A Foundational Study in the Pedagogy of Arithmetic |
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ability abstract accuracy addition arithmetic arrangement association auditory average Beetz Born pictures calculation cards child circles comparative Comparative Graph conclusion consciousness correlation counting Courtis Diamandi difficult digit distance division divisor drill Education efficiency error examples experimental experiments exposure factor figures First-year Pupils four Führer fundamentals George Parker Bidder given grade 5A grasp guessed individual interest large number Lay's major premise marks mathematical measure memory mental mental calculation method metic minuend motor multiplication number concept number forms number names number of mistakes number pictures objects operations pedagogical perception practice presentation problems procedure prodigies psychology Pupils Training School quadratic pictures Quartile quinary quotient reasoning relative rows Russian machine scores standard standard scores strokes subtraction takes Cent teachers teaching tests things tion training school pupils unit vigesimal visual whole ΙΟ
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Page 253 - Do not work the following examples. Read each example through, make up your mind what operation you would use if you were going to work it, then write the name of the operation selected in the blank space after the example. Use the following abbreviations:
Page 255 - Name School Grade In the blank space below, work as many of the following examples as possible in the time allowed. Work them in order as numbered, entering each answer in the "answer" column before commencing a new example.
Page 107 - First, the analysis of the situation by which the essential features of the problems are conceived and abstracted ; second, the recall of an appropriate principle to be applied to the abstract problem, a search among various principles which may suggest themselves for the right one, and, third, involving the second, the inference, the recognition of identity between the known principle and the new situation.
Page 29 - ... 3's, etc. Now in these latter series 2x2, 2x2x2, 3x3, 3x3x3, etc., in short, the powers of the number by which he was counting, were natural resting-places, and awakened his interest, so that before long he began to count in the power series of different numbers (2, 4, 8, 16, 32, etc., 3, 9, 27, 81, etc.) for considerable distances. At first he simply emphasized the powers as they occurred in the complete series of multiples, but gradually he learned to omit the intermediate multiples, and simply...
Page 5 - ... mystical number in the Muses of classical mythology, in Anglo-Saxon aphorisms emphasizing the vitality of the cat and the effeminacy of the tailor, and as a recurring tale in all of the superabundant Celtic lore such as that currently recorded by Seumas MacManus; it even survived in the schoolbooks of the early part of the century in the more curious than useful arithmetic process of
Page 111 - Rule. — Multiply the numerators together for the numerator of the product, and the denominators together for the denominator of the product.
Page 255 - Do not work on any other paper. 1. A party of children went from a school to a woods to gather nuts. The number found was but 205 so they bought 1955 nuts more from a farmer. The nuts were shared equally by the children and each received 45. How many children were there in the party? 2. One summer a farmer hired 43 boys to work in an apple orchard. There were 35 trees loaded with fruit and in 57 minutes each boy had picked 49 apples. If in the beginning the total number of apples on the trees was...
Page 20 - Here we find real mathematical ability, power to take a distinctly algebraic point of view, to generalize, and hence to discover all sorts of ingenious short-cuts and symmetries.
Page 254 - Mul." for multiplication, and " Div." for division. 1. The children of a school gave a sleigh-ride party. There were 9 sleighs used, and each sleigh held 30 children. How many children were there in the party? 2. Two school-girls played a number game. The score of the girl that lost was 57 points and she was beaten by 16 points. What was the score of the girl that won? 3. A girl counted the automobiles that passed a school. The total was 60 in two hours. If the girl saw 27 pass the first hour how...
Page 280 - Grade 2. Grade 3. Grade 4. Grade 5. Grade 6. Grade 7. Grade 8. Grade 9. Grade 10. Grade 11. Grade 12. Grade 13. Grade 14. AMENDED STATUTE Grade 1. Grade 2. Grade 3.