spatial ability and achievement in introductory physics

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 21, NO. 5, PP. 507-516 (1984)

SPATIAL ABILITY AND ACHIEVEMENT IN INTRODUCTORY PHYSICS

GEORGE J. PALLRAND and FRED SEEBER

Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903

Abstract

This research was undertaken to clarify the nature of the relationship between visual-spatial abilities and achievement in science courses. A related purpose was to determine what influence visual-spatial abilities have on the high attribution rate characteristic of many introductory college-level science courses. Three sections of introductory college level physics (S = 136) and one nonscience liberal arts section (S = 52) received pre- and postmeasures of visual-spatial ability in the areas of perception, orientation, and visualization. Increases in visual-spatial abilities were greatest with an experimental section that received a spatial intervention. These gains were related to test items that utilized graphical form and to laboratory work. Substantial gains in visual-spatial ability were also registered by a placebo and by control sections. These increases suggest that taking introductory physics improves visual-spatial abilities. Although students who withdrew from the course demonstrated mathematics skills comparable to those of students who completed the course, their scores on perception tests were appreciably lower. Visual-spatial scores of the liberal arts group were lower than those of the physics sections, suggesting that visual-spatial ability influences course selection.

College represents a period of rapid adjustment for many. Courses frequently cover an extensive range of subject matter and present content in an increasingly abstract and quantita- tive form. This is characteristic of science courses in general and of introductory college level physics in particular. In such courses, the dropout and failure rates are uncommonly high. This problem has been considered from a number of perspectives. This research was conducted to examine how the spatial abilities of students may be related to achievement in such a course.

Psychologists have for some time been interested in the relationship between spatial ability and the choice of careers in science. In her classic study of 64 eminent scientists, Ann Roe (1 952) reported that all possessed the ability to conceptualize visually at unusually abstract levels. Research into the manner in which spatial ability develops has also been strongly influenced by Piaget’s (1954, 1960, 1971) work. Arguing from a constructivist position, Piaget maintains that continuing interaction between the mental structures possessed by the individual and the environment stimulates the generation of increasingly refined representations of the external world. More recently Roger Shepard (1979), in summarizing the thinking processes of scientists such as Einstein, Maxwell, Faraday, and Watson, pointed to their reports of using internal images or visual representations while developing ideas.

Research in such areas as neurology and cognitive psychology has also stimulated studies on the nature of spatial thought. Neurological research has led to a description of the process

@ 1984 by the National Association for Research in Science Teaching Published by John Wiley & Sons, Inc. CCC 0022-4308/84/050507-10$04.00

508 PALLRAND AND SEEBER

of lateralization, the differentiation of functions of the left and right hemispheres of the brain. Linear or verbal information is more likely to be processed in the left hemisphere while spatial or configurational phenomena are processed in the right hemisphere. Cognitive psychologists such as Hunt (1983) point to the fundamentally different ways in which information is coded in working memory. He contends that the hemispheres of the brain are used differently in linguistic and visual-spatial reasoning. Although the importance of visual-spatial ability is increasingly being recognized as an important aspect of thought, its relevance to education has yet to be fully realized.

Previous research has pointed to a strong relationship between visual-spatial ability and success in science. Siemankowski and MacKnight (1 972) found that science students (physics majors in particular) possess more highly developed visualization skills than nonscience students. Similar results are reported by McCee (1979), Bishop (1979), and Mitchelmore (1980). Witkin et al. (1 977) in a longitudinal study followed 1500 college students from the areas of science, liberal arts, and education from their freshman year through graduate school and career selection. Using the embedded figures test as a measure of field independence, they found the science majors to be more field independent than the liberal arts and education students. The further along in college and graduate school, the greater the separation became in field independence-dependence between the science and nonscience students. Those remaining in the sciences were found to be increasingly more field independent. Others have supported the importance of the visual-spatial area. Tobias (1 976) found that when graphic representation of algebraic functions was used in teaching mathematics, performance improved significantly. Tally (1973) reports that when three-dimensional models were used in teaching general chemistry, final grades improved. Poole and Stanley (1972) report that visualization and spatial orientation skills are significantly correlated with final grades in engineering courses. There is a body of evidence that links visual spatial abilities with the selection and subsequent success in the study of science courses.

Although achievement in science and physics in particular has traditionally been associated with ability in mathematics, some investigators have begun to question the nature of the relationship. Hudson and Mclntire (1 976) examined the relationship between mathematics skills and achievement in college-level physics. They found that mathematics appears to be a necessary but not sufficient condition for success in physics. Other skills are apparently needed. Whimbey (1977) reports on a study in which college-level students were asked to visualize and verbalize their thoughts in attempting to solve problems in physics. The approach was introduced to help students conceptualize relationships in a problem before attempting to perform numerical solutions. Such studies suggest that abilities other than those associated with mathematics are involved in physics achievement.

