One problem with this style of investigation is how to reduce the rich and ... A book with a blackboard eraser placed on it was held horizontally ahout 2 m above .... The participants were asked whether they based their answer on observation or ... predictions about the magnitude of the acceleration of the bucket or block, ...
Understanding of Gravity RICHARD F. GUNSTONE AND RICHARD T. WHITE Monash University, Clayton, Victoria, Australia 3168
Purpose
We investigated the knowledge of gravity possessed by first-year physics students at Monash University. Since the investigation took place in the first week of the 1980 lecture year, and the students had not had time to be affected by the university instruction, they can be taken as representatives of the complete range of schools in the State of Victoria, together with a few from interstate and a more substantial number from Malaysia. The context of the investigation is a series of studies and theoretical papers concerned with learning, particularly of the sciences, going back to validation of learning hierarchies (White, 1974), the use of hierarchies to ensure achievement of intellectual skills (Trembath & White, 1975), the specification of different types of elements in memory (Gagne & White, 1978), the description of a model of cognitive processes (White, 1977), and the distinction of achievement, proficiency, and mastery as levels of outcomes (White, 1979a). Within this context, recent attention has heen given to developing methods of probing understanding (White, 1979b), which include both individual interviews and techniques which can be used with large numbers of participants. The present investigation belongs to the latter class. It relies on presenting participants with a physical situation, asking them to make a prediction about what will happen if a certain action is taken, then demonstrating the action and requiring the participants to observe it and explain any discrepancy with their prediction. This procedure was developed at the University of Pittsburgh (Champagne, Klopfer, & Anderson, 1979). The immediate purpose of the investigation is evaluation of a state of affairs: to see how things stand in Victoria with respect to understanding of gravity and related principles of mechanics. As well as being of interest in their own right, the results will influence future development of the theoretical and empirical context outlined earlier, though this aspect will not be touched on further in this paper. Method
The investigation was based on eight physical situations, all involving some aspect of gravity. Nearly all follow the pattern of prediction, demonstration, observation, and explanation mentioned earlier. The first year physics students at Monash University are divided into five groups. Each was available to us for one hour, which was insufficient to present all eight situations. Therefore different sets of situations were presented to the groups, so that each saw five or six situations. The students were told that the purpose of the investigation was to find out more about Science Education 65(3): 291-299 (1981) 0 1981 John Wiley & Sons, Inc. CCC 0036-8326/81/030291-09$01.00
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TABLE I
Summary of Percent Successful on Each Task Situation
..
Forces acting on supported eraser Explanation of motion of falling eraser Predictions of speeds of falling eraser Prediction of times of fall of spheres Relative weights of suspended bucket and block Prediction of effect of addition of sand Prediction of speeds of bucket Releasing of suspended block Releasing of block on plank Spring balance on Mt. Everest
% Correct
86 98 92 76 70
54 90 54 75 29
their understanding of basic physical principles than was possible with a standard formal examination. They were assured that it had nothing to do with their end-of-year assessment. They were encouraged to write a lot in the course of making predictions and observations and in their explanations. The five sessions ran smoothly. Results
One problem with this style of investigation is how to reduce the rich and voluminous data to a reportable size. Our solution is to provide an overall summary, more detailed results for each of the eight situations, illustrative quotes from the students’ responses, and comments. The overall summary is in Table I, which indicates the proportion of students who could perform each task.
Situation A ( n = 175) A book with a blackboard eraser placed on it was held horizontally ahout 2 m above the bench. Students were asked why the eraser did not start moving when the book was under it. Sixteen students (9%) indicated that the book did not exert a force on the eraser, while five (3%) stated that the reaction force acting on the eraser was not equal to the eraser’s weight. The book was then quickly removed. Students were asked to indicate what set the eraser in motion. Adequate answers were given by all but 3. Then the eraser was held next to a marker (the Top marker) about 2 m from the bench. Other markers were about 1 m from the bench (Mid) and just above the bench (Bottom). Students were asked to predict how speed at Mid would compare with speed at Bottom when the eraser was dropped, and to give the knowledge on which the prediction was based. The eraser was then dropped (Table 11). Comments. Only 34 (19%) commented on the difficulty of the observation task. 32 (1 8%) concluded that air resistance had significant effect on the motion and 16 (9%) concluded that the distances between markers were not great enough to allow observable differences in speeds to be reached. Almost all of these 48 students predicted Bottom > Mid and observed Bottom = Mid. ‘ There was a tendency to observe the prediction. For 13 of the 14 predictions other than
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TABLE II Predictions and Observations of the Speed of a Falling Eraser ~
Observation
Bottom > Mid.
