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Effects of differing amounts of visual cues and intervening responses on the acquisition of linear function… Dobson, Leona Nancy 1973

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E F F E C T S O F D I F F E R I N G A M O U N T S O F V I S U A L C U E S A N D I N T E R V E N I N G R E S P O N S E S O N T H E ACQUISITION O F L I N E A R F U N C T I O N R U L E S by Leona Nancy Dobson B . A . , Universi ty of B r i t i s h Columbia, 1957 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A R T S In the Department of Educational Psychology We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A October, 1973 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia Vancouver 8, Canada Date i i E F F E C T O F DIFFERING AMOUNTS OF VISUAL CUES AND INTERVENING RESPONSES ON TH E ACQUISITION OF LINEAR FUNCTION RULES University of B r i t i s h Columbia Leona Nancy Dobson Major Advisor: S.S. Lee ABSTRACT The effect of pointing (presence or absence) as an inter-vening activity, at the salient features of pictorial representations of differing amounts of visual cues (weight, context, both, or neither) for a concrete weighing operation, was investigated on the acquisition rate of three linear function rules. They were a coefficient rule (a. F = S), an intercept rule (F + b = S), and a complex rule (a. F + b = S), in a rule learning paradigm for Grades 4, 5, and 6 school children. The first two rules were presented in a counter-balanced order. Univariate analyses of variance of total error and ratio of error measures indi-cated that the pointing response was more effective than not pointing for the faster acquisition of the first task. Pointing was not significantly-effective for the second task, although the combination of context and weight cues was more effective for this task than was each visual cue presented alone. The effects of training Ss to point on the two tasks, when transferred to the third, Complex-Rule task with no visual cues I l l present, were negative. The findings were interpreted to mean that the calling of the Ss' attention to visual cues by pointing is only effect-ive for the first task undertaken, and the benefit from pointing diminishes thereafter. The negative transfer to the last task can be accounted for by a presumably inevitable change in strategy as the problem, for those who have been accustomed to making the pointing response, switches? from the concrete context of a weighing situation to an abstract problem in numbers. Major Advisor: i v T A B L E O F C O N T E N T S P a g e A B S T R A C T i i T A B L E O F C O N T E N T S i v L I S T O F T A B L E S v i L I S T O F F I G U R E S v i i A C K N O W L E D G E M E N T v i i i P R O B L E M 1 M E T H O D . 7 D e s i g n 7 S u b j e c t s 8 L e a r n i n g M a t e r i a l s 9 A p p a r a t u s 10 P r o c e d u r e 11 R E S U L T S 15 A n a l y s i s o f p e r f o r m a n c e o n the f i r s t t a s k 16 A n a l y s i s o f p e r f o r m a n c e o n the s e c o n d t a s k 18 A n a l y s i s o f p e r f o r m a n c e o n the l a s t ( C o m p l e x -R u l e ) t a s k 19 D I S C U S S I O N 21 B I B L I O G R A P H Y . . . . . . . 30 A P P E N D I X A 32 V T A B L E O F C O N T E N T S (Continued) Page A P P E N D I X B 34 A P P E N D I X C 35 A P P E N D I X D 36 vi LIST O F T A B L E S Table Page I The Observed Mean Numbers of Total E r r o r s and Mean Ratios of E r r o r s by Grade, Treatment Combination, and Task Given as the F i r s t Task (N = 84) 26 II The Observed Mean Numbers of Total E r r o r s and Mean Ratios of E r r o r s by Grade, Treatment Combination, and Task Given as the Second Task (N = 84) 27 III The Observed Mean Numbers of Total E r r o r s and Mean Ratios of E r r o r s by Grade, Treatment Combination, and Task Given as the Third (Complex-Rule) Task (N = 84) 28 v i i LIST O F F I G U R E S Figure Page 1 Est imated Effects of the Interaction on the F i r s t T a s k Between V i s u a l Cues vs . V e r b a l -only Treatment Conditions and Type of T a s k (C-Rule or I-Rule) on 1 in T e r m s of the Ratio of E r r o r s 28a 2 Changes in Est imated Effects of Pointing vs . Not-Pointing Responses over the Three T a s k s in T e r m s of the Total T i m e Spent and the Number of Total E r r o r 29 A C K N O W L E D G E M E N T A d v i s o r : S . S . L e e C o m m i t t e e M e m b e r s : S. B l a n k N . S u z u k i P R O B L E M The acquisition processes of linear function rules in children were initially studied by Lee (1971). His subjects, Grade IV school children, acquired three linear function rules, an intercept rule (I-Rule: S = b + F), a coefficient rule (C-Rule: S = a.F), and a complex rule (Complex Rule: S = a. F + b). Lee's (1971) study was designed to see if the acquisition of these rules could be facilitated by some means of visually represented cues. These cues are referred to as variations in the amount of prompting given a learner in the context of studying verbal learning (Rohwer, in press). In the paired-associate learning task, the cues, whether pictorial or verbal, have been demonstrated to be an effective variable in promoting rapid learning (Rohwer, 1966; Rohwer, Lynch, Levin & Suzuki, 1967; Davidson, 1964). But although researchers in this area have indi-cated the need for practical extensions of this work to other complex tasks (Palermo, 1970; Rohwer, 1973; Paivio, 1971), such extensions have been rare. In Lee's independent line of study the effects of the type and amount of visual cues have been examined in the area of rule learning. The abstraction (or induction) of a linear function rule was considered to be based on the nnumerical instances of the rule; the for-mulated conceptual rule could be expressed in terms of a mathematical 2 sentence. The essence of the rule learning task is to identify relevant attributes, a constant and an operator, and combine them into an appropriate mathematical sentence. The visual cues were established by presenting a set of concrete referents, a set-up of weighing opera-tions involving an easily observable scale along with a manipulable scale pan. A sequence of measuring actions were demonstrated to all subjects. Then, in the absence of the concrete referents, Ss were asked to produce a mathematical sentence involving a given pair of numbers (i.e., two variables) as well as an appropriate constant and a necessary operator. The constant and operator physically corres-pond to the weight of a particular magnitude multiplied by or added to a specific quantity placed on a scale pan, with the result of a specific reading on a scale. The variations in the visually represented cues were produced by a combination of two factors: (1) the presence of the picture of the five different weights vs. its absence, and (2) the picture of the weighing context (scale, etc. ) vs. a graphic presentation of the weighing context vs. no contextual aids. Results varied for each task. The interactive effect of the weight and context facilitated learning of the C-Rule, the first task; whereas in the second task, the acquisition of the I-Rule, the main effects of the visual cues, weight and context, were effective in facilitating learning. 3 Lee (1971) attributed this difference in effect to the development of learners' ability to use the weight and context cues independently. Also investigated was the effect of training on these simpler rules upon the acquisition of the Complex-Rule. This rule was conceived as consisting of two lower-level component rules, the C- and I-Rule, and it was given as a common transfer task. A l l Ss who had received training on the simpler tasks acquired the Complex-Rule faster and with fewer errors than did a control group, who had engaged in a filler task only. The acquisition variables did not affect the learning of the transfer task, as all Ss so trained performed equally well on the Complex-Rule task. In such studies as Paivio & Yarmey (1966), Dilley & Paivio (1968), and Milgram (1967), a paired-associate learning task has been used to evaluate the relative effects on recall performance given pictures or concrete nouns (image-arousing) presented as stimuli, as compared to performance given verbalizations or abstract nouns presented as stimuli. The relevance of such nonverbal processes to concept formation has been studied by Reed & Dick (1968), who inves-tigated learning by adults of abstract and concrete concepts, and learning by children by Lee (1971). Their results indicate that easily imagined instances and high imagery cues can facilitate concept learning. Developmental dif-ferences were not examined in these studies, but there is some evidence in the P-A studies that children do not necessarily respond to 4 visual imagery. Children have appeared to benefit less from the visual cues than do adults. This effect has been interpreted by some investigators (e.g., Rohwer, in press) to mean that children develop the capacity to derive maximal profit from imagery representation later than they do the capacity to profit from verbal representations. Reese (1970) contends that imagery is a less effective mnemonic at young ages. He suggests that the reason children benefitted less from the visual material than adults did, was that imagery might not have been effectively aroused in these studies for children at these ages. In order to ensure that the children were attending to the visual cues provided so as to arouse 6fffective images, Lee (1971) required them to make a pointing response to the relevant features of the pictorial material as an intervening activity. This response fol-lowed the presentation of the stimulus instance and preceded the written response. It was assumed that this pointing response required the £> to pay attention to the visual material and further, increased the likelihood that the S would make effective use of the visual cues in an encoding process whereby the numerical instances, as the nominal stimuli, become functional via an internal representation of the con-crete operation. The effect of this pointing response upon performance was suggested, but not investigated, by Lee (1971). The main purpose of the present study was to evaluate the role of this pointing response as an aid to promoting the encoding processes. To evaluate its role in 5 the acquisition procedure, it is possible to vary the intervening activity by having Ss engage, or not engage, in a series of pointing responses during the acquisition trials of the C- and I-Rule. When such a learning task is undertaken the S is assumed to need to perform on two operations before he can formulate the rule. He must notice the constancy of an operend throughout the instances and select that constant number, and he must also select the appro-priate operator for the task. The operend and the operator will then be available for insertion into the mathematical sentence and the rule can be formulated. When the pointing procedure is used, the S, having been presented the numerical instances as stimuli, is required to point to the weight which represents the constant, and then to the part of the pictured scale relevant to the choice of operator (the balance pan and the scale indicator). Thus, the order of operation and the constant weight being used is indicated. Given the logical description of the series of task require-ments, it was hypothesized that the selective attention inducing activity would augment the image-evoking value of the visual cues in encoding the nominal stimuli to aid rule formulation. If children can get benefit from high image-evoking materials, as has been suggested (Paivio, 1970; Rohwer, 1973; Lee, 1971), then the more potential the visual cues have for bringing the event closer to the concrete referents, the more accurate and rapid the learning should be. According to the reasoning along these lines, there should 6 be the main effect of the pointing responses as intervening activities and further, the more nearly the visual cues resemble the concrete weighing situation (weight and context present), the greater the f a c i l i -tation of learning when the pointing response is present. This would be the case at least during the acquisition phase of the C- and I-Rule. [Lee (1971) found the visually represented cues are effective variables for the acquisition of a rule rather than for transfer . J When either the weight or the context cue is missing, the _S must imagine the missing part for the integration to be complete. The crucial role of the intervening activity of pointing at the pictured aspects of a verbalization which follows the logical sequence of the weighing process as a determinant of the effectiveness of these visual cues was of primary concern. In order to control the effect and determine whether the order of presentation of the rules or the nature of the different rules themselves would account for any dif-ferential effectiveness of the visual cues, the presentation of the two rules (C- and I-Rule) needed to be counter-balanced. Finally, it was also of interest to see if the intervening activity and visual cues would become less effective as the grade level increases. 