Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

ARITHMETICS

PRIMARY BOOK

BY

[ocr errors]

THOMAS ALEXANDER
Professor of Education, Teachers College, Columbia University
Formerly Professor of Elementary Education, George

Peabody College for Teachers

AND

CHARLES MADISON SARRATT
Associate Professor of Mathematics, Vanderbilt University
Formerly Assistant Professor of Applied Mathematics, Syracuse University

JOHNSON PUBLISHING COMPANY

RICHMOND, VIRGINIA

[merged small][ocr errors][merged small][merged small]

Lo

Introduction

Principles Underlying the Series

The authors have kept the following principles in mind in making these books:

1. That children should be able to solve problems dealing with life situations and that these problems are ordinarily simple and concrete.

2. That accuracy and speed in the fundamental operations in whole numbers and fractions are highly essential and should receive the chief emphasis since almost nine tenths of our arithmetical experiences involve nothing more than the simple operations applied to one- and two-step problems.

3. That drill material should be specific, the amount of drill varying with the individual ability of the child.

4. That the laws of habit formation should be employed throughout the texts.

5. That the problem material should be interesting and real.

6. That problem tests should contain more work than any child can finish in the allotted time in order to make provision for individual differences in ability and performance.

7. That the sequence of topics should be psychological.

8. That practice on any given arithmetical process should be distributed at gradually lengthened intervals throughout the texts.

9. That the rationalization of processes should be introduced after the processes have been learned.

10. That the natural tendencies of children should be utilized.

11. That interest, instinctive or acquired, should be employed in drills and in the problem material.

12. That habits of language and procedure which later must be broken should not be formed.

iii

00:00

13. That books should train the child to verify results.

14. That wasteful and harmful topics, such as arbitrary units of measure, multiples of eleven, the difference between concrete and abstract numbers, obsolete and rare terms and processes, and linguistic difficulties should be avoided.

15. That arithmetic should provide for a gradual development of mathematical concepts, such as the idea of function and the equation, which the child will need in later work.

Psychological Principles Employed 1. Interest is elicited by an appeal to:

(a) The child's instinctive tendencies, as, for example, his desire to excel, to win out in competition, to improve, to secure definite results, to solve puzzles, to manipulate and construct.

(b) The child's needs as they are felt by him in his play, in school work, and in his duties at home or in the community.

(c) The child's own experience, as, for example, the arousing of interest in arithmetic through interest in batting averages,

tennis scores, Boy Scout work, etc. 2. The processes in general are introduced inductively.

3. The principles of habit formation are utilized in teaching arithmetical processes. Habits are formed in such a way as to be of the greatest possible use in the working life.

4. The difficulties of children are diagnosed and remedial drills are provided.

5. Provision is made for individual differences in ability and achievement by furnishing specific drills and by providing for problem material subject matter of a wide range of difficulty.

6. Through the projects and activities suggested, arithmetical concepts are approached concretely and inductively.

7. Reasoning is called for in the problem sections, with such provisions that pupils will not be able to solve problems merely by following the model at the first of the list.

Drill

1. All the exercises have been motivated by appeals to the instincts and needs of children.

2. Supervisory tests have been devised to discover the weaknesses of individual pupils and drills have been made of such character as to train the child in those arithmetical processes that need development. They have been arranged in such a way that in a given lesson each child will get the drilling he needs. In other words, the text provides specific rather than general drills.

3. Drills are distributed throughout the year, with the result that they cannot be overlooked or overemphasized by careless teachers.

4. It is intended that drills on any given process should be mastered before one on a new process is begun. Thereafter the drill is reintroduced as nearly as possible at gradually lengthening intervals in order to prevent pupils from forgetting principles once learned.

5. The books contain specific drills for every known arithmetical difficulty.

6. The drill material in the fundamentals is the same for all intermediate and upper grades except that the time allowed for them is gradually shortened in successive grades.

7. The drills are so regulated that any teacher will be enabled to know whether the children in a certain class may measure up to standards commonly accepted throughout the country.

8. They appeal to the instincts of children in that they are generally put on a competitive basis.

9. The drill material utilizes simple, easy, commonly-used numbers.

10. The material is graded and indices are provided in order that the teacher may know what drills to use.

11. Special difficulty drills are featured.

« ΠροηγούμενηΣυνέχεια »