Author: Clute, Pamela S.
Title: Mathematics anxiety, instructional method, and achievement in a survey course in college mathematics.
Source: Journal for Research in Mathematics Education
Year: 1984,15, 5~58.

This study examines the relationships of mathematics anxiety (MA) and instructional method to mathematics achievement. Previous research has shown that high achievement in math is related to low anxiety, and that teacher behavior in the classroom is related to student achievement. Direct instruction is one such teaching behavior. Direct instruction can be divided into two specific teaching methods: expository lectures and discovery lessons. The authors hypothesized that students with low MA would perform better on a Mathematics Achievement Test (MAT) when using the discovery approach, whereas students with high MA would do better under the expository method. 44 students from the University of California, Riverside, and 37 students from California State College, San Bernadino, were used as subjects. The sample was pooled when it was discovered that there were no significant differences between the campuses. The results revealed a significant interaction between method of instruction and level of anxiety. Students with high MA did benefit more form the expository approach, while low MA students performed better using the discovery approach.

Ho₁: Teaching behavior has no effect on achievement of low or high MA students; i.e., there will be no difference between the scores of low or high MA students regardless of the teaching style used to present the material.

Ho₁: m_AB = m_AB

Ho₂: Achievement scores for low MA students will not differ significantly from high MA scores.

Ho₂: m_AL = m_AH

Ho₃: Scores will not differ because of teaching method.

Ho₃: m_BD = m_BE

The a level was not pre-stated. The ANOVA F-ratio was significant at the p < .01 level for anxiety effect and .01 for interaction between method and anxiety level.

N = 81 Sample was pooled after preliminary analysis revealed non-significant college effect.

Discovery Method:

14 low
14 medium
13 high


Expository Method:

14 low
13 medium
13 high

5. Instrument, briefly comment on reliability and validity

Three instruments were used:

The Mathematics Anxiety Rating Scale (MARS) to rate level of anxiety; the University of California and California State University (UC/CSU) Mathematics Test to assess the computational knowledge of each student and to determine the equality of the two subject pools; and the MAT to test the students on course content at the end of the course.

The reliability and validity of the MARS was well-documented by the researcher. The internal consistency was reported as having an alpha of .97 from a study done by Richardson and Suinn (1972). Validity was established through comparisons with other anxiety measures resulting in Pearson r's ranging from .68 to .80.

The UC/CSU Mathematics Test was substantiated with a .71 correlation done by Mattison (1982) and a Kuder-Richardson K-R 21 estimate of .87 for reliability.

The MAT was developed by the researcher. It had been used in two previous quarters and K-R 20 reliability estimates were reported as .89 and .90. The content validity was sufficiently established in a description of the researcher's method for creating the test.

6. Procedure

At the beginning of the semester each student took the MARS. The students were then rank ordered according to their MARS scores and randomly assigned to one of the two treatment groups. The UC/CSU was then administered to all students. The researcher was also the instructor and she presented the same treatments to both schools: one expository and one discovery at each school. Identical objectives and topics were used for each group. A Survey of Mathematics was the textbook used. The instructional time was 3 hours a week for 10 weeks. Attendance counted for 15% of the students' final grade; thus absences were at a minimum - no one dropped the course. A 3-hour final exam was administered to all students at the end of the semester. Each treatment was implemented according to established procedures for the teaching method.

7. Statistical Analysis and Conclusions

In the beginning t tests were done to compare each treatment group within each level of anxiety at each college. None of the differences were statistically significant at the p < .05 level so the results from the two groups were pooled.

A factorial analysis of variance was done on the results. A significant anxiety effect was found, F (2,69) = 10.11, p < .01 revealing that students with high MA had lover achievement than students w low MA. The difference between methods was not significant, but there was a significant interaction between method and anxiety level, F (2,69) = 4.96, p < .01. Students with low or medium MA scored higher with the discovery method.

A second ANOVA was done to see if results changed when low cognitive level items on the MAT were scored separately from high level items. The ANOVA on level items supported the original findings. The ANOVA on high level items revealed a significant main effect for method, a significant main effect for anxiety, and no significant interaction.

8. If you were the researcher, how would you improve the study?

Overall, I thought the study was well done. However, the study might have been improved by: