Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Many mathematics teachers and students are familiar with the typical "box problem." In this type of problem, one takes a rectangular (or a square) sheet of paper and cuts out four squares from the four corners of the sheet and then folds the four strips up to form a box. Math problems like this are seen in middle school, high school,…

In this article, the authors share activities designed to help students make a connection between the complex roots of X[superscript 2] - 2x + 5 = 0 and the graph of y = X[superscript 2] - 2x + 5. We piloted these activities in three precalculus classes. The activities involved both concrete and technological representations of the mathematical…

Effective mathematics teaching elicits and uses evidence of student thinking to assess progress toward mathematical understanding and adjusts instruction continually to support and extend learning (National Council of Teachers of Mathematics, 2014). However, as teachers march through content in precalculus, they tend to rely heavily on traditional…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

Students' procedural knowledge and conceptual understanding of matrices can improve when they use technology, in particular spreadsheets, as a tool. Complex real-world applications of matrix calculations are time-consuming and prone to errors if done by hand, yet calculations can be performed easily with spreadsheets. In this article, the author…

The contexts of the problems educators choose can affect students' mathematical identities by affecting their abilities to relate to the mathematics (Middleton, Jansen, and Goldin 2017). Moreover, these choices send powerful messages to students about the relevancy of mathematics to their own lives (Felton 2010). Eliciting and drawing on student…

Mathematics and technology serve the health sciences as demonstrated in this article, cowritten by one of our calculus students. Creating a lesson based on dosing an antibiotic allows teachers and students to see the immediate value of high school calculus and technology.

During professional development, the authors learned about strings--a powerful instructional routine used in elementary classrooms to elicit students' mental mathematics strategies and use those strategies to build conceptual understanding. Strings provided the authors with a way to make relatively small changes to guided notes in algebra 1,…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…