Prediction Bottom = Mid.
98 48 2
12 0
8 5 161
1 0 13
Bottom > Mid Bottom = Mid Bottom < Mid Could not observe No observation
Bottom < Mid.
0
0 0 1
98 60 3
0
9 5 175
0 1
Bottom > Mid, observation confirmed the prediction. Although reaching terminal velocity was the most common reason for predicting equal speeds, mathematics was used in some cases (e.g. “ u 2 = u2 2as; a is constant, s is constant, hence u is constant.”) Some students who had made quantitative predictions claimed remarkable powers of observation: of the 25 who had predicted a difference of &!times, 9 observed it to be J2 times faster, and one that it was “about 1.2.”
+
Situation B ( n = 176) An iron sphere and a plastic sphere of the same diameter (10 cm) were held next to each other 2 m above the bench, beside the top mark used in Situation A. The participants were asked “How will the time it takes for the metal sphere to fall from the mark to the bench compare with the time it takes the rubber sphere to fall from the mark to the bench?” They were asked to write down the knowledge used in making the prediction. The spheres were then dropped three times, and the participants were asked to record their observations and to explain any discrepancy with their prediction (Table 111). Comments. 25% predicted there would be a difference in speeds. Of these, 3/5 said this is due to air resistance and 2/5 said it is because a bigger weight will cause bigger acceleration. Those who predicted the metal ball would take less time were much more likely than the others to see it arrive first. Of the 131 who predicted equal times, only 7 referred to personal experience as the basis of their knowledge; 21 invoked Galileo as an authority. Most of the 131 simply asserted that all things fall at the same rate. A minority “proved” it mathematically. TABLE 111 Predictions and Observations for Falling Spheres Observation
Equal
Equal Metal faster Plastic faster
128 2 1 131
Prediction Metal faster 28 10 4 42
Plastic faster 0 0 0
156 12
5
0
Note: In addition, two predicted the metal would be faster but recorded no observation, and one predicted they would be ”different” and saw them as being equal.
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TABLE IV Opinions About Weights of Bucket and Block
n % ~~
Weights equal
Block heavier
Bucket heavier
320 70
122 27
17 4
~
Note: In addition, two said they could not tell, one said the weights were different, and one made an uninterpretable reply
Incorrect reasoning was present in at least 10%of the cases; e.g., “Metal sphere will accelerate more than rubber :. time for metal < time for rubber. Gravity exerts the same force on all objects no matter what their weight.” Where the observation conflicted with the prediction, the usual response was to say air resistance was less (or more) than anticipated. Next most common response was to ignore the discrepancy.
Situation C ( n = 463) The apparatus was a bicycle wheel mounted as a pulley with its axis about 2 m above the bench, and a bucket of sand and a block of wood of the same mass which were connected by a cord. The participants were shown that the pulley rotated freely, and then the cord was placed over the pulley so that the bucket was markedly higher than the block. The participants were asked “How does the weight of the bucket compare with the weight of the block?” (Table IV). The participants were asked whether they based their answer on observation or knowledge or both, and if knowledge was used they were asked to describe it. Most of those who said the block was heavier said they relied on observation, and gave no further reason or merely a circular one. The tone of their replies is that it is self-evident that the block is heavier: “The block is heavier than the bucket. Since the block is nearer to the floor, hence it must be heavier.” The next largest group among those who said the block is heavier contains those classed as giving uninterpretable reasons. These are diverse. “In the string used to link both the bucket and the block together over the pulley, tension exists in both its end. At the end towards the bucket, the tension is less than at the end towards the block. This then causes the block to pull itself down and thereby raising the bucket.” “F = ma. Acc. is uniform for both. Since mass of block is greater the block will pull up the bucket.” A few drew inappropriate analogies, to seesaws, beam balances, or spring balances. Another small group operated on a principle of equipartition of energy between the block and bucket: “Total energy is the same throughout, i.e., conservation of energy. mlghI = mzgh2. P.E. of bucket is same as P.E. of the block. But hl > h2 :. m2 > ml.” The 17 who said the bucket is heavier can be classified in a similar way to those who say the block is heavier. About 80% of those who said they are of equal weight gave acceptable reasons; the rest gave incorrect or no reasons.
:.
