Basic Facts�Alternative Activities for MasteryJon M. Engelhardt

Department of Elementary EducationArizona State UniversityTempo, Arizona 85281

Mastery of basic facts was valued in the past as good mentaldiscipline. It provided exercise for man’s mental muscle and therebyimproved his quantitative thought processes. Today, although mem-orization of basic facts is rarely mentioned, it still has value, butfor a different reason. If a child lacks mastery of basic facts, heuses time-consuming and distracting ways of finding products or sumsof larger numbers. His attention is drawn from the larger task ofthinking through the computational procedure for multiplication oraddition. He appears to be uncertain about where he is in the processand frequently proceeds at random, having lost his way. As Ashlock(1972) stated, "If a child is to use arithmetic to solve quantitativeproblems, it is important that he master the basic facts of arithmetic[P. 6].-Once students have derived basic facts from meaningful manipulative

experiences, teachers should help students commit them to memory.This is ordinarily accomplished by providing numerous activities whichrequire the use of such basic facts; the idea is that students willuse basic facts so often that they will naturally commit them to memoryand readily recall them.D’Augustine (1968) indicated that teachers most commonly use

flashcard activities to help children master basic facts. Since othertypes of activities exist, it is the purpose of this article to identifyand give examples of various alternatives appropriate for helpingchildren memorize basic facts. It is hoped that by informing teachersof such alternatives they will provide children a greater variety ofexperiences. Briefly, activities intended to help students master basicfacts may be classified in three ways: problem-solving laboratoryexperiences, games, and open number sentence activities.

Problem-Solving Laboratory Experiences

Problem-solving laboratory experiences are child-centered, sensoryexperiences in which children explore and solve problems. One exampleof a laboratory experience which provides students with many oppor-tunities to compute basic facts is placing a small group of childrenin charge of a classroom toy sale. To obtain toys for the sale, eachchild in the class could be asked to donate several small, used toys(e.g., small trucks or cars, toy soldiers or animals, trading cards,

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or marbles). Depending upon the students and the situation, varyingamounts of guidance may be required.1 Students must, however, begiven at least the following operating rules:

1) no toy may be sold for more than 9 cents;2) toys may be sold (or purchased) only in pairs;3) students must keep a sales receipt for each purchase; and4) all purchases must be in pennies.

By keeping such receipts, the students operating the toy sale willbe practicing an addition fact each time a purchase is made. Studentswishing to purchase toys, faced with the decision of finding twotoys which they like and whose cost totals the amount of moneythey have (or less), must also perform many addition facts.

In order to get the classroom toy store operating, activities otherthen computing basic addition facts are required. Students mustconcern themselves with pricing each toy, determining the best timeand place in the room for the store, organizing the display of theirmerchandise, and advertising that merchandise.To add more structure to the experience, the teacher may designate

special sale days like ’Ten Cent Day," where students may onlybuy pairs of toys whose cost totals ten cents. The teacher may alsoinsist that the store operators provide a list of all permissable toypurchases (thus providing practice with all of the basic addition facts).At the end of the toy-store activity, students could have other

mathematics experiences by preparing elementary graphs representingtotal sales, sales per day, and most popular toy prices. They couldeven make suggestions for future such stores.

Alternative versions of this experience might involve sale of otheritems, such as books, goodies, school supplies, class-made games.Coins other than pennies might be used, thus acquainting studentswith nickels and dimes; making change will help prepare studentsfor subtraction. Items would not have to be sold; they could be rented.With a little experience, students might even wish to expand theirstore operations school-wide.

It should be recognized that such an experience is beneficial tocontent areas other than mathematics. Art is involved in the preparationof advertisement; language arts in the preparation of a final reportand recommendations; and social studies in the role playing of astore keeper. With thought, this experience could be modified oraugmented to involve most of the curriculum.

1. In general, students will need closer supervision and guidance when getting organized. Besides the teacher,perhaps the use of an older child (preferably one from an upper grade who still has trouble with addition facts)could be used.

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Games

Games provide an interesting way for teachers to help childrengain mastery of basic facts. Features which distinguish games fromthe miriad of other activities are (1) competition, (2) chance, and(3) strategy. In a game, a student may compete with himself or withothers, and the outcome of the game may be more or less dependentupon strategy and chance.One such game intended to help children master basic addition

facts is a variation of dominoes. The game is played with domino-likecards, each card displaying a pair of basic addition facts (figure 1).

