Spatial Ability and Earth Science Conceptual Understanding
By Black, Alice A (Jill)
ABSTRACT
Although spatial ability is related to success in the sciences, relatively little research has considered the relationship of spatial abilities with common misconceptions and broader conceptual difficulties in the Earth sciences. Spatial thinking and abilities have not commonly been directly addressed in traditional education. In this study, I found moderately significant positive correlations between scores on the ESC, a new test of Earth science conceptual understanding, and scores on each of three types, or factors, of spatial ability in university undergraduate non-science majors. Types of spatial ability tested included mental rotation, spatial perception, and spatial visualization. I found mental rotation to be the best predictor of ESC scores of the variables tested. Results suggest that an opportunity may exist to improve Earth science conceptual understanding by focusing on spatial abilities or the spatial aspects of concepts.
INTRODUCTION
Does the Earth’s shadow cause moon phases? What happens to water that evaporates in the water cycle does it dissociate into oxygen gas and hydrogen gas? These explanations for common Earth science phenomena are often offered by university non-majors, as well as the general population. Students may also exhibit conceptual difficulties in interpretation of topographic maps, aerial photos, geologic cross sections, and various two-dimensional diagrams showing three-dimensional or moving phenomena. Many misconceptions and broader conceptual difficulties have been reported (Ford, 2003; Kusnick, 2002; Wampler, 1999,2001; Meyer, 1987; Philips, 1991; DeLaughter, 1998) in all four areas of the Earth sciences, although most are in the geosciences, astronomy, and meteorology. Although many conceptual problems are reported verbally as information-based misconceptions, such as the belief that seasons are caused by differences in Earth-sun distance at various times during the year (Schoon, 1992, 1995; Kikas, 1998), other conceptual difficulties are more broadly based. Examples are interpretation of geologic block diagrams (Piburn et al., 2002; Kali and Orion, 1996), aerial and satellite photos (Hawkins, 2000), and topographic maps (Repine and Rockey (1997), as well as understanding of map projections (Downs and Liben, 1991), and of geologic time (Dodick and Orion, 2002a, 2002b; Trend, 2000,2001). In addition, the principles of the kinetic- molecular theory (KMT), which are basic to an understanding of meteorology, are also a source of many Earth science misconceptions (Chang, 1999; Griffiths and Preston, 1992). Other researchers have studied issues of scale related to Earth science, including models and astronomical distances (Dyche et al., 1993), geologic distances (Gobert and Clement,1999; Gobert, 2000), sizes of scientific objects (Tretter and James, 2003), and time (Friedman, 2000, Dodick and Orion, 2003).
Why are misconceptions important? Constructionist learning philosophy (Chang et al., 1999; Riggs and Kimbrough, 2002; Slater et al., 1999; Carpenter et al., 1999) stresses that learners construct knowledge by assimilating new information with their personal previously held concepts. It is important, therefore, that students’ previously held concepts are consistent with the ideas accepted by scientists, in order to establish a base on which to assimilate further concepts. The presence of erroneous previously-held concepts, or of broader conceptual difficulties, may impede understanding of Earth science concepts. Many Earth science misconceptions have been reported to be extremely difficult to change, even with thorough instruction and increasing age (Schneps and Sadler, 1989); this appears to be especially evident if the scientific explanation of Earth science phenomena is contradicted by intuitive knowledge derived from observations since early childhood.
Spatial ability has been defined as skill in “representing, transforming, generating, and recalling symbolic, nonlinguistic information” (Linn and Petersen, 1985, p. 1482). Spatial ability is a cognitive factor that has been linked to high performance in science and mathematics (Lord and Rupert, 1995). A number of spatial abilities have been identified, although researchers have not reached consensus concerning names and descriptions of ability types, as well as categorization of spatial ability tests in regard to factors measured. Some researchers fail to differentiate between ability factors when drawing conclusions (Linn and Petersen), furthering the complexity of the literature.
In their meta-analysis, Linn and Petersen (1985) devised a classification of three types of spatial ability factors (Table 1). They describe mental rotation as a “Gestalt-like” process involving “the rotation of a two- or three-dimensional figure rapidly and accurately” (p. 1483). Although different strategies might be used to solve rotation test items, it is advantageous to be able to mentally rotate the figure as a whole rather than using more time- consuming analytic verbal clues, such as “if this side is turned here, then that side will be there.” Linn and Petersen suggest the possibility that females, on average, may tend to use such a part- by-part analytic strategy, while males may tend to use a holistic analogue strategy to solve mental rotation problems. In addition, they suggest that females may be more cautious.
Spatial perception involves spatial relationships “with respect to the orientation of the subject’s own body, in spite of distracting information” (Linn and Petersen, 1985, p. 1482). Spatial perception is partially characterized by the “possibility of relying on gravitational/kinesthetic cues” (p. 1490). Linn and Petersen report that “The other feature of spatial perception tasks is a focus on disembedding or overcoming distracting cues” (p. 1482).
Spatial visualization is characterized by an “analytic combination of both visual and nonvisual strategies” that involves . . . “complicated, multistep manipulations of spatially presented information” (Linn and Petersen, 1985, p. 1491). These processes may involve the “processes required for spatial perception and mental rotations but are distinguished by the possibilities of multiple solution strategies” (p. 1484). Linn and Petersen note that “These strategies are more characteristic of general ability than of spatial ability” (p. 1491).
Table 1. Linn and Petersen’s (1985) classification of spatial abilities.
Of these three spatial factors, I hypothesized that mental rotation is most important in understanding Earth science concepts that are associated with common misconceptions and conceptual difficulties. In astronomy, humans are handicapped by their single vantage point from Earth of the moving bodies in outer space. Ability to mentally picture moving air masses from different perspectives is helpful in understanding meteorology, as well as ability to picture invisible moving molecules involved in phase changes. Viewing rock layers from varying perspectives is valuable in geology.
It is less clear how spatial perception is involved in Earth sciences. Possible connections of spatial perception to Earth science conceptual understanding include: a) ability to discriminate angular size, as in sun angles reaching Earth, compared to parallel “horizontal” solar radiation, in meteorology and astronomy, and b) disembedding patterns within in aerial or satellite photographs, such as drainage patterns.
Although a number of different types of tasks are present in various spatial visualization tests (e.g., hole punch patterns on folded paper), the spatial visualization test used in this research not only contains an element of differentiation of views from varying vantage points, but also involves two dimensional to three dimensional conversion. The latter is important in Earth science in interpretation of topographic maps and geologic block diagrams, as well as interpretation of any two-dimensional Earth science diagram that represents a three-dimensional phenomena.
A large body of literature has described mean differences between the sexes, often favoring males, in some types of spatial ability (Halpern and Lamay, 2000). In general, the largest sex differences have been found in mental rotation, smaller differences have been found on spatial perception, and smaller or little difference has been found between the sexes on spatial visualization (Kimura, 1999; Linn and Petersen, 1985). Apparently, most, if not all, tests of mental rotation tend to produce results with a male advantage; most researchers apparently do not consider this result due to gender- biased tests (see Kimura, 1999, p. 182-186). Interestingly, several other types of spatial ability are seldom mentioned in the science education or educational psychology literature. Of these, women tend to perform better with some (e.g., object location) and men with others (e.g., targeting) (Kimura, 1999). In addition, Signorella and Jamison (1978), Brosnan (1998), and Firth and Brosnan (2000) reported that psychological gender, the self-described possession of stereotypically masculine and feminine personality characteristics, is statistically related to spatial ability.
Table 2. Proposed characteristics of Earth Science Concepts (ESC) Test Items.
Mathewson (1999) \and McCormack and Mason (2001) argue that spatial ability has been neglected in traditional education. Although students with weaknesses in verbal abilities are encouraged and given a great deal of practice, usually no specific help is given to students with weaknesses in spatial ability. Such students may eventually abandon the study of spatially-related disciplines, such as mathematics and science, when those topics become more difficult in middle and high school (Geary, 1998).
Public understanding of Earth systems and the ability of citizens to think critically about them is increasingly necessary as new technologies illuminate interrelationships among those systems, and as human influences on Earth systems intensify environmental concerns. University graduates who are non-science majors may eventually occupy positions in business, law, government, communications, and education, and therefore may greatly influence public policy on Earth resource issues. As policy makers, some may influence important decisions more than the scientists who advise them.
It has been established, however, that non-science majors typically have more difficulty understanding various science concepts than do science majors (Nordvik and Amponsah, 1998), and also score lower on tests of spatial ability than do science majors (Lord, 1987). Non-science majors are less likely to be formal thinkers than are science majors (Maloney, 1981), and tend to have both weaker study skills (Ryan, 1989) and more negative attitudes toward science (Grandits and Young, 1975) than do science majors. Instructors of non-science majors, therefore, face many challenges in motivating and teaching this important group of future citizens (Dunnivant and Newman, 1999).
Only a few researchers have studied the relationship of specific types of spatial ability to specific types of Earth science concepts (Kali and Orion, 1996; Downs and Liben, 1991; Piburn et al, 2002; Schofield and Kirby, 1994). I found no studies that attempted to relate Earth science misconceptions to spatial abilities. A number of researchers have reported, however, that spatial abilities can be improved (Baenninger and Newcombe, 1995; Lord, 1985, 1987, Bezzi, 1991; Kyllonen, Lohman, and Snow, 1984; Piburn et al., 2002).
Therefore, I thought that a need existed for additional knowledge concerning the relationship of specific spatial abilities to Earth science conceptual understanding by non-major university students. My hope is that, if such a relationship does exist, it may be possible to develop curricula for use throughout the K-16 educational system that may improve Earth science conceptual understanding through improved spatial understanding.
THE STUDY
I hypothesized that a relationship exists between many Earth science misconceptions and conceptual difficulties and spatial ability, and that mental rotation would be the type of rotational ability most highly related to scores on a test of Earth science conceptual understanding, and spatial perception least related. An understanding of scale also appeared to be part of a many conceptual problems (a situation that is likely not helped by models and diagrams that are not depicted to scale or explained as such), as well as difficulty in transforming twodimensional diagrams to three- dimensional reality.
MEHTODS
Subjects – Subjects were non-science majors enrolled in six undergraduate courses in the College of Natural and Applied Sciences of a midwestern public university in the departments of geosciences, chemistry, physics, and biology. The courses were not designated for students majoring in science. I followed Institutional Review Board informed consent process with all subjects. Of 119 students who signed consent forms, I used data from the 97 students who were administered all five tests used in the study. Of these 97 subjects, 34 were male and 63 were female. Thirty were elementary/middle education majors, the most common single non-science major enrolled, 64 had declared other non-science majors, and 3 were undeclared. Of the non-elementary/middle education majors, most majors were related to business, finance, insurance, computer information systems, nursing and health professions, psychology, and various areas of education other than elementary/middle teaching. Subject ages ranged form 18 to 49, with a mean age of 24.42. Most subjects were upperclassmen, with a mean year of university study of 3.27, with 1.00 indicating freshmen. Earth science classes comprised only 10% of subjects’ high school science coursework; 73% of subjects had taken no Earth science in high school. Earth science courses, however, comprised 34% of previous university science coursework. This may be due, in part, to a required Earth science course for elementary/middle majors previously taken by many of those majors.
Figure 1. Examples of ESC item with diagram.
Figure 2. Example of ESC item with no diagram.
Instruments – Because I was unable to find any instrument with validity or reliability data for testing of Earth science misconceptions and conceptual difficulties, I developed and field tested the Earth Science Concepts (ESC) test. I describe the development, use, and results related to use of this instrument elsewhere (Black, 2005). The 20 multiple-choice item questions and distractors are based on the Earth Science misconception and conceptual difficulties literature. Table 2 presents the proposed characteristics of the ESC, including spatial factors and spatial ability tests that I hypothesized as being involved with each ESC item. Spatial ability factors were based on Linn and Petersen’s (1985) classification. Other characteristics include Earth science disciplines involved, whether the item refers to a misconception or broader conceptual understanding, if a diagram is included in the test item, if the item refers to events normally observed throughout the observer’s lifetime, and if scale or motion are thought to be involved.
All four areas of Earth science are represented, but to varying extents, primarily because oceanography is not highly represented in the misconception literature. Eight items include diagrams, and the others follow the verbal form used in the reporting of most misconceptions. Topics include the causes of seasons, moon phases, and tides, several phase changes as related to the KMT, geologic block diagrams, map projections, movements in the Earth/moon/sun system, relative distances within the universe, interpretation of aerial photos and topographic maps, relative distance to the magma that produces features such as volcanoes, and a three-dimensional drawing of weather fronts and air masses. Figures 1 and 2 are examples of ESC items with and without diagrams, respectively.
I field tested the ESC fifteen times in non-majors science courses for over two years. One class was a physics class and the rest were Earth science classes for preservice teachers. I administered a total of 310 pilot tests. Four versions of the ESC were field-tested, with 33, 32, 22, and finally 20 items. Scantron computer grading provided item analysis. I removed some items with very low or high item difficulty ratings (Anastasi and Urbina, 1997), as well as some unselected distractors when new versions were constructed. I gradually removed some misconception items that appeared to be relatively knowledge-based and tended to replace them with items with diagrams and a broader conceptual base, as well as items that referred to phenomena that subjects witness from early childhood. I removed some items that were reported in the literature as children’s misconceptions, but which were not troublesome with most college students in the pilot tests. Some distractors and items were added or changed as a result of interactions with students in my Earth science classes, including conversations and anonymous written answers to “How?” and “Why?” misconception-related questions I ask before beginning many new topics.
To ensure criterion validity, scores on the final version of the ESC that was field tested with Earth science classes were correlated with averaged Earth science content exam scores throughout the semester for the same individuals. The correlation coefficient was 0.60, which was moderately significant at a level of .01. To assure content validity, I asked content and science education expert faculty members to examine the ESC (Huck & Cormier, 1996). Content faculty consulted were experts in geomorphology, geology, geographic information systems and cartography, meteorology, and physics. I made several revisions following their comments. I assessed the ESC several times for possible ambiguity, and removed one cartography item for this reason. I attached an open-ended question to field tests asking participants to describe any unclear or ambiguous questions. No subjects participating in the pilot tests did so. As I was the instructor of many of the students in the pilot tests, it is possible they did not want to appear unknowledgeable by saying a question was unclear. Furthermore, an “I don’t know” option was available, which was designed to discourage guessing. Because no established Earth science conceptions instrument involving all four areas of Earth science similar to the ESC could be found, a construct validity coefficient could not be established.
