Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…

Making connections between various representations is important in mathematics. In this article, the authors discuss the numeric, algebraic, and graphical representations of sums of absolute values of linear functions. The initial explanations are accessible to all students who have experience graphing and who understand that absolute value simply…

A simple way is given to create residual plots that are words or pictures. Three illustrative examples are presented.

On a recent autumn afternoon at Harmony Leland Elementary in Mableton, Georgia, students in a fifth-grade science class investigated the essential process of classification--the act of putting things into groups according to some common characteristics or attributes. While they may have honed these skills earlier in the week by grouping their own…

Mathematical, scientific, and technological knowledge is critical for people in a 21st Century world that is dependent upon a global interconnectedness and a knowledge-based economy. This is the kind of knowledge that will power innovations and drive decision making in the years ahead. Schools are therefore being called upon to devise a…

An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…

Cell water relationships are important topics to be included in cell biology courses. Differences exist in the control of water relationships in plant cells relative to control in animal cells. One important reason for these differences is that turgor pressure is a consideration in plant cells. Diffusion and osmosis are the underlying factors…

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In designing the simulations, we discuss briefly three pedagogical considerations namely (1) a…

The developing field of academic analytics seeks to turn data from educational systems into actionable intelligence for the improvement of teaching and learning. This paper reports on the implementation of analytics in a new medical school with an integrated curriculum and clinical focus. Analytics addressed two challenges in the curriculum:…

When taking mathematics courses, students will sometimes ask their recurring question, "When will I ever use this in real life?" Educators are often unable to provide a direct connection between what they are teaching in the classroom and a real-life application. However, when such an opportunity does arise, they should seize it and…

Given the importance of algebra, middle school mathematics teachers have a responsibility to help students transition from understanding arithmetic to understanding the algebra that will be necessary for success in high school. One method of transition involves introducing algebraic concepts in concrete ways using meaningful contexts. The series…

Charts and graphs are ubiquitous in business documents, and most students in the author's business communication courses are well aware that they need to be able to create many different types of data representation. Most of them have had a great deal of experience working with spreadsheet applications, and they know how to manipulate data and…

The variety and complexity of potentially-related data resources available for querying--webpages, databases, data warehouses--has been growing ever more rapidly. There is a growing need to pose integrative queries "across" multiple such sources, exploiting foreign keys and other means of interlinking data to merge information from diverse…

When teaching mathematics with technology, the author does so in the belief that technology enables students to experience mathematical ideas in a way that might not otherwise be possible. However, teachers must be careful: Sometimes technology does not produce results in the way that they or their students expect. Rather than allowing unexpected…

This study examined the written work of students in the introductory calculus-based electricity and magnetism course at the University of Arkansas. The students' solutions to hourly exams were divided into a small set of countable features organized into three major categories, mathematics, language, and graphics. Each category was further divided…