Reasoning about Structure and Function: Children’s Conceptions of Gears

Twenty-three second graders and 20 fifth graders were interviewed about how gears move on a gearboard and work in commonplace machines. Questions focused on transmission of motion; direction, plane, and speed of turning; and mechanical advantage. Several children believed that meshed gears turn in the same direction and at the same speed. Many second graders provided very incomplete explanations of transmission of motion. Most children confused mechanical advantage with speed. Yet as the interview proceeded, several fifth graders generalized conceptions about transmission of motion into a rule about turning direction. They increasingly justified their ideas about gear speed by referring to ratio. Children’s reasoning became more general, formal, and mathematical as problem complexity increased, suggesting that mathematical forms of reasoning may develop when they provide a clear advantage over simple causal generalizations. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 3–25, 1998. This study investigates the way that secondand fifth-grade students reason about gears, both in configurations on a gearboard, where no purposeful function is entailed, and in other familiar machines that have a known purpose, such as handheld eggbeaters and bicycles. Despite a growing interest in technology education, little research has been conducted to ascertain how elementary school children reason about the way that mechanical devices work (although for exceptions, see Brandes, 1992; Piaget, 1960). Such knowledge is important because it provides a window into children’s reasoning about the relationship between structure and function, a fundamental concern in nearly every form of scientific reasoning. Because of a concern within developmental psychology for exploring early competence in causal reasoning, there is a research literature exploring how very young children and infants understand the behavior of simple objects and mechanisms (Baillargeon, 1987; Bullock, Gelman, & Baillargeon, 1982; Spelke, 1991). Moreover, a growing literature exists on adults’ mental models of more complex devices such as doorbells, thermostats, steamplants, and handheld calculators (e.g., Gentner & Stevens, 1982). However, relatively little is known about the kinds of transformations in device reasoning that typically occur during middle childhood. Such research has practical as well as scientific significance because much of children’s learning during the elementary years, especially in science and technology, depends on their capability to JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 35, NO. 1, PP. 3–25 (1998) © 1998 John Wiley & Sons, Inc. CCC 0022-4308/98/010003-23 Correspondence to: R. Lehrer or L. Schauble Contract grant sponsor: NSF Contract grant number: RED-9355850 inspect things and figure out how they work—that is, to make inferences about the function of a device from its structure. The importance of this kind of reasoning is emphasized in current science education reform objectives, such as those developed by the American Association for the Advancement of Science and the National Research Council. These objectives target the relation between structure and function as a central organizing theme for science instruction. In this study, gears were the focus for studying children’s understanding of structure and function because gears provide an easy entry point for learning, yet also incorporate some relatively deep scientific (e.g., torque, mechanical advantage) and mathematical (e.g., ratio, proportion) principles. Like other simple machines, some aspects of gears’ operation seem deceptively straightforward, but others are not simple at all. On the one hand, unlike devices such as calculators or sewing machines, the operation of gears is directly inspectable and involves no hidden parts, and the transmission of motion is visible. Research on the development of causal reasoning suggests that even preschoolers are well equipped to understand the simple transmission of motion (Bullock et al., 1982). On the other hand, the literature on naive physics forewarns that developing a robust understanding of how motion is transmitted may require a considerable amount of inference which in some cases may be governed by misapplied intuitive understandings (diSessa, 1993). For example, as we will explain below, some children thought that turning force tends to die away as additional gears are added to a train. According to this interpretation, gears that are farthest from the driving gear will turn noticeably more slowly than gears that are close to the driving gear. Thus, even though gears are open, inspectable devices, reasoning about them can be challenging. One source of the challenge is that gears are typically arranged in trains of two or more meshed gears. Understanding such a system can entail figuring out a rather complex set of constraints. For example, the turning direction of any gear in a configuration is constrained by the position of the others. Moreover, the turning speed of a gear depends on its size relative to the other gears. To make matters yet more complex, what one interprets as a gear’s speed depends on the frame of reference that one adopts. For example, for all gears that mesh, the velocity of their gear teeth will be the same, yet in a given period of time, smaller gears will complete more revolutions than larger ones. Although it is possible through direct observation to learn about speed and direction of turn, some principles of gear functioning, such as mechanical advantage, are not directly observable. In summary, although a superficial understanding of gears can be gained readily by direct observation, a deep understanding is unlikely to emerge without considerable reflection. Such reflection involves the application and coordination of two different but complementary perspectives, referred to as mathematical and mechanistic, respectively. In fact, when people observe regularities in the world, both these perspectives are usually engaged to some degree; here we consider them separately only for explanatory clarity. The perspective we are calling mathematical involves observing and symbolizing patterns and regularities. The perspective we are calling mechanistic involves imputing mechanisms that underlie and explain these observed patterns (the distinction is akin to the one made by Shultz [1982], who distinguished Humean and Kantian interpretations of causality). To illustrate a mathematical perspective, after observing the turning speed of several pairs of meshed gears of different sizes, one might observe that across several such combinations the ratio of the circumferences of the gears equals the ratio of the turning speeds. This search for regularity or pattern in data is thus associated with mathematizing nature. Alternatively, one can think about the same phenomenon mechanistically, noting that each tooth on the driving gear must push one tooth on the gear that it drives. Thus, the turning speeds of the two gears must depend on the number of pushing teeth and the number of teeth that get 4 LEHRER AND SCHAUBLE