Figure 3. Purdue Spatial Visualization Test: Rotations.
Kuder/Richardson (K/R) and Spearman/Brown (S/B) split-half internal reliability statistics were computed in field tests of the final version of the ESC; Spearman/Brown was 0.74 and Kuder/ Richardson was 0.63. Higher scores had been achieved with some previous pilot versions that were longer and that contained more knowledge-based misconception questions. Administration of the ESC to the 97 subjects in this study revealed reliability scores of S/B = 0.65 and K/R = 0.63. Additional administration of the ESC to Earth science \classes for preservice teachers in 2003 revealed S/B = 0.81, K/R = 0.68 and S/B = 0.88 and K/R = 0.54 for two classes. In 2004, reliability statistics were S/B = 0.72 and K/R = 0.69, S/B = 0.66 and K/R = 0.71, and S/B = 0.76 and K/R = O .71. In 2005, S/B = O .80 and K/R = O .71. Higher scores could possibly be achieved if the test were longer and more homogeneous in content (Anastasi & Urbina, 1997). A shorter test was developed due to the time restraints of administering a total of five tests to each subject.
I administered timed paper and pencil tests that measured three types of spatial abilities, based as closely as possible on the three categories of spatial ability described by Linn and Petersen (1985). All tests were cited in the science education literature. Two were commercially available, and I obtained the third from another researcher. Other criteria used to select spatial tests included measurement of spatial tasks that appeared related to avoidance of misconceptions or conceptual difficulties, and suitability for group administration.
To test mental rotation, I selected the test called the Purdue Visualization of Rotations Test (PVOR or VOR) (Guay, 1977) on the test booklet and in the science education literature (Provo et al., 2002; Provo-Klimek and Cash, 2001; Pribyl and Bodner, 1987; Carter, LaRussa, and Bodner, 1987). The test is also called the Purdue Spatial Visualization Test – Visualization of Rotations (Branoff, 1998) and Purdue Spatial Visualization Test: Rotations (Sorby and Baartmans, 1996; Sorby, 1999) in engineering graphics literature, abbreviated as PSVT:R (Sorby and Baartmans; Sorby) or as PSVT (Branoff). The designation PSVT:R will be used here. In this test, subjects first determine the manner in which an initial drawing of a three-dimensional figure has been rotated to produce a second rotated drawing of the same figure. They then view a drawing of a second three-dimensional figure, and must then choose from five possible choices the drawing that shows the second figure rotated in the same manner as the first figure (Figure 3). Therefore, they must visualize the direction and extent of rotation of the sample figure before mentally rotating the second figure in a similar manner. Provo et al. (2002) relate that “the Kuder-Richardson and split- half reliabilities of the Purdue VOR test have been calculated in the range of 0.78 – 0.85 with samples of undergraduate chemistry students.” Battista et al. (1982) found a K-R reliability of 0.80 when testing preservice elementary teachers. Branoff (1998) reports internal consistency coefficient results (KR-20) of 0.87, 0.89 and 0.92 from studies conducted by Guay (1980) on university students, machinists, and university students, respectively. Sorby and Baartmans (1996) reported a K-R coefficient of 0.82 for university students. Provo et al. (2002) reported that “the content validity of this instrument has also been shown to be good” (p. 25).
This test was chosen because it tested rotation of complex figures in three dimensions, which not only more closely simulates situations in Earth and space science, but is considered more difficult that two-dimensional rotation by several researchers (Eliot, 1980; Kimura, 1999; Linn and Peterson, 1985). Of three three- dimensional rotation tests commonly mentioned in the science education literature, this test was more complex (a characteristic Linn and Petersen and Kimura have associated with performance) than one other possible test choice, Cube Comparisons (Ekstron et al., 1976) and more readily available than the other choice, The Mental Rotations Test (Vandenberg and Kuse, 1978). I obtained test from Judy Provo, formerly of Purdue University.
Branoff (1998) developed a computer form of the PSVT:R that added x, y, and z coordinate axes to the three dimensions of each test item, with the intention of adding a contextual clue that might improve scores and response times. The addition of the axes had no significant effect on scores. Branoff states that “the addition of the axes eliminated gender difference on the PSVT” (p. 16). He later indicates, however, that only 17 females, who were divided further into the experimental and control groups, participated in the study. He also suggests that “one explanation for not finding gender differences for response times may reflect the type of students participating in the study. A majority of the students were enrolled in engineering programs. It may be that students in engineering, whether male or female, tend to take the same type of approach to solving mental rotation tasks” (p. 31). Therefore, students may not have been using the analytic approach, although the axes were designed to help persons who used the slower, part-by-part analytic approach.
