A Foundational Study in the Pedagogy of Arithmetic

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Care was used to so distribute the exercises that none should be prolonged to the point of fatigue. In the lower grades particu- larly the exercises were so sectioned off that no section demanded more than 15 to 20 minutes. They were usually given in the morning, but not regularly so, since before proceeding very far with the work it was discovered that the pupils hailed the experiments as a welcome change from the regular routine, what- ever the time of day.
Materials. The materials used were
...number pictures (quad- ratische Zahlbilder) constructed after the manner of Lay's pic- tures. Black circles one inch in diameter were pasted on white cardboard, a separate card being prepared for each number from 3 to 12. The strokes between circles used by Lay to indicate operations were also reproduced, although they possess little or no significance for the investigation. The children were told to disregard them when viewing a card.
The series of cards is pictured on the next page.
In each square group (quadrat) of four circles, on the cards as constructed, the distance between the circles forming the sides of the square was 2 inches; and the distance between the quadrats, 3 inches: the ratio between the two distances was thus made: 2:3=1.


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