

We investigated prospects for reported sustainable adoption and sharing of an educational innovation through survey research including online questionnaires and telephone interviews. This investigation is part of the Scaling-Up SimCalc experimental program, which combines dynamic representational algebra software (SimCalc MathWorlds) with…

Despite the proliferation of mathematics standards internationally and despite general agreement on the importance of teaching for conceptual understanding, conceptual learning goals for many K-12 mathematics topics have not been well-articulated. This article presents a coherent set of five conceptual learning goals for a complex mathematical…

A "math congress" is a pedagogical approach in which students present their solutions from their mathematical work completed individually, in pairs, or in small groups, and share and defend their mathematical thinking. Mathematical artifacts presented during math congress remain on display as community records of practice. Math congress has four…

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both…

In this study we attempt to propose a new model of proportional reasoning based both on bibliographical and research data. This is impelled with the help of three written tests involving analogical, proportional, and non-proportional situations that were administered to pupils from grade 7 to 9. The results suggest the existence of a…

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an…