effects of arithmetic homework upon the attitudes and achievement of fourth, fifth and sixth grade...

Effects of Arithmetic Homework Upon the Attitudes andAchievement of Fourth, Fifth and Sixth Grade Pupils

Norbert MaertensAssociate Professor of Curriculum and Instruction

James JohnstonAssistant Professor of Educational Psychology,University of Oregon, Eugene, Oregon 97403

Although arithmetic homework has been a part of most elementarymathematics programs throughout the country, its demonstratedeffectiveness in improving academic performance has been disap-pointing. Studies by Cooke and Brown [l], Di Napoli [2], Teahan[7], and Maertens [6] have found no significant improvement inperformance among those groups receiving arithmetic homework ascontrasted with no-homework groups. An exception, a study by Koch[5] did find that two groups receiving arithmetic homework signifi-cantly outperformed a group not receiving arithmetic homework, andfurther that those receiving a full page of homework each day didbetter than those receiving a half page of homework daily. However,this study was limited to three classrooms in a single school, and theresults may be confounded by teacher effect. Clearly, the prepon-derence of research indicates that arithmetic homework, as nor-mally assigned and completed, does not significantly effect pupilperformance.

In addition to being an ineffective vehicle to improved arithmeticperformance, homework has often been a source of friction amongteachers and parents. Parents are often confused by the new term-inology and methods of instruction characteristic of modern mathe-matics programs, while teachers are frequently disturbed when theyreceive papers which have apparently been completed by parentsrather than pupils. Further, the attempts of teachers to enforcecompletion of homework assignments by students have often resultedin strained relationships between teacher and child and often betweenteacher and parents. Obviously, if homework in arithmetic is to con-tinue to be assigned to pupils, new efforts must be made to ensure itsefficacy, and to ensure that the involvement of parents becomes apositive, rather than negative, force.

Prior research offers a clue for increasing the effectiveness of home-work. A considerable body of literature has been concerned witheffects of temporal arrangements in the provision of feedback. Twostudies (Johnston, Maertens, and Schooley, [4]; Hillman, [3]) havedealt specifically with effects of various knowledge of results condi-tions on arithmetic performance of elementary school children.

117

118 School Science and Mathematics

In both of these studies, one group of children received knowledgeof results after completing each problem while the other group re-ceived knowledge of results after completion of the entire assignmentor on the following day. Those receiving per-problem knowledge ofresults performed significantly higher than the other groups.The purpose of this study was twofold: (1) to determine the effects

of arithmetic homework involving planned parental participationupon arithmetic computation, problem solving performance, and atti-tudes toward arithmetic, homework and school; and (2) to determinewhether children receiving per-problem knowledge of results fromtheir parents differed significantly in arithmetic performance or atti-tude from those receiving knowledge of results upon completion oftheir total assignment. For the pruposes of this study, arithmetichomework is defined as arithmetic material which has been con-sciously assigned to be completed outside regular school hours.

SUBJECTSBecause this study required extensive parental involvement, it was

necessary to ensure the cooperation of the parents before their chil-dren were selected to participate in the study. To do this, lettersdescribing the purpose of the study were sent to the parents of everyfourth, fifth and sixth grade child in the Sweet Home, Oregon, schooldistrict. Attached to each letter was a form requesting the privilegeof involving their child in the study and also requesting their coopera-tion in the study. A total of 532 letters were sent and approximately78% of the parents returned letters indicating that they wouldbe willing to participate in the experiment. From this group, childrenwere randomly assigned to treatments so that each fourth, fifth andsixth grade teacher in the district had all three treatment groupswithin her room. Each child was told that he was in an experimentand a letter was sent to each parent explaining to which treatmentgroup his child had been assigned. It is assumed that these measureswere sufficient to account for the Hawthorne effect.At the beginning of the experiment there were included in the

study 146 fourth grade pupils, 137 fifth grade pupils and 134 sixthgrade pupils. Attrition due to absences and family relocations reducedthe sample slightly. If a child missed more than one weekly test, hewas not included in that analysis. Only children who took both thepretest and post test were included in those analyses, therefore thoseN’s were equal. Children who missed a post test were given three daysto take it. If they did not complete the test within that time, theywere dropped from the sample. For this reason, slight variations wererealized between the analyses for weekly quizzes and the analyses forpost tests. Also, since the attitude measure was given on a different

Effects of Arithmetic Homework 119

day than the arithmetic test, slight variations in sample size betweenthese analyses were also found. Numbers of students used in eachanalysis are shown in Table 1.

