- Top of page
- 1. Study 1
- 2. Study 2
- 3. Experiment 3
- 4. General Discussion
Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two-dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics-naíve students were administered kinematics problems and spatial visualization ability tests. In Study 2, 17 (8 high- and 9 low-spatial ability) additional students completed think-aloud protocols while they solved the kinematics problems. In Study 3, the eye movements of fifteen (9 high- and 6 low-spatial ability) students were recorded while the students solved kinematics problems. In contrast to high-spatial students, most low-spatial students did not combine two motion vectors, were unable to switch frames of reference, and tended to interpret graphs literally. The results of the study suggest an important relationship between spatial visualization ability and solving kinematics problems with multiple spatial parameters.
There is much historical evidence that visualization plays a central role in conceptualization processes of physics and in scientific discoveries. Research on the cognitive processes underlying physics discoveries such as Galileo's laws of motion, Maxwell's laws, Faraday's electromagnetic field theory, or Einstein's theory of relativity, has implicated the extensive use of visual/spatial reasoning in these discoveries (Miller, 1986; Nersessian, 1995; Shepard, 1996). Furthermore, the majority of physics problems involve manipulating spatial representations in the form of graphs, diagrams, or physical models, and in fact, the United States Employment Service includes physics in its list of occupations requiring a high level of spatial ability, that is, the ability to perform spatial transformations of mental images or their parts (Dictionary of Occupational Titles, 1991). Despite this evidence, however, relatively little attention has been devoted to understanding the role of spatial visualization skills in physics problem solving. Although research on expert-novice problem solving has indicated an importance of visual/spatial representations in physics (e.g., Larkin, 1982; Chi & Glaser, 1988; Ericsson & Smith, 1991), this research has mostly focused on verbal aspects of problem representations as well as semantic and procedural knowledge for solving physics problems. Thus, the goal of the current research was to examine the as-of-yet lesser-studied role of individual differences in spatial ability in physics problem solving.
Spatial ability tests usually involve judgments about the identity of a pair of stimuli presented at different angles (speeded mental rotation tasks) or more complex spatial visualization tasks that require the subjects to generate, maintain, and coordinate information during spatial transformations. Individual differences in spatial ability have been studied since the 1920s when psychometric research first differentiated spatial ability from general intelligence and from verbal and numerical abilities (Smith, 1964). However, the psychometric approach has not provided any clear interpretation of what the differences in spatial ability mean. Beginning in the 1970s, researchers applied the theories and methods of cognitive psychology to the study of spatial ability. One focus of this research has been to interpret individual differences in spatial abilities in terms of working memory. According to Baddeley and Lieberman's (1980) model, working memory consists of separate processing subsystems for visual/spatial and verbal information. Visual/spatial processes such as generating, manipulating, and interpreting visual/spatial images occur in the visual/spatial subsystem called the visuo-spatial sketchpad, whereas verbal processes such as the subvocal rehearsal of words occurs within the verbal subsystem called the phonological loop. Both visual/spatial and verbal subsystems have been shown to have limited processing capacities, and research suggests that spatial ability tests, at least in part, measure differences in visual-spatial working memory capacity. That is, people who differ in spatial abilities also differ in performance on laboratory spatial imagery tasks such as mental rotation (e.g., Carpenter et al., 1999) and measures of spatial working memory (e.g., Salthouse et al., 1990; Shah & Miyake, 1996). Therefore, researchers have proposed that measures of spatial ability tests reflect simultaneous processing and storage demands required to maintain and transform spatial images within the limits of visual-spatial working memory resources (Salthouse et al., 1990; Shah & Miyake, 1996; Miyake, Friedman, Rettinger, Shah, & Hegarty, 2001).
One of the limitations of the above studies, however, was that they ignored “the external validity of the processes that are measured, making it difficult to access the importance of the obtained individual differences in terms of real-world tasks” (Carpenter & Just, 1986, p. 232). Thus, in the current study we focused on examining the relationship between performance on spatial ability tests and solving problems in physics. The domain of physics chosen for this research was kinematics, which describes the motion of objects in terms of such concepts as position, velocity, and acceleration. We chose kinematics because of the diversity of the external visual/spatial representations used in these problems, including graphical schematic representations (vectors of force or velocity; and graphs of motion) and more concrete iconic representations (e.g., of blocks, pulleys, or springs). Additionally, people develop a set of naíve motion principles as a tool for coping with moving objects in everyday life (e.g., Clement, 1983; McCloskey, 1983; Kozhevnikov & Hegarty, 2001), so it is possible to examine their understanding of kinematics, whether correct or incorrect, using qualitative problems that do not require formal knowledge of physics.
