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 this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

The simple process of iteration can produce complex and beautiful figures. In this article, Robin O'Dell presents a set of tasks requiring students to use the geometric interpretation of complex number multiplication to construct linear iteration rules. When the outputs are plotted in the complex plane, the graphs trace pleasing designs…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

One tool for enhancing students' work with data in the science classroom is the measure line. As a coteacher and curriculum developer for The Inquiry Project, the author has seen how measure lines--a number line in which the numbers refer to units of measure--help students not only represent data but also analyze it in ways that generate…

The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Describes how one kindergarten classroom made pictographs and paper graphs of the students' acting preferences for a production of "The Wizard of Oz." Focuses on how the activity led to varied mathematics and literacy connections. Identifies implications from the Oz experience, including relating graphs to classroom contexts, using…

A variety of applications of logarithms are presented along with suggestions about how this topic might be made more interesting and relevant in a secondary classroom. In most cases, the treatment is multi-modal using numerical, graphical and algebraic approaches.

Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

New approaches to the teaching of introductory algebraic concepts are discussed. Their use in the Approaching Algebra Numerically Project in some middle schools in Ohio is reviewed. Some implications for use in Australian schools are considered. (MNS)