TABLE 1

Sample Sizes

Attitude Pre and Post An’th Weekly Tests

4th 5th 6th4th 5th 6th 4th 5th 6th

Per-Problem5538515136445149 47

Delayed5041494836475048 44

No-Homework4833514134484446 46

Total153112151140106139145153 137

All students in the experiment used the same textbook series andfollowed the curriculum suggested by its authors. The text series usedwas Arithmetic published by Laidlaw. All classrooms in the experi-ment were self-contained, and they were not grouped by ability.The Sweet Home, Oregon, school district encompasses a large rural

area, and many elementary students attend school in rural atten-dance centers. Children from a total of eight elementary schoolsparticipated in the experiment. The Sweet Home district is com-posed primarily of modest single family dwellings, and its chief indus-tries are logging and farming. Disregarding consolidations with smallrural areas, the growth of the Sweet Home district has been rela-tively gradual.

TREATMENTS

This study, involving three homework treatments, was conductedover a period of six weeks. A description of the treatments follows:

1) No Homework. Children in this treatment group were not given anyarithmetic homework. Further, they were not allowed to complete un-finished daily assignments at home, nor were they given any additionalhomework assignments from other subject areas to compensate for theirlack of arithmetic homework.

2) Per Problem Knowledge of Results. Children in this treatment group re-ceived daily homework assignments in arithmetic on Monday, Tuesday,Wednesday and Thursday. These homework materials, prepared by theexperimenters were carefully designed to compliment and enrich the ma-terials covered in the students’ textbooks. Each arithmetic assignment pro-vided drill upon materials previously covered in class, and provided childrenwith the opportunity of applying the mathematical principles which hadbeen learned in verbal problem situations. Tivo story problems and eight toten computational exercises were included in each homework assignment.Arithmetic homework assignments were passed out to the children Just


prior to their leaving for home, and the children were instructed to do theirwork at home in the company of their parents.Each Monday, children were given a scaled envelope containing instruc-tions to parents and answers to the problems to be encountered that week.One parent observed the child while he attended to the assigned homework.As each problem or exercise was completed, the parent would say, "Thecorrect answer to problem (exercise) one is . . ., now go on to problem two."The entire homework assignment was completed in this manner. Parentswere instructed not to give assistance to the child, nor were they to givecriticism or praise.

3) Delayed Knowledge of Results. Children in this treatment group receivedhomework assignments identical to those in thepcr-problem treatment andfollowed identical procedures, except that children did not receive knowl-edge of results until the entire homework assignment was completed. Atthat time, the parent read the correct answers to each of the questions.Arithmetic papers for both experimental groups were returned to theteacher on the following morning.

Teachers were instructed to expose students in all three groups tothe same in-class activities. All children were to be taught in thenormal manner with no extra attention given to the treatment groups.

TEST INSTRUMENTSTest instruments used in the study were administered by the class-

room teacher. Prior to beginning the experiment, each pupil was givenan attitude test and an arithmetic test. The arithmetic test includedcontent covered by the Laidlaw series in the preceding year. Thus,the test for fourth grade students was composed of materialscovered by children in the third grade, and so forth. The attitudemeasure used Osgood^s Semantic differential as a model, and testedchildren^ attitudes toward school, arithmetic, and homework.A one-way analysis of variance indicated that treatment means

attained on the pretests did not differ significantly (a<.05). Becauseof the extreme difference in size among schools, and because someschools did not contain a particular grade (for example, one schoolcontained all the sixth grade children for two schools), the experi-menters did not test for between schools differences.

Experimenter-prepared achievement tests designed to measure thecontent covered in class during the week were given each Friday.Each test included fifteen computation problems and five story prob-lems. The tests were designed for power rather than speed. Weeklyattitude measures were not given.

Post attitude measures, designed to measure students’ attitudestoward school, arithmetic, and homework, were given on the Mondayfollowing the completion of the sixth week. The arithmetic post test,designed to measure computation and problem solving skills, wasgiven on the following Tuesday. A brief description of the test instru-ments follows:


Attitude Scale. The attitude scales used Osgood’s Semantic dif-ferential as a model. Eleven bi-polar adjectives were constructed foreach of the school-related structures under consideration. Sevenblanks were included within each item to allow students to expressstrengths of feelings toward each item. Two distractors were includedto discourage children^ patterning of responses, and the position ofpositive and negative alternatives was varied. The concept underconsideration appeared at the top of the page. A sample from the posttest is included below. Directions needed to complete the test wereread by the teacher, and a practice page was completed by everychild to assure understanding of the nature of the task. Children wereinstructed to place an X in the space which best described their feel-ing toward the concept at the top of the page. If children felt verystrongly about arithmetic, they were advised to place an X at theextremes. On the other hand, if arithmetic didn^t arouse much feeling,students were advised to place an X in the middle. Various strengthsof feeling were shown in this manner.

