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Manuals
Conduct of Christian Schools:
FIRST PART - Chapter 5
SCHOOL PRACTICES AND THE MANNER IN WHICH THEY ARE TO BE CARRIED OUT
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CHAPTER 5
Arithmetic
In the study of arithmetic, students will have different lessons according to how advanced they may be. Some of them will be learning addition, others will be learning subtraction, multiplication, or division. Teachers will take care to write on the board a problem for each operation every Saturday or on the last school day if Saturday is a holy day. They will see that all who are learning arithmetic copy their examples on Monday morning at the beginning of the writing lesson or on the first school day if there is a holy day on Monday. For this, each must have a notebook of white paper folded in quarters. Arithmetic will be taught only to those who are entering the fourth level in writing, and it is the duty of the Director or of the Inspector of Schools to promote to this lesson as well as to the others. Arithmetic will be taught on Tuesday and Friday afternoon from one thirty to two o'clock. If there is a holy day on Tuesday, it will be taught on Wednesday, unless there is a holy day on Monday as well as on Tuesday. If there is a holy day on Friday, it will be taught on Saturday.
To teach arithmetic, the teacher will either remain seated on his chair or will stand before it. A student of each lesson will stand in front of the class and solve the problem for the lesson. The student will indicate the steps and, with the pointer, the figures, adding, subtracting, multiplying, or dividing the numbers aloud.
Thus, to make an addition properly, the students will always begin by adding deniers,7 and speaking out loud, saying for example: 10 and 6 make 16, and so on.
While the example of the lesson is being done, the teacher will ask the student several questions concerning it, in order to make the student better understand and retain the lesson. If terms pertaining to the subject are used which the student does not understand, the teacher will explain them and make the student repeat them before going further. From time to time, the teacher will also question some other students who have the same lesson, to ascertain if they are attentive and if they understand. If the one who is doing the example fails in any respect, the teacher will make a sign to another student who is learning the same lesson or one who is learning a more advanced lesson to make the correction. The latter will do this by correcting aloud what the other one had said wrongly. If there are no lessons more advanced than this one and if no student is able to correct the mistake properly, the teacher will make the correction.
The student who is doing the example on the board should, as part of doing the example, write at the bottom both the result of the addition, subtraction, multiplication, or division and the proof of the problem which has just been done. After this, the students will erase all that they themselves have written but nothing more. In this way, another student may do the same example.
In arithmetic, as well as in the other subjects, it is with the most elementary examples that the lesson will begin and with the most advanced that it will end.
When a student is doing an example in arithmetic whatever the grade, all the others who have the same lesson will remain seated facing the board and will pay attention to the figures that the student writes and to what the student says when doing the example. The students who are reading and who are not yet learning arithmetic will also pay attention. The teacher will have a register of all the students who are learning arithmetic, divided according to the lesson that they are studying, and will have each of them, one after another and without any exception, do an example from their lessons on the board in school.
On Tuesday of each week or the first day upon which arithmetic is taught, all the students who are learning it and who are among the advanced students will bring already done on their paper the example for their lesson which the teacher has written on the board for that week. They will also bring some other examples which they have invented for themselves. On Friday, they will bring a certain number of examples from their own lessons as well as from the work of more elementary lessons which they have done by themselves and which the teacher has, according to their capacity, assigned for them to do.
During the writing time on Tuesday and Thursday afternoons, instead of correcting the writing, the teacher will correct the examples which the students of arithmetic have done by themselves on their papers. The teacher will explain why anything is incorrect. Concerning addition, the teacher will, for example, ask them: "Why do we begin with deniers?" "Why do we reduce the deniers to sols and the sols to livres?"8 The teacher will ask other similar questions, as needed, and will give the students a full explanation.
7 The denier is the smallest unit of the old French monetary system.
8 At the time of De La Salle, the living expenses for a Brother were approximately 200-250 livres per year; 12 deniers were the equivalent of 1 sol, and 20 sols equaled 1 livres.
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