Situation D ( n = 463) This was a continuation of Situation C . The participants were shown a very small spoonful of sand, and asked to predict what would happen when it was added to the bucket. After they had written their predictions, the sand was added to the bucket, when, because of the friction in the axle of the wheel, no motion occurred. The participants were asked
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to record their observation, and if it was contrary to their prediction to explain the discrepancy. This procedure was repeated with a large scoop of sand, in which case the bucket accelerated smoothly to the bench. Just over half (249, 54%) of the participants made substantially correct predictions and observations for the two parts of the situation, though some of these made incorrect predictions about the magnitude of the acceleration of the bucket or block, such as a = g, or that they would move with constant velocity. Among the rest there was a predominant belief, that the added weights would cause a small shift of the bucket and block to a “new equilibrium” position. This notion was shown by 140 (30%) participants. “The existing system will be no more and the new system will be one in which the bucket will be ultimately closer to the table and the block higher from the table, but still in equilibrium.” “The bucket will fall slightly and the block will be raised by a similar amount. After they move they will then have a new equilibrium.” The most remarkable feature of these people was that in the case of the scoop of sand not one of them attempted to resolve the discrepancy between their predictions and observations. Most ignored it. For the spoonful of sand some did invoke friction. A few implied that the spoon of sand did cause a movement, but too slight a one to see. Two people actually saw movement, identical to that which they had predicted. Another common prediction (33 people, 7%) was that the large scoop of sand would not be sufficient to overcome the friction in the wheel. This indicates a lack of experience with bicycle wheels, or an inability to relate the forces involved. The rest of the responses were diverse. Some said the sand was insufficient to overcome the inertia of the system, others that the amounts were negligible without explaining in what way they were negligible. There was a proportion of very odd statements: “First the bucket would be pulled down and the block will be pulled up. Then the block will pull the bucket up the pulley until the block reaches the ground.” “Theoretically the bucket of sand weighs heavier therefore it should go higher up in the pulley.” “The small teaspoon of sand would not make much difference to the weight of the bucket. Hence, the bucket would still be lifted higher than the block of wood, showing its lesser density.”
Situation E ( n = 163) The bucket and block were placed on the pulley as in Situations C and D. A scoop of sand was to be added to the bucket, repeating the second part of D, which all the participants had already seen. The participants were asked to predict how the speed of the bucket at two markers would compare. One marker (the High mark) was about 0.6 m below the bucket, the second (the Low mark) was about 1.2 m below the bucket. Most students (144,90%) correctly predicted that the speed at the Low mark would be greater than that at the High. Of these, 4 indicated that their prediction was based on knowledge that the gravitational force acting on the bucket increased as the bucket lowered (or force on block decreased as the block rose), 12 specifically stated that the acceleration of the bucket would be g, and 10 observed the speed to be equal at the two marks. The reconciliations of prediction and observation given by these 10 students included “no net force,” “objects only accelerate in free fall,” “friction,” and “error in observation .”
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TABLE V Predictions in Situation F Prediction
n
1. System will remain stationary’ 2. System will return to original position 3. Bucket will fall 4. Block will fall
253 (54%) 164 (35%) 40 (9%) 9 (2%)
* Note: In 8 of the 253 cases of this prediction respondents indicated that they would have anticipated movement if there was less friction in the pulley.
Of the 16 students giving other predictions, 6 said speed at High would be greater than speed at Low. Five of these 6 students observed speed at Low to be greater than speed at High, but only 1 of these adequately reconciled prediction and observation. The remaining 10 students predicted the speeds would be equal (and 9 observed this).
Situation F ( n = 466) The block of wood and bucket of sand were placed on the pulley so that they were at the same level and hung freely. The block was then pulled down about 0.7 meter and held. Students were asked to predict what would happen when the block was released (Table V). Various reasons were given for predictions 2 to 4 of Table V. Of the 21 3 such predictions 94 were of the general form encompassed by “the system will return to where it was in equilibrium” or “fall back to the equilibrium position” or “it was balanced before, so it will go back” or “it went down because of an applied force, therefore if the force is removed it will go back.” These reasons appear to be intuitive rather than rational. In addition to these 94, another 19 respondents gave no reason at all, 7 indicated “common sense,” and 6 responded “a guess.” Thus a total of 126 students gave statements (or no statement) in support of a prediction of movement which were based on intuition rather than on physics knowledge. There was observational evidence that many students had a strong belief that the system would return to its original position when released. Numerous exclamations of surprise were given when the system remained stationary. The 21 3 students who gave predictions of movement often made unexpected responses to the request to reconcile prediction and observation. Only 27 showed that they were now correctly interpreting the situation, while another 17 talked of notions such as ‘‘new equilibrium” which may have indicated a correct interpretation. This leaves 169 who did not learn from the observation, or learnt incorrectly. Friction was given as the explanation by 54 students (i,e., the system would have returned had there been less friction in the pulley), while 66 gave either no answer or statements indicating exasperation. The remaining 49 students gave a wide variety of reasons including “inertia too large,” “the elasticity of the plastic bucket,” and “the block was held for some time at its new position.” Two students said the block had been given extra mass or weight by being pulled down. Equilibrium was seen in an odd way by many students. It was, during this demonstration, ‘:shattered,” “lost,” “upset,” “destroyed,” “sought,” “immediately reestablished,” “obtained,” systems “wanted to go back to it.” It was apparently seen as some sort of real entity contained in objects rather than as a description of a particular physical state.