7 METHOD Design In order to answer the questions regarding the effective-ness of the pointing response and the amount of visual cues, the two factors were experimentally defined. A series of pointing responses as intervening activities before criterion terminal responses, were made present or absent, constituting the first experimental factor. The visual cues were varied in terms of context (scale) pictures, the five weights pictured, and both context and weights: pictured. Thus, the variations in the two factors resulted in a 2 x 3 factorial design. A seventh condition presented the weighing situation in verbal terms only, and acted as a control to measure the effectiveness of the visual cues. These seven conditions served as the experimental conditions for the evaluation of the effects of the two factors. The two function rules (i.e. , C- and I-Rule) were presented in counter-balanced order and two grade groupings were involved,. Grade 4 vs. Grades 5 and 6. Thus, the design can be described concisely in terms of a 2(Grade: 4 vs. 5 and 6) x [2(pointing response: presence vs. absence) x 3(visual cues: context vs. weight vs. context and weight) along with a verbal condition^ x 2(Task: C-Rule vs. I-Rule) factorial design. The criterion performance on the function rules was ex-pected to show significant main effects due to pointing and visual cues. Significant interactions between the two factors was also expected 8 when the effect of combined weight and context cue was compared with that of either cue singly, weight or context. The effects the training factors have on performance at the Complex-Rule task were not parti-cularly expected to be significant as Lee (1971) detected no transfer effect. Subjects Forty-two fourth-grade children and twenty-one fifth-and twenty-one sixth-grade children in a metropolitan private elemen-tary school were chosen for experimental Ss after a preliminary screening. They were initially asked to play a game. A child was asked to give a number (i. e. , 7); then E answered, with the number 56. The S's comprehension of the relationship was tested by E who now supplied the first number and asked S! to mark the corresponding number on a paper. Any child who correctly identified the relationship was ex-cluded from the experimental Ss sample. Since the purpose of the present study was to study the effects of thecexperimental variables upon the acquisition of linear function rules as new rules, those class of _Ss would not be appropriate. In other words, it was felt that for children so quick to see the relationships, the experimental tasks would involve merely rule identification rather than rule learning. The remaining children were given a 25-item survey test of arithmetic achievement constructed and used by Lee (1971) for the purpose of measuring pre-requisite learning. Information obtained from this test was expected to reflect their pre-experimental individual 9 differences. The 42 Grade 4 Ss who scored highest, were blocked and assigned at random to one of seven treatment groups, the 42 Grade 5 and 6 children, 21 for each grade, were assigned likewise to one of seven treatment groups. A random half of the six Ss assigned to a treatment condition, three Ss, were given the two task in one of two possible orders of the two rules; the other half of the Ss received in the other order. Learning Materials Each of the three learning tasks bearing the C-Rule (4.F = S), the I-Rule (F +- 5 = S), and the Complex-Rule (2 + 3.F = S) consisted of a set of 12 numerical instances for study and 4 criterion test instances. Each numerical instance was a pair of numbers. The second member of the pair would be the corresponding scale reading for S in terms of "gram" resulting from a single weighing operation with the first member of the pair. The four test instances were two letter pairs and two prediction instances, viz., (F, S), (13, ? ), (Y, Z), and (15, ?) for the C-Rule. A letter pair was used as the labels of the independent and dependent variable on the basis of which an unknown value of the dependent variable could be predicted. The task set for S was to express a mathematical sentence by transforming a given pair of numbers or a given letter pair, and predicting the value of S (or Z) from a given value of F (or Y). A l l the numbers used were integers ranging from 0 to 60. Each of the 16 stimulus instances for each task were presented in a pair of 1 x 1. 75-in. rectangular boxes which were 10 drawn in black ink on a white 3. 