ARITHMETICGOOD _________________________________BADHARD _______________________________ EASY

Computation. The computation test included thirty-five items.Students were instructed to complete the entire test without stopping.Space was available for each student to show his work, and scratchpaper was provided. Problems included in the examinations rangedfrom very easy problems to rather difficult problems. Three sampleitems from the sixth grade test are given below:

291 173

67 X 8 5 83)6 1 5 7

+538

Problem Solving. The problem solving test included twenty storyproblems. Some of the problems required the student to perform twooperations, and some included information not needed to solve theproblem. Children were instructed to complete the entire test withoutstopping, and each child was told to show the algorithm he had usedin solving the problem. Space was available for each student to showhis work, and scratch paper was provided for each pupil. Two sampleitems from the sixth grade test are given below:

1. A certain cake mix contains 5 parts flour, 2 parts milk, 1 part shortening,and 2 parts sugar. What fraction of the cake mix is made of milk?

2. In a game of chance you get 3 times as many red chips as blue chips. Youare given 1600 chips. How many are red and how many are blue?


HYPOTHESESThe following null hypotheses were tested:1. There is no significant difference between those groups receiving arithmetic

homework and those groups not receiving arithmetic homework in perfor-mance on tests of arithmetic computation, problem solving performance,and attitudes toward arithmetic, homework and school.

2. There is no significant difference between those groups receiving per-problem knowledge of results and those groups receiving knowledge ofresults at the end of the assignment on tests of arithmetic computation,problem solving performance and attitudes toward arithmetic, homeworkand school.

RESULTSProblem Solving and Computation Tests, Means for the various

groups on both the weekly tests and post tests are presented in Table2. In every case, means on the computation and problem solving testsfor the homework groups were higher than means for the no-home-work groups. However, means between those groups receiving per-problem knowledge of results and those groups receiving end of theassignment knowledge of results showed little consistent variation.The weekly test means reported in Table 2 represent the sum of thesix weekly tests for each pupil divided by the total sample.Two planned orthogonal comparisons were performed (see Table

3) to test for the significance of differences between (1) means of thehomework groups vs. the no-homework groups, and (2) means of thegroups receiving per-problem knowledge of results and the groups

TABLE 2

Problem Solving and Computation MeansComputation Problem Solving

4th5th6th 4th 5th 6th

Weekly Tests

Per-Problem 57.04 61.80 74.32 15.31 18.27 18.89

Delayed 57.22 62.31 74.75 16.74 16.13 18.25

No-Homework 48.82 52.96 71.46 14.23 13.22 17.61

Post Tests

Per-Problem 25.39 29.58 30.48 9.06 8.78 11.30

Delayed 27.40 28.11 30.83 9.58 8.39 11.06

rio-Homework 20.10 24.09 28.31 7.02 7.09 9,35


receiving end of the assignment knowledge of results. The methodsuggested by Winer [8] was used. Results of these analyses are pre-sented in Table 4.

TABLE 3

Weights for Orthogonal ComparisonsComparison Weight

Per-Problem vs. Delayed

Per-Problem + Delayedvs* No-Homework

1

1

-1

1

0

-2

TABLE 4

F Values for Orthogonal Comparisons

Post Tests Weekly Tests

Computation Problem SolvingComputation Problem Solving

Grade 4

Per-Problem NS USvs. Delayed

Per-Problem + Delayed 17.49** 5.37*vs. No-Homework

Grade 5

Per-Problem NS NSvs. Delayed

Per-Problem + Delayed 12.80** 3.03 (.10)vs. No-Homework

Grade 6

Per-Problem NS NSvs. Delayed

Per-Problem + Delayed 6.67* 4.06*vs. No-Homework

NSNS

17.42**3.15 (.10)

NSNS

6.40*15.21**

NSNS

NSNS

* a < .05

**a < .01

"Weekly Quizzes"�Significant differences between homework andno-homework groups were found on both the problem solving and thecomputation tests for grades 4 and 5. For the sixth grade, however,differences between homework and no-homework groups on both testswere not significant. Differences between means of the two homeworkgroups were not significant at any grade level.

124School Science and Mathematics

"Post Test^�Significant differences between homework and no-homework groups were found on both the problem solving and thecomputation tests for all three grade levels. However, for the fourthgrade problem solving, differences were only significant at the .10 level.

In every case for both the weekly quizzes and for the post test, thereported significant differences favored the homework groups over theno-homework groups.