Despite the large number of studies on students' difficulties in solving kinematics problems (e.g., Clement, 1983; McCloskey, 1983), very few attempts have been made to relate students' susceptibility to the errors in kinematics problem solving to their spatial ability. However, there is evidence that competing visual/spatial processing demands are more likely to arise as to-be-described kinematics events become more complex. For instance, Isaak and Just (1995) found that participants' susceptibility to incorrect judgments about rolling motion was related to their spatial visualization ability and proposed that the simultaneous processing of the rotation and translation components of the motion overloaded available visual-spatial working memory. Furthermore, Hegarty and Sims (1994) found that the ability to infer how different components of a mechanical system move was related to spatial ability, and Hegarty and Kozhevnikov (1999) showed that this was particularly true when the motion was complex (e.g., a component's motion was constrained by the motions of several other components). Kozhevnikov & Thornton (2006) found that spatial ability was also related to the ability to interpret motion characteristics of an object from a kinematics graph.
To investigate the relationship between physics problem solving and spatial ability, Kozhevnikov, Hegarty, and Mayer (2002a) administered to students a series of different types of kinematics problems along with a number of spatial ability tests. Factor analysis revealed that various types of kinematics problems loaded on different factors. Two particular types of kinematics problems loaded on the same factor as the spatial ability tests. These were problems requiring the extrapolation of an object's trajectory when the correct extrapolation involved combining two vectors of motion, and problems requiring inferences about the characteristics of an object's motion from a different frame of reference. In contrast, other types of kinematics problems, namely one-dimensional motion problems and problems that required the evaluation and calculation of the speed of a single moving object, loaded on a different factor that was interpreted as representing general knowledge of physics laws. Thus, it appears that in addition to conceptual knowledge, spatial ability is particularly related to solving kinematics problems requiring predicting the two-dimensional motion of an object and translating from one frame of reference to another.
The current study focuses on investigating the relationship between performance on spatial ability tests and performance on the above types of kinematics problems in more detail. In Study 1, we investigated the quantitative relationship between students' spatial abilities and patterns of correct and erroneous solutions to different types of kinematics problems. Study 2 further specified the differences in performance between individuals of high and low spatial ability in kinematics problem solving by using a protocol analysis methodology. Finally, in Study 3, we examined the relationship between students' spatial ability and patterns of eye fixations while solving kinematics problems.
3. Experiment 3
- Top of page
- 1. Study 1
- 2. Study 2
- 3. Experiment 3
- 4. General Discussion
To further investigate how spatial ability affects the solution of kinematics graph problems and two-dimensional motion extrapolation problems, we examined students' eye fixations while solving these problems in Experiment 3. Eye movements have been used to study visual imagery processes (Brandt & Stark, 1997; Spivey & Geng, 2001; Laeng & Teodorescu, 2002) as well as cognitive processes underlying visual/spatial tasks, such as mental rotation (Carpenter & Just, 1986) mechanical reasoning (Hegarty, 1992), and graph comprehension (Carpenter & Shah, 1998). In this study we examined differences in the eye fixations of low-spatial and high-spatial students as they solved motion extrapolation and kinematics graph problems.
Recent eye-movement studies have found that mental imagery is often accompanied by eye movements. For example, when viewing a static scene and imagining motion, people's eye-fixations mimic the direction of imagined motion (Spivey & Geng, 2001). In Study 3 we used this observation to examine differences in visualization processes between high- and low-spatial students in solving motion extrapolation problems. We predicted that if the students use spatial imagery rather than just conceptual physics knowledge to predict the trajectory, they would make eye fixations in the direction of the trajectory of motion.
