children to focus on a single relevant dimension, Siegler developed the following cognitive model, which incorporates four different rules children use to solve such problems:
Rule I—If the weight is the same on both sides, predict that the scale will balance. If the weight differs, predict that the side with more weight will go down.
Rule II—If one side has more weight, predict that it will go down. If the weights on the two sides are equal, choose the side with the greater distance (i.e., the side that has the weight farther from the fulcrum).
Rule III—If both weight and distance are equal, predict that the scale will balance. If one side has more weight or distance, and the two sides are equal on the other dimension, predict that the side with the greater value on the unequal dimension will go down. If one side has more weight and the other side more distance, muddle through or guess.
Rule IV—Proceed as in Rule III unless one side has more weight and the other more distance. In that case, calculate torques by multiplying weight times distance on each side. Then predict that the side with the greater torque will go down.
SOURCE: Siegler (1976, p. 482). Used by permission of Academic Press.
siderably better understood in some domains, such as physics and reading, than in others, such as history and chemistry. Moreover, the models developed by cognitive scientists will need to be recast in ways that are easily understood and readily usable by assessment developers and teachers.
Every assessment is also based on a set of beliefs about the kinds of tasks or situations that will prompt students to say, do, or create something that demonstrates important knowledge and skills. The tasks to which students are asked to respond on an assessment are not arbitrary. They must be carefully designed to provide evidence that is linked to the cognitive model of learning and to support the kinds of inferences and decisions that will be based on the assessment results.