We argue that people compare values in graphs with a "visual routine"--attending to data values in an ordered pattern over time. Do these visual routines exist to manage capacity limitations in how many values can be encoded at once, or do they actually affect the relations that are extracted? We measured eye movements while people…

In this article Dave Vernier describes how he turned the total eclipse on August 21, 2017 into a science, technology, engineering and mathematics (STEM) lesson by taking data. He asked teachers and former teachers to join in collecting data and to share it. The most frequently monitored parameters were illuminance (a measure of light brightness as…

The objective of this design case was to describe the development of an online graph-oriented tool to support the representation of collaborative argumentation for middle school students from a faculty expert's perspective and discuss the processes that were instrumental in developing the tool. Supported by the professional staff in the Digital…

This article advances the prerequisite network as a means to visualize the hidden structure in an academic curriculum. Networks have been used to represent a variety of complex systems ranging from social systems to biochemical pathways and protein interactions. Here, I treat the academic curriculum as a complex system with nodes representing…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

Mobile device accelerometers are a simple and easy way for students to collect accurate and detailed data on an amusement park ride. The resulting data can be graphed to assist in the creation of force diagrams to help students explain their physical sensations while on the ride. This type of activity can help students overcome some of the…

The purpose of the current study was to examine the degree to which instruction based on stimulus equivalence procedures could be used to teach single-subject design methodology to graduate-level professionals through a Web-based course management system known as Blackboard (see http://www.blackboard.com). Specifically, we used the stimulus…

The authors explore the role of comparison in improving graph fluency. The ability to use graphs fluently is crucial for STEM achievement, but graphs are challenging to interpret and produce because they often involve integration of multiple variables, continuous change in variables over time, and omission of certain details in order to highlight…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in reading. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

The "Measuring College and Career Readiness" report for each state represents a snapshot of the ACT-tested graduates in the class of 2009 and focuses on their readiness for college and careers. Designed to inform policymakers and practitioners about selected indicators of effectiveness, the report is not intended to be comprehensive but…

This volume is designed for teachers preparing to teach upper elementary students using the Comprehensive School Mathematics Program (CSMP) curriculum. It begins with a discussion of the importance of graph theory in mathematics and science. A mathematical development of graph-theoretic concepts and theorems is presented, followed by a set of…

This study attempted to determine the relationship between average daily attendance (ADA) and costs in 72 Illinois high schools having only one attendance center. Costs included administrative, instructional, and operational costs. The schools were divided into three populations, namely all those under 5,000 ADA, those less than 2,000 ADA, and…

The sixteen chapters of this book provide the core materials for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Compares Illinois' funding formula with a mathematical model for resource compensating formulas. Describes the variables used (including district enrollment, wealth, tax effort, and state guaranteed valuation). Uses graphs to illustrate varying equity effects of the formula for K-12, K-8, and high school districts, both statewide and in selected…