In the case of graph comprehension, Carpenter and Shah (1998) have proposed that graph comprehension occurs through integrative processing cycles in which learners identify visual patterns in the graph (e.g., positive slopes vs. negative slopes), translate the patterns into quantitative and qualitative interpretations (e.g., interpreting an upwardly curved line as an accelerating function), and then relate the interpretations to the referents inferred from the labels on the graph. They provided evidence for this process by examining participants' eye-fixations on graphs during comprehension. A striking result of their study is that participants spent most of their time fixating the axes and labels of the graphs, and that graph comprehension involved frequent switches of gaze between the graph patterns, axes and labels, presumably to integrate the information in the graph patterns with that presented in the axes and labels. We expected high spatial individuals to interpret the motion graphs in this way, showing frequent fixations and a high proportion of time on the axes and labels of the graph. This should be particularly true if they break the graph down into intervals showing different motion events. On the other hand, because low-spatial individuals appear to interpret graphs as pictures and view them holistically rather than interval by interval, we predicted that they should spend less time and have fewer fixations on the axes and labels.
We did not investigate the frame-of-reference problem in Study 3, because this problem required the use of more complex, dynamic visual/spatial imagery (e.g., imaging the cart moving, the ball being released, and the perspective changes), and we could not make predictions about the eye-movement patterns that would accompany such complex visual/spatial imagery processes.
Fifteen students were recruited from the general participant pool in the Psychology Department at Rutgers-Newark. The participants were selected based on their Paper Folding test scores, and the Paper Folding Test was administered under a variety of contexts for studies to be reported elsewhere. Six low-spatial (M paper folding = 1.99) and nine high-spatial (M paper folding = 8.22) students agreed to participate in the eye-tracking study.
There were two kinematics problems used in this study. The first problem was the hockey puck problem in Fig. 1a, which was not accompanied by any text other than the labels for points a and b. When Fig. 1a was presented, the experimenter read the description and asked the student to imagine and describe in as much detail as possible the path that the puck was likely to travel after receiving the kick. The second problem showed a position-versus-time kinematics graph, similar to the graph in Fig. 2a. It was not accompanied by any text other than the labels for the axes, and the experimenter stated only that it was “a graph of an object's motion” and that the student was to study the graph and to describe in as much detail as possible what was depicted.
The graph and figure were presented on a 17-inch Dell monitor. The students' eye-movements were measured via an iView-X RED eye tracking system designed by SensoMotoric Instruments, Inc. (Boston, MA), and their descriptions were recorded on audiotape. A chin-cup and headrest were used to keep the students' viewing distances constant and to reduce the students' head movements, although the eye-tracking system was set to accommodate slight head movements. Finally, the eye-tracking system was calibrated for each student at the beginning of the session using the 9-point iView-X calibration system, and, if necessary, the eye-tracking system was adjusted for drift between the presentations of the problems.
The students were tested individually. They were told that they would be shown some figures and would be asked to answer some questions about the figures while their eye-movements and answers to the questions were recorded. Prior to showing each figure, the student was asked to fixate on a set of cross-hairs. After the student fixated on the cross-hairs, the experimenter gave the student a verbal “get ready” prompt and started recording the student's eye-movements. The experimenter then pressed a key on the keyboard to display the figure, and after it appeared, the experimenter read the problem to the student. If asked, the experimenter re-read the problem.
The position-versus-time graph problem was presented first, followed by the motion extrapolation problem. For each problem, the student was given unlimited time to respond. When a student's description was ambiguous, the experimenter asked the student to elaborate, and at the end of the session, the experimenter had the students sketch the trajectory for the motion extrapolation problem.
3.2.1. Extrapolation problem
None of the low-spatial students accurately described the puck's trajectory; however, seven of the nine high-spatial students did. A likelihood ratio revealed that the association between spatial ability and correctly describing the puck's trajectory was significant, L2 (df = 1, N = 15) = 11.19, p < 0.01, Φ = 0.76. The two high-spatial students who incorrectly described the trajectory failed to integrate the horizontal motion component (i.e., they predicted that the puck would move only in the direction opposite to the kick), and the data for these students were not further analyzed.
If students are solving this problem by visualization (imagery) strategies, we might expect them to make eye fixations in the direction that the puck would travel (Spivey & Geng, 2001). Thus, we examined whether a student made eye movements and fixations in the correct direction. This was considered to have occurred if the gaze path was in the direction of motion and the fixation fell within a region of interest (ROI) defined as a rectangular space beginning 1 cm to the right and 1 cm above point b and extending to the top and right edges of the display (see Fig. 7). Fixations were defined as periods in which the eye remained within a circular area (diameter = 19.5 cm) for at least 50 ms.
Figure 7. The fixations and scan paths of two low-spatial and two high-spatial ability students while solving the hockey puck problem. Circles represent fixations; the diameter of the circle represents the duration of the fixation. Lines represent the scan paths. Rectangles mark regions of interest (ROI) that we defined.
