By Joseph V. Collins

Excerpt from An uncomplicated Exposition of Grassmann's Ausdehnungslehre, or idea of Extension

The sum qf any variety of vectors is located by means of becoming a member of the start element of the second one vector to the top aspect of the 1st, the start aspect of the 3rd to the top aspect of the second one. etc; the vector from the start element of the 1st vector to the tip aspect of the final is the sum required.

The sum and distinction of 2 vectors are the diagonals of the parallelogram whose adjoining aspects are the given vectors.

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**Extra resources for An elementary exposition of Grassmann's Ausdehnungslehre, or Theory of extension**

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New York: Teachers College Press. This chapter describes two algebra lessons involving pattern tasks that were taught in an urban high school classroom. The first is similar to the activity used by Catherine Evans and David Young. The second employs a nonlinear pattern involving staircases and the number of cubes used to build them. The role of the teacher and students is discussed as students explore the patterns, develop their understanding of variable, explain their mathematical reasoning, and create strategies (including recursion, direct-modeling, and relating the formula to the figure) for finding the general rule.

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1996). A function as a mail carrier. Mathematics Teacher, 89, 468–469. This article discusses some of the difficulties secondary students have understanding the concept of function. In particular, the article addresses the ideas that a function is an object rather than a process and that a function does not always have to be defined by a symbolic rule. The author then suggests the metaphor of a function as a mail carrier, as a way to help students understand the concept of function. Scanlon, D.