Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function…

Graph representations underlie many modern computer applications, capturing the structure of such diverse networks as the Internet, personal associations, roads, sensors, and metabolic pathways. While the static structure of graphs is a well-explored field, a new emphasis is being placed on understanding and representing the way these networks…

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,…

Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers,…

If educators want to interest students in mathematics (and science), they must engage them in the lower forms of high school or even earlier (Fisher, 2012). So, teachers should always consider a topic's ability to interest students in the early years of instruction in high school and its topicality. Networks have come into prominence recently with…

This article describes how we used the context of mailing a package with seventh-grade students to explore and connect the different representations of step and linear functions. (Contains 2 tables and 7 figures.)

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

Introduces students to the study of dynamical systems through a number of learning activities that explore functions in general and linear and exponential functions in particular. Students use calculators to interpret graphs, find patterns in tables of data, and also use algebra. (DDR)

Describes the use of step-functions in modelling instruction. Classifies modelling into three categories: direct, analogical, and creative application. Provides and discusses modelling postal rates and other problems as examples. (YP)

This paper has two goals. The first is to present a model of the acquisition of a concept image of function. Theories describing the objectification of function are outlined through two different but related paths, and both stem from the conception of function as a process. The first path to objectification involves the generalization of the…

Presents 24 activities related to the theme of area to illustrate how algebra can empower students, not impede their progress. Activities use grid tools, manipulatives, computational tools, and paper-and-pencil tools to facilitate access, discourse, independence, and multiple representations. Well-chosen themes offer connections, motivation,…

The 9th International Conference on Educational Data Mining (EDM 2016) is held under the auspices of the International Educational Data Mining Society at the Sheraton Raleigh Hotel, in downtown Raleigh, North Carolina, in the USA. The conference, held June 29-July 2, 2016, follows the eight previous editions (Madrid 2015, London 2014, Memphis…

A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…