Can math concepts be experienced through the sensory modality of balance? Balance Board Math (BBM) is a set of pedagogical math activities designed to instantiate mathematical concepts through stimulation to the vestibular sense: an organ in the inner ear that detects our bodily balance and orientation. BBM establishes the different ways children…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

If the goal is to move beyond the shape of the graph to consider the dynamic aspects of functions, students need to explore dynamic representations of functions. To address this, the authors combined the use of a dynamic representation of function with the instructional routine, Which One Doesn't Belong? [WODB]. In this article, they briefly…

This article explains how explorations into the quadratic formula can offer students opportunities to learn about the structure of algebraic expressions. In this article, the author leverages the graphical interpretation of the quadratic formula and describes an activity in which students derive the quadratic formula by quantifying the symmetry of…

Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from…

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

This article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

As a parent, the author stepped into his child's class on a Friday morning to a room buzzing with activity. Parents walked around the room, coffee and bagel in hand, reading stories that their child (and others) had drafted, revised, written, and illustrated. Students eagerly shared their stories and drawings, cherishing the comments and praise…

This article encourages approaches that develop children's understandings of data representations. In particular, when children develope flexibility in their approaches to data representation and understanding, the same data can be represented in different ways. Flexible and adaptive use of representations is part of mathematics competence which…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

Every day, students collect, organize, and analyze data to make decisions. In this data-driven world, people need to assess how much trust they can place in summary statistics. The results of every survey and the safety of every drug that undergoes a clinical trial depend on the correct application of appropriate statistics. Recognizing the…

Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

The project models the conductive heat loss through the ceiling of a home. Students are led through a sequence of tasks from measuring the area and insulation status of a home to developing several functions leading to a net savings function where the depth of insulation is the input. At this point students use calculus or a graphing utility to…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…