The TPACK of Dynamic Representations

Dynamic Representations And Teacher Knowledge

The K-12 school curriculum presents a significant amount of content to students that they are expected to understand without being able to see firsthand, especially in the middle school and secondary levels. This content may require abstract thinking (e.g., place value, solving equations, and linear programming in mathematics), or it may require them to internalize concepts and processes that are invisible or too fast or too slow or too far away to be observed from the classroom (e.g., molecular structure, Newtonian physics, distant geographic landforms, etc.). Visualization, spatial thinking, and the ability to understand and translate representations in multiple forms are highly valued skills for success in school, especially if students are not just to memorize but understand what they are supposed to be learning (Jiang & McClintock, 2000; Linn, 2003; National Council of Teacher of Mathematics, 2000; Newcombe, 2010). Yet, students have long struggled with curriculum requiring these skills, and many fail to develop conceptual understanding of the content (e.g., see Leinhardt, Zaslavsky, & Stein, 1990; White & Mitchelmore, 1996).

Visual representations, such as illustrations, photographs, graphs, maps, analogies, physical manipulatives, and three-dimensional models, are often used by effective teachers to promote conceptual understanding, but these static representations remain insufficient for conveying adequate information to novice learners about motion and dynamic processes (Rohr & Reiman, 1998). The advent of personal digital technologies has created new possibilities for more fully supporting visualization, however. Pictures and graphs may be animated, displaying changes in space over time; interactive simulations can set into motion models based on real data; three-dimensional maps and models can be rotated and zoomed in or out; two- and three-dimensional geometric figures can be resized, rotated, and reshaped; and digital video, which is easier than ever to access and create, can capture actual events for repeated viewing and analysis. Multimedia environments can even combine multiple dynamic representations, linking them so that users can see the effects of changes made to one representation in all the others.

Some educators see all this capability for motion as intuitively beneficial, asserting that a dynamic representation of a dynamic phenomenon is more authentic and should be an obvious means for increasing student comprehension and conceptual understanding (e.g., McKagan et al., 2008; Ploetzner & Lowe, 2004). The literature includes numerous small-scale studies that support this conclusion (many of which will be cited in this chapter). In their meta-analysis of 26 studies, for example, Hoffler and Leutner (2007) found that representational animations produced significantly superior learning outcomes in students than did representational static pictures. The authors defined representational animations as explicitly presenting the topics to be learned and not there merely as motivational devices.

On the other hand, a number of researchers have presented students with animations and other dynamic representations and found their learning outcomes to be inferior to the learning of students viewing one or more static images of the same phenomenon (Lewalter, 2003; Lowe, 2003; Tversky, Morrison, & Betrancourt, 2002). As Ploetzner and Lowe (2004) concluded,