25 x 7-in. paperboard card and labelled with " F i r s t " and "Second", respectively. The three experimental variations of the visual cues were drawn on white 28 x 28-in. paperboards. One display included a schematic picture of a Jolly balance scale with a vertical scale stick. This stick was appropriately scaled and labelled with the measurement unit (gram) at values ranging from 0 to 60. A visual weight cue of size 01 75 x 3-in. was a schematic drawing of a series of ordered 1 - 5-gram weights standing for a row of a 5 x 5 matrix of weights used in the observation phase of the weighing operations. The weight cue was placed beside the balance pan of the pictorial Jolly balance. Another display contained a picture of the balance scale only; another, the weight cue only. A common warm-up task consisted of a set of 10 pairs of numbers from 1 to 10 and was presented in the verbal context alone. Apparatus A Jolly balance scale with a 60-cm. vertical scale and a round balance pan of 2-in. in diameter and five rows of 1 - 5-gram brass weights was used for the observation phase. A plywood foldable cubicle, 38 x 38 x 38-in. , was installed on a long table. A metal blackboard, 24 x 36-in. , with two signal lights lay against the far end of the cubicle. The two lights were connected to E's monitoring console with a set of switches. Two sets of white magnetic numerals ranging 11 from 0 to 9, two pairs of white magnetic letters (F, S, Y, Z), and a pair of white magnetic operators (y, x), were placed on the bottom half of the blackboard. Two stop-watches were used, one for E to control the presentation time of each instance and the other for recording the total time needed to complete each task. Procedure There were two phases to the experiment: observation and learning. The observation phase was intended to establish the concrete referents for the second phase. (1) Observation phase Each S was introduced to the Jolly balance scale set of weighing operations. E first named for him the parts of the instrument, such as "weight", "balance pan", "Indicator", and "scale", one by one and had him repeat naming after E. E demonstrated a sequence of measuring actions, while verbally describing each action in a verbal context, "When I put this weight on the balance pan then the indicator points to grams". _S identified the weight in grams. E demon-strated wijth each weight and had S repeat E's verbalizations and copy exactly the same sequence of E's actions. (2) Learning phase Upon completion of the observation phase S was taken into the cubicle and instructed how to respond to a stimulus instance. 12 This involved an intervening response, if required, and an overt terminating response. Each S from the three treatment groups which were trained to give a pointing response as an intervening activity were instructed to point to the relevant visual cue or cues displayed on their particular paperboard, while saying audibly a verbal context, "When I put this weight on the balance pan, the indicator points to grams. ", for the C-Rule. A l l other groups were taught in the verbal context but no response to the visual displays was allowed. The sequence of stimulus instance - pointing response, if required -writing response, was followed for the C- and I-Rule tasks. The visual cues were removed for the Complex-Rule task, otherwise the routine was similar. The terminating response was a composition of a. ma'thernatrcal sentence in two rectangular boxes drawn on the blackboard, the boxes being connected by an equality sign and labelled as " F i r s t " and "Second" (gram). _S was asked to f i l l in the two boxes with the provided magnetic numerals, operators, and letters so that both sides were equal. He was told that a white light signifies a correct response; a red light, an incorrect one. Immediately after the common warm-up task, given to aid the Ss in following the general instructions, the C-Rule and I-Rule tasks were presented in a counter-balanced order within each treat-ment condition. The Complex-Rule task common to all Ss and pres-13 ented in a verbal context only, followed. Three books of stimulus cards, each embodying the C-Rule, the I-Rule, or the Complex-Rule, was placed on the left-hand side of the table. The cards were arranged in three random orders within each task. A set of two numerical instances was followed by a test instance (F, S) and a prediction instance, except that the two test instances were omitted in the presentation of the first six numerical instance s. Each J! was asked to turn over a stimulus card in a book one at a time and make the sequence of responses per instructions. He was reinforced for the correct response with a white light. A l l other responses were given negative feedback with a red light. When all the numerals, operators, and letters had been returned to their origi-nal positions, a learning trial was completed. Ss paced the stimulus presentation and the response, though E gave negative feedback indica-ting S was to go onf to the next instance if S did not complete the trial in one minute. The learning 'trials for the C-Rule and I-Rule tasks con-tinued until S had reached the criterion of six consecutive responses to a set of two numerical instances and two sets of two criterion test instances. The last set of test instances, viz. , (Y, Z) and the other prediction instance, were presented only when S had correctly res-ponded to the first set of test and prediction instances. The learning trials for the Complex-Rule task continued for a maximum of 20 14 minutes. _Ss who had not reached criterion in this time were scored as failing this task. Upon completion of the three tasks, S was warned not to discuss the experiment with others, and released. 15 RESULTS Ss 1 performance was initially observed in terms of three dependent measures, the total time to the mastery of a task, the number of numerical instances used before the mastery of criterion test instances, and the number of total errors made to the mastery of a task. In addition, two additional measures were observed, the number of errors made over the criterion test instances and a derived measure of the number of errors in the test instances divided by the number of errors in the numerical instances. The principal component analysis of the error correlation matrices of these measures indicate that the first two components loaded saliently by the total number of errors and the derived measure of the error ratio account for 95% and 83% of the total variations in these measures observed given the first two and the last task, respectively. It seems quite clear that the number of total errors is informative enough to measure the accuracy and efficiency of what other measures could measure (84, 80, and 62%), even under the semi-Ss' self paced presentation condition. It is also worthy noting that the derived ratio measure reflects something that other measures do not (11%, 15%, and 11%). The ratio measure should index the relative difficulty with abstracting or formulating a rule as compared to the difficulty with getting the numerical instances correct. Thus, the logical as well as empirical considerations of the measurements taken 16 indicate the validity of the two measures to be used in the following analyses of the present data in terms of the total number of errors and ratio of errors, unless indicated otherwise. The two major statistical hypotheses, one the main effect of the pointing response and the other its interaction effect with the amount of combined visual cues, are tested at the overall type I error of . 