1. Math Metaphors • Atif Chaudhry • Malvin Hiew • Ruth Limberg • Thi Nguyen

2. Abstract Math: Images and Metaphorshttp://www.abstractmath.org/MM/MMImagesMetaphors.htm

3. This website contains mathematical metaphors. Math metaphors argue that people use metaphors and images to better understand math. • ¨  “Continuous functions don’t have gaps in the graph”. As a student, this helps you to visualize and understand continuity of functions. • ¨  You may think of the real numbers as lying along a straight line (the real line) that extends infinitely far in both directions. This is both a visual and a metaphor (a real number “is” a place on the real line).

4. Understanding without Proofhttp://www.rattlesnake.com/notions/math-metaphor.html

5. People use math metaphors in our day to day life from toddlers to adults. • There are actually four ‘grounding’ metaphors (metaphors based on experiences many of us had as a child).: • Adding and taking away objects from a collection (playing with pebbles); • Construction of a larger whole from smaller objects (playing with blocks); • Measuring the width or height of something (by stretching our hands to the ends of the object or standing up to see how high it is); • Moving from one place to another (by crawling or walking). • These experiences provide us with four metaphors that work with arithmetic. Four inference-preserving cross-domain mapping mechanisms that work consistently with each other and the world.

6. Understanding Integrated Mathematics Using Living Metaphorshttp://www.nctm.org/resources/contnet.aspx?id=1674

7. Grow rather than build • This is an article written by F.Merlino, project director of the Greater Philadelphia Secondary Mathematics Project at La Salle University. In this article, Merlino is disputing the learning methods of math that he grew up with and embracing the new mathematical era; which involves metaphors and analogies rather than repetition and “laying a good foundation.” He has proved that mathematical metaphors have been outdated and should be done away with.

8. Grow rather than build con’t Some quotes from Merlino’s article include: • “Metaphors can also limit how we think, can prevent us from "thinking outside the box," can constrain our imaginations, and can veil our eyes from seeing things as they really are.” • Integrated curricula can be better understood if we view the act of thinking as a living system, like a growing tree, rather than like a structure made of bricks and mortar. Using "living" metaphors has enormous implications for how we think about mathematics education.

9. Dictionary.comhttp://dictionary.reference.com/browse/metaphorDictionary.comhttp://dictionary.reference.com/browse/metaphor

10. Metaphor: A Definitionhttp://dictionary.reference.com/browse/metaphor • Metaphor: • a figure of speech in which a term or phrase is applied to something to which it is not literally applicable in order to suggest a resemblance, as in “A mighty fortress is our God.” • Something used, or regarded as being used, to represent something else; emblem; symbol. • Dictionary.com is a website where anyone can come and find definitions for words that they don't understand the meaning to. One can type in almost any words and find the meaning to that word.