A quiz for arithmetic teachersAuthor(s): B. G. PAULEYSource: The Arithmetic Teacher, Vol. 10, No. 3 (March 1963), pp. 141-142Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41186727 .

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A quiz for arithmetic teachers

B. G. PAULEY Kanawha County Schools, Charleston, West Virginia Mr. Pauley is associate superintendent of Kanawha County Schools.

JVlany curriculum planning groups and school systems are studying the mathe- matics offered in the elementary schools. As a result, more and more of the topics and terminology commonly called "the new mathematics" are appearing in print for use by elementary teachers. Presently most of these materials are designed for enrichment, but it is likely that the new topics and terminology will begin to ap- pear more and more in basic textbooks. Many elementary teachers whose prepa- ration programs have been traditional or who do not consider themselves to be as adequately prepared to teach mathe- matics as they should like to be are finding the "new mathematics" difficult to use. However, if the present trend continues and the number of books containing "modern topics" are an index, elementary teachers will have to accept the fact that this new kind of mathematics is here to stay.

Fortunately, some National Science Foundation institutes and other forms of in-service training are available to ele- mentary teachers. Most school systems in which the "new mathematics" is intro- duced into the elementary schools make some provision for in-service education. While the new topics and new terminology are different, they are not so difficult that they are beyond the comprehension of elementary teachers. Certainly teachers should be able to master concepts that are intended for intermediate grade pupils, even though the teacher may have to relearn or even unlearn some things.

The "quiz" below is designed to stimu- late interest in the new topics and ter-

minology that are appearing in elementary school mathematics programs. Teachers may wish to take the "test" themselves as well as to administer it to their pupils. It is a "fun quiz." Some choices that are included are obviously ridiculous. There are no norms. No one can pass or fail. The questions and problems used have been selected to illustrate topics and terminology that are now in use in the intermediate grades in many schools.

The author's answers will be found following the last question. The test has in no sense been standardized. It has no known validity nor reliability, but can serve as a basis for discussion and explora- tion.

1. The statement that 2+2 = 4 is a. always true b. true in the United States only c. true under some conditions d. an axiom

2. Addition, subtraction, multiplication and division are methods of perform- ing what operation?

a. arithmetic b. homework с computations d. regrouping

3. Which of the following forms is cor- rect for the indicated multiplication? a. 24 b. 24 с 24 d. 24X3 = 72

ХЗ ХЗ ХЗ 60 12 72 11 ^2. 72 72

March 1963 141

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4. Which of the following fractions makes the statement f >n>| true? a. 16 b. 11 с. Ш d. 13

19 16 17 22

5. What is an algorism? a. a palace in Granada b. an Arabian mathematician c. a form for computation d. a branch of modern algebra

6. A numeral is a. a small number b. a symbol that stands for a num-

ber c. the name of a number d. a word that represents a number

7. We say six eights are forty-eight be- cause

a. it can be represented as a set of four tens and eight units

b. it is six times as great as one eight

с it is the set of six eights d. everyone knows it is true

8. Why do we invert the divisor and multiply when we divide fractions?

a. As a convenient short cut b. Because it gives the answer c. We do not have to; we can invert

the dividend d. In order to be able to use can-

cellation

9. The relation of the product of a multiplication to the factors mul- tiplied is described as:

a. unrelated b. equal to c. greater than d. less than

10. In the decimal system, things are collected

a. by addition b. into sets of tens c. for charitable purposes d. through withholding

11. A null set is a. something sweet to the ear b. nothing с the set of all nulls d. an empty set

12. An example of a subset of the set of all natural numbers is:

a. 7, 8, 9 ... 16 b. 6-3, 6-1, 6-love с 2¿, 2i 2' . . . 2+Ì d. -1, -2, -3 ... -n

13. In what kind of arithmetic could the following statement be true? 11+4 = 3

a. arithmetic with a duodecimal base

b. the binary system с modular arithmetic d. None; the statement is nonsense

14. The associative law is illustrated by which of the following?

a. 3 + (2+l) = (3+2) + l b. aXb = bXa c. n(a+b)=an+bn d. Birds of a feather flock together

15. The natives of the Zenobian Islands have developed a number system which they represent as follows:

X, Л, О, 7г, +, XI, XX, ХЛ, XO, Хтг, X+, Л1, ЛХ, ЛЛ, etc.

If a native chief paid + gritos each for his 7Г wives, how much did they cost him all together?

a. X X gritos b. O O gritos c. Л я" gritos d. О Л gritos

Answers for quiz

1. с 6. b 11. d 2. d 7. a 12. a 3. a, b, 8. a 13. с

с and d 9. b 14. a 4. b 10. b 15. d 5. с

142 The Arithmetic Teacher

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