NUMBER LESSONS Number by Development CAROLINE HAGAR, State Normal School, Fitchburg, Mass. T HE little group of children standing around the table eyed Miss Hepsey and the objects in front of them with keen interest. Inch cubes, 3-inch and 4-inch kindergarten sticks, colored splints and blocks were placed before each child with ample space to arrange these as directed by their teacher. "Now," said Miss Hepsey, "no one must touch anything until I tell him he may do so. Let us see how many can do just what I ask. These are blocks (touching the objects as she named them), "these are sticks, these cubes and these splints. Show me two blocks." Children do so (00). Miss Hepsey Show me another two. Children show another two (oo oo). Miss Hepsey Show me another two. Children do so and now have this arrangement: (00 oo 00.) Miss Hepsey Good. Now how many twos have you? Miss Hepsey Count them. (Children point to each of their twos in order, beginning, of course, at the left with the first two put down.) Children (touching each two and counting) One, two, three - three twos. Miss Hepsey This is the way the crayon says three twos -(3 2's). (Written by Miss Hepsey on the blackboard.) Miss Hepsey Now clear away the blocks you have been using, putting them all together again. That is right. Now show me a three. Children (ooo.) Miss Hepsey Show me another three. Children (ooo 000.) Miss Hepsey Show me another three. Children (ooo 000 000.) Miss Hepsey Now how many threes have you? Class Three threes. Miss Hepsey This is the way the crayon says three threes. She writes on the blackboard (3 3's). Miss Hepsey Clear away the blocks again. What shall we use this time? Mary Little sticks. Miss Hepsey This time we will take the little sticks. Miss Hepsey Make the crayon say a three and a three. Miss Hepsey Show me a two. Miss Hepsey Show me another two. Miss Hepsey Show me another two. Miss Hepsey How many twos? Miss Hepsey Mary write it for me. Mary writes (3 2's). Three twos. Miss Hepsey Count for me what you have. Class Two and two and two. Miss Hepsey Make the crayon say it that way. Miss Hepsey Read this for me. (Three twos.) Miss Hepsey Read this. (2 + 2 + 2.) (Two and two and two.) (NOTE There should be a way of speaking of each of these read- Miss Hepsey Show me a four and a two. Miss Hepsey This is the way the crayon says it, or, Children (4+2). Miss Hepsey Show me three threes. Children Four. Miss Hepsey What is the fourth group? Miss Hepsey Are the groups alike? Miss Hepsey Read it the short way then. Miss Hepsey Make the crayon say it the short way. Miss Hepsey constructs (ooo ooo ooo). Miss Hepsey Make the crayon say it. Miss Hepsey What is the first group? Miss Hepsey What is the second group? Miss Hepsey The third? Miss Hepsey Are the groups alike? Miss Hepsey Read it the short way. Miss Hepsey Read it the long way? Miss Hepsey Make the crayon say it the long way. After some time spent in drill of this kind, Miss Hepsey puts Reading Lessons in Written Work on the blackboard, the purpose being simply to give practice in reading written work. Such exercises are reading lessons in number, there being no object work connected with it. 3 +3+3 2 3's 2 2's Miss Hepsey Now I will have the crayon tell you what to 4 + 4 5 + 1 make on the table. ( Miss Hepsey writes (2 + 2 + 2.) Miss Hepsey Read what you have. Children Two and two and two. Miss Hepsey Count them. Children count "One, two, three three twos. Miss Hepsey Laura, write this for me the "s" way. Laura writes (3 2's). The pupils constructed this on the left half of their desks, leaving the right half clear for them to use in the written work which followed. If a child made a mistake in construction, Miss Hepsey did not correct the mistake, but simply pointed to the wrong construction, leaving the child to discover and rectify the error himself. Each child was made to rely as much as possible upon himself. When Miss Hepsey had finished dictating the expressions and all had been constructed correctly on the desks, she gave to each child a piece of paper and told him to write the whole exercise from the construction work on his desk. She did not expect or desire that the pupils' written work should be an exact reproduction of the original dictation or that two pupils should agree in all the written expressions of an exercise. In the unequal-group expressions the written work would be the same, but in the equal-group expressions on the desk or blackboard, the work on the children's papers may differ. When she looked over the papers, Mary had written for this expression (00 00 00) (∞0 oo oo) while John had written (3 2's), both being correct interpretations of the desk construction. For this construction (o o oo) Laura had written (4 1's) while Ruth had (1 + i + 1 + 1), both papers being correct. The next day Miss Hepsey wrote on the blackboard a dictation exercise of twenty expressions for the children to construct on their desks without assistance or oversight. These she wrote on the blackboard before school and now had her time free for the "A" class while the "B" class were at work upon their constructions. When all had finished the constructions Miss Hepsey examined the work of each to see that it was correct. She now erased the dictation and the children were given paper and pencil to write the exercises from the object work upon their desks. While the children were doing this, Miss Hepsey was once more free for other school work, but the children were told that the object work must remain on the desks after the written work was done in order that she might compare it with the completed written work. In order that the child might find the place quickly in glancing from the desk to the board, Miss Hepsey wrote every fourth expression in the dictation column with colored crayon. The child read the first expression, constructed it on his desk, read the next, constructed it, and so on. MISS HEPSEY'S BLACKBOARD DICTATION 5 4's 35's 2 + 4 2+5 5 2's 23's ing. Day after day for three or four weeks Miss Hepsey continued this seat construction and written work, always looking carefully over each child's work and allowing him to rectify his mistakes alone. Each child was provided with two or more classes of objects for counting material. Beans, peas, small sticks, large sticks and pegs were used. C Third Grade Number January ΚΑΤΕ Κ. Ο'NEILL OUNT by sixes beginning with o, 1, 2, 3, 4, 5, 6. Either two rings or two sets of figures should be in sight until the children can count rapidly without. o, 6, 2, 8, 4 and 1, 7, 3, 9, 5. If they know their combination, this counting or adding will not be hard. Teach them to see that the counting is only a review of their combinations in addition in a different form. A great deal of time is frequently wasted by not making the children see the different ways of doing the same thing, instead of letting granted. Know that the children know what you want them them imagine everything is new. Never take anything for to know. Take the sevens in the same way as soon as the sixes are learned. Give frequent drills on how many can be left over. How many can be left when you divide 4, 6, 9, 2, 10, 3, II, 5, 7, 12, 8? Drill, drill, drill and then drill some more on o divided by; divide by o; o multiplied by; multiply by o; add o; and subtract o. Simple as this seems children make many mistakes unless much care is taken in all three lower grades. Continue reading and writing numbers, and dollars and cents. Also continue to ask about the terms of the different combinations, leaving the sample lesson in sight for reference. If there is a lack of board room make charts of Manila paper, using a marking crayon. Cheaper than these are the large sheets of paper obtained at a printing office for a cent a sheet, and a one-cent rubber tipped pencil dipped in ink for the marking. Do not allow the children to use signs when working examples. It is unnecessary and the higher grade teachers complain that it is not easy to break the children of the habit. Why have them work: 2+4 2+3 4 2's 3+2 32's 42 21 +16 4 + I 79 |