10, each at . 05 level. Other find-ings are stated with significance probability levels as may be necessary. Analysis of performance on the first task The mean numbers of total errors and ratios of errors, as defined previously, are shown in Table I. Two separate univariate Insert Table I about here analyses of variance were performed on the estimated means, observed in terms of the two criterion measures in the 2 x (2x3 with a verbal condition) x 2 design, as shown in Appendix B. The results of the univariate analysis of the total errors indicate that the main effect of the pointing response (i.e., -2.89) was significant, as predicted, F(l,56) = 4.48; P <.039. This means that the _Ss under the pointing response conditions made fewer errors to the mastery of the task than those under no pointing response conditions. The same main effect in terms of the ratio of errors (i.e., -1.40) was not significant, although approaching to the significance level, F ( l , 55) = 2.43; P < .12. The predicted interaction effect between the pointing response and the amount of visual cues was nonsignificant in terms of the total error 17 and the ratio of errors, F ( l , 56) = 1. 34 and . 89. However, when the verbal-only condition was contrasted with the six treatment conditions that involved varying amounts of visual cues, the effect of the contrast in terms of both total error and ratio of errors (i.e., -11.33 and -4. 51) was significant, F( 1, 56) = 9.85 and 4. 14; P < . 003 and < . 057, respectively. This means that the amount of visual cues are effective in facilitating the acquisition of the linear function rule as might be expected from the previous study. There was also a significant grade effect for the total error only (i.e., 3. 18), F ( l , 56) = 6. 28; P<.015, indicating that Grade 5 and 6 Ss made fewer errors, as would normally be expected. There was a highly sig-nificant task effect in terms of both measures (i.e., 6.93 for total error and -3. 57 for ratio), F ( l , 56) = 30. 05 and 18, 35, P < . 0001 and •( .0001, which indicates that the C-Rule task is more difficult than the I-Rule with respect to both numerical and criterion test instances. The two-way interaction between visual cue vs. verbal-only and the two tasks was found significant only in terms of the ratio of errors, F ( l , 56) = 6. 24; P < . 016, as can be seen in Figure 1. This means that the Ss under the conditions of visual cues had as much difficulty with the numerical as with the criterion test instances, given the difficult C-Rule task, as the Ss under the verbal-only. Given the easy I-Rule task, the Ss had more difficulty with the criterion test instances. A l l other remaining effects were found nonsignificant. 18 Analysis of performance on the second task The mean numbers of total errors and ratios of errors, as defined previously, are shown in Table II. As for the first task, Insert Table II about here two separate univariate analyses of variance were performed on the estimated means, as shown in Appendix C. Those Ss making the point-ing response have again appeared to make less errors than the other Ss (see Figure 1), but the main effect of the pointing response (i.e., -.74) was not statistically significant in terms of%oth total error and ratio of errors, F( 1, 56) = . 54 and 1. 85j P <. 4643 and <.1790. The two-way interaction between grade and pointing response was significant for the total error, _F(1, 56) = 5.64; P < .0211. This means that the Grades 5 and 6 children made less total error (i.e., -3.2) as predicted, when the pointing response was present, but the Grade 4 children did not benefit from the intervening activity (i.e., 1. 7). Again the predicted interaction between the pointing response and the amount of visual cues was nonsignificant. However, the combined cues of weight and context when contrasted with the presentation of each cue singly (i.e., -2.92) is now significant for the total error, F(2, 56) = 3.65; P < .0323. The combined visual cues effectively facilitated the acquisition of the second linear function rule. Again there was a highly significant task effect for both measures, F ( l , 56) = 20. 23 and 10. 77; P < . 0001 and 19 < .0018, in favour of the I-Rule (i.e., 4.23 and -1.34). The two-way-interaction between the presence or absence of the combined cues and the two tasks was significant in terms of total error, F(2, 56) = 3. 86; _P < .0278. When the C-Rule was the second task, the presence of the visual cues greatly reduces error (i.e., -5.76). When the I-Rule is ^second, the facilitation is minimal (i.e., -.08). The pointing response was also more effective for the more difficult task (i.e., -5.73) than it was for the easy one (i.e. , -2. 00), but this interaction effect was not significant, _F(1, 56) = 3.43; P < .0728. A l l other remaining effects are found nonsignificant. Analysis of performance on the last (Complex-Rule) task The mean numbers of total errors which were made within the first 20 minutes, and ratio of errors are shown in Table III. Insert Table III about here The results of the univariate analysis of the total errors and ratio of errors, as shown in Appendix D, indicate that the main effect of train-ing the Ss to use the pointing response during the acquisition trials (i.e., 2. 09 and . 29) is significant, F ( l , 56) = 7.43 and 15.57; P < . 0086 and < .0003, respectively. This means that Sis perform with fewer errors on the test criterion, in particular, when they have not been trained to make the pointing responses while performing on the previous two tasks. In terms of the total error the main effect of grade (i.e. , -4.05) was highly significant as would be expected F ( l , 56) = 32.73; P < . 