Visual-spatial abilities have been influenced by a number of investigators. Dawson (1967) employed the technique of drawing outdoor scenes in proper proportion and dimension. The visualization ability of the experimental group improved significantly over that of the control group. Brickmann (1 966) used a short course in geometry involving points, lines, angles, plane and solid figures, and transformations instead of formal proofs. The visualization ability of the experimental group increased significantly. Anderson (1 976) using SCIS level-four materials investigated the influence of these materials on the students’ visual-spatial abilities. Significant gains in orientation abilities were registered. Some find that while success is obtained in train- ing for a particular task, little transfer is realized (McFie, 1973).

Problem Statement Findings from several fields point to the importance of visual-spatial ability although it

remains unclear how this ability may be related to instruction. I t should be noted that this

SPATIAL ABILITY AND ACHIEVEMENT 5 09

ability is frequently treated as a single factor. This practice may mask aspects of its relationship to achievement in science courses. Which visual-spatial abilities are most utilized in college-level science courses such as physics? Assuming the existence of some relationship, how can these abilities be developed in an instructional program? How is the availability of development of visual-spatial ability related to the high attrition rate prevalent in many introductory college level science courses, particularly physics courses?

Experimental Design and Procedures

The subjects in this investigation were drawn from a two-year community college in a suburban area of a large industrialized state. The distribution of students at the beginning and end of the experiment is contained in Table I. Three groups were drawn from the student popu- lation taking an introductory course in physics. The course was the first semester of a four- semester calculus-based physics course with laboratories. Standard topics such as elementary mechanics, molecular forces, and heat were treated. All sections proceeded from an outlined course of study and used the same text and lab manual. An experimental group received a spatial intervention in addition to the regular classes and labs. A second group, referred to as the placebo group, was exposed to lectures on the history of physics by the same individual who conducted the spatial intervention. This group was established to examine the effect of the additional instruction period. A third group, referred to as the control, received no instruction other than the normal class and laboratory periods. A fourth group, consisting of liberal arts students, was selected to measure any test-retest effects that might occur during the experimental period. These students had not taken and did not intend to take physics.

The experimental, placebo, and control groups each consisted of two sections of students taking introductory physics. Three physics faculty members taught these groups. Each taught two sections, no more than one section in any group. One additional faculty member who did not participate in the physics instruction conducted the spatial intervention and history of science sessions with the experimental and placebo groups, respectively.

Several instruments were used to establish visual-spatial abilities in the areas of perception, orientation, and visualization. The measures are described in the “Manual for the kit of factor- referenced cognitive tests” by Ekstrom et al., (1976). All three sections of physics students and liberal arts students were given pre- and post-visual-spatial tests. The posttests were administered at the end of the semester, approximately four months later.

Visual-Spatial Tests (Reliabilities in Parentheses) (1) Perception-the ability to search a distracting field and find a given configuration. Per-

(a) Identical pictures test P-2 (0.82). (b) Number comparison test P-3 (0.82). (c) Hidden figures test CF-2 (0.83). The P-2 and P-3 tests emphasize perceptual readiness and decision speed and are frequently

regarded as measures of perceptual speed. The CF-2 test emphasizes the ability to hold a given precept in mind while disembedding it for the other well-defined perceptual material. This is regarded as a measure of flexibility of closure.

(2) Spatial Orientation (Rotation)-the ability to mentally rotate solid figures in all planes and to orient spatially with respect to a given object or scene.

(a) Card rotation S-1 (0.80). (b) Cube comparisons S-2 (0.84).

ceptual memory and decision speed are critical.


TABLE I Distribution of Students

January Group I September Number I Number

Experimental I M-42 I F13; I F- 7 1 M-39 I M-30 1 F- 3 F- 1

Control

Llberal Arts M-27 M-17 F- 16

(3) Spatial Visualization-The ability to determine what a given pattern or configuration

(a) Paper folding test VZ-2 (0.84). (b) Surface development test VZ-3 (0.82). ‘

would be if it were altered so that the parts occupied a different relationship to one another.

Additional Tests Administered

(1) Mathematics Test-The physics course lists as a prerequisite two years of high school mathematics including algebra and trigonometry. All students upon entering physics take a departmental mathematics test that is used for advisement purposes. The test consists largely of items in intermediate algebra and graphical analysis. The test has a reliability of 0.83.