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Five of the seven high-spatial students who answered this problem correctly made at least one fixation within the ROI, whereas only one of the low-spatial students made a fixation within the ROI. A likelihood ratio revealed that the association between spatial ability and fixating within the ROI was significant, L2 (df = 1, N = 13) = 4.16, p < 0.05, Φ = 0.55. Thus, the high-spatial students who correctly described the trajectory showed evidence, in the form of eye movements and fixations, of imaging the path that the puck would travel. One of the other high-spatial subjects who answered correctly did not make any eye movements away from the elements shown in the figure. The seventh high-spatial subject made upward and rightward eye movements and fixations from point b, suggesting that he was actually visualizing the results of the two motion components.
Three students who reported that the puck would move opposite to the direction of the kick did make at least one fixation in that direction, but none made eye-movements and fixations in the direction of the horizontal motion component, thus failing to show evidence of visualizing this horizontal component.
3.2.2. Kinematics graph
None of the low-spatial students gave correct schematic descriptions of the graph. Five of the six low-spatial students gave “graph-as-picture” descriptions, and one failed to describe the graph in terms of an object's motion. Six of the high-spatial students, however, gave correct schematic descriptions of the graph. Two gave “graph-as-picture” descriptions, and one incorrectly described the graph in terms of an accelerating object. Because our primary interest was in the more typical low-spatial students who gave “graph-as-picture” descriptions and high-spatial students who gave correct schematic descriptions, and because the number of low- and high-spatial students giving other types of responses was small, only the data for the low-spatial students who gave “graph-as-picture” descriptions and the high-spatial students who gave correct schematic descriptions were further analyzed.
For the position versus time graph, regions of interest (ROI) were defined in an attempt to isolate fixations on the x- and y-axes, the labels for the axes, and the line segments within the graph (see Fig. 8) and then to calculate the proportion of fixations made on the axes, labels for the axes, and the line segments out of the total number of fixations made and the proportion of time spent studying these features out of the total duration spent studying and describing the graph. Fixations were defined as periods in which the eye remained within a circular area (diameter = 19.5 cm) for at least 50 ms.
Figure 8. The fixations and scan paths of two low-spatial and two high-spatial ability students while studying a kinematics graph. Circles represent fixations; the diameter of the circle represents the relative duration of the fixation. Lines represent the scan paths. Rectangles mark areas of interest that we defined.
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Separate between-groups ANOVAs were calculated for the proportion of fixations within and proportion of time spent studying each graph element (axes vs. labels vs. line segments) for the low and high spatial ability groups (see Table 2, and for examples, see Fig. 8). The analyses revealed that the high-spatial students spent a greater proportion of time studying the axes than the low-spatial students, F (1, 9) = 7.00, p < 0.05, partial η2 = 0.437, and they also tended to make a greater proportion of fixations along the axes, F (1, 9) = 3.11, p = 0.11, partial η2 = 0.258. The groups, however, did not significantly differ in the proportion of time spent studying or the proportion of fixations made along the line segments or axis labels, all ps > 0.22. Due to some potential uncertainty regarding the focus of some of the fixations along the line segment and x-axis segment on the right of the graph, we calculated the proportion of time studying and proportion of fixations made along just the horizontal line segment on the right and slanted line segment, but the differences between the low and high-spatial groups were still not significant, both Fs (1, 9) < 1.
Table 2. Mean proportion of fixations and proportion time spent studying the regions of interest on the graph by low-spatial students who gave pictorial descriptions and high-spatial students who gave correct abstract descriptions
| || ||Proportion of Fixations||Proportion of Time|
|Region of Interest||Spatial Ability||M||SE||M||SE|
Thus, the data showed that high-spatial students who accurately described the kinematics graph studied the graph differently from low-spatial students who gave “graph-as-picture” interpretations of the graph. In terms of Carpenter and Shah's (1998) model of graph comprehension, the fixation data and descriptions from the present study show that high- and low-spatial students spent equal proportions of time studying the line segments, suggesting that both at least engaged in pattern encoding. High- and low-spatial students also spent similar proportions of time studying the axis labels, which suggests that both considered the importance of interpreting the patterns according to the variables. However, the finding that the high-spatial students studied the axes more than the low-spatial students and that they gave interval-by-interval descriptions of the functional relations depicted in the graph (e.g., In the first couple of seconds, the object it is staying still, and then for like 2 seconds it's moving, the position is changing, and then it's still again) suggests that the high-spatial students engaged in the second and third processes of Carpenter and Shah's (1998) graph comprehension model (i.e., translation the visual pattern into conceptual relations and by identification of the referents of the relations). That is, they relied more extensively than low-spatial students on the scales when deriving the functional relations depicted in the graph and when associating those relations to the concept of an object's position changing over time. Consistent with the integrative processing proposed by Carpenter and Shah, high-spatial students tended to study the axes, axis labels, and line segments repeatedly.
