This experiment was designed and successfully introduced to complement the nanochemistry taught to undergraduate students in a useful and interesting way. Colloidal Ag nanoparticles were synthesized by a simple, room-temperature method, and the resulting suspension was then used to study the surface-enhanced Raman scattering (SERS) of methylene…

This paper describes a new approach for learning from homework called Peer-Assisted Reflection (PAR). PAR involves students using peer feedback to improve their work on open-ended homework problems. Collaborating with peers and revising one's work based on the feedback of others are important aspects of doing and learning physics. While notable…

In order for students to move from using concrete materials to using mental strategies and from additive to multiplicative thinking, the use of arrays and visualisation is pivotal. This article describes a lesson in which students are taken through a Concrete-Representational-Abstract (CRA) approach that involves noticing structure, using…

General chemistry and introductory chemistry students were presented with a laboratory exploration for the determination of the mass percent of copper in rock and mineral samples. They worked independently in the laboratory, which involved multiple lab (pipetting, preparing standard solutions by quantitative dilution, recording visible spectra…

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

When students earn good grades and high praise without having to make much effort, they may not learn the values and skills needed in order to be productive, caring citizens who contribute positively to the world. Some of the most important concepts for a successful life may not be taught to gifted children early in life because they are not…

During the summer, we interviewed Tony Bryk, Author of Learning to Improve: How America's Schools Can Get Better at Getting Better and head of the Carnegie Foundation for the Advancement of Teaching. His work was seminal in the creation of the Framework for Great Schools, which has spurred New York City schools to rethink the structures and…

This article demonstrates how to consider differentiating instruction for diverse learners while maintaining the cognitive demand of a mathematics task. The authors present scenarios involving hypothetical cases of students in inclusive classrooms who engaged in productive struggle within the differentiated task. The authors specifically focus on…

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…

Design thinking is a methodology that emphasizes reasoning and decision-making as part of the problem-solving process. It is a structured framework for identifying challenges, gathering information, generating potential solutions, refining ideas, and testing solutions. Design thinking offers valuable skills that will serve students well as they…

Gifted middle school students in sixth, seventh, and eighth grades engaged with a community activism curriculum designed and implemented by the author, their gifted education facilitator, as part of their gifted programming. This authentic learning experience asked students to follow a creative problem-solving process that fostered thoughtful…

Computational thinking is an important and necessary way of thinking for computer programmers and other professionals in science, technology, engineering, and mathematics (STEM). Research on emerging practices around computational thinking that is developed through coding initiatives in schools reports that elementary children typically learn how…

This article describes the implementation of a collaborative--competative pedagogy in a Year 10 class and the productive motivational outcomes that followed.

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

The Mathematics Practicum has been offered at St. Olaf College for over 30 years. The Practicum is a 4-week, January Interim course where three teams of five students work on consulting problems solicited from area businesses, government agencies, and non-profit organizations. These problems have significant mathematical, statistical, and…