Two other questions arise in regard to choosing whether to use Branoff’s version of the test. First, is the altered test still measuring the ability of rapid mental rotation of a figure using the Gestalt-like process that Linn and Petersen described? They noted that “mental rotation items are used to measure the time required for solution” and “conditions of measurement encourage an analogue process” (p. 1484). secondly, does the addition of the letters x, y, and z, which add verbal cues, further change the basic nature of the test? Ironically, Piburn et al. (2002) developed a computer version of the Cube Comparisons to eliminate the pre-existing lettered sides of the cubes, which they feared added verbal cues.
I used the Group Embedded Figures Test (GEFT) (Witkin et al., 2002) to test spatial perception. In this test, subjects must locate a previously seen simple geometric figure within a larger complex geometric figure that has been organized to obscure or embed the simple figure within the complex figure. Only straight lines that are horizontal, vertical, or diagonal compose either simple or complex figures. Because the subject must match the angles of the hidden figure with its duplicate within the complex figure, discrimination of angles or comparison to horizontal or vertical appears necessary to perform the task, as well as separation of figure from distracting ground. The test is the group-administered version of the original individually-administered parent test, the Embedded Figures Test (EFT) (Witkin et al., 1971). The manual for the GEFT (p. 1) relates that “the [EFT] is a perceptual test.” Linn and Petersen (1985), however, do not list the EFT as a test of spatial perception, but as a test of spatial visualization. They state, however, that “the other feature of spatial perception tasks is a focus on disembedding or overcoming distracting cues” (1482). They note a high correlation between the EFT and the Rod and Frame Test (RFT) (Witkin, 1948), an unavailable individually-administered earlier test of spatial perception and field dependence- independence which requires complicated equipment (a darkened room, and in one version, a tilted room). Field dependence-independence is described as the ability to discriminate relevant stimuli from distracting stimuli, the “field.” Several other researchers (Kimura, 1999; Eliot, 1980; Ekstrom et al., 1976) disagree with Linn and Petersen’s designation of the EFT. The two tests mentioned by Linn and Petersen as tests of spatial perception, the RFT and the water- level task (Inhelder and Piaget, 1958; DeAvilla et al, 1976) are both individually-administered with physical objects, and neither is currently available. Therefore, the categorization of the EFT and GEFT by their developers as a perceptual test was followed. Although some researchers (Vasta et al, 1996) devised paper and pencil water level tests, no reliability and validity data have been offered. Furthermore, it is unknown if any kinestheticgravitational aspects of the physical-object tests would be as applicable to paper and pencil tests.
Witkin el at. (2002) reported that because the GEFT is a timed test, an appropriate method of estimating reliability is the correlation between parallel-forms with identical time limits. Correlations between the nine-item first section scores and the nine- item second section scores were computed and corrected by the Spearman-Brown prophecy formula, producing a reliability estimate of 0.82 for both males and females. Reliabilities for three groups of college age students completing the parent EFT were 0.82 for males and 0.79 for females in the first group, 0.90 for males and 0.82 for females in the second group, and 0.85 for a third male-only group. Regarding validity, Witkin et al. (2002, p. 21) stated that “the most direct criterion measure is the ‘parent’ form of the test, the EFT.” Correlations of the GEFT with the EFT are -0.82 for males and – 0.63 for females. The validity coefficients “should be negative because the tests are scored in reverse fashion” (p. 21). Additionally, the GEFT and EFT have exhibited criterion validity by correlations with the RFT. Researchers who have reported use of the GEFT include Piburn et al, 2002; Kwon and Lawson (2000), Brosnan (1998), Firth and Brosnan (2000), and Signorella and Jamison (1978).
Discrimination of angles is likely more important in understanding spatially-related concepts on the ESC and in Earth science than is the specific ability to discriminate vertical and horizontal lines from lines at other angles. In comparison to mental rotation and two- to three-dimensional transformations, relatively few concepts and commonly held misconceptions in Earth science appear to directly involve disembedding skill, although possible associations include map and aerial and satellite photo interpretation.
