#### Abstract

ABSTRACT

The accurate calculation of drug dosages is a critical skill for nurses. This study compared two different treatments, algorithmic-based instruction (ABI) and teacher-directed instruction (TDI), as ways of providing instruction in dosage calculation. The ABI treatment relied exclusively on the use of a written study guide with algorithms, whereas the TDI treatment utilized lecture. Both treatments included an equal number of practice sessions structured via a whole or part method.

The sample included 55 nursing students who were randomly assigned to either the whole or part method, and to TDI or ABI treatment. Initial learning and retention were measured by the use of two post-tests.

Analysis of covariance indicated that neither of the treatments nor methods were statistically different for initial learning or retention. Both treatments, however, were found to be effective. The ABI treatment, moreover, was very efficient since it eliminated 75 minutes of instruction presented by a lecturer. Implications of this finding are considered.

Introduction

Several studies have cited problems with the mathematical proficiency of nursing students. Bindler and Bayne (1984) reported that, after testing 741 nursing students with a teacher-constructed examination, 9% to 38% in each group tested were unable to pass all parts of the examination at a 70% level.

Dexter and Applegate (1980), referring to the associate degree program at Indiana University, encountered a dosage calculation problem in the clinical setting. They attributed the problem to several factors: students entered the program less well prepared in mathematics, consistent with the national trend of declining SAT scores; students tended to be a heterogeneous group with a wide variety of backgrounds and ages; the program switched to an integrated curriculum without a pharmacology course per se and with mathematics content not specified at any point; and studente spent less time actually giving medications.

Timpke and Janney (1981) introduced a successful computer-assisted program in drug dosages after six unsuccessful years using traditional methods of remediation at California State University. The traditional methods used by these authors consisted of testing, counseling, and a review text. Groves (1985) also reported success with the use of a computer-assisted program in mathematical calculations for nurses.

The problem of continued remediation and retesting of dosage calculations can also be observed in the associate degree nursing program at Armstrong State College in Savannah, Georgia. Because of the students' ability to pass the college-wide basic skills examination in mathematics and to pass the calculation tests in the freshman year, the problem is believed to be retention and/or incomplete understanding rather than lack of ability.

Purpose of the Study

The purpose of the study was to compare algorithmic and teacher-directed instruction of dosage calculation for associate degree nursing students. These two treatments included equal practice sessions and were instituted via a whole or a part method. Initial learning was measured by the use of a post-test. Retention was measured by the use of a second post-test given 3\k months after completion of the instruction.

The teacher-directed instruction was defined as a treatment that used lecture as the method of instruction followed by written practice for the five types of dosage calculations. The algorithmic-based instruction (study guide with algorithms) was defined as a treatment in written form that contained an explanation for each type of dosage calculation, directions for using the algorithms, and demonstration problems. This treatment also included supervised written practice for the five types of dosage calculation.

The whole method of instruction is a technique in which all content is presented at one time (in this study, either through the teacher-directed or algorithmic-based treatment) followed by distributed practice on all of the content (in this case, distributed over a five week period). The part method of instruction is a technique in which part of the content is presented (in this study, either through the teacher-directed or algorithmic-based treatment) then followed by massed practice on that one area, then the next part is presented and followed by massed practice on that area. This process is repeated until all areas of content have been presented and practiced separately. Since the research literature provided little direction for presenting the algorithmic treatments, the whole/part presentation modes were included as variables in this study.

Background

The theoretical basis for the selection of algorithmicdirected instruction can be traced to the research of Landa (1974, 1976, 1983, 1987). Landa (1974) defined algorithms as "a precise, generally comprehensible prescription for carrying out a defined sequence of elementary operations in order to solve any problem belonging to a certain class."

Algorithms break down operations into categorical yes/ no steps. Landa (cited in Cook, 198Oa) found the following reasons for the use of algorithms: the application of a simple algorithmic rule can often save countless hours that are wasted in an attempt to understand complex prose; algorithms are designed to categorize information so that an individual only has to read what is relevant; instruction with algorithms allows the development of master-level decision making processes in the very beginning with a higher degree of reliability (only a small portion of nonmasters are able to discover all of the operations necessary to become masters); instruction with algorithms forces the educator to clearly define the operations that must be carried out to arrive at a solution; and instruction with algorithms allows educators to develop methods of instruction that can produce "masters in mass."