Attitude Tests. Means for the attitude measures are reported inTable 5. Little variation among means was noticed either betweenhomework vs. no-homework groups or between the two homeworkgroups. No significant differences were found on any of the orthogonalcomparisons among treatment means, indicating that the treatmentshad no significant effect on measured attitudes.

TABLE 5Attitude Means

Pretest Post Test

Grade 4

Arithmetic

School

Hom2work

Grade 5

Arithmetic

School

Homework

Grade 6

Arithmetic

School

Homey/ork

Per-Problem

51.22

52.71

51.35

51.18

53.74

50.03

50.59

54.22

44.82

Delayed

53.00

55.56

50.76

52.85

54.93

48.85

50.12

52.22

47.29

No-Homework

50.50

54.59

50.04

49.03

53.33

47.64

49.06

51.43

42.73

Per-Problem

50.93

53.00

46.84

49.66

51.71

44.16

47.84

52.04

40.47

Delayed

53.46

53.38

45.50

51.37

50.85

46.83

49.41

51.45

44.92

No-Homework

49.29

52.10

48.81

52.55

54.73

47.36

48.67

50.20

38.59

DISCUSSIONResults of this study indicate that homework combined with

parental involvement as described in this study does have a signifi-


cant effect upon both computation and problem solving performances.Since other homework studies have not found this result, the effec-tiveness of the homework treatment may perhaps be attributed to avariable not found in previous studies�planned parental involve-ment. Whether the parent is involved in giving immediate knowledgeof results or end-of-assignment knowledge of results seems to makeno difference.

Parents were instructed to do no more than provide the correctanswers to problems at the appropriate time, and to do so withoutemotion. Informal responses from parents indicate that they becamevery much aware of both the strengths and weaknesses of theirchild’s mathematical competencies. Further, involvement of theparent resulted in pupils consistently completing the assignments.

Certain inconsistencies in the results are difficult to explain. Re-sults on weekly tests for grade 6 do not show significant results favor-ing the homework over the no-homework groups. This may be afunction of the psychometric power of the tests used or it may indi-cate the presence of other, untested variables.The question also arises as to why the per-problem group failed to

perform better than the end of assignment group when previous re-search by Johnston, Maertens and Schooley [4], and Hillman [3]indicated this as a strong variable. Although not a variable for thisstudy, it is possible that parental per-problem feedback to pupils isless powerful as a reinforcer than teacher feedback.On the basis of this study and related research the experimenters

recommend that w^en homework is assigned, parents be encouragedto become involved, at least to the extent of providing feedback tothe child.

IMPLICATIONS FOR FUTURE RESEARCHThis study did not differentiate whether the significant results

favoring the homework groups were attributable to provision ofknowledge of results or to parental involvement. It may be that bothare essential. Future research could be designed to sort out influencesof these variables.Although no significant results were obtained from attitude mea-

sures, post hoc observation of the data suggest some interesting hy-potheses for future research. A general decline can be noted in meanattitude scores for all groups at all grade levels from the time thepretest was administered at the beginning of the school year until thepost test was given six weeks later. There is also a consistent declinein attitude scores from the fourth through the sixth grades. Theseresults seem to hold for all three areas measured.


REFERENCES[1] COOKE, DENNIS H., AND BROWN, GREGORY B., JR., Home study has many

angles. Journal of Education, 1935, 118, 409-410.[2] Di NAPOLI, PETER, Homework in the New York City elementary schools.

Teachers College, Columbia University Contributions to Education No. 719,1937, Bureau of Publications, Columbia University.

[3] HILLMAN, BILL W.j Two methods of facilitating classroom learning: Im-plications for the counselor consultant. The School Counselor, 1969, 17, No. 2.,131-137.

[4] JOHNSTON, JAMES, MAERTENS, NORBERT, AND SCHOOLEY, DANIEL, When tocorrect arithmetic problems�A critical variable. School Science and Math-ematics, 1969, 69, 799-805.

[5] KOCH, ELMER A., JR., Homework in arithmetic. The Arithmetic Teacher,1965, 12, 9-13.

[6] MAERTENS, NORBERT W., An analysis of the effects of arithmetic homeworkupon the arithmetic achievement of third grade pupils. The ArithmeticTeacher, 1969, 16, 383-389.

[7] TEAHAN, GLADYS, E., Required home study is unwise. The American SchoolBoard Journal, 1935, 91, 41.

[8] WINER, B. J., Statistical principles in experimental design. New York: Mc-Graw-Hill 1962.

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effects of arithmetic homework upon the attitudes and achievement of fourth, fifth and sixth grade...

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