USE OF ARITHMETIC VERBAL PROBLEMS

SARA RODGERSBurnside School^ Chicago 19, Illinois

This talk will epiain the use of Verbal Problems at the BurnsideSchool, Chicago under the supervision of our principal Mr. TurnerC. Chandler and the cooperation of all the teachers from Grades 4-8.I shall indicate the philosophy and principles of the selection of theproblems, the technique of giving the lessons and the follow-up.These lessons, with variations, have been a procedure for manyyears.The philosophy underlying the principles involved in the selection

and solution of Verbal Problems is:First, problems should ordinarily involve processes that have

been taught. However, to increase the difficulty of the last half ofthese lessons in some situations new applications of processes may beadded to provide the child with experiences he needs in getting a newfact or procedure. Care should be taken to keep these problems withinthe experience, interest, and understanding of the pupils and basedupon significant social situations.

Second, Verbal Problems can be used to show the child that heneeds certain facts and processes in daily life.

Third, Verbal Problems may be used in particular situations forpractice in the processes being taught.

Fourth, Verbal Problems will illustrate any necessary reteaching.Fifth, Verbal Problems should be used to teach meanings, not

only the meanings involved in the abstract processes, but meaningsin concrete situations.There has been considerable investigation by organizations, com-

mittees and individuals in grade-placement of abstract operations inArithmetic but comparatively little has been done in the way ofobjective studies in grade-placement of Verbal Problems. Someyears ago the Committee of Seven of the Northern Illinois Confer-ence on Supervision, made a preliminary study and came to theconclusion that this topic should be further investigated. Mr.Chandler was a member of this committee and some of the experi-ments were carried on in our school. Even this preliminary studyshowed conclusively that the grade-placement of verbal problemscannot be determined very accurately by subjective methods, and sothe selection of problems must be done with a great deal of care andnever extemporaneously.At the Burnside School each teacher in Grades 4-8 has at least one

lesson each week consisting of sixteen Verbal Problems. These

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lessons in most cases include a certain process which has just beentaught and one or more review processes. An example of this wouldbe twelve or thirteen problems involving Case 2 in Percentage andthree or four involving Discount. The first eight problems usuallyrequire easy one-step operations; and the last eight are more difficult,to tax the ability of the better students. These problems may betaken from textbooks or prepared by the teacher. When, severalyears ago, our school began its project in verbal problems our text-book was inadequate and so many of the lessons had to be preparedby the school. Many modern textbooks have abundant material inverbal problems, and so the problems may be taken from the bookand not necessarily from one page. A fundamental point to rememberis that these problems should be worded to necessitate carefulreading and thinking. No lesson should contain one process so thatputting down numbers and choosing a process as a matter of routinewill allow the pupil to solve the problem without careful thinking.The technique of giving these lessons is divided into four parts:

I. PreparationII. Launching or Presentation

III. The Lesson, andIV. Follow-up

In preparing for the lesson the teacher should anticipate anydifficulties in computation and reading. Time is an important factoras the lesson should care for individual differences in ability, andinvolve remedial and follow-up work. The period if possible, shouldimmediately precede an enrichment period. This enrichment periodmight be gymnasium, library, movies in correlation with anotherteacher, art or recreational reading. The materials needed are (1)a score card with answers for the sixteen problems, (2) two colorsof marking pencils or crayons, (3) two sheets of paper for each child.Notebook paper is the most convenient size. Assign to each pupil apermanent serial number to correspond with his place on the officialclass roll.

In launching or presenting the lesson do the preliminary teachingin anticipation of difficulties. Then pass two sheets of paper to eachchild. Give specific directions about the lesson including the prepara-tion of the paper (division into eight spaces by drawing a centerhorizontal line and three vertical lines); usual headings; using pencilto solve problems; showing ALL work on the paper, even if it can bedone mentally. Now pass the sixteen problems and tell the pupils togo to work as soon as they receive them.At the beginning of the lesson, that is when the pupils begin to

solve the problems, note the time. The main lesson is to be twentyminutes of actual problem solving. This time may be extended to

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twenty-five minutes if no one has completed correctly the sixteenproblems at the end of twenty minutes. As the pupils work theteacher moves from desk to desk and puts a check with a coloredpencil on each solution that is correct. When a child fails to solve theproblem correctly, the teacher tells him it is incorrect and to tryagain before going on to new problems. If the second attempt is afailure, the teacher tries to discover the trouble and give whateverinstruction she thinks is necessary for the pupil to solve the problem.When a pupil has completed all sixteen problems correctly, theteacher writes an eight across each of the sheets. Such pupils becometeacher-assistants to help score other papers, using their own papersas a score card and the same color marking pencil as used by theteacher.At the end of twenty (or twenty-five) minutes ALL work stops.

The teacher completes the scoring and writes on the face of eachsheet the number of problems correctly solved�8 if all are correct.The total of these two numbers is the pupil’s score to be entered onthe official record sheet. The pupils who have completed twelve ormore problems go to the enrichment work. (This number may bechanged by the teacher if in her judgment the lesson seemed partic-ularly difficult.) The remaining pupils continue to work under theteacher’s direction and assistance. If the other marking crayon isused a recount is unnecessary at time of copying the scores. Thesechildren may go to the enrichment activity at the discretion of theteacher, but never if the pupil does not have AT LEAST eight prob-lems correct. Usually they should not go until they have twelvecorrect solutions. Each pupil’s OFFICIAL score is the number ofproblems correct at the end of the twenty or twenty-five minuteperiod.The follow-up work consists of a period of remedial work and in-

dividual instruction for the pupils who do not go to the enrichmentperiod. Keep a record of the official scores on your class roll and insome cases it is desirable to keep the unofficial scores. In our schoolwe are asked to record at least five of the scores on the official classroll in the office, and a total of the scores for the semester. Frequentconferences with the principal about the work are desirable andhelpful.

The most important day I remember in all my life is the one on which myteacher . . . came to me. I am filled with wonder when I consider the immeasur-able contrast between the two lives which it connects.

�HELEN KELLER