posted by:
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Mack McCary
on June 27, 1998
at 1:37PM
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subject:
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why do we need more than math tests?
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I've just come back from almost a week of assessing student portfolios with 4th, 8th and 10th grade teachers from seven districts in North Carolina. As we predicted, we found much more evidence of student competence in writing than we did in math.
What we did find in math caused us to rethink the evidence needed to judge whether a student is demonstrating competence in meeting grade level standards in math. Prior portfolio reviews in Vermont coupled with our own experience showed that objective measures, such as multiple choice, short answer and most word problems, do an adequate job of assessing fundamental knowledge of math concepts and procedural skills. Some (rare) well constructed multiple choice can also indicate more sophisticated conceptual knowledge. The biggest problem we encountered was that individual teacher-made tests were not very helpful in determining whether students had mastered such core knowledge and procedures unless it was summarized by a comprehensive list of grade or course objectives, such as that provided by an instructional management system.
But we concluded that overall these traditional objective measures do not do an adequate job of monitoring the development of student understanding. We decided that this developing understanding is best revealed on two ways: 1) application of concepts to solve structured and ill-sturctured problems (structured problems are typical school problems in which the problem and usually the strategies to solve it are evident in the problem, and usually there is only one right answer. Ill-structured is more like real life, in which even the problem, much less how to solve if, are not evident, and there may be a range of both strategies and solutions) 2) communication, including oral, written and visual, in which students must explain their logical reasoning, strategies and steps, links to other math concepts, and/or conclusions to a variety of audiences.
Prompts (shorter time span, more school like problems) and tasks (more authentic, real world and usually longer term projects) do a much better job of revealing developing conceptual understanding than most objective measures.
Our focus of work during the coming year will incorporate work we are doing with our project with similar statewide work. We will be focusing on classroom assessment tools which teachers find useful to monitor their students' achievement of standards and make instructional decisions, as well as useful for providing feedback to students and their parents which will help students understand what they need to learn.
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