Methodology

Subjects

The subjects were those students enrolled in the second fundamentals nursing course (Nursing 101) at Armstrong State College in the winter and spring quarters of 1987 who were willing to participate. Thirty students participated in the study during the winter quarter and 25 students participated during the spring quarter.

Students who agreed to participate in the study were asked to sign an informed consent form approved by the University of Georgia. All of the students enrolled in the course participated in the study with the exception of one student who began the instruction and later dropped out of the study and the nursing program. All of the subjects had completed the Scholastic Aptitude lest (SAT) prior to admission to the nursing program.

The 55 subjects in the study ranged in age from 19 to 51. All of the subjects were female except for two males who were both in the algorithm-whole group. The subjects' Scholastic Aptitude Verbal Test scores ranged from 270 to 660; their Scholastic Aptitude Mathematics Test scores ranged from 250 to 690.

Treatments

Lecture, a programmed text, small group review, and frequent explanations in the clinical setting have traditionally been used to teach dosage calculation in the associate degree nursing program at Armstrong State College. These approaches were very time consuming for faculty and did not produce the accuracy on initial learning or retention needed by the practicing nurse.

Prior to this study, students receiving instruction on dosage calculations had lectures covering the various tasks as occur in the part method. The programmed text was also subdivided, but was assigned as a whole so that a student might complete the book in part or in one sitting. Practice sessions had never been formally arranged, but consisted of practice in the programmed text and small group review as needed. Thus, there was a need to determine which method of presentation was superior (whole or part) and to formally arrange practice sessions.

Lecture for the teacher-directed instruction was written by the primary investigator and reviewed for content validity by three other faculty members in the department. The same three faculty members served as observers during the lecture presentation to ensure consistency and objectivity.

Past experience at the college indicated that many students who could correctly solve a dosage calculation problem in one class session could not do so at the next class session. For this reason, and the large amount of faculty time being consumed by this problem, a performance aid was sought for independent use during practice.

A review of the Literature concerning performance aids for dosage calculation was not fruitful. This review did, however, identify algorithms as an effective treatment for teaching procedural information. For this reason, algorithms were chosen for use as performance aids.

Books by Horabin and Lewis (1978) and Wheatley and Unwin (1972) were reviewed. Development of the first algorithm took approximately 6 hours (4 hours to develop and 2 hours to test). The other algorithms took considerably less time for development and testing (2 to 3 hours each). The study guide with algorithms was also reviewed by the three faculty members for accuracy and content validity.

Instructions were provided to the students utilizing the study guide with algorithms and included a definition of algorithms as performance aids. The students were told how to use the algorithms during their practice sessions, the schedule for the practice sessions, and that teacher support would not be provided.

TABLE 1 WEEKLY ACTIVITIES |

Procedures

The 30 students enrolled in Nursing 101 in the winter quarter were randomly assigned to the whole or part method. The treatment for these groups was teacherdirected (lecture) with practice. Length of instruction was held constant for both groups although one had the content presented as a whole with distributed practice and the other had content presented in five parts with massed practice following each part. Table 1 outlines the weekly activities. At the end of the treatment, these students were given a post-test to assess initial learning and a second post-test at the end of the spring quarter (3Vfc months later) to assess retention.

The lecture for the teacher-directed treatment was written and divided into the five tasks. The whole method group received all of the lecture in 75 minutes. The part method group received five, 15-minute lectures over five weeks. Lectures were delivered by the primary investigator without the use of any prepared audiovisual aids. Lectures for both groups were taped and reviewed or observed by a fellow faculty member, and were found to be consistent and objective. Practice sessions were limited to 20 minutes and monitored by faculty members in the department.

Students enrolled in Nursing 101 during the spring quarter were randomly assigned to the whole or part method. The treatment for these two groups was study guide with algorithms and practice (presented in written form as a whole or in five parts). Table 1 outlines the weekly activities. At the end of the treatment, these students were given a post-test to assess initial learning and a second post-test at the beginning offall quarter (3Mi months later) to assess retention.

All groups received feedback from practice in the form of a completed practice sheet with the correct answer and correct method for solving the problem. The number of practice problems and length of practice sessions were held constant. Students who were in the whole method practiced all five tasks weekly with two practice problems for each task totaling 10 weekly and 50 for the 5-week period. Students in the part method practiced one task weekly with 10 practice problems on that task for a total of 50 practice problems.

Instruments

The instruments used in this study were a post-test to assess initial learning and a second post-test to assess retention. Each test consisted of 25 dosage calculation problems, five problems for each of the five tasks in the study. Three, 25-question tests were piloted with fourth quarter nursing students (65 sophomores) who had completed dosage calculation testing one month earlier. These students were randomly assigned to one of the three tests. The two tests with the highest reliability estimates (KR-20) were used for the two post-tests. Reliability estimates for the two post-tests were as follows: first post-test, .87; second post-test, .85. A written form was designed and used with each group of subjects to elicit comments about the subjects' opinions of the specific treatment in which they participated.

TABLE 2 SUMMARY OF UNADJUSTED SCORES FOR POST-TEST I (LEARNING) |

TABLE 3 ANALYSIS OF COVARIANCE FOR POST-TEST I (INITIAL LEARNING) |

Research Design

This study used an experimental design (post-test only without control groups) with four equivalent treatment groups. The study was conducted for students entering Nursing 101 during two consecutive quarters (winter and spring). This approach eliminated the possibility that the teacher-directed groups might gain access to the study guide with algorithms since this latter treatment was not used until the second quarter. The groups were considered equivalent because they were beginning the same course and courses taken in the quarter interim for both groups did not contain any dosage calculations or mathematical content.

Results

Post-test I was given to all four groups after the treatmenta to assess initial learning. A summary of the descriptive statistics for this post-test is presented in Table 2.

Using the students1 Scholastic Aptitude Mathematics Test Scores as a covariate, analyses of covariance (ANCOVA) were run. Scholastic Aptitude Mathematics Test scores were found to be a significant covariate in the study. The results for Post-test I, shown in Table 3, indicated no significant treatment effects for initial learning. Adjusted means based on percentage scores for each treatment group were as follows: teacher whole, 93.83; teacher part, 94.63; algorithm whole, 93.87; algorithm part, 91.90.

Post-test II was given 3Y2 months after the treatment to assess retention. A summary of the descriptive statistics for this post-test is presented in lable 4.

The ANCOVA for Post-test II, shown in Table 5, indicated no significant treatment effects for retention. Adjusted means for each treatment group were as follows: teacher whole, 81.69; teacher part, 81.38; algorithm whole, 88.68; algorithm part, 81.36.

Discussion

Treatment: Initial Learning and Retention

The data related to the examination of the effects of treatment for initial learning and retention yielded no significant results. Both treatments, however, were found to be effective, producing an overall adjusted mean for initial learning of 94.23 for teacher-directed and 92.89 for study guide with algorithms. Although a statistically significant retention loss over a 3 ½ month period was found for both treatments (p<.0001), the adjusted means remained at a high of 81.54 for teacher-directed and 85.02 for study guide with algorithms.

The associate degree program in nursing at Armstrong State College requires 88% correct as the passing criterion on dosage calculation tests. In the past 6 years, approximately 20% of the students needed to take the dosage calculation test four times during the quarter they received initial instruction to achieve the required passing grade. In contrast, 83.64% of the subjects in this study achieved the required passing grade on Post-test I and 45.45% were still able to achieve or exceed this grade after 3 ½ months. Of the sophomore students who took the pilot tests, 55.38% were able to achieve the required passing grade even though they had completed dosage calculation testing one month prior to the pilot tests. The adjusted grand means for the subjects in this study were 93.56 for Post-test I and 83.28 for Posttest II (unadjusted means were 93.60 and 83.05, respectively). The mean for students taking the pilot tests was 78.36.

TABLE 4 SUMMARY OF UNADJUSTED SCORES FOR POST-TEST II (RETENTION) |

It is interesting to note that the algorithm-whole group was the condition that seemed to facilitate retention (p<.10). The majority of the students in this group achieved or exceeded the department's required passing grade on Post-test I (11 out of 12) and Post-test II (10 out of 12). The Figure illustrates the effects of treatment and method on initial learning and retention. The literature, although limited on the subject of algorithms, does support the use of algorithms for subject matter that can be broken down into operations (Romiszowski, 1981; Landa, 1974; Landa, 1976; Landa cited in Cook, 1980a, 1980b). Since neither of the treatment groups were statistically superior to the other, the use of the study guide with algorithms can be considered equal to the more traditional treatment of lecture (teacher-directed). A substantial savings of teacher time (75 minutes each time the lecture was repeated or a total of 450 minutes for the study), however, was obtained by using the study guide with algorithms treatment. The literature does provide similar evidence for a savings of work hours through the use of algorithms in place of traditional instruction (Horabin & Lewis, 1980; Landa cited in Cook, 1980a, 1980b).

Method: Initial Learning and Retention

The data related to the examination of the effects of method for initial learning and retention yielded no statistically significant results. Both methods, however, were found to be effective, producing an overall adjusted mean for initial learning of 93.85 for the whole method and 93.27 for the part method. Although a statistically significant retention loss over a 3Vfe month period was found for both methods, the adjusted means remained at a high of 85.19 for the whole method and 81.37 for the part method.

Conclusion

The use of algorithms in other areas of nursing curricula should be investigated. Criteria for these areas should consist of selecting topics that can be broken down into categorical yea/no steps, skills that frequently need practice by students, and content areas that require the application of a rule or problem solving. A few of the many areas that meet these criteria include interpretation of laboratory results (acid-base balance would work especially well), determining a patient's nursing diagnosis, assessing a diabetic for diabetic ketoacidosis, assessing a burn patient for fluid shifts and extent of burn injury, treatment of arrhythmias, and dietary planning for patients with dietary restrictions.

TABLE 5 ANALYSIS OF COVARIANCE FOR POST-TEST II (RETENTION) |

The findings of this study indicate that neither of the treatments (teacher-directed and study guide with algorithms) nor methods whole and part) were statistically different for initial learning or retention of dosage calculations. The study guide with algorithms was found to save faculty time and was an effective performance aid. Both treatments and methods were effective and were well-received by the subjects in the study.

This study suggests that the use of algorithms is a feasible alternative to more traditional methods of instruction (lecture) for dosage calculation. Combination of the two treatments, however, offers yet another potential approach. Moreover, regardless of which instructional treatment is initially used, algorithms may well be an effective way to help students retain their initial high levels of achievement by providing opportunities after instruction for quick and accessible reference, review, and practice. Additional research on their potential application is needed.

### References

- Bindler, R., & Bayne, T. (1984), Do baccalaureate students possess basic mathematica proficiency? Journal of Nursing Education, 23(5), 192-197.
- Cook, M.H. (1980a). Algorithmization - A shortcut to learning (and to savings). Training and Development Journal, 34, 4-8.
- Cook, M.H. (1980b). Algorithmization - A shortcut to learning (part 2). Training and Development Journal, 34, 4-7.
- Dexter, P., & Applegate, M. (1980). How to solve a math problem. Journal of Nursing Education, 19(2), 49-53.
- Groves, G.E.G. (1985). The effects of linear and diagnostic computer based formats in teaching mathematics for drug administration to nursing students with high and low math aptitudes. Unpublished doctoral dissertation, University of Georgia, Athens
- Horabin, I., & Lewis, B. (1978). Algorithms. Englewood Cliffs, NJ: Educational Technology Publications.
- Landa, L.N. (1974). Algorithmization in learning and instruction. Englewood Cliffs, NJ: Educational Technology Publications.
- Landa, L.N. (1976). Instructional regulation and control. Englewood Cliffs, NJ: Educational Technology Publications.
- Landa, L.N. (1983). The algo-heuristic theory of instruction. In C.M. Reigeluth (Ed.), Instructional design theories and models: An overview of their current status, pp. 163-211. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Landa, L.N. (1987). A fragment of a lesson based on the algoheuristic theory of instruction. In C.M. Reigeluth (Ed.), Instructional theories in action: Lessons illustrating selected theories and models, pp. 113-159. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Romiszowski, A.J. (1981). Designing instructional systems. New York: Kogan Page/Nichols.
- Timpke, J., & Janney, C.P. (1981). Teaching drug dosages by computer. Nursing Outlook, 29, 376-377.
- Wheatley, D.M., & Unwin, A.W. (1972). The algorithm, writer's guide. London: Longman Group.

TABLE 1

WEEKLY ACTIVITIES

TABLE 2

SUMMARY OF UNADJUSTED SCORES FOR POST-TEST I (LEARNING)

TABLE 3

ANALYSIS OF COVARIANCE FOR POST-TEST I (INITIAL LEARNING)

TABLE 4

SUMMARY OF UNADJUSTED SCORES FOR POST-TEST II (RETENTION)

TABLE 5

ANALYSIS OF COVARIANCE FOR POST-TEST II (RETENTION)