(2) Physics Final Examination-This test was developed by the physics department faculty and included sections on kinematics, dynamics, momentum, and heat. The test consists of two sections, one of multiple-choice questions, and one of problems requiring several steps for solution.

Spatial Intervention The spatial intervention consisted of 11 additional hours of instruction. Students met with

the instructor for one 65-minute session weekly for 10 weeks. These sessions took place at the end of regular laboratory periods. Materials used in the intervention were adopted from several sources. Subjects were asked to draw outside scenes by viewing through a small square cut in a piece of cardboard. They were encouraged to draw the dominant lines of the scenery and to re- duce the scene to its proper perspective (Dawson, 1967). Subjects were also given a short course in geometry involving lines, angles, plane and solid figures, and geometric transformations (Brickmann, 1966). In addition the “Relative Position and Motion” module from the Science Curriculum Improvement Study (Karplus, 1971) was used. Subjects locate positions of objects relative to a fictitious observer, Mr. 0. Individuals learn to reorient their perceptual framework with respect to observers with different orientations. A series of ten lectures based on The His- tory of Science by William Dampier was presented t o the placebo group.

Results

Test scores for the pre- and post-visual-spatial measures are contained in Table 11. To determine the degree of homogeneity in visual-spatial ability of the physics sections, the pretest scores were analyzed in a analysis of variance. The groups were found to be homogeneous on all

-.

vi

s~

~z

a-

ul c

Y

j Pos

t! 59

5 28

9 14

3.71

5.5T

47

8 23

4 16

.3

1.78

,5

31

220

15.7

3.02

405

263

17.1

t1.75

iPos

t I

693

, 17

9 12

.9(3

.79*

62

3 16

4 18

.2

, 4.

66*

665

202

15.1

3.

.24*

56

9 21

2 9.

2 2.80*

Post

! 77

3 j 2

32

29.9

7.7

r 7

04

253

15.2

I3

.63*

.70

7 I2

40

14.6

3.

7?

545

302

9.4

1.85

I VZ

2 ' P

re

614

168

I 52

7 16

9 , 57

8 21

6 52

1 19

5

I VZ

3 Pr

e \ 5

95

277

611

238

, 617

22

9 49

8 27

0


the measures except the CF-2. The difference in means for this test score was statistically significant at the p < 0.001 level. The Waller-Duncan Post Hoc K-Ratio t-Test indicated that the pretest mean for the experimental group was significantly lower on the CF-2 test than were means of the other groups. The posttest visual-spatial scores for all groups increased. These scores were analyzed in a one-way analysis of variance. The results are contained in Table 111. Statistically significant differences in all posttest measures were found. The Waller-Duncan K ratio Post Hoc [-Test indicates that the means of the liberal arts group for S-1, S-2 , VZ-2, and V2-3 were significantly lower than those of the other groups. The means for P-2, P-3, and CF-2 were significantly higher for the experimental group. The scores of the liberal arts group were generally lower in the perception, orientation, and visualization areas than were those of the three physics groups.

The changes from pre- to posttest scores were greatest for the experimental group. Sub- stantial gains were realized in the areas of perception, orientation, and visualization on all seven measures. These changes were significant at the p < 0.001 level except for those on the VZ-2 tests which were significant at the p < 0.01 level. Gains were also realized by the control and placebo groups and were distributed over the areas of perception, orientation, and visualization. These gains may in part be related to test-retest effects which would also account for the gains registered with the liberal arts group. The increases found with the control and placebo groups are, however, greater and more consistently distributed across the range of measures used. The increases by the control and placebo groups suggest that taking introductory physics may itself influence the visual-spatial abilities of students. This was unantic- ipated.

A number of students withdrew from the three physics groups during the semester. With- drawals are due to a number of reasons, difficulty with the course being only one of them. The pretest scores of these students were compared to those completing the semester course in physics. A one-way analysis of variance indicated that the differences in the means on P-2, P - 3 , and CF-2 were significant. The Waller-Duncan Post Hoc K Ratio t-Test indicates that the mean scores of the withdrawal group in the perception tests were significantly lower than were the scores of those completing the course.

All students taking introductory physics are required to take a test in mathematics for advisement purposes. The means for the mathematics test of the withdrawal group were comparable to those of the experimental, control, and placebo groups. Any differences in the means between these groups were not significant at the p < 0.05 level. The students who withdrew from the physics course had mathematics skills that were comparable to those who completed the course. The visual-spatial scores in the perception area of this group were significantly lower than those of students completing the course. This suggests that cognitive abilities other than those associated with mathematical ability are utilized in an introductory physics course.

