linear and curvilinear relationships between student practice and achievement in physical education

Teachrng & Teacher &ducanon. Vol. 6. No. 4. pp. 3OS314, I!?90 Printed I” Great Britam

LINEAR AND CURVILINEAR RELATIONSHIPS BETWEEN STUDENT PRACTICE AND ACHIEVEMENT IN PHYSICAL EDUCATION

STEPHEN SILVERMAN

The University of Texas at Austin, U.S.A.

Abstract-The purpose of this study was to examine relationships between student practice trials and achievement in physical education classes. Middle school/junior high school students (N = 202) were pretested and posttested on two volleyball skills. Between tests students received seven classes of instruction. Data were collected from videotapes on the quantity and quality of individual student practice trials. Linear, quadratic, and cubic relationships of practice with residualized achievement were determined. For both skills, appropriate practice trials were positively related to achievement and inappropriate trials negatively related to achievement. Other linear and curvilinear relationships were found.

The study of time and practice variables has produced powerful results in investigations of relationships to student achievement in classrooms. Generally, the amount of time students spend at an appropriate level or with a high suc- cess rate has correlated with student achievement (for reviews see Brophy & Good, 1986; Denham & Lieberman, 1980; Fisher & Ber- liner, 1985). Both the variables-time and the appropriateness of the task to the student - interact in their relationship with achievement.

A subject matter area in which some investi- gation of time variables related to student achievement has occurred is physical education (for reviews see Lee & Poto, 1988; Metzler, 1989). Differences exist, however, between the environment of physical education and the typi- cal environment where much of the classroom research has been conducted. Although categories for measuring time related variables may be different in the research conducted in gym- nasia, results of studies indicate that many of the relationships found in classrooms also may apply in physical education (Silverman, Tyson, & Morford, 1988).

As a number of authors have discussed

(BI oom, 1985; Carroll, 1963, 1985, 1989; Smyth, 1985) and studies have documented

(Brophy & Good, 1986; Fisher, Filby, Mar- liave, Cahen, Dishaw, Moore, & Berliner, 1978) allocating time for student learning is not sufficient to produce learning. Students must be engaged with the subject matter during that time. Silverman et al. (1988) found that the time devoted to student practice was related to achievement, but that some organizational pat- terns did not relate, or had a negative relationship, to learning. A number of studies have shown that students in physical education classes spend large amounts of time waiting for opportunities to actually practice the skill being taught and that there is much variability in the amount of time students spend on task (Costello & Laubach, 1978; Godbout, Brunelle, & Tousignant, 1983; Metzler, 1980; Pieron, 1983; Placek, Silverman, Shute, Dodds, & Rife, 1982; Shute, Dodds, Placek, Rife, &Silverman, 1982; Silverman, Dodds, Placek, Shute, & Rife, 1984). Variables related to individual student practice may be important in understanding those variables which are important in learning motor skill.

One variable which often has been investi- gated in laboratory motor learning studies and which has been found to be related to learning is practice trials (Magill, 1989; Schmidt, 1988).

This study was supported by a grant from the University Research Institute, The University of Texas at Austin The author would like to acknowledge Terri Johnson and Connee Howard for their help with this study.

305

306 STEPHEN SILVERMAN

Two studies with moderate sample sizes, conducted in actual physical education settings, have shown that appropriate practice trials relate to student achievement (Ashy, Lee, & Landin, 1988; Silverman, 1985). Practice trials may be strongly related to motor skill learning. These two studies, however, provide only limited data on the relationships of interest.

In studies of practice and motor learning a “plateau effect” has been found-where learning is linear up to a certain point and then levels off or plateaus (Magill, 1989). Similar effects have been seen in classrooms where curvilinear relationships of process variables to achievement have described the relationship in stronger terms than the linear relationship (Brophy & Evertson, 1974). Since laboratory studies of motor learning and classroom process studies both indicate nonlinear relationships may exist in learning, it is likely that the investi- gation of both linear and curvilinear relationships of process variables to achievement will yield greater understanding of practice- achievement relationships in physical education.

