Arithmetic of Words: Physics of Measurement Volume I

School Science and Mathematics, Feb 1999 by Abdi, S Wali

Arithmetic of Words: Physics of Measurement Volume I

Author

Aggelos Kotas Afytos

630 77 Kassandra

Greece

1997; 255 pages

One way to get new ideas for improving mathematics teaching is to see what is being done in other countries. Arithmetic of Words: Physics of Measurement provides some insight into how its Greek author believes "natural arithmetic" should be introduced to students and what related knowledge their teachers should have of this content.

Reviewing this book was made difficult by two factors: (a) the translation of the book from Greek into English (by the author) was sometimes imperfect, and (b) only a translation of a part of the original text was submitted for review.

One of the basic ideas appearing throughout the book is named "arithmetical words" by the author. What these words are, their rank, classification,and usage are discussed for numbers, multitude-quantity, weight-mass, time, value-money, distance-length, width, height, depth, and thickness.

Two aspects of the book I found of special interest were the examples and homework problems it contained. To provide you with some idea of their nature, two examples and two problems are reproduced as follows.

Examples

The apricots (p.172)

Helen and Costas have bought apricots. Helen ate half of the apricots she bought. Costas gave half of his apricots to Eli and three of the remaining apricots to Helen, who now has as many apricots as Costas. How many more apricots did Costas buy than Helen?

Time for exams (p. 126)

The students of the second grade in high school took the math exam the day before yesterday. Two days before the math exam, they took the physics exam. Tomorrow they will be tested on geography and 3 days after that the Biology exam follows. The chemistry exam comes 1 day after the biology exam. How many days are there between the day of the physics exam and the day of the chemistry exam?

Problems

The cookies (p. 85)

Christine's mother made a tray of cookies for her daughter's birthday. Just when the cookies were out of the oven, Christine ate one and her sister ate three of them. Some cookies were broken while trying to take them out from the tray, and as a result, Christine and her another ate them, taking half each. Finally, of the 54 cookies that were baked, 42 were left for guests. How many cookies did Christine eat?

How old is he? (p. 123)

Costas is 2 years older than Helen. Helen's brother was born in 1980. If Helen is 2 years older than her brother, how old was Costas in 1995?

Editor's Note: S. Wali Abdi's postal address is The University of Memphis, Department of Instruction and Curriculum Leadership, 401 A Ball Hall, Memphis, TN 38152, ande-mail address is abdi.wali@coe.memphis.edu.

Reviewer

Bob Prielipp

University of Wisconsin Oshkosh

Oshkosh, WI