Trade Publication Article

Mathematics borrows from everyday language

Thorpe, Jim

2019

Overview

In textbooks we see these definitions (figure 7): although the following interpretation of exterior angle is plausible in the light of the provided definition of interior angle (figure 8): I see one text proclaims, \"This is not an exterior angle\". In response to a task asking for the distance a ball is thrown and which is found from a quadratic equation with solutions -300 and 67, students who are aware that the negative value has to be ignored, sometimes write, \"The distance is 67m. Learners may be told that a solution to a quadratic equation should not be written x = 3 and x = 2, on logical grounds, but as x = 3 or x = 2, as seen in the texts, although on the next line the text announces, \"So the solutions are x = 3 and x = 2\", returning from logical to everyday. Which of the subtleties and refinements can be deferred until later, without actually misleading, in order to make the broad ideas accessible to beginners? (p. 221) Perhaps Thornton has it about right, there is no single answer, decisions about everyday and mathematical classroom talk being, to turn a phrase, \"horses for cases\".

• Publisher: The Association of Teachers of Mathematics
• Subject: Classrooms / Etymology / Geometry / Horses / Language / Learning / Mathematical analysis / Mathematicians / Mathematics / Mathematics Instruction / Native Language / Open Universities / Prior Learning / Quadratic equations / Semantics / Textbooks / Topology / Undergraduate Students