This study analyses a standards-based textbook series to investigate how slope is presented across seven sequential textbooks in a secondary mathematics curriculum. Analysis of the expository content across the textbooks shows that slope is covered in all seven books, is frequently described as a "Constant Parameter" or…

In this study, we investigate a sample of in-service teachers' professional noticing of slope. The analysis focuses on which elements of students' statements about slope teachers attend to, and how teachers interpreted those elements. Study results suggest that teachers attended to the vocabulary and mathematical focus of students' statements.…

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which…

This study reviews how slope is developed in expository materials across a seven-textbook series. Slope development is analyzed using a framework of five slope components to describe which components are used and connected, and by investigating accompanying levels of covariational reasoning. Findings suggest that the series describes slope from…

In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of…

This study focuses on how students in different postsecondary mathematics courses perform on domain and range tasks regarding graphs of functions. Students often seem to focus on notable aspects of a graph and fail to see the graph in its entirety. Many students struggled with piecewise functions, especially those involving horizontal segments.…

This paper describes seven in-service teachers' interpretations of student statements about slope. The teachers interpreted sample student work, conjectured about student contributions, assessed the students' understanding, and positioned the students' statements in the mathematics curriculum. The teachers' responses provide insight into their…

To understand the mathematical concept of function, students must understand certain subconcepts, such as domain and range. Many researchers have studied students' understanding of functions, but no study has focused on how students come to understand the domain and range for the graphs of functions. In this study, we identified four common…

Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…

In this study, we build on previous work on conceptualizations of slope to suggest a framework of slope across the landscape of the mathematics curriculum. Data from multiple studies on students', teachers', and college instructors' conceptualizations of slope are revisited in light of theory on procedural versus conceptual understanding and…

This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…

A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…

What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…

Curricular policy documents generally communicate guidelines regarding the teaching of algebra. Those policy documents may not represent what teachers, currently teaching mathematics, consider significant. Teachers' views are more likely to provide information about what they emphasise in their mathematics classrooms. This paper reports on…

Since slope is a fundamental topic that is embedded throughout the U.S. secondary school curriculum, this study examined standards documents for all 50 states to determine how they address the concept of slope. The study used eleven conceptualizations of slope as categories to classify the material in the documents. The findings indicate that all…