This study is part of a large, multifaceted in- vestigation of the correlates of student achievement in physical education (Silverman, 1988; Silverman et al., 1988). The purpose of the study was to examine linear and nonlinear relationships between amount and appropriateness of student practice and achievement for two skills with a large number of student subjects.

Method

Students and teachers in 10 middle school/ junior high school physical education classes in central Texas were the subjects for this study. Students in the classes were pretested, received instruction, and then were posttested on the forearm pass and underhand serve volleyball skills. Instruction was videotaped for subsequent coding of process variables. A systematic observation instrument was developed to collect data on the quality and quantity of student practice. Both linear and nonlinear relationships were determined between the practice variables and student achievement.

Subjects

Students enrolled in 10 physical education classes taught by seven teachers in one middle school and one junior high school were the subjects for this study. Students (N = 202) who completed the pretest and posttest and missed no more than two classes were initially included in the study. During the collection of the process variables, students who could not be observed during one or more classes were elimi- nated from the sample. This resulted in 194 student subjects for the forearm pass skill, and 192 for the serve skill. The teachers were the regularly assigned physical education teachers who would normally teach these students in this unit of instruction. Four teachers each taught one class and three teachers each taught two classes.

Skill Testing

Students were pretested and posttested on each of the two skills to be taught. Both tests have been previously shown to be reliable and valid for this age group (Carlisle, 1982) and in pilot studies were shown to be practical, in that they could be completed in one class session with junior high aged children in the school gymnasium setting. With the help of several trained assistants, the investigator performed all testing. The pretest for the students took place in the class session prior to instruction, and the posttest on the day following com- pletion of instruction.

Serve test. The American Alliance for Health, Physical Education, Recreation and Dance serve test (American Alliance for Health, Phys- ical Education, Recreation and Dance, 1965) was used to determine skill in serving. Students stood in a designated area behind the service line and had 10 serving trials. The court was marked so that the subject received from 0 to 4 points for each serve depending on where the ball landed. The total number of points was summed and used for analysis.

Forearm pass test. The Brumback forearm pass test (Carlisle, 1982) was used to determine skill on the forearm pass. The test consisted of passing the ball above an 8 foot line and against a wall as many times as possible in one minute.

Practice and Achievement 307

Instruction

Instruction took place over 7 consecutive school days. All instruction occurred as part of the regularly scheduled physical education class. All class sessions for each class were videotaped using a two-camera split screen video set-up such that virtually all activity in the gymnasium could be recorded. Elapsed time was superimposed on the video image prior to recording on a VHS videocassette recorder. Teachers wore a small, cordless microphone and the audio signal was recorded simultane- ously. Each of the classes participating in the study would normally receive instruction in volleyball during the time period in which the study was conducted.

and net- when the student attempts to get the ball over the net; (d) forearm pass without ball

when the movement is practiced without a ball; (e) f orearm pass with ball - when the student attempts the skill by passing to him or herself or to another student; and (f) forearm pass with ball against wall - when the movement is practiced against a wall similar to the testing conditions. Trials where difficulty could not be discerned also were recorded. A technical report (Silverman & Johnson, 1986) is avail- able from the author to provide further detail.

Data Collection

Teachers were instructed to use the time as best they could for maximum student improve- ment in the two skills that were being tested. Teachers conducted the normal routines (role taking, warm-up, etc.) that were a part of the class. In all classes, the only skills taught were the forearm pass and the underhand serve; however, teachers spent varying amounts of time on lead-up skills and knowledge of volleyball rules and strategy.

All student practice trial data were collected by viewing the videotapes. The investigator and one other individual completed all coding. Dur- ing data collection the coders identified the student by the numbered pinafore being worn and observed the student throughout the class session. Practice trials were recorded on a specially prepared sheet. Each student was observed in each of the seven class sessions. Due to the time intensive nature of collecting data on each student in each class, data collection took approxi- mately 900 hours over a 12-month period.

