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The Effect of Testing Frequency uponthe Achievement of Students in HighSchool Mathematics CoursesParsia DineenJohn TaylorBryan Senior High SchoolOmaha, Nebraska 68157

Larry StephensDepartment of Mathematics & Computer ScienceUniversity of Nebraska at OmahaOmaha, Nebraska 68182-0243

The purpose of this study was to investigate the effects of two evaluationmethods on the learning process in mathematics courses. In one method,students were given daily quizzes or tests. The second method relied on weeklyquizzes or tests. The two methods were employed by two teachers over a1-semester period to look for differences in the performance of students.Mathematical competency of each student was compared at the beginning ofthe study while mathematical achievement was compared at the end. Studentsgiven daily quizzes or tests showed improvement, although not statisticallysignificant, over students taking weekly quizzes.

In a previous study (Stephens, 1977), it was found that giving short weeklytests as opposed to two major tests or four monthly tests did not increasesignificantly the average performance of college students in a traditional16-week semester course. However, in a subsequent study (Stephens, 1987),students enrolled in the same course, but during a 5-week summer session,were compared. Those students quizzed daily for four days and tested thefifth day significantly outperformed students who were tested each fifth dayonly. The intense nature of the summer session, where the pace is muchfaster, seems to lend itself to daily quizzes. To determine whether daily testswould improve the performance of high school students during an 18-weeksemester course, two teachers and nine different classes were used. Students ofvarying mathematical abilities and courses of varying difficulty werecompared.

Methods

The subjects used for the study were ninth through twelfth graders at asuburban high school. The school, consisting of 1,350 students, is located in arapidly growing white middle-class neighborhood. The students come from all

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198 Testing Frequency in Mathematics

economic backgrounds. Students living on the fringe of the enrollment areaare from low-income working-class families. Approximately 200 students froma predominantly black neighborhood are bused to the school. The schooldistrict itself is affluent and is populated by students with slightly-above-the-national-norm achievement scores.One hundred eighty-four students were involved in the study. There were

three classes of Introduction to Algebra 1, two classes each of Introduction toAlgebra 2, Algebra I and 2, and Pre-Calculus and Trigonometry.

Introduction to Algebra 1 and Introduction to Algebra 2 comprise acomprehensive program in first-year algebra that is to be studied over a 2-yearperiod. Introduction to Algebra 1 and Introduction to Algebra 2 cover in twoyears the same material that Algebra 1 & 2 covers in one year. The two yearprogram is recommended for the college-bound student who is notmathematically oriented.The control and experimental groups were randomly determined. There was

one control and at least one experimental group for each of the courses. Oneteacher taught all Introduction to Algebra 1 and Algebra 1 & 2 classes. Theother teacher taught the Introduction to Algebra 2 and Pre-Calculus andTrigonometry classes.At the beginning of the semester, the students were given The Beckmann-

Beal Mathematical Competencies Test for Enlightened Citizens. The test has48 questions measuring achievement on identified mathematical competencies.The Beckmann-Beal Test was given to determine the relative competency ofthe experimental and control groups at the beginning of the study. The testwas chosen because it has been shown to be a valid and reliable measure ofcompetency (Edwards, 1972).For the control and experimental groups two different evaluation methods

were used. Students in the experimental groups w^ere evaluated using Method 1where they were quizzed after each new topic. Almost every day, thesestudents completed a short 1- to 3-question quiz. No make-up quizzes wereallowed, but at the end of each quarter, the five lowest quiz scores weredropped. Students in the control groups were evaluated using Method 2. Thesestudents were quizzed just once a week and no quizzes were dropped.

All other aspects of teaching and grading the experimental and controlgroups were the same. After each unit, the students were given a chapter test.Classroom lectures, computer activities, audio visual aids, and homeworkassignments were comparable. At the end of the semester, each class was givena final examination to measure each student’s comprehension of the materialpresented that semester.

Results

The SPSSX package was used to perform the two-sample t-test on the testscores for each of the courses. The results are shown in Table 1. Students inthe Algebra 1 & 2 control group had significantly greater competency than

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Testing Frequency in Mathematics 199

students in the Algebra 1 & 2 experimental group. There was no difference inmathematical competency between control and experimental groups for any ofthe other courses.

Table 1

Mean Competency Scores for the Experimental and Control Groups for theDifferent Courses

CourseT value

Introduction to

Algebra 1Introduction to

Algebra 2Algebra 1 & 2Pre-Calculus& Trigonometry

*p<.05

Table 2

ExpeN

41

13

2021

�rimentalMean

21.00

23.77

26.5537.91

CoN

19

16

2222

ntrolMean

18.84

25.44

31.3239.52

Computed

1.13

.72

2.61*1.08

Two-Sample T-Test Comparison of the Semester Test Scores for theExperimental and Control Groups for the Different Courses

Course

Introduction to

Algebra 1

Introduction to

Algebra 2

Algebra 1 & 2

Pre-Calculus &Trigonometry

Group

ExpConComputed T valueSignificance level ==

ExpConComputed T valueSignificance level =

ExpConComputed T valueSignificance level =

ExpConComputed T valueSignificance level =

N

4119

= 1.09.279

1613

= .81.424

2022

= .13.901

2122

= .04.966

Mean

60.5953.21

33.3129.75

66.8065.73

31.7331.62

St Dev

3.2766.998

13.6068.835

22.39031.799

9.6676.511

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200 Testing Frequency in Mathematics

The results of the students’ performance on the semester tests are given inTable 2. The scores for students in Introduction to Algebra 1 and Algebra 1 &2 were based on percentages. The scores for students in Introduction toAlgebra 2 and Pre-CalcuIus and Trigonometry were based on points.

There were no significant differences between the test results of the twomethods of evaluation; however, the experimental groups had higher meanson the semester test in all the courses. At the beginning of the study, three ofthe control groups had higher means on The Beckmann-Beal Test�significantly higher in the case of Algebra 1 & 2.

Conclusions

Even though no statistically significant differences were found between theexperimental and control groups for any of the four courses, certain trendswere apparent.The mean test score for the experimental group was greater than the mean

for the control group in each of the classes even though the differences werenot significant. Also, it was noted that the mathematical competency scoresparallel the level of difficulty of the four courses. That is, students inIntroduction to Algebra 1 had the lowest mathematical competency scoreswhile students in Pre-Calculus and Trigonometry had the highest mathematicalcompetency scores on the average.The difference between mean semester test scores for experimental and

control groups was greater for the less difficult courses, indicating thatfrequent testing was more effective for the weaker students than the strongerstudents. This result is extremely important since students in the Introductionto Algebra courses are extremely difficult to motivate with respect to studyingmathematics.

References

Edwards, E. (1972). Mathematical competencies and skills essential forenlightened citizens. The Mathematics Teacher, LXV, 671-677.

SPSSX users guide: A complete guide to SPSSX language and operations.(1985).

Stephens, L. (1977). The effect of class evaluation method on learning incertain mathematics courses. International Journal of MathematicalEducation in Science and Technology, 5, 477-479.

Stephens, L. The effect of testing frequency upon performance in mathematicscourses. International Journal of Mathematical Education in Science andTechnology, 18, 611-613.

School Science and MathematicsVolume 89 (3) March 1989