844 SCHOOL SCIENCE AND MATHEMATICS

THE SOCIALIZED RECITATION IN MATHEMATICS.By F. E. Buss,

High School, Madison, Wis.During the last two or three years the socialized recitation

has been the subject of many a conversation of worthy peda-gogues and enthusiastic teachers, so much so in fact that ateacher with but a normal interest in his work could not helpbeing curious about it, as to what it really is and why it shouldbe.The term, ^the socialized recitation,^ implies more or less

freedom of speech on the part of the pupils during the classperiod, also an opportunity for actually doing things wheneverpossible. The purpose of such a recitation, according to Wm.Whitney, is twofold: to substitute for the passivity of most ofthe pupils in the classroom actual activity and to provide oppor-tunity for developing the initiative of the children. All teachers,of course, agree that the ideal class is one in which every childis actually thinking about the subject under discussion everyminute of the time. If the pupils are given an opportunityto voice their thoughts and are even encouraged to do so, therenaturally is an added incentive for thinking about the subject.If the other members of the class express their opinions, eachindividual desires to do likewise, hence tries doubly hard to havean opinion. In recent years, initiative on the part of an in-dividual seems to have been a growing factor in his struggle forsuccess. Thus far it has been an incidental or accidental resultof our teaching. But the socialized recitation recognizes itsworth and provides for its development.Now, how manipulate a socialized recitation? It is very evi-

dent that by permitting and encouraging this greater freedom,utter confusion might easily result. The teacher must have avery definite plan in mind, must outline it to the pupils and makethe necessary regulations to achieve his aim. The actual methodof procedure may vary, but the usual tendency of teachers whohave tried out the socialized recitation is to have the class workin groups. The number in a group may vary from two to sixand the groups may be arranged so that poor students form onegroup, those of moderate ability another, etc.; or each groupmay contain an excellent student as leader, a few mediocre ones,and one or two poor ones. Still other teachers who favor thegroup plan, arrange these groups with no thought of their rankas students, but from the point of view of getting together

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those that will work well as a group. Groups may be broken upand rearranged daily or whenever the teacher sees fit. Theyusually work as units in different parts of the room, but maybe called together for a class recitation or a group report to theclass, for a whole period or part of one at any time. When a

group reports to a class, its leader may do the talking, or he maycall on one of his co-workers to do so, while the others will fillin his recitation. The rest of the class may ask questions, criti-cize, etc., being called on by the group leader or by the pupilreciting.The other plan of the socialized recitation which has usually

found favor is the one according to which the class conductsitself. A leader is usually appointed by the teacher for theperiod or part of it, to open the discussion, call on others to con-tribute information, to correct, to criticize, or to question; orthe members of the class may volunteer. The danger, in thelatter case, of course, is a monopoly of the recitation by capablepeople to the exclusion of the weaker ones. This the leadermust guard against. Both this method and the group plan de-pend for their success on the fact that the pupils recognize theirresponsibility; that it is their duty not only to keep things going,but to work towards some end and thus cover a certain amountof ground in the recitation. True, the teacher, as a member ofthe class, can step in whenever he chooses, but he naturallyconsiders himself most successful when it is unnecessary. Thisleads to the question as to whether one should have the socializedrecitation in every class. I should say, ^No.^ Sometimes ithappens that a class group is entirely lacking in leaders, in thekind of pupils who recognize what they are working toward andmake an effort to attain that end. In such a class a socializedrecitation would fail utterly. Any kind would, except one inwhich the teacher directs the class constantly. Sometimes, too,a teacher, through no apparent fault of his own, fails to instillinto his class a desirable class spirit. Under such circumstances,the socialized recitation would hardly be successful, for classspirit, the desire to accomplish, to make and not to mar, is moreessential to the socialized recitation than to any other.Now, to what extent can we use the socialized recitation in

mathematics? Is it feasible to have socialized recitations everyday, or shall we have them only occasionally? Shall we .use thegroup or the class method? And, if we socialize, how best shallwe begin? As yet we have few records of what has’been done in

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socialized mathematics recitations. To me it seems that in so faras there are certain principles to be taught in algebra, we canreasonably expect that there must be a certain number of lessonswhich must be developed by the teacher with the cooperationof the pupils, ratherv than to be worked out by the pupils alone,but that for a large amount of drill work, the group form of thesocialized recitation is decidedly advantageous.

In my algebra classes I have made use of the group form ofrecitation both for drill on mechanical processes, as for example,addition and subtraction of fractions, and in solving concreteproblems. The number in a group varied from two to five, onemember of the group usually working at the board, the otherssometimes standing by to assist, or following the work at theirseats. Each group usually had its own exercises. For me-chanical work, when a process had just been taught, I liked hav-ing two in a group, thus giving half of the class opportunityfor immediate practice, the other half, occasion to get the meth-od a little more firmly fixed in mind before attempting the workthemselves. Then, if the pupil working became confused, hispartner could help him, giving any necessary explanation. Thepupils took turns in working at the board, so that as far as pos-sible there was an equal division of labor, although when a strongand a weak pupil were linked together, the give and take ad-justed itself along natural lines.