Process Data

A systematic observation instrument was designed and validated to provide data on the quality and quantity of student practice trials. The author was interested in collecting data which would provide information on the type of practice in which the student engaged as well as the quantity of appropriate and inappropriate trials. Initial categories for defining and classify- ing each practice trial by each student were developed. Pilot testing of the observation instrument occurred and modifications to the categories and definitions were made. Piloting and testing of the system continued until practice trials could be easily categorized and the system had demonstrated high reliability.

Coders were trained by viewing videotapes and discussing categories, simultaneous coding followed by discussion, separate coding of videotapes for comparison, and separate coding with interobserver agreement checks. Actual coding of the videotapes did not begin until interobserver agreement was at the .90 level for three subsequent coded classes. Interobserver agreement was calculated by ANOVA with scored categories to obtain an intraclass correlation coefficient (Winer, 1971). Throughout the actual data collection 82 random observer agreement checks were performed. Ail interobserver agreement checks were .87 or higher, with a mean of .93.

Data Analysis

Each practice trial by an individual student Achievement data. For each skill, a residual was categorized as either appropriafe (a good score was calculated for each student as the practice trial) or inappropriate (a difficult or measure of student achievement. For the entire poor trial) for the following: (a) serve without sample a posttest on pretest regression equation ball-when the movement is practiced without was determined. Based on this equation pre- a ball; (b) serve with ball but without net- when dicted scores were calculated. The actual post- the student attempts the skill without attempt- test score minus the predicted posttest score was ing to get the ball over a net; (c) serve with ball the achievement score adjusted for entry skill

308 ST!ZPHEN SILVERMAN

level (the residual gain score). Therefore, if a student did better than predicted the student would have a positive residual score and if worse than predicted a negative residual score. Residual gain scores were selected because they partial out pretest skill level, and are reliable, uncorrelated with entry skill, and not subject to ceiling effects.

Process data. For each student, the categories of practice trials were summed across the seven class sessions. Categories then were summed so the number of appropriate, inappropriate, and total trials for each skill could be entered into subsequent statistical analyses. In addition, since previous research (Fisher, Berliner, Filby, Marliave, Cahen, & Dishaw, 1981) has shown that the ratio of appropriate to inappropriate trials was related to achievement, the ratio of appropriate to inappropriate trials for each skill also was calculated.

Statistical analysis. The data summed across classes (e.g., appropriate serve trials with a net), the summed variables (e.g., all appropriate trials), and the ratio of appropriate to inappropriate trials were correlated with residual achievement using the Pearson product-mo- ment correlation technique. This analysis determined linear relationships. The procedure of correlating residual scores with other variables is similar to calculating part correlation coeffi- cients. The technique used here was chosen because it is slightly more powerful than using increments of R for significance in part correlation and for consistency of analysis. Based on research hypotheses, one-tailed tests of significance were used.

In instances where there were significant linear relationships, curvilinear relationships of the process variables to achievement were tested. Quadratic and cubic functions were separately added to a multiple regression equation (residualized gain on the linear function) to determine if (a) the quadratic equation ac- counted for a significantly greater R’ than the linear equation; and (b) the cubic equation ac- counted for a significantly greater R’ than the quadratic equation (Pedhazur, 1982). When a curvilinear equation was found to be significant, the least squares line was graphed for easier de- scription of the relationship.

Results

Descriptive Data

For the forearm pass, the mean number of appropriate practice trials was 196.8 with the mean for inappropriate trials 221.5. Nearly all trials were with the ball, with the great majority not using the wall for practice. For the serve, the mean number of appropriate trials was 21.3 and the mean for inappropriate trials was 27.3. Nearly all of the serve trials occurred with the ball and with the student attempting to serve over the net. Great variability was found in the number of practice trials per individual student. The means and standard deviations for each class and the total sample are presented in Table 1 for the forearm pass and Table 2 for the serve.