The low-spatial students who gave incorrect descriptions, on the other hand, relied less on the scale information available on the axes, and their descriptions show that they failed to translate the patterns into integrated functional relationships. Instead, they appeared to have retrieved memories of a motion event that matched the general shape of the line segments (e.g., Well, someone could be diving off a diving board into a pool and then swimming to the end of the pool), giving pictorial responses consistent with the patterns of the low-spatial students in Studies 1 and 2. The difference between the high- and low-spatial students in translating the patterns into integrated functional relationships suggests that spatial resources are important for such translations.
4. General Discussion
- Top of page
- 1. Study 1
- 2. Study 2
- 3. Experiment 3
- 4. General Discussion
The current research provides insights into the nature of individual differences in spatial ability as well as the types of physics problems that might require high visual-spatial processing resources. Study 1 showed that there was a significant relationship between visual-spatial abilities and the solutions that students gave to kinematics problems. In particular, high-spatial students were more likely to take into account and successfully integrate several motion parameters, to interpret kinematics graphs as abstract representations of an object's motion, and to reorganize one spatial problem representation into another coordinated, corresponding representation. In contrast, the low-spatial students were more likely to consider a single motion parameter at a time, to interpret graphs as picture-like representations, and to hold multiple, uncoordinated representations of the same problem. The results of Study 2 were consistent with the findings from Study 1 in that students' solutions to the kinematics problems presented in these studies were related to spatial visualization ability. In particular, the students' transcripts showed that low-spatial students did not integrate the two motion components in the case of the extrapolation problems, did not decompose graphs into intervals with different motion characteristics, and did not spatially transform one problem representation to another.
Finally, the results from Study 3 provided further insight into the influence of visual/spatial ability on solving kinematics problems. First, the fact that most of the high-spatial students made upward and rightward eye movements as well as eye movements in the diagonal direction that puck would travel suggest that they were actually visualizing the results of integrating two motion components. In contrast, most of the low spatial students did not make eye movements in the direction of the horizontal motion component showing no evidence of visualizing the horizontal component. Second, consistent with Studies 1 and 2, the availability of spatial resources predicted how the low- and high-spatial students studied and interpreted the graphs. High-spatial students who interpreted the graphs as a schematic representation of an object's motion spent a greater proportion of time studying the axes of the graph than low-spatial students who interpreted the graph as a literal representation of an object's motion, and the high-spatial students were able to integrate both the position change and the time dimensions.
The data reported in this paper are correlational in nature, so we cannot rule out the possibility that some other variable covaries with spatial ability in our samples and is causing the differences in kinematics problem solving that we observed. Some plausible correlates that might cause differences in performance include general intelligence, mathematical ability, and conceptual knowledge. It is unlikely that the difference reported in our studies were due to the differences in intelligence or mathematical ability. We measured verbal intelligence in Study 1 and found no significant difference on this measure between our high- and low-spatial groups. Furthermore students in all of our studies reported their SAT Quantitative scores and again there was no significant difference between high- and low-spatial students on this measure.
To control for possible differences in conceptual knowledge, we recruited as participants only students who had not taken physics in high school or college. However, we cannot be sure that our high- and low-spatial groups did not differ in conceptual knowledge and, in fact, some of the responses in the protocol study suggested that they did. It is possible that the high-spatial students, as a result of informal education or through interactions with moving objects, had already developed a more sophisticated conceptual understanding of physics concepts and laws, and that this expertise (rather than specific spatial competences) affected their solutions to physics problems. However, it is unlikely that the differences reported in our studies were entirely due to differences in conceptual understanding. First, a factor-analysis study (Kozhevnikov et al., 2002a) has shown that the physics problems studied here load on the same factor as spatial visualization tests, whereas other physics problems load on a separate factor, which was unrelated to spatial visualization ability. If conceptual knowledge of physics was the only relevant variable at play here, we would not expect these physics problems to share common variance with spatial ability tests. It is also interesting to mention that a correlation between spatial ability and kinematics problem solving is no longer present after students receive physics instruction (Kozhevnikov & Thornton, 2006). This suggests that when conceptual knowledge has been already developed, spatial ability is no longer a predictor of their performance on the kinematics problems.
