The interpretation of single-case data requires systematic visual analysis across and within conditions. Graphs are a vital component for analyzing and communicating single-case design data and a necessary tool for applied researchers and practitioners. Several articles have been published with task analyses for graphing data with the new versions…

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were…

No person, place, or thing can capture the attention of a class of sixth graders like "man's best friend." To prompt students' interest in a series of lessons on proportional relationships, the authors brought in a unique teaching aid--a dog. A family dog was used to supply the measurements for scatter plots and variables so that students could…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

Chemistry students in Israel have two options for studying chemistry: basic or honors (advanced placement). For instruction in high school honors chemistry courses, we developed a module focusing on abstract topics in quantum mechanics: Chemistry--From the Nanoscale to Microelectronics. The module adopts a visual-conceptual approach, which…

As anyone who has taught or taken a statistics course knows, statistical calculations can be tedious and error-prone, with the details of a calculation sometimes distracting students from understanding the larger concepts. Traditional statistics courses typically use scientific calculators, which can relieve some of the tedium and errors but…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

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…

The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know…

Making time for science is a genuine complaint among classroom teachers. As a former fifth-grade teacher and district curriculum coordinator, the author's moment of truth came one morning while juggling classroom housekeeping tasks. Her students were set to work on their "bell work," which consisted of some type of assignment that required little…

One tool for enhancing students' work with data in the science classroom is the measure line. As a coteacher and curriculum developer for The Inquiry Project, the author has seen how measure lines--a number line in which the numbers refer to units of measure--help students not only represent data but also analyze it in ways that generate…

The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion…

One measure of the impact of a new idea in geography education is how well it is incorporated into teachers' everyday practice. "Spatial thinking" is not really a new idea in geography education; spatial analysis has long been one of its core traditions, but the use of the term is novel and only beginning to be widely used. By spatial thinking the…

The world is filled with information delivered through graphical representations--everything from voting trends to economic projections to health statistics. Whether comparing incomes of individuals by their level of education, tracking the rise and fall of state populations, or researching home ownership in different geographical areas, basic…