Relationships with Achievement

Linear relationships. For both skills, the number of appropriate practice trials was positively related to achievement (forearm pass, r = .653, p < .OOl; serve, r = .654, p < ,001). All categories of appropriate forearm pass trials were positively related to achievement (without ball, r = .27O,p < .OOl; with ball, r = .566,p < .OOl; with ball against wall, r = .-CO. p < .OOl). For the serve only, the appropriate trials with a ball and net category had a significant positive relationship to achievement (r = .675, p < .OOl).

All inappropriate practice trials had a low, but significant negative correlation to achievement for the forearm pass (r = -.185, p < .OOS). A much stronger negative relationship between residualized achievement and inappropriate practice trials was found for the serve (r = -.615, p < .OOl). Those categories in which the greatest number of inappropriate trials occurred for both skills also showed significant negative relationships with achievement. Table 3 provides a summary of the relationships of all categories to achievement.

For both skills, the total number of practice trials was positively related to achievement (forearm pass, r = .427, p < .OOl: serve, r = .138, p < .05). The ratio of appropriate to inappropriate trials also showed significant positive relationships for both skills (forearm pass, r = .535, p < .OOl; serve, r = .-I%, p < .OOl).


Table 1

Means and Standard Deviations for Forearm Pass Practice Trials

Without ball With ball Against wall Total trials

Individual classes M (SD) M (SD) M (SD) M (SD1

Class 1 -appropriate (N = 15) -inappropriate Class 2 -appropriate (N = 27) -inappropriate Class 3 -appropriate (N = 10) -inappropriate Class 4 -appropriate (N = 19) -inappropriate Class 5 -appropriate (N= 16) -inappropriate Class 6 -appropriate (N= 31) -inappropriate Class 7 -appropriate (N = 12) -inappropriate Class 8 -appropriate (N = 24) -inappropriate Class 9 -appropriate (N = 17) -inappropriate Class 10 -appropriate (N = 23) -inappropriate Total -appropriate (N = 191) -inappropriate

3.1 (0.4)

0.9 6.0 $:Z;

1.8 (0.8)

0.0 0.0 iS:!$ 12.5 (2.3)

0.0 (0.0) 0.0 (0.0) 0.0

13.2 3.2 0.0 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 4.4 0.8

Table 2

Means and Standard Deviations for Serve Practice Trials

246.1 217.5 316.7 203.7 141.7 239.6 200.1 246.1 228.1

83.6 95.4

137.6 185.9 29.7 48.7 59.7 97.1 38.7 80.7

137.2 159.7

(204.7) 26.7 (24.6)

(i37.3j (220.0)

(72.6) w;:;j

(152.9) (123.3)

I:;::; (126.2) (120.6)

;:;:;; (89.8) (31.3)

;;;:;; (157.7) (124.5)

29.3 8.3

12.3 0.0 0.0 0.0 0.0

82.3 76.4

194.9 202.0

87.7 117.7 69.3

114.0 0.0 0.0 0.0 0.0

55.2 63.9

(0.0)

g::; (51.2) (41.4)

(161.7)

(iZ:t;

i::::;

(4:::;

;:::1

(0.0)

253.9 276.2 231.8 330.8 203.7 141.7 252.1 200.1 328.1 304.6 291.7 300.7 225.3 303.6

98.9 162.7 59.7 97.1 38.7 80.7

196.8 224.5

(229.6) (143.0) (206.5) (143.3) (220.0)

(72.6) (168.5)

(89.4) (204.1)

i:::;; (199.8) (206.3) (197.0)

(72.5) (66.3) (89.8) (31.3) (34.5) (29.8)

(199.8) (157.8)

-

Individual classes

Class 1 -appropriate (N = 14) -inappropriate Class 2 -appropriate (N = 26) -inappropriate Class 3 -appropriate (N = 10) -inappropriate Class 4 -appropriate (N = 19) -inappropriate Class 5 -appropriate (N = 16) -inappropriate Class 6 -appropriate (N= 31) -inappropriate

