#### Abstract

ABSTRACT

Eighty learners were randomly selected from 160 first-year nursing students enrolled in an urban community college nursing program in Ontario. They were subsequently divided into control and treatment groups to investigate the effects of different teaching methods on mathematics anxiety and the students' ability to accurately calculate fractional drug doses. The results obtained in this study indicated that there were no statistically significant differences between the control and treatment groups in either mathematics anxiety levels or in arithmetic test performance. These findings counter many of those found in previous investigations. Reasons for these discrepancies are provided along with recommendations for present practice and future research.

Introduction

Schools of nursing have long been concerned with ensuring that their graduates are able to consistently calculate the correct amount of medication that the patient receives. Inaccurate doses, however, have been administered (Dexter & Applegate, 1980). Reasons for these errors vary, but evidence suggests that most are due to poor teaching methods, mathematics anxiety, or a combination of these. The purpose of this article, therefore, is to examine these claims as they relate to first-year nursing students in a 2 ½-or 3-year program at Mohawk College of Applied Arts and Technology in Hamilton, Ontario, Canada.

Literature Review

To date, there have been few studies in this area. Lazarus (1975), who coined the word "mathophobia," believes that math avoidance is caused primarily by social factors. For example, he posits that current teaching methods make math useful to only a very few bright people; little is done to make it relevant to everyday life. Further, he concludes that being poor at arithmetic is in "good taste" and therefore socially acceptable.

Others would concur. Tobias (1976), for instance, found that women chose careers in nursing because they feared number manipulation. Moreover, this fear is believed to be society related. Specifically, it is,

A culture that makes math ability a masculine attribute, that punishes women for doing well in math, and that soothes the slower math learner by telling her she does not have a "mathematical mind." It all adds up to math anxiety of which avoidance is but a symptom (p. 57).

Tobias' solution was mutual support groups (1978). Here, learners could discuss their feelings about arithmetic. They frequently revealed vivid memories of disturbing situations that occurred as early as sixth grade. For example, they often failed to understand a concept such as division of fractions and were afraid to ask for help for fear of being ridiculed by the teacher or their peers. Her sessions were accompanied by mathematics input that was carefully and gently explained, often using English instead of mathematical symbols.

In a further study on sex differences and mathematical ability, Betz (1978) found that females experienced greater math anxiety than males. In addition, older women reported more anxiety than younger ones. She concluded that "...math anxiety is a problem for a large proportion of college students" (p. 446).

Hendel and Davis (1978), in a study of 69 female participants in a math anxiety program, discovered that although there were few sex-related cognitive differences toward mathematics, there were many attitudinal ones. They also discovered that high anxiety students do not, as a rule, enroll in mathematics courses. In the end, the researchers implemented a desensitization program that lowered anxiety levels and improved performance.

Timpke and Janney (1981), after 6 years of frustration with traditional drug dose calculation teaching methods, decided to implement computer-assisted instruction. The students found this approach less embarrassing and less overwhelming than the one they had previously experienced. They attributed this change to the fact that they could work in privacy, at their own pace, and receive direct feedback in relation to their success or failure in that segment of the program. The learners' observations were verified by the test results: the failure rate on the final examination was reduced from 11 out of 22 students to O out of 32.

It would seem, then, that nursing students, who are more than 90% female, carry with them a number of social and cultural predeterminants that impair their computational abilities in mathematics. Moreover, this impairment is supposedly compounded by methods traditionally used to teach arithmetic.

Problem Statement and Hypotheses

This study will investigate these postulates as they relate to fractional drug dose calculation among first-year nursing students. In particular, this inquiry will address the following questions:

1. Will a teaching method that includes disclosure of feelings related to mathematics, and different modes of representation, reduce mathematics anxiety?

2. Will a teaching method that includes disclosure of feelings related to mathematics, and different modes of representation, increase the learner's ability to accurately calculate fractional drug doses?

Stated in the affirmative, the research hypotheses become:

1. There will be a statistically significant difference between the post-treatment and the post-control math anxiety scores.

2. There will be a statistically significant difference between the post-treatment and the post-control arithmetic test scores.

Stated alternatively, the null hypotheses become:

1. There will be no statistically significant difference between the post-treatment and the post-control math anxiety scores.

2. There will be no statistically significant difference between the post-treatment and the post-control arithmetic test scores.

Research Design

Study Locale

Mohawk College of Applied Arts and Technology is located in an urbanized, highly industrialized region with a population of approximately 500,000. The surrounding area is largely mixed farming, although in recent years there has been an increase in cottage and secondary industry.

The college has approximately 12,000 full-time students working at 15 teaching locations in a wide variety of programs ranging from general interest to trades, technology, and professional disciplines such as nursing and occupational therapy. The nursing group, from which the sample for this study was taken, has a total of 700 full-time students who work through three levels during &/z semesters. The nursing group is different from the main college body in that the program is oversubscribed, which leads to a more stringent process than if it was undersubscribed. The program is based on a modular design. First-year students work in small groups of 11 with one instructor who is responsible for their total nursing theory, biology, and clinical practice. The students stay with the same instructor for the first semester; thereafter, they change every half semester.

