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APPLICATIONS OF THE FILM IN MATHEMATICS
dramatized with tickets and with play pennies. Each situation should be represented by the use of the new symbolism.
It should be pointed out that the aim of the procedure described above was not to teach any specific group of number
relations, such as 3 15 3 | 12 4 j 20, etc. Rather, the aim was to teach the nature of division as the process which requires the separation of a larger group into equal smaller groups of a given size, and to introduce the arrangement of numbers and a frame which may be used to express this division idea. The plan aimed also to relate division to subtraction as the mathematical way of finding out how many of the equal smaller groups could be formed from the larger group.
Pupils need experiences in utilizing the division idea and its symbolism in a variety of situations. A film which pictured the following activities might well be shown after the children had participated in the buying of seeds:
Social situation: The pupils have planted tomato seeds in the seed box in their room, and a total of 24 plants of one kind have come up and are ready for transplanting. Pupils wish to transplant them into flower pots with 4 plants in each pot.
Concrete stage: Pupils take groups of 4 plants out of the seed box and plant them in pots until all are planted. The successive subtraction of groups of four is emphasized. Since a group of four could be taken away six times, there were enough to fill 6 pots.
Semi-concrete stage: 24 lines appear to stand for 24 plants. The narrator asks, "How many 4's in 24?" The lines group themselves in 4's by the successive subtraction of 4. Each time a group of 4 separates a subtraction example appears on the screen.
Symbolism of division: The 24 lines appear in a continuous row, then they disappear and the number 24 appears. About the 24 the frame appears and the 4 outside the frame appears. For a moment the 24 lines appear again and group themselves into fours. The number six appears above the frame
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