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The game rules consist basically of placing dominoes end-to-endto form a train. A domino may be added to the train if a missingsum on one of the dominoes in the player’s hand is the same asthe missing sum on the end of the domino train. As in regular dominoes,if a double is played (a domino in which both facts have the samesum), it is placed crosswise and the train begins to branch. The gamemay be played so that the student competes with himself (to seeif he can get rid of all the dominoes in his hand) or so that studentscompete with each other (the winner being the first to get rid ofall the dominoes in his hand). In either case, the student draws adomino from the drawing pile only when it is his turn and he isunable to make any play with the dominoes in his hand. Studentsreceive additional practice by checking their own or their opponentsmoves.Chance affects the game insofar as the dominoes are randomly

drawn. Even though one student may have an edge by having bettermastery of the addition facts, he can’t win unless he draws the rightdominoes at the right time; on the other hand, a student who lackscomplete mastery may, by having a little luck, still experience successat winning the game.Many other games may be created to help children master the

basic facts. Variations of bingo and parcheesi, as well as card gameslike war and rummy, offer much potential for the innovative teacher.

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Open Number Sentence Activities

Open number sentence activities designed to help students masterbasic facts usually involve either worksheets or flashcards. Worksheetsgenerally consist of sets of open number sentences for which thestudent is to supply the appropriate sums or products. The mostcommon form of a worksheet is the workbook-type page. While thepage may only contain open number sentences, student interest canbe heightened by surrounding them with drawings (figure 2) ororganizing them into appealing diagrams (figure 3).

FIG. 2. FIG. 3.

Worksheets may take forms quite different from the printed page.They may even have moving parts. For example, different sized pizzawheels may be joined at their centers and numerals written nextto each other on the two wheels. By rotating the center wheel, anentirely new set of open number sentences is generated (figure 4).

FIG. 4.

Flashcards are cards in which a stimulus problem is printed onone side of a card and an appropriate response on the other sideof the card. In practice students examine the stimulus, respond in

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some way, and then flip the card to check their response. Althoughflashcards may be used by an individual alone or an entire classof students, they are usually used by pairs of students, one childlistening to and checking the responses of the other. They essentiallydiffer from worksheets in that they provide immediate feedback onthe correctness of the student’s response.

Flashcards designed to help students master basic facts consistof an open number sentence on one side of each card (e.g. |2 + 3 = D|

or I 2 x 3 = D|) and the appropriate sum or product on the otherside of the card.

Unfortunately, if a student does not have a pretty good conceptof addition or multiplication, flashcards do not provide any way forthe student to associate the correct response with an open numbersentence other than pure memorization. If the child responds incor-rectly and is not able, for example, to mentally reconstruct theunionizing of sets, he has no way to logically arrive at the correctresponse; he must rotely memorize it or fail.

Since rote learning is not retained very long (Willoughby, 1970),flashcards would be much improved if they provided ways for theunsure child to arrive at correct responses. One way might be tohave diagrams printed on the back of each flashcard which suggestthe meaning of the open number sentence. For example, besides thecorrect response to the number sentence 2 + 3 = D, a flashcard mighthave a set diagram, a number-line diagram or both (figure 5). If

FIG. 5.

the child is unable to respond to the open number sentence, he can(by strategically grasping the right side of the card) flip it to exposeonly the diagram(s), which can then be examined to help him makethe correct response. The emphasis is still upon an abstract response,but the child is provided with a model to help him make sense ofthat response. If flashcards can remind the unsure child of a meaningfulapproach for obtaining a correct response, he will likely master basicfacts more easily and retain them longer.

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Summary

Children have long found memorization of basic facts to be a dulland boring task. In this article three types of learning activities whichteachers can use to help students master the basic facts have beenidentified. One type of activity was problem-solving laboratory experi-ences; a classroom toy sale was explored as an example of this typeof activity. Games were identified as a second type of activity; avariation on dominoes was indicated as an example of such games.The third type of activity was open number sentence activities, whichincluded worksheets and flashcards; examples of novel ways to designworksheets were presented and a new approach to flashcard designwas suggested.Teachers have an opportunity and an obligation to provide numerous

activities which help children master basic facts. These activities,however, do not have to involve only flashcards, games, or any otherparticular kind of activity. If you believe the saying "variety is thespice of life," try adding a little spice in your classroom life.

REFERENCES

ASHLOCK, R. B. Error Patterns In Computation. Columbus, Ohio: Merrill, 1972.D’AUGUSTINE, C. H. Multiple Methods of Teaching Mathematics in the Elementary School.New York: Harper and Row, 1968.

WILLOUGHBY, S. S. Issues in the Teaching of Mathematics. In E. G. Begle (Ed.), TheSixty-ninth Yearbook of the National Society for the Study of Education. Part 1.Mathematics Education. Chicago: University of Chicago Press, 1970

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