Table 3. Pearson correlation matrix for ESC, PVOR, GEFT, and DAT, with p values. *p < 0.05, **p<0.01
I tested spatial visualization using the Differential Aptitude Test: Space Relations (DAT) (Bennett et al., 1991). I selected this test due to the required task of two-dimensional to three- d\imensional transformation. The test asks the subject to visualize a two-dimensional pattern as it would look after being folded into a three-dimensional figure, and then to select the correct drawing of the three-dimensional figure from choices that are viewed from various perspectives. This type of test is often termed a surface development test. Other types of spatial visualization tests, such as paper folding and punching tests, do not seem as applicable to Earth science concept understanding. Bennett et al. (1991) report a K/R internal consistency reliability of 0.94. They also report a part-whole correlation of the formerly used DAT Form V with the currently available shortened version, that was used in this research, of 0.96. Criterion validity was obtained by examination of correlation coefficients between DAT test scores and criterion scores on job training tests. These included 0.59 for draftsman applicants, 0.49 for freshman engineering students, 0.55 for dental hygiene students, and 0.52 for electricians. Construct validity was shown by a correlation coefficient of 0.68 with the spatial relations subtest of another multiple aptitude battery, the General Aptitude Test Battery.
Earth science involves a number of concepts that require mental visualization of three-dimensional phenomena, which may be viewed from various vantage points, using two-dimensional representations; such concepts appear to require skills similar to those used to answer DAT items. These include understanding of geological block diagrams, air and satellite photos, map projections, and contour maps. Researchers who have reported use of the DAT include Feingold (1988), Provo-Klimek and Cash (2001), Huit and Brous (1986), and Fennama and Sherman (1977).
Subjects also completed a questionnaire that queried them about demographics and past science coursework. I administered the short form Bern Inventory (BI) (Bern, 1974) to determine the psychological gender category and BI-t score of each subject. I administered this test due to questions raised by past researchers (Provo-Klimek and Cash, 2001; Signorella and Jamison, 1978; Brosnan,1998; Firth and Brosnan, 2000).
ANALYSIS AND RESULTS
ESC Scores – Many Earth science misconceptions and conceptual difficulties were revealed in this population of university non- science majors. The mean score for these non-majors on the 20 item ESC was 6.82, or 34%, with a minimum of 1 and maximum of 16 (SD = 3.03). Difficulty ratings, which indicated the percent of students selecting non-scientific explanations, were determined for each item. Ratings ranged from 96.42 to 33.04.
Spatial Ability and ESC Scores – I found significant positive correlations at a moderate level between scores on the test of Earth Science concept understanding and scores on each of the three spatial ability tests (Table 3). For mental rotation, (r(97) = 0.52, p = < 0.01. Subjects who scored higher on the PSVT:R tended to score higher on the ESC. For spatial perception, (r(97) = 0.34, p = < 0.01. Subjects who scored higher on the GEFT tended to score higher on the ESC. For spatial visualization, (r(97) = 0.43, p = < 0.01. Subjects who scored higher on the DAT tended to score higher on the ESC. Low to moderate correlations were found among the three spatial ability tests.
Stepwise regression was conducted first using all three spatial test scores as independent variables, and then using the three spatial test scores and number of completed university Earth science courses as independent variables. In both procedures, models were produced that indicated that PSVT:R score is the independent variable that is the best predictor of ESC score, of the variables used in the regression. In the first model, with the three spatial tests as independent variables, an R value of .52 indicated as estimate of a 52% relationship between ESC score and the best linear combination of independent variables. The R2 of .27 indicated that 27% of the total variation in ESC scores can be accounted for by the three types of spatial ability. In the second model, with the three spatial tests and number of past university Earth science courses as independent variables, an R value of .56 indicated as estimate of a 56% relationship between ESC score and the best linear combination of independent variables. The R2 of .31 indicated that 31% of the total variation in ESC scores can be accounted for by the three types of spatial ability and number of past university Earth science courses.
Demographic Analysis – Table 4 is an expanded version of Table 3; it shows correlations among all tests and most demographic variables. I found a weak correlation between number of previous university Earth science courses and ESC scores (r(97) = 0.25, p < .01). Statistical analysis revealed that neither sex, age, university grade level, or major (preservice elementary/middle majors in comparison to all other majors) was significantly related to scores on the ESC or any of the spatial ability tests. Independent samples t-tests (Table 5) determined if a significant difference existed between female and male test scores on tests and demographic variables. Results revealed that although males outperformed females on the ESC, the PSVT:R, and the GEFT, the differences were not significant. Females and males performed nearly identically on the DAT. Females had taken significantly more science classes at the university level, were significantly older, significantly more likely to be elementary/middle education majors, and had significantly higher Bern numbers and T-scores, indicating greater femininity.
Pearson correlations of Bern Inventory T-scores revealed no significant relationships between psychological gender with any of the three spatial ability scores or ESC scores. Further t-tests comparing each possible combination of the four psychological gender categories in regard to all other demographic characteristics and test scores revealed no significant relationships between psychological gender and test scores.
Table 4. Pearson correlation matrix for demogrpahic variables and tests, with p values.