Sample

The sample consisted of eight groups of 10 first-year nursing students (N=SO) chosen at random from 16 possible groups. Four groups, in turn, were randomly selected as the treatment and control groups, respectively. No one was required to participate if he did not wish to do so. All the instructors agreed to cooperate. Faculty and student anonymity were guaranteed.

Most of the students came from the surrounding area and are thus representative of the region in general. All, with the exception of a few mature students, held a diploma from a secondary school (grade 12) with advanced level credits in English and science. A breakdown by age indicates that 55% were between the ages of 17 and 20; 23% were between the ages of 21 and 25; and 22% were between the ages of 26 and 40.

Methodology

The method adopted was taken, in part, from Bruner (1964). His approach to the problem takes into account the cognitive, cultural, maturational, and personal factors of the learner. This task is best achieved by moving the student from a concrete phase of learning to a more abstract phase where mathematical symbols are implemented in the process. The teacher must also consider the anxiety levels of the student. If stress levels are high, students are assisted with their feelings before the sessions continue. The process entails three steps: the students are first moved through a set of actions appropriate for achieving a certain result (enactive representation); next, the students are moved through a set of summary images or graphics that stand for a concept without defining it fully (ikonic representation); the students are then moved through a set of logical propositions drawn from a symbolic system that is governed by rules and transforming propositions (symbolic representation).

Although five steps were employed in this study, they parallel those of Bruner. The teachers of the four treatment groups were given specific verbal and written instructions related to the procedures that were to be followed when teaching the mathematics package. The studente were first given the opportunity to verbalize their feelings: Were they anxious? Why were they anxious? Where were the feelings coming from? The students then demonstrated the amounts involved using a kit that included teaching aids such as syringes, bottles, and medicine cups and were encouraged to develop mental images of the amounts. Next, the students were asked to make sample conversions using the learning aids provided, and then they solved the problems related to the modular exercises of the program using either the mathematical formulae provided or others with which they felt more comfortable.

In contrast, the instructors of the control groups were not given directions on how to teach the materials. Rather, they were told to continue as they had in the past. Basically, this meant that the students were required to complete the learning modules on their own. The traditional method contains few lectures; any consultation that does occur is in small groups or on an individual basis. The students are given a series of standardized formulae that they apply to the problems. If they are successful, they move to the next unit. When difficulties arise, problems of a similar nature are given to the student. This procedure is repeated until the student grasps the concept.

Instrumentation

The Mathematics Anxiety Scale (MARS) (Richardson & Suinn, 1972) was administered to both the treatment and control groups before the unit was taught and again in three weeks after the unit was completed. The instrument is a 98-item, self-rating tool with a five-point Likert type scale ranging from "not at all" to "very much." Respondents indicate the degree of anxiety precipitated by each statement. Sample items included:

* Having someone watch you as you add a column of figures;

* Registering for a math course;

* Working on an income tax form;

* Raising your hand in a math class to ask a question;

* Reading a formula in chemistry;

* Thinking about an upcoming math test the day before;

* Receiving a final math grade in the mail;

Data concerning the reliability and validity of the instrument have proven it to be consistent over time and accurate in measuring what it purports to measure. For example, the internal consistency coefficient (coefficient alpha) was found to be 0.97 (N=397). Also, Suinn, Edie, Nicoletti, et al (1972) found the test-retest reliability coefficient after a 2week interval to be 0.78, significant at p < .001. Based on these results, Richardson and Suinn (1972) claim "... that the test items are heavily dominated by a single homogenous factor, presumbly (sic) mathematics anxiety" (p. 553).

TABLE 1 MEANS, STANDARD DEVIATION AND T-TESTS FOR MARS SCORES: PRERETIREMENT AND PRECONTROL GROUPS |

TABLE 2 MEANS, STANDARD DEVIATION AND' T-TESTS FOR MARS SCORES: POST-TREATMENT AND PPST-CONTROL GROUPS |

Validity studies between MARS and other tests of math anxiety (concurrent validity) have likewise been encouraging. For instance, Suinn et al (1972) found that the correlation between MARS and the Differential Aptitude Test (DAT) "to be - .35 (p < .05) for the original testing and -.32 (p < .05) for the retesting" (p. 374). This negative relationship means that a high anxiety level is associated with low performance on DAT.

The arithmetic scores of the two groups were measured by a standard math test that is routinely administered by the department at the end of this module. The test is a mix of 34 items that include 20 equivalency conversions and 14 dosage and solution calculation problems. No stringent time limit is set although the learners usually complete the examination within one hour.

Data Analysis

The analysis included eight steps. After the MARS scores were computed, the means and standard deviations for both the pretest and post- test treatment and control groups were calculated and a two-tailed test was used to determine if differences in the scores between the groups were statistically significant. The arithmetic test scores were tallied; the means and standard deviations for the treatment and control groups were calculated and a two-tailed test was run between the means to determine if the results were statistically significant.

Results

Table 1 presents the means, standard deviations, and t values for the pretest groups. The t value of 2.45 is not significant (p =e .01) and therefore it can be concluded that there is no initial difference between the mean anxiety scores of the two groups.

TABLE 3 MEANS, STANDARD DEVIATION AND T-TESTS FOR THE ARITHMETIC SCORES: POST-TREATMENT AND POST-CONTROL GROUPS |

Table 2 shows the means, standard deviations, and t values for the post-test groups. The t value of 1.22 is not significant (p ≤ .01) and thus the authors were unable to reject the first null hypothesis (ie, there are no statistically significantly differences between the post-treatment and post-control math anxiety scores).

Table 3 reveals the means, standard deviations, and t values for the post-treatment and post-control arithmetic test scores. Again, the t value of 1.21 is not significant (p=s .01) and hence the authors were unable to reject the second null hypothesis (ie, there are no statistically significant differences between the post-treatment and the post-control arithmetic test scores).

Discussion

Clearly, variations in teaching approaches did not affect either the levels of math anxiety or the arithmetic test scores of the two groups of students in this study. In other words, planned and systematic interventions designed to lower the students' math anxiety levels and to improve their calculation abilities were not significant. The question, of course, is why the results of this study differ from those suggested in the literature.

The answer can, no doubt, be attributed to a number of factors, not the least of which is time. Perhaps this generation is not as math anxious as its predecessors. In fact, evidence would indicate that this is indeed the case. For example, Richardson and Suinn (1973) initially found the mean score on MARS to be 215 whereas in the present investigation it was 171. This is a difference of approximately 44 score points or 17 percentile points. Thus, this group was less anxious overall than those employed earlier.

But the question of why this group less math anxious than its predecessors remains. One suspects that it has much to do with socialization. Fifteen years have passed since the development of MARS. In the interval, there have been many changes in attitudes towards sex roles. Improved counseling facilities and consequent attempts by the school system to encourage enrollment in mathematics and science courses may be having some visible effects. In short, mathematics may no longer be viewed, at least by this group, as the domain of the male student.

The second finding, that there were no significant differences hi the students' abilities to accurately calculate drug doses, suggests that perhaps there is no need to change the program, that the modular approach is an effective format. Or, it could mean that the students learn the content despite the teacher or teaching method; essentially, these students are independent achievers.

Caution must be exercised. It must be remembered that this investigation was confined to one college, and hence the results may not be applicable to the larger society. More studies with diverse populations are needed before unconditional conclusions can be drawn. Still, this inquiry does challenge conventional wisdom. It should no longer be assumed, for instance, that female students are math anxious and that this, in turn, inhibits their ability to calculate drug doses.

Teachers must realize that people and social conditions change, that what was once assumed to be true may no longer be so. They must guard against false impressions engendered by armchair speculation, hearsay, or idle inference. Is math anxiety really a problem, or is it merely "thought" to be a problem? And how do we know?

Assuredly, we know best through the compilation of a body of systematic, scientific research. It is hoped that others will launch similar studies that will provide further insights into the question of math anxiety and its effects on drug dose calculation.

### References

- Betz, N. E. (1978). Prevalence distribution and correlates of math anxiety in college students. Journal of Counselling Psychology, 25(5), 441-448.
- Bruner, J.S. (1964). Some theorems on instruction illustrated with reference to mathematics. Sixty- Third Yearbook of the National Society for the Study of Education (part 1, pp. 306-335). Chicago: University of Chicago Press.
- Dexter P., & Applegate M. (1980). How to solve a math problem. J Nurs Educ 19(2\ 49-53.
- Hendel, D.B., & Davis, S.O. (1978). Effectiveness of an intervention strategy for reducing mathematics anxiety. Journal of Counselling Psychology, 25(5), 429-434.
- Lazarus, MJ. (1975, June). Rx for mathophobia. Saturday Review, 2(20), 46-48.
- Richardson, F.C., & Suinn, R.M. (1972). The mathematics anxiety rating scale. Journal of Counselling Psychology, 19(6), 551-554.
- Suinn, R.M., Edie, CJi., Nicoletti, J., & Spinelli, P.R. (1972). The MARS, a measure of mathematics anxiety: Psychomatic data. J Clin Psychol, 28, 373-375.
- Timpke, J., & Janney, C.P. (1981, June). Teaching drug dosages by computer. Nurs Outlook, 29(6), 376-377.
- Tobias, S. (1976). Math anxiety. Ms, 5(3), 56-59, 92.
- Ibbias, S. (1978). Overcoming math anxiety. New York: Norton.

TABLE 1

MEANS, STANDARD DEVIATION AND T-TESTS FOR MARS SCORES: PRERETIREMENT AND PRECONTROL GROUPS

TABLE 2

MEANS, STANDARD DEVIATION AND' T-TESTS FOR MARS SCORES: POST-TREATMENT AND PPST-CONTROL GROUPS

TABLE 3

MEANS, STANDARD DEVIATION AND T-TESTS FOR THE ARITHMETIC SCORES: POST-TREATMENT AND POST-CONTROL GROUPS