For giving weak pupils a bit of extra drill, the socialized reci-tation is particularly useful. Then I have just as many groupsas there are weak pupils, with one of the latter in each group.The weak pupils are the board workers for their respectivegroups, the others remaining seated to watch them. The firstone to note an error or a standstill on the part of his board workergoes to him with the necessary explanation. The pupil workingcorrects his error. Anyone in the group may ask the workerany question concerning his work. Such a recitation may becriticized as wasteful of time for the capable pupil and thecriticism would be just if a great deal of time were spent thisway. But for an occasional fifteen minutes it has its goodpoints. Short cuts are sometimes explained that would other-wise never be mentioned. Then, too, the pupils see that thereis more than one way of doing a certain piece of work.

This is especially brought out in working concrete problems.For example, when the leader of one group wrote his openingstatement, ^Let L represent the larger number,^ some of the

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group objected, saying if should be, ^Let 8 represent the smallernumber.^ But after the problem had been solved both ways,th*e members of the group were ready to readjust their thoughtsto the leaders opening statement, even if they would have begunthe other way. In solving concrete problems, however, groupwork has a disadvantage. Pupils do point out errors and tryto show why they are errors, and they give the correct forms,but they fail to ask the reconstructive questions which helpto set the mistaken pupils right. The teacher in supervisingthe work has not time to do this for every group, hence more oftensuch questions are omitted. For concrete problems I ordinarilyprefer a class recitation with plenty of free discussion by thepupils, but under the immediate direction of the teacher (hencenot a strictly socialized recitation). Into such a recitation manyof the good points of the socialized recitation may be introduced,such as board work with explanation of steps by one pupil, cor-rection of his work with reasons for the change by another,another possibility of solution mentioned by a third, etc., so thateverybody is constantly on the qui vive, but instead of havingthe discussion between pupils, the teacher is the intermediarybetween them.

In geometry as well as in algebra there will be many entirelessons or parts of lessons for which it seems advisable for theteacher to direct the class, to develop the proof of the theoremwith the aid of the pupil, rather than to let them stumble aroundaimlessly for a while, thus wasting precious class time, justbecause the recitation is to be socialized. This is as bad on theone extreme as to assign the next proposition, let the classmemorize the proof from the book and recite it verbatim the nextday, is on the other. But for drill or review work especially,after a class has been well trained in the fundamentals of geom-etry, group work, with five or six in a group does make for effi-ciency. Jf a class of twenty-five is divided into five groups, therewill be five recitations in progress in different parts of the room.The leader of the group may be given the advantage of recitingwhen he chooses, and calling on the other members at other times.All members should be ready to continue, to commend, or tofind fault with the previous recitation. Should a whole groupbe unable to continue, the teacher may be called on as a lastresort. But the obvious advantages are there, the pupil has fivetimes as many opportunities to recite; he is less timid before his2:roup than before the whole class plus the teacher; he does not

848 SCHOOL SCIENCE AND MATHEMATICS

resent criticism, because everybody in the group gets his share.For easy originals the group recitation is also good; for more

difficult ones, I like to have the class as a whole in a socializedrecitation. We need all the minds, then, concentrated on thesame task in order to make headway. The pupils begin work attheir seats. When the first member thinks that he has a solutionhe goes to the board, draws the figure, calls the class to atten-tion, and proceeds with his proof. As soon as there is a flaw,hands go up, and he calls for information. If the flaw throwsout his proof, another may begin or continue with the work-Should every one be on the incorrect track, the teacher, as a mem.ber of the group may give a suggestion.

In both algebra and geometry, then, the socialized recitationmay be used to advantage at times, either for an entire periodor for a part of it; either in the class or group form. But fre-quently throughout the year and continually for a time duringthe beginning of the year, lessons in which the subject matteris developed under the direction of the teacher are necessary.The pupils like the socialized recitation, for it gives them powerand self-reliance; they like to talk directly to each other; theylike to feel that they can explain things so that their classmatescan understand them; and they develop an unusual keenness incriticism. The older the students, of course, the greater is theirsense of responsibility, and the greater will be the success of themethod.

CLASS ROOM SAYINGS.Why does an aeroplane rise?"An aeroplane rises because of the action of its wings beating upon

the air. It is lighter than the air, and thus it may (to speak unscientific-ally) place its wings upon a layer of air, and by leverage raise itself to ahigher position, in precisely the same manner as a bird flies."

Define volt, ampere, ohm."A volt is the electromotive force that will carry a current through a

distance of one ampere with a resistance of one ohm.""An ampere is a volt flowing through one ohm per second.""An ohm is the quantity of resistance against one volt flowing at the

rate of one ampere per second."(The above answers were collected from tests given to first-year students

in a university in a required course.)Of what are clouds composed?"Liquid air.""I don’t know what an East Indian Typhoon is, but there is only one in

captivity.""If a ray of white light is passed through a glass prism there will be

seen all the colors of the solar rectum."