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addition problems and two multiplication problems does not provide convincing evidence that a student can subtract, multiply or divide.
Content-related evidence should also be considered when developing scoring rubrics. The task shown in Figure 1 was developed by the Quantitative Understanding: Amplifying Student Achievement and Reasoning Project (Lane, et. al, 1995) and requests that the student provide an explanation. The intended content of this task is decimal density. In developing a scoring rubric, a teacher could unintentionally emphasize the nonmathematical components of the task. For example, the resultant scoring criteria may emphasize sentence structure and/or spelling at the expense of the mathematical knowledge that the student displays. The student's score, which is interpreted as an indicator of the student's mathematical knowledge, would actually be a reflection of the student's grammatical skills. Based on this scoring system, the resultant score would be an inaccurate measure of the student's mathematical knowledge. This discussion does not suggest that sentence structure and/or spelling cannot be assessed through this task. If the assessment is intended to examine sentence structure, spelling, and mathematics, then the score categories should reflect all of these areas.
Figure 1. Decimal Density Task
Dena tried to identify all the numbers between 3.4 and 3.5. Dena said, "3.41, 3.42, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48 and 3.49. That's all the numbers that are between 3.4 and 3.5."
Nakisha disagreed and said that there were more numbers between 3.4 and 3.5. A. Which girl is correct?
Answer:
B. Why do you think she is correct?
Construct-Related Evidence
Constructs are processes that are internal to an individual. An example of a construct is an individual's reasoning process. Although reasoning occurs inside a person, it may be partially displayed through results and explanations. An isolated correct answer, however, does not provide clear and convincing evidence of the nature of the individual's underlying reasoning process. Although an answer results from a student's reasoning process, a correct answer may be the outcome of incorrect reasoning. When the purpose of an assessment is to evaluate reasoning, both the product (i.e., the answer) and the process (i.e., the explanation) should be requested and examined.
Consider the problem shown in Figure 1. Part A of this problem requests that the
student indicate which girl is correct. Part B requests an explanation. The intention of
combining these two questions into a single task is to elicit evidence of the students'
Rudner, L. and W. Schafer (2002) What Teachers Need to Know About Assessment. Washington, DC: National Education Association.
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