0001. 20 No other results are significant, but it is noteworthy that the effect of the two-way interaction between grade and the presence or absence of combined visual cues on the training tasks approaches sig-nificance, F(2, 56) = 2. 13 and 2. 00; P < . 1284 and < . 1453. Grade 4 children and the presence of the combined visual cues on the training tasks make for more errors on this transfer task (i.e., 1.33), while Grades 5 and 6 children so trained, perform better on the transfer task (i.e., -1.34). Other interactions approaching significance are: combined visual cues, grade, and task for ratio of errors, F(2. 56) = . 0854; P •< . 0854, in favour of Grade 4's making more equal errors on test and numerical instances when they had had the combined visual cues and the C-Rule first, two-way interaction between visual cue vs. verbal-only and task for total error, F ( l , 56) = 2.58;;P < .1136 in the direction of more errors for verbal-only when the C-Rule has been first, and two-way interaction between combined visual cues and task, F(2, 56) = 2.20; P < .1199, in the direction of more error when the I-Rule was first and the combined cues were absent. 21 DISCUSSION The pointing response as defined in the present study-independently facilitated the acquisition of the first task, as predicted. This means that the hypothesized role of the attention-inducing activity in the encoding process is confirmed. However, the predicted inter-action between the pointing response and the combined visual cues did not occur, which means the disconfirmation of the other hypothesized extended role of this activity. Presumably, it could be sufficient to draw the Ss attention by pointing to any one of the pictorial representa-tions of the concrete referents in order to decrease the number of errors made by S prior to the discovery of the first rule. Any image-evoking value the visual cues might have, was present, whether or not the pictorial representation was complete. This could mean the potential the visual cues have for bringing the event closer to the con-crete referents is unimportant for reducing errors or, more likely, that in this case the degree of difference between the presence of both cues and the presence of either cue alone was not great enough to cause a significant difference in the number of errors made. On the second task the Grade 5 and 6 children continued to benefit from the intervening activity; however, the Grade 4 children did not. It could be that the Grade 4 children did not realize the sig-nificance of the pointing activity to the same extent that the older students did. The experience that Ss gained from their exposure to the 22 visual cues on the first task may also have resulted in better use of those cues. On the second task the combined context and weight cue was functional independently of the other factors. On the Complex-Rule task, contrary to the prediction, those Ss that had been trained to make that pointing response made more er r o r s than the other J!s with no training received. This failure of the pointing response to assist in the transfer to the third task could be attributable to the conditions under which Ss had to perform, the absence of the visual cues and the previously-learnt pointing activity that they were used to. More specifically, a question arises as to why the performance of those Ss so trained shows a significant increase in error (error on the test instances, in particular) when contrasted with the performance of those Ss not so trained (see Figure 2). This training Insert Figure 2 about here must have interfered with performance. The degree of learning attained on the first two tasks may have been insufficient for these groups, or the lack of the usual motor response to the numerical stimuli may have interfered with their performance. It is more likely that the interference could be accounted for by the change in strategy necessary for those Ss. Previously, they had been forced to incorporate the stimulus numbers into the pictorial representation of the weighing situation before making the written response. On the third task, it was necessary for them to go directly from the stimulus numbers to 23 the written response. In other words, the solution became an abstract one. This change from the concrete to the abstract could account for the interference. These results seem to support the notion (Reese, 1970) that children of these ages can profit from imagery representations when acquiring a rule but that imagery may not effectively be aroused if their attention is not drawn (i.e., by pointing) to the visual cues in such a way that they become functional. But if this initial benefit becomes a deterrent to performance on subsequent tasks, its introduc-tion would be disadvantageous to overall learning. The evidence for this conclusion; is inconclusive in the present study. It should be pos-sible to train Ss on a number of tasks involving similar rules before, switching them to the learning of a new rule. The degree of learning on the simpler rules would then become greater and the effect of this upon the acquisition of a complex rule would be clarified. An aspect of the effect of the change from concrete to abstract solution that could also be investigated is the possibility of taking the situation one step further. In the present study, the progres-sion has been from the concrete weighing situation to numerical reasoning involving an abstract rule. The Ss who used abstract reasoning on the simpler rules made fewer errors on the complex one. A more important practical outcome to be considered would be the effect of the type of training given for the acquisition of the simpler rules upon the application of that rule to a concrete situation. If this 24 additional activity should favour pointing as an intervening activity, the advantages of an attention-inducing response to visual cues would be indicated. Further thought could also be given to the creation of an attention-inducing activity which does not involve a motor