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TABLE VI Predictions for Situation G Prediction
n
1. Bucket falls to floor 2. BucketlBlock remain stationary 3. Block moves a bit
216 (75%) 69 (24%) 4 (1%)
Situation G ( n = 289) This task used the block of wood and a bucket of sand of weight equal to that of the block. Students were told that the weights were equal. The block and bucket were connected by a piece of cord. The block was held on a horizontal board with a reasonably smooth surface, and the bucket left to hang freely. Students were asked to predict what would happen when the block was released (Table VI). For predictions 2 and 3 of Table VI, 58 of the 73 predictions were supported by either some form of the argument that “the weights are equal and hence cancel,” or “friction between the block and the horizontal surface will prevent motion,” or a combination of these two. When these 73 students came to reconcile their prediction with the rather dramatic motion which was observed when the block was released, there was considerably more evidence of learning from the demonstration than was the case in section F. In all, 25 students gave quite acceptable explanations, while another 17 gave a clear indication of having seen something of the explanation even though they had made incorrect statements in their reconcilation. That is, their responses suggested that one or two appropriate questions from an instructor would have resulted in the students having a reasonable understanding of why motion occurred. Among the small number of particularly unusual reconciliations of observation and prediction were “Gravity overcame the inertia of the system,” “Probably that swinging of the bucket allowed the bucket to gain momentum such that, on release, the momentum is greater than the limiting friction of the wooden surfaces,” “. . . height difference ( U = mgh).” Attempts at rationalizing the unexpected observation were much less common than in F, perhaps because the demonstration is much more dramatic. That is, in the face of somewhat spectacular motion, a student who predicted that the system would remain stationary was likely to start from the assumption that the prediction was wrong. In the case of F many students who had predicted movement started their attempts at reconciling prediction and observation from the assumption that the prediction was correct. This result in attempts to rationalize the observation, e g , friction was such that the pulley couldn’t turn, otherwise the system would have returned. Situation H ( n = 458) The participants were shown a large spring balance on which hung a bucket of sand so that the pointer was at the middle mark of the 40-mark scale. They had a sheet of paper on which were four copies of the scale. They were asked to mark the observed position of the pointer on the first copy. On the other copies they had to mark predicted positions of the pointer if the apparatus were taken to the tops of the University’s tallest building, Mt Kosciusko, and Mt Everest, the heights of which were given as 44 m, 2200 m and 8800 m respectively. They were asked what knowledge they used to make their predictions.
