This paper reports the results of the experimentation of a didactic engineering for the treatment of the sense of variation of functions with pre-university students. The theoretical references of the investigation are grounded in the theory of didactic situations and the methodological elements in the didactic engineering, the use of…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

Action-Process-Object-Schema (APOS) Theory is applied to study student understanding of directional derivatives of functions of two variables. A conjecture of the main mental constructions that students may do in order to come to understand directional derivatives is proposed and is tested by conducting semi-structured interviews with 26 students…

Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

The mean can be interpreted as a fair-share value and as a balance point. Standards documents, including Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), suggest focusing on both interpretations. In this article, the authors propose a sequence of five activities to help students develop these understandings of the mean, and they…

The rapid growth of digital technology, including the worldwide adoption of mobile and embedded computers, places new demands on K-grade 12 educators and their students. Young people should have an opportunity to learn the technical knowledge of computer science (e.g., computer programming, mathematical logic, and discrete mathematics) in order to…

After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…

Calculus instruction is an important topic for high school and college teachers alike. A prime target for attention is integration, which, unfortunately, students too often treat as a rote procedure. Understanding the integral better will support students' application of their mathematical knowledge to science, technology, and engineering…

To understand multiple representations in algebra, students must be able to describe relationships through a variety of formats, such as graphs, tables, pictures, and equations. NCTM indicates that varied representations are "essential elements in supporting students' understanding of mathematical concepts and relationships" (NCTM…

Much of what is taught, especially in college, is designed to support other disciplines. To determine the current mathematical needs of twenty-three partner disciplines, the Mathematical Association of America (MAA) conducted the Curriculum Foundations Project (Ganter and Barker 2004; Ganter and Haver 2011), as discussed in the appendix…

There are urgent calls for more studies examining the impact of Professional Development (PD) programs on teachers' instructional practices. In this study, we analyzed how grades 5-9 mathematics teachers used graphs to teach mathematics at the start and end of a PD program. This topic is relevant because while many studies have investigated…

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

This article suggests an activity, called the epsilon-strip activity, as an instructional method for conceptualization of the rigorous definition of the limit of a sequence via visualization. The article also describes the learning objectives of each instructional step of the activity, and then provides detailed instructional methods to guide…