A significantly positive correlation was found between number of completed Earth science courses at the university level, age, university grade level, and elementary/middle education major, as well as ESC scores. No significant relationships were found between number of completed high school or university science courses or number of high school earth science courses with any test scores.
DISCUSSION
The results of this study provide preliminary data that suggest a possible relationship of selected spatial test scores and Earth science misconceptions and conceptual understanding. They are also consistent with the proposed idea that mental rotation is a type of spatial ability that is associated with a number of Earth science misconceptions and conceptual difficulties. Of the variables tested, regression analysis indicates that between one fourth and one third of the total variation in ESC scores can be accounted for by spatial ability, an ability that has not been systematically fostered in traditional education.
Low to moderate correlations among scores on the three spatial ability tests is consistent with the notion that all are measures of spatial, rather than verbal ability. They were not highly correlated, as they might be if they were measuring the same spatial abilities.
PSVT:R score, or mental rotation, is the variable studied that best predicted ESC performance. This result is consistent with the aspects of movement involved in many Earth science concepts on the ESC, and the necessity to visualize the position of objects from varying vantage points. Some of the most persistent misconceptions exhibit these characteristics, including the mechanism of moon phases, the mechanism of seasonal change, and the invisible movement of molecules during phase changes. The PSVT:R requires three- dimensional thinking, which is also required in understanding these concepts
Many subjects completed the PSVT:R before the suggested 20 minute time limit had expired. This may have somewhat diminished the capacity of the test to measure the ability of subjects to rapidly and accurately rotate objects mentally in a Gestalt-like manner, rather than in an analytic manner (Linn and Peter sen, 1985). Linn and Petersen suggested that females may, on average, tend to use analytical strategies rather than a holistic Gestalt-like ability, which is more common with males. This time limit may have allowed more time for persons who tend to use analytic strategies to do well on the test. This study’s result of a non-significant male advantage on the PSVT:R is inconsistent with most findings that males exhibit a significant advantage on all tests of mental rotation (Linn and Petersen, 1985; Kimura, 1999; Geary, 1998). It is unknown if this time limit was related to this result. I have seen no other references to the time limit in the literature.
Table 5. Independent sample t-test comparison of means by gender, also showing means of all subjects.
DAT results are consistent with the idea that conversion of two- dimensional images to three-dimensional reality in the Earth sciences is a component of several misconceptions and conceptual difficulties, as well as the viewing of phenomena from different vantage points. The highest correlation between spatial ability tests occurred between the PSVTiR and DAT. This is not surprising, as both have components of viewing three-dimensional objects from differing vantage points, although other aspects of the tests are not similar.
A contrasting pattern of DAT results compared to PSVT:R and GEFT results is evident in several respects. Males outperformed females on the other two tests, although the advantage was not significant, but male and female scores on the DAT were nearly equal. This result is consistent with the observation that spatial v\isualization tests are characterized by use of analytic strategies and often show little, if any, difference in male and female performance (Linn and Petersen, 1985).
The possible relationship of spatial visualization to verbal factors and general ability indicated by Linn and Petersen (1985) may also be partially responsible for the disparity between mean percentage scores on the three spatial tests. Mean scores on the PSVT:R and GEFT were 52% and 48%, respectively, but the mean score on the DAT was 67%. This represents 15% and 19% higher mean scores on the DAT than on the PSVT:R and GEFT, respectively.
A contrasting pattern of DAT results compared to PSVT:R and GEFT results is also evident in regard to past science coursework. DAT scores were significantly related to the number of Earth science classes completed at the university level, but the other two tests’ scores were not. Also, elementary/mid die majors, who had taken significantly more university Earth science and science courses than all other majors, scored quite similarly to all other non-science majors on the ESC, PSVT:R and GEFT, but scored higher on the DAT than all other non-science majors, although the differences were not significant. These differences between results on the PSVT:R and GEFT in comparison with the DAT are consistent with Linn and Petersen’s (1985) description of spatial visualization in comparison to mental rotation and spatial perception. Linn and Petersen observed that spatial visualization depends on meta-strategy for selecting processes rather than an individual’s relative proficiency for using any particular process. As mentioned, they considered visualization strategies to be more typical of general ability and more closely related to verbal factors than are mental rotation and spatial perception strategies. University coursework may help develop some of these more general, and more verbal, strategies. Most preservice elementary/middle teachers in the study had completed the required Earth Science for Teachers course, a fact that contributed to the significant correlation between that major and number of completed university earth science and science courses. Elementary/middle majors in this study also showed significantly higher university grade level, which is perhaps indicative of the tendency of many preservice teachers to delay taking physics and Earth science courses until later semesters in their university careers, as well as the biology prerequisite. Because the great majority of elementary/middle majors were female, it is possible that some relationships exist between the additional Earth science and university training received by this subgroup of subjects and female performance on some of the tests. To further assess gender and major differences, further investigation may be indicated of preservice teachers at both earlier and later years in their university careers, as well as non-major populations that do not include preservice elementary /middle teachers.