response. It is noteworthy that in this particular study, the criterion for marking the correctness of Ss 1 responses was binery, that is, either correct or incorrect. This means that some of true omission responses might have been recorded as incorrect ;l'Iri;this connection, it would be interesting to use a different criterion with three alternatives (i.e.,' correct, incorrect, or omission) than the one used in a future study in an attempt not to force Ss to make any response or guess. The sample of Ss in the present study differs somewhat from the sample in the Lee (1971) study. In that study there was no attempt to screen off the most knowledgeable Ss, so that his Ss were the top two-thirds of the Grade 4 children in the school. The school from which his Ss were drawn was in a higher socio-economic area. But if the three treatment conditions in this study which involve pointing (context, weight, or both) and the verbal task, are analyzed in a 2 x 2 factorial design, the combination of weight and context cues are significant on the 1st task as in Lee (1971). On the second task these effects continue, so that for all the treatment groups which received visual cues, the combination of weight and context cues show statistidal'ly significant effect in reducing errors. These findings appear to support the suggestion by Lee (1971) that the effects of the 25 visual cues on the acquisition of simple linear function rules vary, depending upon the extent of S's experience in utilizing such rules. T A B L E I T H E OBSERVED MEAN NUMBERS OF T O T A L ERRORS AND MEAN RATIOS OF ERRORS BY GRADE, T R E A T M E N T COMBINATION, AND TASK GIVEN AS THE FIRST TASK (N = 84) Pointing Response Visual Cues Presence Absence context(c) weight(w) c w context(c) weight(w) c & w verbal only Grade 4 C-Rule Total E r r o r Ratio of E r r o r s 13. 67 1. 72 12. 33 1. 26 6.67 .82 12. 00 1. 31 20. 67 1.12 11. 00 1. 78 24. 00 1. 16 I-Rule Total E r r o r Ratio of E r r o r s 5. 67 55. 83 1. 67 2. 67 2. 00 1. 28 9. 33 6. 75 7. 33 6. 11 8. 67 7.44 11.67 9. 00 Grade 5 and 6 C-Rule Total E r r o r Ratio of E r r o r s 15. 33 .91 10. 67 2. 21 5. 00 1.42 13. 33 1. 74 88. 33 1. 04 9.67 1. 22 10. 33 . 50 I-Rule Total E r r o r Ratio of E r r o r s 4. 67 3. 67 . 00 1.00 2. 00 1.67 4. 33 2. 93 2. 00 3. 00 7. 67 6. 83 9. 00 10. 00 Mean Square E r r o r (Total E r r o r ) = 33.55 Mean Square E r r o r (Ratio of E r r o r s = 14. 59 The error correlation coefficient between pretest achievement score and the ratio of errors = . 396 P ( . 002 The error correlation coefficient between pretest achievement score and the raterrors on test instances = = .272 P < . 04 T A B L E II ' T H E O B S E R V E D M E A N N U M B E R S O F T O T A L E R R O R S A N D M E A N R A T I O S O F E R R O R S B Y G R A D E , T R E A T M E N T C O M B I N A T I O N , A N D T A S K G I V E N AS T H E S E C O N D T A S K (N = 84) Pointing Response V i s u a l Cues Pre sence Absence context( c) weight( w) c &: w context( c) weight( w) c w verbal only Grade 4 C - R u l e Total E r r o r 10.67 Ration of E r r o r s .44 5. 33 . 72 3. 33 1.67 11. 00 . 32 5. 00 . 80 1.0 . 75 9. 00 1. 19 I-Rule Total E r r o r Ratio of E r r o r s 2. 67 1. 33 3.67 4. 0 3. 67 4.67 1. 33 2. 33 . 0 1.0 1.0 2. 0 2. 33 2. 08 Grade 5 and 6 Total E r r o r C - R u l e Ratio of E r r o r s 4. 00 1.42 3. 00 1.11 33 83 7. 33 1. 14 15. 00 1. 68 3. 00 .83 7. 33 1. 18 I-Rule Total E r r o r Ratio of E r r o r s 1. 33 2. 33 3. 0 4. 0 . 33 1. 33 . 33 1. 33 3. 00 2. 22 2. 33 2. 22 2. 1. 00 00 Mean Square E r r o r (Total E r r o r ) = 18.64 Mean Square E r r o r (Ratio of E r r o r s ) = 3.51 T A B L E III T H E O B S E R V E D M E A N N U M B E R S O F T O T A L E R R O R S A N D M E A N RATIOS O F E R R O R S BY G R A D E , T R E A T M E N T C O M B I N A T I O N , A N D T A S K G I V E N AS T H E THIRD ( C O M P L E X - R U L E ) T A S K (N = 84) Pointing Response V i s u a l Cues Pre sence Absence (context( c) weight(w) c &: w context(c) weight(w) c &t w verbal only Grade 4 C - R u l e Total E r r o r Ratio of E r r o r s 9.67 . 74 11. 33 . 82 11. 00 . 86 4. 33 .79 6.67 .41 11. 33 . 82 11. 00 . 56 I-Rule Total E r r o r Ratio of E r r o r s 11. 00 .44 10. 33 .97 10. 00 . 72 8. 67 . 74 8. 00 .48 -8. 00 .48 8. 67 . 74 Grade 5 and 6 C - R u l e Total E r r o r Ratio of E r r o r s 6. 0 . 57 5.67 1. 18 5. 33 . 83 6. 00 . 26 3. 67 . 75 5. 00 .39 8. 33 .89 I-Rule Total E r r o r Ratio of E r r o r s 9. 33 1.13 5. 33 .87 3. 00 . 65 4. 00 .42 5. 00 . 54 3. 33 . 72 4. 33 . 83 Mean Square E r r o r (Total E r r o r ) = 10.51 Mean Square E r r o r (Ratio of E r r o r s ) = . 09 CO oo 10 9 8 4 u o u W O 3 4 3 -2 -L e g e n d : C - R u l e I - R u l e x X V i s u a l C u e s V e r b a l O n l y -F i g u r e 1. E s t i m a t e d E f f e c t s o f t h e I n t e r a c t i o n o n t h e F i r s t T a s k B e t w e e n V i s u a l C u e s v s . V e r b a l - o n l y T r e a t m e n t C o n d i t i o n s a n d T y p e o f T a s k ( C - R u l e o r I - R u l e ) o n 1 i n T e r m s o f t h e R a t i o o f E r r o r s ro 00 30 25 ft! 20 1 2 a 1 5 -o H G 2 10 -5 -1 F i r s t Task Second Task 1 Third Task 15 -10. o -5 a G a 2 Legend; Pointing *-Not Pointing Verbal-only A-Pointing Not Pointing • M V T i m e -A x>Erro H Verbal-onlyA A Figure Z. Changes in Estimated Effects of Pointing vs. Not-Pointing Responses over the Three Tasks in Terms of the Total Time Spent and the Number of Total E r r o r 30 BIBLIOGRAPHY Arbuckle, T.Y. Mediation instruction in P-A learning. Journal of Experimental Psychology, 1971, 88, 396-401. Davidson, R.E. Mediation and avility in paired-associate learning. Journal of Educational Psychology, 1964, 55, 35Z-356. Dilley, M. G. , and Paivio, A. Pictures and words as stimulus and response items in paired-associate learning of young children. Journal of Experimental Child Psychology, 1968, _6, 231-240. Lee, Seong-Soo. The effects of visually represented cues on learning of linear function rules. Journal of Experimental Child Psychology, 1971, 12, 129§145. Milgram, N. A. Verbal context versus visual compound in paired-associate learning by children. Journal of Experimental Child Psychology, 1967, _5, 597-603. Paivio, A. Imagery and Verbal Processes. New York: Holt, Rinehart, and Winston, Inc., 1971. Paivio, A., and Yarmey, A.D. Pictures versus words as stimuli and responses in paired-associate learning. Psychonomic Science, 1966, 5, 235-236. Palermo, D.S. Imagery in children's learning: Discussion. Psychological Bulletin, 1970, 73, 415-421. Reed, H.B., and Dick, R.D. The learning generalization of abstract and concrete concepts. Journal of Verbal Learning and Verbal Behaviour, 1968, 7, 486-490. 