


Does the material include accurate and comprehensible representations of the key ideas? Explanation. This criterion highlights the importance of using a variety of representations to make abstract ideas intelligible to all students. Different representations highlight different aspects of an idea and provide a variety of opportunities for the idea to connect to other students' ideas and become embedded in a student's knowledge system. Possible modes of representation include drawings, diagrams, graphs, images, analogies and metaphors, models and simulations, and roleplaying. Representations need to be clear so that students can understand fairly quickly which ideas are being represented and how. In addition, because representations typically highlight only some aspects of an idea, care must be taken that they represent the real thing as accurately as possible (or that they involve students in considering which aspects of the real thing are represented by the model and which are not). The number of representations that would be considered "sufficient" will depend on the complexity and level of abstractness of the idea being presented. For example, the idea that "About two thirds of the weight of cells is accounted for by water. . . ." (Benchmark 5C6–8#4) probably requires fewer representations (if any) than the complex and highly abstract idea that "Atoms and molecules are perpetually in motion. Increased temperature means greater average energy of motion, so most substances expand when heated. . . ." (Benchmark 4D6–8#3). 