Achievement

The three physics groups all received the same examination, which was developed by departmental faculty. The examination had a reliability of r = 0.80, established with the Kuder- Richardson formula #20. The test consisted of two parts-multiple-choice items and problems (Prob.). The multiple-choice items were identified for purposes of analysis into two categories, those utilizing spatial ability (Spt.) such as graphical analysis, and those that were essentially propositional (Prpt .) or verbal statements emphasizing information recall. A final course grade (Crg.) was established by averaging the examination score (Fex.) and laboratory grade (Lab.) into a scale ranging from 1.00 to 4.00. To analyze the differences in achievement scores and

SPATIAL ABILITY AND ACHIEVEMENT

Visual i ra- t i o n

TABLE 111 One-way Analysis of Variance of the Visual-Spatial Posttest Means of

the Experimental, Control, Placebo, and Liberal Arts Groups

Variable S.S. M.S. F Exp.Var. (%)

213786.1 71262.0 5.62** 11.8 p2

p3 897806.6 299268.8 12.89*** 23.5 Percep t t on

CF2 419001.6 139667.2 4.80** 10.3

VZ3 904235.7 301411.9 4.50- 9.7

513

166408.1 3.92* 8.5 I I s1 499224.5

Or ientat ton I 624313.8 208104.6 3.23* 7.1 j s2

~~~ ~~

(df= 3,126). * p < 0.05.

**p < 0.01. ***p < 0.001.

which aspects of achievement were related to the experimental group, a one-way analysis of variance was performed within the three sections. The results are contained in Table IV.

These results indicate differences in the means of the variables Spt., Lab., and Crg. that are significant at the p < 0.05 level. The Waller-Duncan Post Hoc K Ratio t-Test indicates that the means for these variables were higher for the experimental group. The achievement measures that were related to improved visual-spatial ability were the multiple-choice items requiring

TABLE IV One-way Analysis of Variance of the Means of Physics

Achievement Scores for Experimental, Control, and Placebo Groups with Variables Spt, Prpt, Probl, Fex, Lab, and Crg

Variable S.S. M.S. F Exp.Var.(%)

Spt (Spat ia l 298169.4 149084.7 4.61* 8.9

Prp t (Propostttonal) 15329.6 7644.8 .22

Probl (Problem) 157631.4 78815.7 1.19

Fex (F ina l examt nation) 194068.5 72034.2 2.37

Lab (Laboratory) 262764.5 131382.2 4.33* 8.4

Crg (Course grade) 11.58921 5.7946 4.16* 8.1

(df= 94). * p < 0.05.

5 14 PALLRAND AND SEEBER

graphical analysis and the laboratory work. The higher course grades result from higher scores in these areas.

Since multiple tests of significance have been conducted, it is possible that some of the results indicating statistical significance may represent random rather than real effects. However, the consistency of results across variance spatial measures strongly suggests that the effects are real and not statistical artifacts.

Discussion

The three physics and the liberal arts sections registered gains in visual-spatial abilities over the experimental period. The gains in the control and placebo groups were more extensive than were the gains in the liberal arts group, suggesting that the visual-spatial abilities of those who take such a course improve. The experimental group made the most substantial gains in the three areas investigated. The intervention apparently directly influenced performance in this area.

Perception as defined in this investigation can be broken down. The literature frequently regards perceptual speed as measured by P-2 and P-3 as one factor and disembedding as measured by CF-2 as a second factor. Perceptual speed may be utilized in recognizing patterns and relationships. Disembedding may be more related to isolating components or aspects of a situation. Regarding the perception factor as consisting of perceptual speed and disembedding does not affect the results of this experiment. I t does enable us to refine the interpretations when considering the relationship of the factor to achievement in physics.

The gains in visual-spatial abilities for the experimental group were most related to the spatial items on the examination and to the laboratory phase of the course. The items that were identified as spatial utilized diagrammatic and graphical representations. With such items it was necessary to extract and operate upon relevant information. Similar skills are apparently utilized in the laboratory. The nature and form of course material makes certain demands upon the manner in which students extract, organize, and process information. Increases in spatial- visual abilities are manifest in those areas in which diagrammatic and graphical representation are found as well as in the laboratory phase of the program.

'

Conclusions

Introductory level science courses such as physics contain extensive amounts of subject matter. Drawings, diagrams, and graphs are increasingly being used to present and analyze phenomena in such courses. The visual-spatial abilities of students taking such a course improved. Increases were realized in the areas of perception, orientation, and visualization with both control and placebo groups. It is one thing to recognize that such abilities are needed to succeed in such courses. It is quite another to find that such abilities may develop as a result of taking such a course.

