# Explaining the Roles of Definitions in Mathematics II

Share Cognitive Science Implications for Teaching Mathematics
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Role #2: They provide the foundation for new learning.   See 21 Feb blog.  Study the blog on 15 MAR 2018 and 10 July 2018.

No longer is there any doubt that:

“All new learning requires a foundation of prior knowledge.”

Memorization of stipulative mathematics definitions provides a form of foundational knowledge upon which to build a complete concept. I will provide a detailed example or two in future blogs.

Words are the tools students use to access background knowledge, to make necessary connections, to learn about new concepts, and to express those ideas in everyday life. In fact, the more terms you know about a specific subject, the easier it is to understand and learn new information related to that subject. One builds upon the other as established in the introductory paragraphs in the website.

If a student has learned (stored in long-term memory and is retrievable) the definition of linear equation, then that student will not be tempted to apply a property of linear equations to a quadratic equation.

If a learner has learned the definition and attending elaboration of “equivalent equations” then the statement “If any expression is added to both sides of an equation the resulting equation is equivalent to the original equation” will be easily learned.  Without a knowledge of “equivalent equations”, the statement “If any expression is added to both sides of an equation the resulting equation is equivalent to the original equation” will be nearly impossible to understand.