Students' success in solving problems involving proportional reasoning is an indication that they have moved beyond additive thinking to multiplicative thinking. However, classroom work indicates that many students do not reason proportionally in many practical contexts. The authors discuss a particular task that reveals students'…

Middle school students' mathematical understanding benefits from connecting mathematics to other content areas in the curriculum. This month's activity explores the issue of the scarcity of freshwater, a natural resource (activity sheets are included). This activity concentrates on the critical areas mentioned in the Common Core State…

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a "black box" to the students. Thus, although correct models are…

Recently, with the development of more powerful and accurate computational tools, the inclusion of new didactic materials in the classroom is known to have increased. However, the form in which these materials can be used to enhance the learning process is still under debate. Many different methodologies have been suggested for constructing new…

Generating, collecting, and analyzing data is an essential practice in the science classroom (NRC 2012). Taking this data and using it to craft an explanation that demonstrates understanding of content is another essential practice. But both practices can be challenging, and students often require teacher support to succeed. Accordingly, the…

How do children use physical and virtual tools to develop new numerical knowledge? While concrete instructional materials may support the delivery of novel information to learners, they may also over-simplify the task, unintentionally reducing learners' performance in recall and transfer tasks. This reduction in testing performance may be…

Math games bring out kids' natural love of numbers. Yet in the waning days of school, students can't wait for that final bell to ring. Each summer, most students lose about two months of mathematical computation skills. So how do teachers keep their students focused on math up till the end? Before sending them off for the summer, get them hooked…

Learning styles are increasingly being integrated into computational-enhanced earning environments and a great deal of recent research work is taking place in this area. The purpose of this study was to examine the impact of the computational experiment approach, learning styles, epistemic beliefs, and engagement with the inquiry process on the…

In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…

Understanding counting rules is challenging for students; in particular, they struggle with determining when and how to implement combinations, permutations, and the multiplication rule as tools for counting large sets and computing probability. We present an activity--using ideas from the games of poker and pinochle--designed to help students…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

A hands-on activity can help multivariable calculus students visualize surfaces and understand volume estimation. This activity can be extended to include the concepts of Fubini's Theorem and the visualization of the curves resulting from cross-sections of the surface. This activity uses students as pillars and a sheet or tablecloth for the…

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

In this activity, I show how high school students apply their knowledge of density to solve an unknown variable, such as thickness. Students leave this activity with a better understanding of density, the knowledge that density is a characteristic property of a given substance, and the ways density can be measured. (Contains 4 figures and 1 table.)

How do teachers teach students to count rhythms? Teachers can choose from various techniques. Younger students may learn themed words (such as "pea," "carrot," or "avocado"), specific rhythm syllables (such as "ta" and "ti-ti"), or some other counting method to learn notation and internalize rhythms. As students grow musically, and especially when…