The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Discusses several philosophies of linguistics and semiotics that debate the importance of words and their relationship to signs, language as the primary modeling system, and the historical primacy of verbal versus visual communication. Describes human communication as both language-based and nonverbal, both aspects inviting arbitrary and abstract…

Despite the central role of risk assessment in analyzing and making decisions about many environmental issues, most people are poorly equipped to understand key concepts about risk or apply them successfully. I present three class activities in which students develop a better appreciation for the magnitude of a one in a million increased risk of…