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…

Every day, students collect, organize, and analyze data to make decisions. In this data-driven world, people need to assess how much trust they can place in summary statistics. The results of every survey and the safety of every drug that undergoes a clinical trial depend on the correct application of appropriate statistics. Recognizing the…

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

Data visualization is the term used to describe the methods and technologies used to allow the exploration and communication of quantitative information graphically. Data visualization is a rapidly growing and evolving discipline, and visualizations are widely used to cover politics. Yet, while popular and scholarly publications widely use…

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

The "Toolbox" column features content adapted from ReadWriteThink.org lesson plans and provides practical tools for classroom teachers. This issue's column features a lesson plan adapted from "Graphing Plot and Character in a Novel" by Lisa Storm Fink and "Bio-graph: Graphing Life Events" by Susan Spangler. Students retell biographic events…

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…

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

The written lab report--a concise and accurate accounting of an experiment, including a summary of the procedure, presentation of the results, reasoned analysis, and thoughtful explanation--is essential to the scientific endeavor and a key expression and product of inquiry. Generally, however, students and teachers dislike these reports, the…

Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing…

In this paper, we present materials and teaching ideas utilizing multiple representations in the contexts of kinematics and the force concept. These ideas and materials are substantiated by evidence and can be readily used in teaching with no special training. In addition, we briefly discuss two multiple-choice tests based on physics education…

This teaching brief describes a 30-minute game where student groups compete in-class in an introductory time-series forecasting exercise. The students are challenged to "beat the instructor" who competes using forecasting techniques that will be subsequently taught. All forecasts are graphed prior to revealing the randomly generated…

Two problems from high school mathematics on finding minimum or maximum are discussed. The focus is on students' approaches and difficulties in identifying a correct solution and how dynamic geometry systems can help.

In the Fall semester of 2009, I taught a first-year course that focused on skills required to successfully complete undergraduate research. This paper will discuss the Simpson College first-year course requirements, my course goals, the graph theory topics covered, student feedback, and instructor reflection.