Class 7 -appropriate (N= 12) -inappropriate Class 8 -appropriate

(N = 24) -inappropriate

Class 9 -appropriate (N = 17) -inappropriate

Class 10 -appropriate (N = 23) -inappropriate Total -appropriate (N= 192) -inappropriate

Without ball With ball With net Total trials

M (SD) M (SD) M (SD) M (SD)

0.0 I:::; 0.0 (0.0) 14.6 ;I:::; 14.6 0.0 0.0 (0.0) 38.5 38.5 I ::::; 0.0 (0.0) 0.0 (0.0) 19.2 0.0 (0.0) 0.0 (0.0) 37.5

i:::;; 19.2 (22.7) 37.5 (17.2)

0.0 (0.0) 0.0 36.9 (32.5) 36.9 (32.5) 0.0 ii:;; 0.0

;oO::; 28.6 (24.5) 28.6 (24.5)

4.3 0.0 (0.0) 37.7 (29.9) 42.3 (30.3) 0.0 0.0

ii::; 0.0 (0.0) 27.3 0.0 (0.0) 30.9

;E:; 27.3 (25.6) 30.9

0.0 (0.0) 0.0 (0.0) 33.1 33.1 i:;:;; 3.6 15.1 (15.8) 6.3

(1::;; 24.9 (22.7)

0.0 [::oo;

29.1

0.0 0.0

(1,;:;; 10.7 (4.9) 39.8 (18.2)

28.0 28.0 0.0 i::oO; 0.0 28.8 ::24::; 28.8 ;::::; 0.0 i:::; 2.7 [Y:J 4.7 (6.7) 7.4 (10.6) 0.0 6.3

I;::;

10.5 (3.6) 16.8 (5.9)

0.0 0.0 17.8 (13.1) 17.8 0.0 I;:oO{ 0.0 (0.0) 10.7

;;:48;

10.7 (‘(Ej

0.0 (0.0) 0.0 5.7 5.7 0.0 (0.0) 0.0 I:::{ 10.3 (5.8) 10.3 I::;; 1.0 (1.9) 2.3 (8.4) 17.5 21.3 0.0 (0.0) 5.5 (11.9) 21.9 27.3


.Table 3

Correla(ions and Quadratic RL between Practice Trials and Achievement

Forearm pass (N = 194) All appropriate

without ball with ball against wall

All inappropriate without ball with ball against wall

Total trials Appropriate/inappropriate

Serve (N = 192) All appropriate

without ball with ball with net

All inappropriate without ball with ball with net

Total trials

r

.653tt

.270tt

.566tt

.420tt -.llw -.036 - .237tt

,003 .427tt .535tt

.654tt ,026 ,059 .675tt

-.615tt .OOO

-.277tt -.473tt

.138* Appropriate/inappropriate .454tt

*p < .05, **p < .Ol, ;p < .005, ttp < .OOl.

R2 R? Quadratic Increase

.427 ,050

.097 ,024

.364 ,055 ,213 ,036 ,039 .005

,057 ii0 - -

,183 ,001 ,413 ,127

.432 - -

,473 ,421 -

,079 .277 .049 .346

,004 - -

,012 .043 -

,003 ,051 ,030 ,140

F

18.30tt 5.03’

16.61tt 8.78t

.93

ii3 -

.12 41.32tt

1.33 - -

5.99’ 13.87.V

- .51

13.74tt 5.96*

40.46::

Curvilinear relationships. As indicated in Table 3 a variety ofquadratic relationships were found between practice variables and residualized student achievement. No cubic relationships were found. All appropriate forearm pass trials had a quadratic relationship with achievement (R’quadratic = .427, R’increase = .050, F = 18.30, p < .OOl). As the graph of this relationship (Figure 1) indicates there was a positive relationship between appropriate practice and achievement and then a plateau occurred indicating that more practice did not increase achievement. Similar quadratic relationships were found for the non-summed forearm pass appropriate practice trial categories with achievement.

