From the National Mathematics Advisory Council of 2008 final report:

The use of “real-world” contexts to introduce mathematical ideas has been advocated, with the term “real world” being used in varied ways. A synthesis of findings from a small number of high-quality studies indicates that if mathematical ideas are taught using “real-world” contexts, then students’ performance on assessments involving similar “real-world” problems is improved. However, performance on assessments more focused on other aspects of mathematics learning, such as computation, simple word problems, and equation solving, is not improved.

It seems to me that if a real world focus in mathematics makes students more able to use mathematics to solve problems from the real world, then this would make much of the mathematics instruction we do more useful. What exactly is the goal of those simple word problems anyway? Aren’t they an effort to add some context to the learning of computations, so that students are able to use mathematics to solve problems? And if students are going to graduate from school, aren’t the problems they are most likely to face going to come from the real world?

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