COMPOSITION OF NUMERAL SYSTEMS ACROSS LANGUAGES (MATHEMATICAL PROBLEMS IN NUMBERS)

The number system is investigated in this study as a small yet typical semiotic system of a larger one, i.e. language. The double-faceted nature of signs is self-evident: most numbers have two senses, one being morphological and the other being lexical. Underlying the different additions and multiplications in numbers is peoples’ mathematical and linguistic thought. While the Vietnamese reveal their mathematical thought in “mười”, “mươi”, “một chục” (ten) on the basis of decimal numeration, the French are opted for vigesimal numeration (80=4x20 – quatre vingt), and the Taiwanese merely rely on their hands and fingers. The systematicity and national peculiarities are also visible, even though numbers may have been borrowed from other languages. In this paper, we use data from ethnic languages in Vietnam, Austroasiatic and Austronesian languages, or, to be accurate, Austro-Tai languages which are closely related to Vietnamese. Some languages beyond Vietnam’s borders are also referred to when necessary. We compare and contrast the number systems in isolating, analytic languages in Vietnam and Southeast Asia with those in Indo-European languages, including such typical inflectional, synthetic languages as French, English and German before drawing general conclusions. Finally, the paper offers an overview of the evolution of number systems across languages spanning from about 10,000 years ago to the last millennium, as well as ancestral relations among languages.

Notations, Conventions, and Constraints: Contributions to Effective Uses of Concrete Materials in Elementary Mathematics

Twenty fourth-grade children were matched according to performance on a whole-number calculation and concepts pretest and assigned at random to one of two groups: wooden base-ten blocks and computerized microworld. Instruction in each group was designed to orient students toward relationships between notation and meaning. Instruction given the two groups was based upon a single script that extended whole number numeration to decimal numeration, and emphasized solving problems in concrete settings while inventing notational schemes to represent steps in solutions. Neither group changed in regard to whole-number notational methods. Blocks children understood decimal numerals as if they were funny whole numbers; Microworld children attempted to give meaning to decimal notational methods, but were largely in a state of disequilibrium at the end of the study.

By Way of Introduction

Some things need to be learned in the sense of being simply memorized—the forms and order of the letters of the alphabet, a, b, c, …, x, y, z; the ten digits of the decimal numeration system, 0, 1, 2, …, 8, 9; months of the year; and day of the week, for example.

Money—A Key to Mathematical Success

In a poll reported several years ago on the Phil Donahue Show, children rated money as the most important item on a list that included peers, school, and family. Children are fascinated with money from a very early age, so why not capitalize on this prevailing interest in money by using money to teach other topics such as fractions, percents, decimals, and non-decimal numeration.

What am I ever going to use that for?

What am I ever going to use that for?” is an often-heard complaint in the mathematics classroom. One of the topics about which such a complaint is voiced is that of nondecimal bases. And, perhaps, such a complaint is not unreasonable, for the only answer that most teachers seem to have is some vague comment that the study of nondecimal numeration will help the student better understand the decimal numeration system.

The quest for an improved curriculum

For the past several years teachers have been almost overwhelmed by successive waves of propaganda that has generally been critical of our “traditional” mathematics programs. Unless set notation and symbolism, non-decimal numeration, modular arithmetic and strict attention to correct terminology (such as distinction between number and numeral) were included in our courses of study, we were not up-todate. Our students would be ill-prepared for their responsibilities in the Space Age and we were effectively sabotaging the future of our country.