Sciences (Pashler et al., 2007), and a review of problem-solving transfer in the Handbook of Educational Psychology (Mayer and Wittrock, 2006).

Before describing various research-based principles for instructional design, it is worth noting that recent research on teaching and learning reveals that young children are capable of surprisingly sophisticated thinking and reasoning in science, mathematics, and other domains (National Research Council and Institute of Medicine, 2009; National Research Council, 2012). With carefully designed guidance and instruction, they can begin the process of deeper learning and development of transferable knowledge as early as preschool. As noted in Chapters 4 and 5, this process takes time and extensive practice over many years, suggesting that instruction for transfer should be introduced in the earliest grades and should be sustained throughout the K-12 years as well as in postsecondary education. Thus, the principles discussed below should be seen as broadly applicable to the design of instruction across a wide array of subject matter areas and across grade levels spanning K-16 and beyond.

Research-Based Methods for Developing Transferable Knowledge

Using Multiple and Varied Representations of Concepts and Tasks

Mayer (2009, 2011b) has shown, based on 11 experimental comparisons, that adding diagrams to a text (or adding animation to a narration) that describes how a mechanical or biological system works can increase student performance on a subsequent problem-solving transfer test by an average of more than one standard deviation. Allowing students to use concrete manipulatives to represent arithmetic procedures has been shown to increase transfer test performance both in classic studies in which bundles of sticks are used to represent two-column subtraction (Brownell and Moser, 1949) and in an interactive, computer-based lesson in which students move a bunny along a number line to represent addition and subtraction of signed numbers (Moreno and Mayer, 1999).

Research suggests that the use of multiple and varied representations is also effective in informal learning environments. For example, a recent National Research Council (2009a) study found that visitors to museums and science centers commonly report developing a deeper understanding of a concept through the concrete, sensory, or immersive experiences provided by the exhibits. One investigation reported in this study found that children who interacted purposefully with exhibits about magnetism gained conceptual understanding of the concept of magnetism (Rennie and McClafferty, 2002).

While adding diagrams or animations to text can enhance learning and transfer, researchers have found that how multimedia learning environments are designed strongly influences their effectiveness. Based on dozens

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