© '98, Agnes Azzolino
Introduction, Activity 1: Find a partner before you read any further, then, have one person read and the other listen to the next paragraph.
From simplest to most sophisticated, we speak mathematics in concrete, pictorial, written, and verbal terms. Within each of these broad families are similar, overlapping, languages. Many teachers use a language from each group in everyday math class communication. Many teachers use predominantly the spoken family. Many use predominantly the spoken and written families. This text lists and examines the use of each language family, the languages in the group, the interrelations between them and suggestions for maximal language use.
If you read the above paragraph, the message was not communicated or received in the same way as if you were the one listening to the paragraph being read. Listening is different from reading.
Verbal communication is different from written communication.
If you look at the figure on the left, above, the message is very different than if you look at the figure in the middle, above.
Each has exactly the same words. In each the words are in the same order from top to bottom.
We recognize conventions in pictorial presentation. The words in the middle picture are ordered and the words in the left appear to float or assume nebulous positions. Floating and listed imply different ideas, different organization structures.
The right most figure, above, is closest to a concrete representation since the words are placed before the viewer one at a time, bottommost picture first - CONCRETE, then CONCRETE and PICTORIAL, then CONCRETE and PICTORIAL and WRITTEN, then CONCRETE and PICTORIAL and WRITTEN and VERBAL.
Please discuss your reaction to these statements with your partner, DTWYP.
The terms spoken, written, pictorial, and concrete have been introduced as broad catagories or families as a means of grouping the 18 math classrooms languages listed in this text. The next page will list the languages grouped in families, begin the introduction of each language, and suggestion how the language might best be used.
Verbal, Written, Pictorial, and Concrete (the Hundreds Board, for example) are the four broad mathematics language families discussed in this electronic monograph found at www.mathnstuff.com/papers/langu/page0.htm and additional pages (ISBN: 1-929-870-01-9 © 1998, Agnes Azzolino).
© 2005, Agnes Azzolino