The Language of Comparisons: Communicating about Percentages
This paper describes an approach used to explicitly teach students how to analyze arguments based on comparisons of numbers and percentages, and how to write such comparisons with the necessary precision.
While comparisons between percentages or rates appear frequently in journalism and advertising, and are an essential component of quantitative writing, many students fail to understand precisely what percentages mean, and lack fluency with the language used for comparisons. After reviewing evidence demonstrating this weakness, this experience-based perspective lays out a framework for teaching the language of comparisons in a structured way, and illustrates it with several authentic examples that exemplify mistaken or misleading uses of such numbers. The framework includes three common types of erroneous or misleading quantitative writing: the missing comparison, where a key number is omitted; the apples-to-pineapples comparison, where two subtly incomparable rates are presented; and the implied fallacy, where an invalid quantitative conclusion is left of the reader to infer.
This article gives teachers much to think about in terms of truly understanding percentages as they relate to comparisons. The author does an exemplary job of showing where student and teachers weaknesses are in analyzing and interpreting data sets.
Some discovery methods of teaching mathematics rely almost completely on what the student brings to class in terms of problem-solving abilities and mathematical knowledge. This method helps students develop the ability to analyze and apply mathematics in a way that will help them both in future math classes and in the world outside the classroom.
The implications for instruction in this resource stretch beyond the lessons in data and communicating about percentages. The way these lessons are taught will strengthen student awareness of data, mathematics, and real world analysis.
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