This article examines a common proportional reasoning problem used in schools, often referred to as the Orange Juice task. The authors show how these six strategies described by Nikula (e.g., Unitizing, Norming, etc.) and one additional strategy can be used to either solve or make progress in the Orange Juice task. The article presents work from…

The goal of this article is to give examples of high school students exploring parameters of quadratic functions using different tools as a catalyst to discuss the pros and cons and demonstrate the mathematical power of each. The authors illustrate how teachers' learning goals should navigate them toward a productive option.

Various studies have indicated that incorporating origami activities into a geometry lesson can promote elementary and middle school students' mathematical reasoning, enhance their ability to use precise mathematical terminologies, and increase their communication skills. The authors wondered if origami activities have a place in high school…

We present a sequence of two physics experiments, designed for use with secondary students, which investigate the specific heat of sand, both qualitatively and quantitatively, without a calorimeter. We use two LM35 temperature sensors and an Arduino prototype board for data acquisition. The results are good and allow teachers to discuss the…

Experimental teaching is essential for a good understanding of science, especially on Physics. Practical activities play an important role for engaging students with science, mainly when they interact directly with equipment, collect experimental data with computers and/or use interactive software for data analysis. In this work, we present the…

The real time PCR (qPCR) method provides a powerful method to assess levels of particular species of DNA. When combined with reverse transcription (RT-qPCR) it is the predominate technique to measure expression of gene transcripts. While this approach is very powerful, particular care must be taken in the design of the primers to facilitate…

Mathematics has been taught throughout history without much more than a straightedge, a compass, and an abacus. So there is little question that all the major concepts of mathematics can be delivered without the aid of modern technology. But clearly, just the time-saving aspect of using technology can greatly enhance the art of teaching. In this…

In 1827, Robert Brown noticed pollen suspended in water bouncing around erratically. It wasn't until 1905 that Albert Einstein provided an acceptable explanation of the phenomenon (Kac 1947): Brownian motion is the random movement of particles (e.g., pollen) in a fluid (liquid or gas) as a result of collisions with atoms and molecules. Movement of…

Investigating real-world phenomena in a playful, exploratory setting is a natural process for young children. Teachers can capitalize on children's curiosity to foster their understanding of science ideas and their engagement in science practices, such as predicting, experimenting, observing, comparing, and contrasting. Force and motion…

During the COVID-19 pandemic, an at-home laboratory program was created and implemented for a section of the general chemistry course at the University of Southern California. The experiments were designed to only utilize safe household items and no special equipment. These laboratory activities, spanning over 4 weeks, focused on concepts usually…

Over the past 25 years, the Davidson College Physics Department has developed small computer programs called Physlets. These programs were written in Java and distributed as Java applets embedded in HTML pages. Physics teachers from around the world used Physlets to author interactive computer-based curricular materials for the teaching of…

A Rube Goldberg device is a complicated, yet comically involved machine that performs a simple task such as closing a door, watering a plant, or typing a key on a keyboard. Creating one is an open-ended activity that challenges students to use prior knowledge, resourcefulness, investigatory skills, and imagination. This reverse engineering…

In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

In this article, the authors discuss the potential of the icon-based mathematical games, emoji math and mobile math, to promote student engagement with and understanding of algebra. They describe how these games serve as accessible entry points for algebraic thinking and that, in contrast to traditional symbolic algebra, the use of these…