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• #### Index 363-374

##### Formats for Assessing Understanding

Teachers have limited time to assess students’ performances and provide feedback, but new advances in technology can help solve this problem (see Chapter 9). Even without technology, however, advances have been made in devising simple assessments that measure understanding rather than memorization. In the area of physics, assessments like those used in Chapter 2 to compare experts and novices have been revised for use in classrooms. One task presents students with two problems and asks them to state whether both would be solved using a similar approach and state the reason for the decision:

1. A 2.5-kilogram ball with a radius of 4 centimeters is traveling at 7 meters/second on a rough horizontal surface, but not spinning. At some later time, the ball is rolling without slipping 5 meters/second. How much work was done by friction?

2. A 0.5-kilogram ball with a radius of 15 centimeters is initially sliding at 10 meters/second without spinning. The ball travels on a horizontal surface and eventually rolls without slipping. Find the ball’s final velocity.

Novices typically state that these two problems are solved similarly because they match on surface features—both involve a ball sliding and rolling on a horizontal surface. Students who are learning with understanding state that the problems are solved differently: the first can be solved by applying the work-energy theorem; the second can be solved by applying conservation of angular momentum (Hardiman et al., 1989); see Box 6.2. These kinds of assessment items can be used during the course of instruction to monitor the depth of conceptual understanding.

Portfolio assessments are another method of formative assessment. They provide a format for keeping records of students’ work as they progress throughout the year and, most importantly, for allowing students to discuss their achievements and difficulties with their teachers, parents, and fellow students (e.g., Wiske, 1997; Wolf, 1988). They take time to implement and they are often implemented poorly—portfolios often become simply another place to store student work but no discussion of the work takes place— but used properly, they provide students and others with valuable information about their learning progress over time.

##### Theoretical Frameworks for Assessment

A challenge for the learning sciences is to provide a theoretical framework that links assessment practices to learning theory. An important step in this direction is represented by the work of Baxter and Glaser (1997), who

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