Experiences associated with analyzing graphs and resolving vector diagrams apparently influence the cognitive skills of students in ways not normally recognized. The relevance of these changes is even more germane when it is recognized that students who do not take such a course or who enroll and subsequently withdraw are deficient in visual-spatial skills. Students who withdrew from the experimental sample were found to be lower in perceptual ability even though their mathematical skills were comparable to those who completed the course. These students lacked abilities to recognize patterns and relationships as well as to isolate components or aspects of an overall pattern. These skills, apparently utilized in such a course, are not normally addressed in counseling or remediation programs. Science teachers working with in-

SPATIAL ABILITY AND ACHIEVEMENT 515

troductory-level students need to consider this broad range of cognitive skills that may be utilized in such courses. This is particularly appropriate when such skills are subject to improvement as was indicated in the intervention described in this experiment.

The relation of visual-spatial abilities to particular test items as well as to the laboratory phase of the course raises other questions. Test items are frequently narrowly constructed to fit the needs of quick scoring and distribution requirements. Items that emphasize word recall and utilize standard algorithm solutions may not adequately reflect changes in student comprehen- sion. The differential relation of improved spatial-visual performance to particular test items and laboratory work suggests that attention be given to procedures which more adequately assess the kinds of abilities utilized and developed in such courses.

Implications

The transmission of subject matter suchas that contained in a physics course is a formidable task. As knowledge in such areas continues to advance and as the role of science in the society increases, the challenge becomes even more demanding. Increasingly students will need to learn how to organize and analyze data in various forms. Concomitant with such procedures is the ability to generate abstractions in the form of some internal representation which can then be built upon and altered with additional educational experiences. The processes associated with spatial-visual thought appear to be closely related to those involved in data analysis as well as to those utilized in abstract representation. An understanding of the mental processes involved in such undertakings will become increasingly important.

References

Anderson, B. Science teaching and the development of thinking. Gothenburg, Sweden:

Bishop, A. Developing spatial abilities. Educational Studies of Mathematics, 1979, 10(2),

Brickmann, E. H. Programmed instruction as a technique for improving spatial visualization.

Dawson, J. I. M. Cultural and physicological influences upon spatial perceptual processes in

Ekstrom, R., French, J., Harmon, H., & Derman, D. Manual for kit of factor-referenced

Hunt, E. On the nature of intelligence. Science, 1983,219,141-146. Hudson, H. T., & McIntire, W. R. Correlation between mathematical skills and success in

Karplus, R. Science curriculum study. Berkeley, CA: University of California, 1971. McGee, M. Human spatial abilities: psychometric studies and environmental, genetic,

Mitchelmore, M. Three-dimensional geometrical drawings in three cultures. Educational

Piaget, J. Construction of reality in the child. New York: Basic Books, 1954. Piaget, J., & Inhelder, B. The child’s conception of geometry. London: Routledge and

Piaget, J., & Inhelder, B. Mental imagery in the child. New York: Basic Books, 1971. Poole, C., & Stanley, G. A factorial and predictive study of spatial abilities. Australian

Acta Universitatis Gothoburgensis, 1976.

135- 146.

Journal of Applied Psychology, 1966, 50(2), 179-1 84.

West Africa-Part I. International Journal of Psychology, 1967,2(2), 11 5-128.

cognitive tests. Princeton, NJ: Educational Testing Service, 1976.

physics. American Journal of Physics, 1977,45(5), 470-471.

hormonal, and neurological influences. Psychological Bulletin, 1979, 86(5), 889-91 8.

Studies in Mathematics, 1980, 11(2), 205-216.

Kegan Paul, 1960.

Journal ofPsychology, 1972,24(3), 317-320.


Roe, S. A psychologist examines 64 eminent scientists. Scientific American, 1952, 187, 21-22.

Siemankowski, F., & MacKnight, F. Spatial cognition: success prognosticator in college science courses. Journal of College Science Teaching, 1971,59,1-56.

Talley, L. The use of three-dimensional visualization as a moderator in the higher cognitive learning of concepts in college level chemistry. Journal of Research in Science Teaching, 1973, 10,263-269.

Tobias, S . Math an. MsMagazine, September 1976. Whimbey, A. Teaching sequential thought: the cognitive skills approach. Phi Delta Kappan.

Witlun, H. et al. Role of field dependent and independent cognitive styles in academic eval- 1977, 59(4), 255-259.

uation: A longitudinal study. Journal of Educational Psychologv, 1977,69, 197-21 1 .

Manuscript accepted August 31,1983

spatial ability and achievement in introductory physics

Documents