mathematical principles that underlie common digital communication and information technologies. Binary numbers, matrix operations, polynomials, and other forms of mathematics are presented as essential content for synthesizing music, compressing video, and encrypting data, and mathematical concepts and equations are presented as tools used by engineers to create or improve a given digital technology or system. In addition, the laboratory activities require that students use mathematics and mathematical reasoning to design, simulate, and explore digital communication and information technologies.

Engineers often develop mathematical models featuring the key variables in a process, system, or device. The variables include forces that act on a structure, the length of time required for a process, or the distance an object moves. The relationships between variables are represented by equations that can be used to test ideas, predict performance, and inform design decisions. However, our review of curricula did not find any projects or units in which students were instructed to develop and use mathematical models to assist them in designing solutions to problems.

The Science Thread

We defined “science” as the study of the natural world, including the laws of nature associated with physics, chemistry, and biology and the treatment or application of facts, principles, concepts, or conventions associated with these disciplines. Our analysis suggests that science is a moderately thick thread composed of two strands, (1) science concepts related to engineering topics and problems and (2) scientific modes of inquiry that build knowledge and inform design decisions.

The First Strand

The most common science topics in the first strand found in K–12 engineering curricula relate to materials, mechanisms, electricity, energy, and structures and typically involve concepts such as force, work, motion, torque, friction, voltage, current, and resistance. In the curricula, most of these concepts are presented in the form of encyclopedia-like explanations that are subsequently reinforced in laboratory activities.

“Engineering is Elementary” includes concepts related to water, sound, plants, and organisms. At the high school level, “Material World Modules” address natural degradation processes, bioluminescence and chemilumi-



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