The purpose of this article is to describe the development of elementary school teachers' mathematical knowledge for teaching as they participated in a Modeling Instruction environment that placed heavy emphasis on improving their subject-matter knowledge as a basis for affecting the development of their pedagogical content knowledge. We…

Contributing to a growing body of research addressing secondary students' quantitative and covariational reasoning, the multiple case study reported in this article investigated secondary students' quantification of ratio and rate. This article reports results from a study investigating students' quantification of rate and ratio as…

We combine Peirce's rule, case, and result with Toulmin's data, claim, and warrant to differentiate between deductive, inductive, abductive, and analogical reasoning within collective argumentation. In this theoretical article, we illustrate these kinds of reasoning in episodes of collective argumentation using examples from one…

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…

This article examines pre-service secondary school teachers' responses to a learning situation that presented a student's struggle with determining the area of an irregular hexagon. Responses were analyzed in terms of participants' evoked concept images as related to their knowledge at the mathematical horizon, with attention paid…

International calls have been made for reasoning-and-proving to permeate school mathematics. It is important that efforts to heed this call are grounded in an understanding of the opportunities to reason-and-prove that already exist, especially in secondary-level geometry where reasoning-and-proving opportunities are prevalent but not thoroughly…

Despite extensive scholarship about the importance of teaching mathematics with multiple strategies in the elementary grades, there has been relatively little discussion of this practice in the middle and high school levels or in the context of introductory algebra. This article begins our exploration of this practice by addressing the following…

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…

Some problems exist at the intersection of statistics and probability, creating a dilemma in relation to the best approach to assist student understanding. Such is the case with problems presented in two-way tables representing conditional information. The difficulty can be confounded if the context within which the problem is set is one where…

Context personalization refers to matching instruction to students' out-of-school interests and experiences. Belief in the benefits of matching instruction to interests is widely held in the culture of schooling; however, little research has empirically examined how interest impacts performance and learning in secondary mathematics. Here we…

In this article I explore high school students' perspectives on working together in a mathematics class in which they spent a significant amount of time solving problems in small groups. The data included viewing session interviews with eight students in the class, where each student watched video clips of their own participation, explaining and…

Three experiments used multiple methods--open-ended assessments, multiple-choice questionnaires, and interviews--to investigate the hypothesis that the development of students' understanding of the concept of real variable in algebra may be influenced in fundamental ways by their initial concept of number, which seems to be organized around the…

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…

In this article we consider data arising from student-teacher-researcher interactions taking place in the context of an experimental teaching program making use of multiple modes of communication and representation to explore three-dimensional (3D) shape. As teachers/researchers attempted to support student use of a logo-like formal language for…

Transitions from middle school to high school mathematics programs can be problematic for students due to potential differences between instructional approaches and curriculum materials. Given the minimal research on how students experience such differences, we report on the experiences of two students as they moved out of an integrated,…