Only a weak correlation, the lowest correlation between any two of the spatial ability tests, was found between the DAT and GEFT. This finding is consistent with the use of the GEFT as a test of spatial perception, rather than a test of spatial visualization, as suggested by Linn and Petersen (1985). It is also consistent with the observations of several researchers (Kimura, 1999; Ekstrom et al, 1976, Eliot,1980) that disembedding may not be classified as spatial visualization. In addition, the GEFT requires only two- dimensional thinking, while both the DAT and PSVT:R require three- dimensional thinking. Linn and Petersen’s description of spatial visualization includes “multistep manipulations” (p. 1484); Eliot (1980) considers embedded figures tasks to be matching, rather than manipulation tasks, as the subject must match angles and line lengths.
Students with ability to discriminate angles and discrepancy from vertical or horizontal may find it easier to understand Earth science concepts that involve angles, such as sun angle during different seasons and the relative angles of the ecliptic and Earth’s equatorial plane, as well as bedding planes and strike and dip. Disembedding may be related to ability to discern individual features on aerial or satellite photographs.
Much work remains to be done, including further delineation of spatial ability factors and tests. Not only is there a great deal of overlap and ambiguity among classification methods proposed by various authors (McGee, 1979; Linn and Petersen, 1985; Eliot, 1980; Kimura, 1999), but other researchers have identified possible additional spatial factors. Kali and Orion (1996), for example, have described a visual penetrative ability, VPA, which they have associated with successful interpretation of geologic block diagrams, and which they consider a subset of spatial visualization.
Spatial visualization itself is a somewhat nebulous category. Linn and Petersen (1985) do not delineate spatial visualization by the same criteria as spatial perception and mental rotation, which apparently involve specific abilities. They describe spatial visualization, instead, as often using the same abilities attributed to spatial perception and mental rotation. They delineate spatial visualization by choice of multiple strategies rather than by ability type.
Much of the development of spatial ability tests used in education and a large body of research occurred in the 1970s and 1980s, and subsequently a number of cited tests are not now easily available to researchers. Commercially available tests are primarily used for employee testing. Although research on spatial ability has continued in the following decades, little additional development of tests has apparently occurred, other than the production of group- administered forms of several tests. A need exists for both clarification of factors measured by specific tests and development of tests.
Much additional research is implicated by this preliminary study, including a similar study using many more subjects. I am analyzing any relationships between individual ESC items and scores on individual spatial ability tests, and intend to continue this study as I collect more data. I am also currently planning and piloting a number of spatially-related activities for use in my Earth Science for Teachers course that I will implement next year, as part of a university grant, and will employ the three spatial tests and the ESC as pre- and post-tests. I also plan to test preservice teachers at an earlier stage in their university careers.
Understanding of scale in both distance and time appear to be related to many Earth science conceptual problems. Several researcners have begun work concerning the cognitive basis of student understanding in this field (e.g Dodick and Orion, 2002, with geologic time). Additional work will hopefully be enlightening.
Although many factors are certainly associated with understanding of Earth science concepts, the contribution of spatial ability that is suggested by these results should not be overlooked, nor should studies that indicate that spatial ability can be enhanced. A word of caution may be in order, however. Although research indicates that spatial ability can be improved, those results, as well as many others concerning spatial ability, may require further research and clarification. Some studies do not differentiate between types of spatial ability (Linn and Petersen, 1985). A few intervention studies that do differentiate between spatial ability factors (Piburn et al, 2002; Zavotka, 1987) found improvement in some spatial or Earth science abilities, but no improvement in mental rotation. Interestingly, mental rotation is the factor I found that best predicted ESC scores. Many questions remain, such as the possible influence of age at which interventions begin. A great deal of future work in many related areas is indicated, and could prove exciting.
Therefore, this study’s results suggest that an opportunity may exist to improve Earth science conceptual understanding by development of curricula and interventions that focus on spatial aspects of concepts. Perhaps the neglect of educators to foster spatial ability is related to its history of association with practical, rather than academic, skills. Perhaps educators have assumed that nothing can be done to improve spatial ability. The known association of success in science with spatial ability underscores the importance of additional research and of attempting a more deliberate and informed focus on spatial aspects of science concepts by K-16 teachers.
ACKNOWLEDGEMENTS
I would like to thank Dr. Judy Provo for kindly sending me a copy of the PVOR (PSVT:R), and my dissertation advisor, Dr. Lloyd Barrow, for his comments while writing my dissertation on this topic.
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Alice A. (Jill) Black Department of Geography, Geology, & Planning, Southwest Missouri State University, Springfield, MO 65804, aab208f@smsu.edu
Copyright National Association of Geoscience Teachers Sep 2005