BOX 2–2 Methods for Observing Children’s Rules for Solving Balance-Scale Problems

Below are descriptions of the kinds of problems Siegler (1976) crafted to observe which rules children are using to solve balance-scale problems. Children who use different rules produce different patterns of responses to these six problems:

  1. Balance problems—The same configuration of weights on pegs on each side of the fulcrum.

  2. Weight problems—Unequal amounts of weights, equidistant from the fulcrum.

  3. Distance problems—Equal amounts of weights, different distances from the fulcrum.

  4. Conflict-weight problems—One side with more weight, the other side with its weight farther from the fulcrum, and the side with more weight goes down.

  5. Conflict-distance problems—One side with more weight, the other side with more distance, and the side with more distance goes down.

  6. Conflict-balance problems—The usual conflict between weight and distance, and the two sides balance.

SOURCE: Siegler (1976). Used by permission of Academic Press.

competency. In the context of classroom assessment, the interpretation is often made less formally by the teacher, and is usually based on an intuitive or qualitative model rather than a formal statistical one.

Returning to the example of Siegler’s balance-scale problems, one example of an interpretation method is presented in Box 2–3. In this example the interpretation framework specifies patterns of response to the six problems and the corresponding rule, if any, that one can infer a student is using.

Relationships Among the Three Vertices of the Assessment Triangle

A crucial point is that each of the three elements of the assessment triangle not only must make sense on its own, but also must connect to each of the other two elements in a meaningful way to lead to an effective assessment and sound inferences.

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