In order to study the conceptions, and their evolutions, of the tangent line to a curve an updating workshop which took place in Mexico was designed for upper secondary school teachers. This workshop was planned using the methodology of cooperative learning, scientific debate and auto reflection (ACODESA) and the conception-knowing-concept model…

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students' learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented…

Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory--the domains…

We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual…

This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…

This study addresses the measures chosen by students when selecting or constructing indices to properties of distributions of data. A series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students' conceptualizations of distribution over the course of 8 weeks of instruction.…

Frequently, in the US students' work with proofs is largely concentrated to the domain of high school geometry, thus providing students with a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof in mathematics, there is a lack of studies addressing how to…

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

This study investigates teachers' argumentation aiming to convince students about the invalidity of their mathematical claims in the context of calculus. 18 secondary school mathematics teachers were given three hypothetical scenarios of a student's proof that included an invalid algebraic claim. The teachers were asked to identify possible…

This paper highlights the value of student collaboration in doing mathematics, demonstrates how urban, middle-school students, working together, co-constructed justifications for their solutions, and shows that certain conditions are associated with the promotion of a culture of reasoning. It is documented that students collaboratively built…

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers' shoulders. This paper focuses on one secondary school teacher's reactions to students' suggested proofs and justifications in elementary number theory. To determine…

This study is part of a large research and development project aimed at observing, describing and analyzing the learning processes of two seventh grade classes during a yearlong beginning algebra course in a computer intensive environment (CIE). The environment includes carefully designed algebra learning materials with a functional approach, and…

The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie-Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school…

Non-attendance to meaning by students is a prevalent phenomenon in school mathematics. Our goal is to investigate features of instruction that might account for this phenomenon. Drawing on a case study of two high school algebra teachers, we cite episodes from the classroom to illustrate particular teaching actions that de-emphasize meaning. We…