SELECTIONS ILLUSTRATING GENERAL EXCELLENCE
From each of two systems ranking among the lowest five in course of study.
3 B. Speer work. Simple work in addition and subtraction, following the plan in the Elementary Arithmetic.
3 A. Primary Book. First half page 26, second half page 41.
Grade III, Number
Exercises, mental and written, in addition, subtraction, multiplication, and division of numbers.
The processes will be explained.
The multiplication table up to 12 will be made by the pupils and thoroughly committed to memory.
Drill in rapid addition.
Notation and numeration to five periods.
Table of weights, United States and English money. Problems in all tables learned.
Square and cubic measure. Troy and apothecaries’ weights. Principles of multiplication.
From the system standing best in course of study.
Grade III B
Scope: Review the work taught in preceding grades. (This review may require from four to six weeks.)
Addition and subtraction of numbers through twenty. Multiplication and division tables through 4’s. Give much practice upon the addition of single columns. Abstract addition, two columns; the result of each column should not exceed twenty. The writing of numbers through one thousand. Roman notation through one hundred. Fractions ½, ¼, and ⅓. The object of the work of this grade is to make pupils ready in the use of the simple fundamental processes.
Book: Cook and Cropsey’s New Elementary Arithmetic (for use of teacher), pp. 1 to 46.
The chief difficulty in the work of this grade is in teaching the arithmetical forms as applied to concrete processes. Pupils should know very thoroughly the work given on pages 1 to 23, Cook and Cropsey’s Arithmetic, before any new forms are taught. They have up to this time used the arithmetical signs and the sentence, and have stated results only. New forms for addition and subtraction are first applied to concrete processes on page 24. No other forms should be taught until pupils are very familiar with these. A drill should be given showing that these two forms are identical and that we must first know what we wish to use them for, if applied to problems. Write
9
2
upon the board and indicate your thought by the signs + and -.
| 9 | 9 | 9 | apples | 9 | apples |
| + 2 | - 2 | + 2 | - 2 | ||
| 11 | 7 | 11 | 7 | apples |
Pupils should be very familiar with these forms before any written concrete work is given.
When the new form for multiplication is introduced, this drill should be repeated:
| 9 | 9 | 9 |
| + 2 | - 2 | × 2 |
| 11 | 7 | 11 |
Nothing new should be added to this until pupils can use these forms without confusion.
When presenting the new forms for division and partition the same method may be used, but pupils should use the form for division some weeks before using the same form for partition. It is not necessary to use the division form for partition until the last four weeks of the term, and not even then, if there seems to be any danger of confusion in using the same form for both processes. The terms division and partition should not be used. The terms measure and finding one of the equal parts can be easily understood. Pupils should be able to read arithmetical forms well, before any use is made of these forms in their application to written concrete work.
All concrete problems should be simple and within the child’s experience.
Grade III A
Scope: 1. Review the work of Grade 3 B.
2. Abstract addition of three columns. Subtraction, using abstract numbers through thousands. Addition and subtraction of United States money. Multiplication and division tables through 6’s. Multiplication and division of abstract numbers through thousands, using 2, 3, 4, and 5 as divisors. Addition and subtraction by “endings” through 2 + 9, last month of term. Writing numbers through ten thousands. Roman notation through one hundred. Fractions ½, ¼, and ⅓.
3. Application of fundamental processes to simple concrete problems, of one step.
4. Measures used—inch, foot, yard, square inch; pint, quart, gallon; peck, bushel; second, minute, hour, day, week, month, year. Use actual measures.
Books: (In hands of pupils) Walsh’s New Primary Arithmetic, pp. 1 to 68.
(For teachers’ use) Cook and Cropsey’s New Elementary Arithmetic, pp. 46 to 85, Article 105.
Even with only the work of a single grade to judge from, one has no difficulty in recognizing the wide difference in the excellence of these courses. As may be seen from Table XXVIII, page 73, in the rating they stand about thirty steps apart, i.e. the one from which the third illustration was taken has a score of 65, while the others have scores of 32 and 39, respectively.