This study describes how a secondary school teacher in Trinidad and Tobago implemented opportunities for reasoning and proof in Geometry. Data were collected via teaching observations, teacher interviews, audio, and video recording. The analysis of the data suggested that the teacher used open-ended questioning, revoicing, group work, and…

This article reviews the history of thought on how intelligence and creativity, two individual differences important to teaching and learning, are connected. For decades, intelligence and creativity have been seen as essentially unrelated abilities. Recently, however, new theories, assessment methods, and statistical tools have caused a shift in…

Our high school optics course finishes with an assignment that students usually appreciate. They must take pictures of everyday situations representing optical phenomena such as reflection, refraction, or dispersion, and post them on Instagram. When the photos were presented to the class, one student revealed an intriguing photo, similar to Fig.…

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

This column presents ideas and techniques to enhance science teaching. In today's classrooms, teachers face numerous challenges. They are preparing students for jobs and careers that are not even conceived of yet. Assessments are being used to address students' college and career readiness and to promote critical thinking and problem solving.…

The degrees of freedom (DOF) concept is a powerful tool that has been taught since at least the '70s in undergraduate curriculum, typically introduced in the context of a first course on material and energy balances. The concept, however, has not been widely applied beyond the material balance domain and in general is not taught as a unified…

In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…

This article will share the intellectual journey E. Paul Torrance and I traveled in 2001, in which we explored psychology, science and ancient wisdom and traditions, including Native American and indigenous traditions, to establish a foundation for spiritual intelligence. This section will be followed by ways to develop and nurture spiritual…

Assessment and instruction are interwoven in mathematically rich formative assessment tasks, so employing these tasks in the classrooms is an exciting and time-efficient opportunity. To provide a window into how these tasks work in the classroom, this article analyzes summaries of student work on such a task and considers several students'…

Design is a powerful weapon for modern companies so it is important to have excellent designers in the industry. The purpose of this study is to explore the learning problems and the resources that students use to overcome problems in undergraduate industrial design studio courses. A survey with open-type questions was conducted to collect data.…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

After teaching the concept of division with remainders for many years, Vanessa Battreal, Vanessa Brewster, and Juli Dixon noticed that interpreting remainders in contextualized problems is particularly challenging for elementary school students. To effectively interpret remainders, students must attend to problem context and consider carefully…