For the serve, appropriate practice trials with the net had a quadratic relationship (R’quadratic = .473, R’increase = .012, F= 5.99,~ < .05) which was in the same direction, but was much less pronounced than those found for forearm pass categories. The opposite trend occurred

10

j 2o;/-y

0

T 2 ~ -10 -

-20 I I I I I I I I 0 200 400 600 600

Appropriote trials-pass

Figure 1. Quadratic relationship of forearm pass appropriate trials with residualized student achievement.


for inappropriate practice trials where no curvilinear relationships were found for the forearm pass, but all inappropriate trials had a quadratic relationship with residualized student achievement (R’quadratic = .421, R’increase = .043, F = 13.87, p < .OOl) for the serve. As Figure 2 indicates, up to a point there is a negative relationship between the variables and then further inappropriate trials do not cause a greater decrement in performance. As would be expected, since the majority of trials in the serve were with a net, this variable had a similar quadratic relationship with achievement.

-201 0 10 20 30 40 50 60 70 80 90

Inappropriate trials-serve

Figure 2. Quadratic relationship of serve inappropriate trials with residualized student achievement.

There was no curvilinear relationship for total forearm pass trials. For the serve, however, total practice trials had a quadratic relationship with achievment (R’quadratic = .049, R’increase = .030, F= 5.96,~ < .05). Although this relationship did not account for a large part of the total variance in residualized gain, the graph of the relationship (Figure 3) indicates that there was a slight negative relationship between total practice trials and achievement and then the relationship turned positive.

Finally, the ratio of appropriate to inappropriate practice trials had a quadratic relationship with achievement for both the forearm pass

20

r

-201 ’ 1 1 1 1 1 1 1 1 ! I 1 0 20 40 60 60 100 120

Total trials-serve

Figure 3. Quadratic relationship of serve total trials with residualized student achievement.

(R’quadratic = .413, R’increase = .127, F = 41.32, p = .OOl) and the serve (R’quadratic = .346, R’increase = .140, F = 40.46. p < .OOl). As Figure 4 indicates, for both skills the relationship was positive and then levelled off and, in fact, turned downward. It is important to note that although the increments of R’ and the graphs look similar, the range in the X-axis was much larger for the serve than for the forearm pass.

Discussion

The results of this study show great variability in the number of practice trials across classes and for students within a class. This is consistent with previous results showing variability in the time students spend on task (Costello & Laubach, 1978; Godbout et al., 1983; Metzler, 1980; Pieron, 1983; Placek et al., 1982; Shute et al., 1982; Silverman et al., 1984).

The average student had many more forearm pass than serve practice trials. A previous study with this data base showed that about two-thirds of practice time was spent on the forearm pass (Silverman et al., 1988). Students on the average, however, completed more than eight times


0 10 m 30 40 50 60 70 60 so 100 0 2 4 6 8 10 12 14 16

Appropriote / inoppropriote-serve Appropriate/ inappropriate - pass

Figure 4. Quadratic relationship for serve and forearm pass appropriate to inappropriate ratio with residualbed student

achievement.

the number of trials for the forearm pass than the serve. Teachers used organizational strate- gies for the serve which often only allowed one or two students to execute practice at a time. This resulted in far fewer trials for this skill. It is interesting that students rarely practiced the serve without a net, resulting in very few trials where the complexity of learning was reduced. It is probable that this contributed to the number of inappropriate trials. Models such as those suggested by Bloom (1985) and Carroll (1963) emphasize the need to reduce complexity in learning. The teachers in this study did not provide skill breakdowns to help students learn. The serve is a closed motor skill, where students do not have to react to an outside influence to initiate the skill (such as moving to the ball for the pass), and teachers may have felt students should learn the skill very quickly.