Rather than considering spatial abilities and conceptual knowledge as alternative explanations of the performance differences that we observed in these studies, we speculate that the two factors may be interrelated. That is, high spatial ability may enhance people's ability to gain conceptual knowledge of physics principles in informal situations. Previous studies have shown that high-spatial individuals are better able to perceive and predict complex motions (Law et al., 1993; Isaak & Just, 1995; Kozhevnikov et al., 2002a). Furthermore, the analysis of students' transcripts revealed that, in the case of the frame of reference problem, both low- and high-spatial students started with the same misconception, but the ability of the high-spatial students to maintain different spatial representations appeared to be critical in bringing about a conceptual change. Thus, it is likely that both spatial competence and conceptual understanding are at play. Some basic abilities in spatial processing (e.g., the ability to integrate two components, to decompose images into parts; and to perform spatial transformations) might bring about significant changes in students' conceptual understanding, and this, in turn, might influence students' future strategies and responses. This would also explain why high-spatial students in our studies exhibited more advanced conceptual understanding while attempting extrapolation and graph interpretation problems.
The findings of this research support the idea that spatial ability tests can reflect visual-spatial working memory capacity (Miyake et al., 1991; Shah & Miyake, 1996) in the sense that people who differ in spatial abilities also differ in their ability to solve physics problems that involve multiple spatial parameters. What do multidimensional physics problem solving and spatial visualization ability have in common, and what are other types of physics problems that might require high visual/spatial resources? Both multidimensional physics problems and spatial visualization tasks require the problem solver to simultaneously process multiple pieces of spatial information that tax the supplies of visual/spatial working memory resources. Indeed, all the studies reporting differences in the performance of low- and high-spatial students have examined physics problems with multidimensional spatial parameters (Law et al., 1993; Isaak & Just, 1995; Kozhevnikov, 1999; Kozhevnikov et al., 2002a). Interestingly, however, differences in performance between high- and low-spatial students on these higher dimensional problems disappeared after formal physics instruction with rich visualization technologies (Kozhevnikov & Thornton, 2006). Thus, a curriculum that provides external visualizations via technologies to students who have difficulty generating such visualizations on their own can compensate for such shortcomings.
The finding that spatial ability is related to solving many types of physics problems raises questions about the properties of visual displays that should facilitate the use of visual/spatial processing strategies, particularly to help low-spatial students learn from spatial physics concepts and diagrams. Visualization alone and even dynamic simulations do little to help people understand the dynamics of systems that involve multiple parameters or multiple objects (Kaiser et al., 1992), and low-spatial students in particular have more difficulties than high-spatial students in extracting necessary visual information from animations (Isaak & Just, 1995). However, it has been suggested that animations possessing specific features (e.g., allowing students to break a system down into a point-particle system with a single dynamically relevant parameter or drawing students' attention to a single element of the problem and thus minimizing the influence of other elements) should facilitate the development of spatial understanding and competence (Kaiser et al., 1992). The results from our studies also have some practical applications for the design of visual displays. First, our research suggests that visual simulations should illustrate how velocity vectors change along horizontal and vertical dimensions while an object is moving and demonstrate how these vectors combine to produce an object's overall trajectory. Second, for kinematics graphs, visual simulations should highlight segments of data and associated tick-mark ranges along the axes, rather than the overall shape of the graph, and should lead the learner to analyze and imagine event changes occurring with the subintervals.
Finally, the studies presented here specifically focused on the relationship between spatial ability and kinematics problem solving. Spatial visualization ability should also be useful when solving problems in other physics and science domains. For instance, spatial ability might be especially important in order to visualize invisible phenomena and processes such as electric or magnetic field lines or electric current when solving electricity and magnetism problems. Although some of the implications of our findings should generalize to other domains, further research is needed to explore the specific relationships between visualization skills and students' performance in these domains. The results of this research may reveal important instructional implications for the development and the use of different visualization aids that generalize across physics and science domains and may reveal implications that are specific to a particular domain.