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TABLE VII Shift in Position of Pointer for Mt. Everest
Shift up Shift down Total
1
2
3
4
5
6
17
18
4 6 3 6 3 6 2 2 2 9 1 2 8 5 1 0 2 8 5 6 1 5 1 5 2 1 1 5 3 4 3 0 0 3 3 5 2 0 0 0 3 1 136 57 41 39 26 32 12 8 8 13 33 7 6 1 5 18 3
3 0 3
4 0 4
7
8
9
10
12 13 14 15 16
0
11
19 20 1 0 1
4 1 5
Knowledge that gravity decreases with height is widespread, but responses to this situation reveal ignorance of the scale of reduction. At the top of Everest gravity has fallen by about one part in 400, or about 0.05 of a scale division. Only 136 (29%) indicated a shift of zero to half a scale division. Of these, 36 gave no reason and 44 gave wrong reasons. “Gravitation attraction is constant everywhere”; “Newton’s law of motion. Gravity and mass was constant therefore the force extended exerted must be the same”; “Weight = mg and is independent of height”; “Gravitational pull is the same at whatever altitude.” Thus only 56 (1 2%) gave a reasoned correct response. There were 44 ( 1 0%) who showed the pointer getting lower with increasing height. Their written reasons show that they thought gravity was decreasing, so these responses must be considered as aberrations or as indicators of lack of experience with spring balances (Table VII). The responses for Kosciusko were a smaller version of those for Everest. The responses for the building further illustrate the lack of sense of scale commented on above. Although 402 (88%) show no shift, there are 46 who predict a shift of 1 scale division, 5 who predict 2, and 5 who predict more than 2 . Most of those who showed shifts, for Mt. Everest at least, gave either no reason or said it was because gravity decreased with height. The next most common type of reason was confused thoughts about the effect of air (12, only a small proportion but still remarkable that there are any at all): “Common sense that the rarefield air will make the bucket weigh less thus rising the marker to the appropriate levels’’-this student made a shift for Everest up 20 marks to zero; “When using spring balances the air resistance affects the reading. As the height increases the reading on the balance decreases”; “Atmospheric pressure is decreasing but the spring’s tension (stiffness) remains the same so the downward force decreases allowing the spring to contract further I think.” A few others gave a motley of reasons such as the effect of temperature or distance from the equator. General Observations
The summaries given for Situations A to H and the osmotic effect of reading several times through 468 protocols lead us to make some general observations. Perhaps the most important and general of these is the conclusion that the students know a lot of physics but do not reiate it to the everyday world. This is shown in the widespread errors of scale in estimating the effects of friction and air resistance and the relation between height and gravitational field strength, in the minimal number who used experience to support their prediction in Situation B, and in the large number who related the pulley system incorrectly to see-saws, beam balances, and the like. This conclusion has a vital implication for the teaching of physics: much more attention may have to be given to integrating the knowledge acquired in school to general knowledge. The second point is really another aspect of the first. In many instances the students
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used mathematical equations to explain predictions, though often inappropriately, which indicates that they had lots of physics knowledge to hand but were unskilled in seeing which bit applied to the given situation. A serious deficiency is the inability to explain a prediction. Many of the attempts were narrowly circular, or reflected intuition rather than rational assessment. Another related aspect is the failure to resolve discrepancies between predictions and observations, which was particularly noticeable in Situations D and F. Some, of course, avoided the discrepancy by observing what they had predicted, even when hardly anyone else saw it that way. Some even managed not to observe at all and gave mathematical equations when asked what they had seen. This is one instance of anti-scienceamong the students; another is their reliance on authority, such as Galileo, as support for a prediction. We would not have been surprised to find misuse of the concept of inertia. However, inertia was invoked rather rarely. What was surprising was the prevalence of the notion of equilibrium, as a state of Nirvana which systems seek. It was the most obvious fixation of a large proportion of students. These observations have implications for research experiments as well as for teaching. They suggest that dependent variables in investigations cou!d include the degree of integration of school learning with general knowledge, the ability to explain, and the accuracy of observation. Finally, it must be emphasised that the students in this investigation are the successful fraction from 13 years of schooling. Their shortcomings are likely to be compounded in the less successful majority. Certainly these first year university students did not show much evidence of some of the unfortunate characteristics observed in 1lth grade physics students in our preliminary study (Champagne, Gunstone, & White, 1980), such as confusion of quantities, reification, and animism. While this might indicate that the instruction in 12th grade diminishes these shortcomings, the over-all performance of the participants in this large scale study remains a matter for concern. References
Champagne, A. B., Gunstone, R. F., & White, R. T. Knowledge of basic principles of dynamics. Monash University, 1980. Champagne, A. B., Klopfer, L. E., & Anderson, J. Factors influencing the learning of classical mechanics. University of Pittsburgh, 1979. Gagni, R. M., & White, R. T. Memory structures and learning outcomes. Rev. Educ. Res., 1978, 48,187-222. Trembath, R. J., & White, R. T. Use of learning hierarchies in promoting mastery learning. Res. Sci. Educ., 1975, 5 , 135-142. White, R. T. The validation of a learning hierarchy. Am. Educ. Res. J . , 1974,11, 121-136. White, R. T. A model of cognitive processes. Res. Sci. Educ., 1977, 7 , 25-32. White, R. T. Achievement, mastery, proficiency, competence. Studies in Science Education, 1979a, 6, 1-22. White, R. T. Describing cognitive structure. Paper given at the meeting of the Australian Association for Research in Education, Melbourne, November 1979b.
Received 18 June 1980 Revised 20 November 1980 Accepted for publication 19 January 1981
