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The myth of objectivity in mathematics assessment

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Bell & Howell Information and Learning: Formulae omitted. THE ASSESSMENT PRINCIPLE: Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

JR wide array of alternatives to traditional quiz-and-test assessment of students' mathematical understanding has been proposed in the last decade (e.g., Stenmark [1991]; NCTM [1995]; Greer et al. [1999]). Adding open-ended problems, performance tasks, writing assignments, and portfolios to teachers' assessment repertoires is important, these documents argue, because "assembling evidence from a variety of sources is more likely to yield an accurate picture of what each student knows and is able to do" (NCTM 2000, p. 24).

The decision by teachers to incorporate some of these less familiar assessment techniques is often framed as a trade-off between objectivity and subjectivity. Traditional assessment methods, which are sometimes narrowly focused on skills and procedures, are at least objective measures of those skills and procedures. By contrast, alternative approaches-which have the potential to assess students' conceptual understanding and their problem-solving and reasoning ability-are unfortunately subjective.

What does it mean for an assessment technique to be objective? The American Heritage Dictionary of the English Language defines the word as follows: Ob.jec.tive adj. 1. Of or having to do with a material object as distinguished from a mental concept, idea, or belief. Compare subjective. 2. Having actual existence or reality. 3. a. Uninfluenced by emotion, surmise, or personal prejudice. b. Based on observable phenomena; presented factually: an objective appraisal.

A student's mathematical understanding-for example, knowledge of linear functions or the capacity to solve nonroutine problems-is a "mental concept" and as such can be observed only indirectly. Further, a teacher's appraisal of this knowledge cannot help but be influenced by emotion or surmise. Objectivity, like the mythical pot of gold at the end of the rainbow, would...