Helping Students to Recognize and Evaluate an Assumption in Quantitative Reasoning: A Basic Critical-Thinking Activity with Marbles and Electronic Balance
There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively about a situation, they usually do not consider which implicit assumptions they have made and,
consequently, they do not evaluate if these assumptions are acceptable in the related problem task. In order to show to students the importance of being aware of assumptions making and their consequences in the quality of judgments, a simple Predict – Observe - Explain active-learning sequence was designed. In it students are supposed (a) to observe the mass measurement of 10 marbles on an electronic balance and (b) to predict the future balance
readings related to 7 and 12 marbles. They would be also asked explicitly (c) to state all assumptions they had made in order to predict the readings and (d) to propose a method to verify assumptions’ acceptability. After they have observed actual readings, they would be asked to explain the differences and verify their explanations. Informal pilot tries of this learning sequence was carried out by a few high-school physics teachers during their regular classroom sessions and they considered that it gave good results with students.
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