scientists, engineers in different areas of engineering require different sets of specific skills and concepts. The reviewers focused on core concepts and skills that are usually considered essential, defining features of “engineering.” Although it is impossible to separate concepts from skills in engineering practice, the research literature tends to treat them separately. Thus, for the sake of simplicity, this chapter follows that dual structure.

The discussion of each skill or concept addresses (1) difficulties encountered by K–12 students in learning that particular concept or skill; (2) the development of students’ understanding and cognitive capabilities during their K–12 years; and (3) the experiences and teaching interventions that facilitate an increasingly sophisticated understanding of each concept or skill. Based on the these three issues, the committee identified common principles: (1) the allocation of sufficient classroom time; (2) student engagement in iterative design activities; (3) sequencing of instruction that moves from easier-to-learn concepts to more difficult-to-learn concepts; and (4) the integration of tools (e.g., computer software or computational devices). These principles are discussed in more detail at the end of the chapter.

ENGINEERING CONCEPTS

Engineers generally agree that the prototypical engineering process is design and redesign. However, engineering design is not the same as trial-and-error “gadgeteering.” Engineering design involves the following essential components: identifying the problem; specifying requirements of the solution; decomposing the system; generating a solution; testing the solution; sketching and visualizing the solution; modeling and analyzing the solution; evaluating alternative solutions, as necessary; and optimizing the final design. These essential components can be categorized into three type-specific groups of engineering concepts: basic science and math concepts, domain-specific concepts, and concepts common to most areas of engineering. Though this review does not focus on the social aspects of engineering design, engineering design is an inherently social enterprise, since those involved typically are working in teams and must communicate with clients or other stakeholders.

Research on the development of science and math concepts is not discussed in this chapter but has been extensively reviewed in recent studies by the National Research Council (e.g., Taking Science to School: Learning and Teaching Science in Grades K–8 [Duschl et al., 2007] and Adding It Up: Helping Children Learn Math [NRC, 2001]). Very little research has been



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