Appropriate practice trials clearly relate to residualized student achievement. For both skills, all appropriate trials showed strong positive correlations. This result is consistent with the model of learning proposed by Carroll (I963), with results of classroom studies (Brophy & Good, 1986; Fisheret al., 1978), and the two previous studies conducted in physical education (Ashy et al., 1988; Silverman, 1985).

This result also was found for all categories of forearm pass practice and for serve practice with the net. The other appropriate serve variables did not relate to achievement since few students had trials in these categories, causing a restriction in the range of scores.

As with the previous research conducted in classrooms (Brophy & Evertson. 1974). nonlinear relationships were found. Appropriate practice of the forearm pass showed curvilinear relationships to achievement where a plateau occurred after many practice trials. This quadratic relationship was found only for serve trials which occurred with a ball and net. There was much less of a plateau effect with more trials - just less gain as appropriate trials increased. Although these plateau effects have been found often in the motor learning literature (Magill, 1989; Schmidt, 1988), for studies conducted in laboratories, it would be poor advice to caution practitioners to limit the number of appropriate trials because of this effect. Very few students practicing the pass completed enough trials to plateau and the scores of most students were located at a point on the curve where appropriate trials were related positively to achievement.

The lack of similar curvilinear results for the

Practice and Achievement 3I3

serve suggests that students did not receive enough appropriate trials for a plateau effect to occur. Even for trials with a ball and net, the positive trend attenuated and did not level off. It is likely that if students had many more appropriate trials with the serve the same trend would occur.

Inappropriate practice was negatively related to achievement for both skills. Silverman (1985) found a similar phenomenon in swimming classes. The relationship in this study was much stronger for the serve than the pass. The relationship for the forearm pass was significant, but weak. It is possible that the large number of appropriate practice trials students had for the forearm pass lessened the effect of the inappropriate trials. For the serve, however, where few trials were received, inappropriate trials did not contribute to learning.

For the serve, all inappropriate trials and trials with a ball and net showed a quadratic relationship to achievement. After a certain point the negative relationship showed no further decrement in achievement as inappropriate trials increased. This inverse of the plateau seems reasonable considering relationships found in other studies in motor learning (Magill, 1989; Schmidt, 1988) and in classrooms (Brophy & Evertson, 1974) and for the appropriate trials in this study. Although the plateau occurred, it was clear that inappropriate practice did not contribute to learning.

The data for total practice trials presents mixed results. There was a moderate linear relationship for the pass and a weak relationship for the serve. In addition, the quadratic relationship found for the serve indicated a slight negative relationship and then a positive turn to the slope. Previous studies by Ashy et al. (1988) and Silverman (1985) showed no significant relationships between total trials and achievement. These other studies included much less instructional time and far fewer subjects. The increase in time to accumulate practice and the effect of a very large N may contribute to relationships found in thisstudy. It is likely, however, that the relationship of the total number of trials to achievement depends on the relative number of appropriate and inappropriate trials which are summed to reach that total.

For both skills, the relationship of appropriate to inappropriate trials had both a positive

linear relationship and a quadratic relationship with achievement. The linear relationship makes sense when the other results of this study are considered. A similar finding occurred for the Beginning Teacher Evaluation Study (Fisher et al., 1981). Although the curves look similar the ratio is much larger for the serve than for the forearm pass. The difference between the two skills in the total number of trials may have influenced both the magnitude of the ratio and the point at which leveling effects occurred. It is interesting that for both skills there was a negative curve at the high end of the ratio. Very few students had ratios high enough to hit the downward turn of the curve. As with the other nonlinear relationships, this result should be in- terpreted cautiously.

The results of this study provide strong evi- dence that practice is related to achievement in physical education. More specifically, appropriate practice is positively related to achievement and inappropriate practice is negatively related to achievement. Similar curvilinear relationships to those found in motor learning and classroom studies were found. The results also demonstrate that when research is designed in consideration of the findings of these related areas, similar, but certainly not the same results, may be found in physical education.

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