31 Reese, H. W. Imagery and contextual meaning. Psychological  Bulletin, 1970, _73_, 404-414. Rohwer, W.D. Jr. Constraint, Syntax, and meaning in paired-associate learning. Journal of Verbal Learning and Verbal  Behaviour, 1966, 5, 541-547. Rohwer, W.D. Jr. Children and adolescents: Should we teach them or let them learn? Wittrock, M.C. (Ed.). Changing  Education: Alternatives from Educational Research, Englewood Cliffs, N.J., Prentice-Hall, Inc., 1973. Rohwer, W.D. Jr. Elaboration and learning in childhood and adoles-cence. H. W. Reese (Ed.). Advances in Child Development  and Behavior. New York: Academic Press, in press. Rohwer, W.D. Jr., Lynch, S. , Levin, J.R., and Suzuki, N. Pictorial and verbal factors in the efficient learning of paired associates. Journal of Educational Psychology, 1967, 58, 278-284. 32 A P P E N D I X A INSTRUCTIONS G I V E N T O S U B J E C T S DURING T H E L E A R N I N G P H A S E O F T H E E X P E R I M E N T There are cards on your left hand side. If you look at the first card, it wil l tell you the case, "When I put 1 of this kind of weight on the balance pan, then the indicator points to 1 gram on the scale. " (Point to (Look at) the balance pan in the picture - point to the scale. ) I wil l be asking you to write this case on the chalkboard using the necessary numbers, signs, or letters f rom the ones supplied here. Say the sentence with me (and point to (look at) the part on the picture when it is mentioned). "When I put 1 weight on the balance pan (point), then the indicator points to 1 gram on the scale" (point). (Say twice in unison), How many weights are there? (1) What size is it? (1) (Point at (look at) the weight in this picture. ) Now, first f i l l in the empty box on the left of the equals sign with the number of weights I put on the balance pan, and f i l l in the right box with the number of grams the indicator points to. That's right, the number of weights is 1, and the number of grams is also 1. F i l l in the remaining box with the size of weight used and f i l l in the c irc le with the 4- or X sign. Be sure both sides are equal. Many answers may be possible but only one is correct . If your answer is the correct one, the white light will go on - like this - and if your answer 33 is not the one I want, the red light wil l go on - like this. Immediately after you get either light, please place the numbers and signs you used back in their original positions. When the light goes off, turn the first c a r d over and do the same thing with the next card. We are going to continue this until you can get al l the answers correct . StouswillifeelattjO-wed only a short time for each answer. If you take longer, I wil l put on the red light and you should go on to the next problem. Sometimes there wil l be letters on the cards . These take the plaee of numbers and should be treated in the same way as the numbers. Now, for the rest of these cards - say the sentence, (point to (look at) the picture) and write down the results . F o r the I-Rule the following sentence was said, "When I add 2 grams more to one of the weights, the indicator points to 4 grams on the scale. " The S said the sentence and, as before, pointed to or looked at the visual mater ia l . 34 APPENDIX B UNIVARIATE ANALYSIS OF VARIANCE OF T H E NUMBER OF T O T A L ERRORS AND T H E RATIO OF CRITERION TEST ERRORS TO NUMERICAL ERRORS MADE ON T H E FIRST TASK (N = 84) Criterion Measure Number of Total E r r o r Ratio of Two Kinds of E r r o r Source of Variation d.f. Mean Square F P< Mean Square F P< Grand Mean 1 6642.95 198.02 .0001 799.66 54.80 .0001 Grade 4 vs. (5 and 6) (G) 1 210.58 6. 28 .0152 10. 92 . 75 . 3906 Visual Cue vs. Verbal-only(Q 1 330.29 9. 84 . 0028 60.45 4. 14 . 0466 Pointing vs. No Pointing (P )1 150.22 35. 52 . 0388 35. 52 2.43 .1244 Visual Cues (V) 2 62. 54 1.86 . 1645 4. 00 . 27 . 76 P x V q 2 45. 26 1. 35 . 2678 12. 98 .89 .4165 C-Rule vs. I-Rule (T) 1 1008.11 30. 05 . 0001 267.83 18.35 .0001 G x C 1 87. 50 2. 61 . 1120 2. 78 . 19 . 6642 G x P 1 46. 72 1. 39 . 2430 3. 16 . 22 .6434 G x V 2 38. 37 1. 14 . 3259 3. 62 . 25 . 7813 G x P x V 2 12. 96 .39 . 5367 10. 39 . 71 . 4024 C x T 1 . 03 . 00 .9756 91. 11 6. 24 . 0155 P x T 1 18.00 . 54 .4670 36.49 2. 50 .1194 V x T 2 80. 68 2.40 . 0996 4. 14 . 28 . 7538 P x V x T 2 2. 79 .08 . 9203 11. 24 . 77 .4677 G x C x T 1 77. 79 2. 32 . 1335 8. 23 . 56 .4559 G x P x T 1 . 50 .01 .9033 1. 23 . 08 . 7726 G x V x T 1 25. 12 . 75 .4776 3. 59 . 25 . 7826 G x P x V x T 2 11. 79 .35 . 7052 .98 . 07 . 9354 E r r o r s 56 33. 55 14. 59 35 APPENDIX C UNIVARIATE ANALYSIS OF VARIANCE OF T H E NUMBER OF T O T A L ERRORS AND T H E RATIO OF CRITERION TEST ERRORS TO NUMERICAL ERRORS MADE ON THE SECOND TASK (N =84) Criterion Measure Number of Total E r r o r Ratio of Two Kinds of E r r o r Source of Variation d. f. Mean Square F P< Mean Square F P< Grand Mean 1 1328.05 71. 24 . 0001 236.03 67. 20 . 0001 Grade 4 vs. (5 and 6)(G) 1 8. 05 .43 . 5139 . 01 . 00 . 9552 Visual Cue vs. Verbal-only (C) 1 12. 38 . 66 .4186 . 06 . 02 . 8948 Pointing vs. No PointingCP) 1 10. 12 .54 .4643 6. 51 1.85 . 1790 Visual Cues(V) 2 68. 10 3.65 . 0323 2.41 .69 . 5071 P x V 2 7. 29 .39 . 6782 1. 32 . 38 . 6881 C-Rule vs. I-Rule (T) 1 377.19 20. 23 . 0001 37. 82 10. 77 . 0018 G x C 1 2. 72 .15 . 7042 . 02 . 01 . 9400 G x P 1 105. 12 5. 64 . 0211 2. 03 . 58 .4505 G x V 2 48. 51 2. 60 . 0831 4. 56 1. 30 . 2814 G x P x V 2 15. 04 .81 .4514 4. 16 1. 18 . 3137 G x T 1 .43 . 02 . 8801 1.95 . 56 .4592 C x T 1 17. 91 .96 . 3313 . 80 . 23 . 6351 P x T 1 62. 35 3.43 . 0728 4. 34 1. 24 . 2707 V x T 2 71. 26 3. 82 . 0278 . 85 . 24 . 7869 P x V x T 2 19. 85 1. 06 . 3518 3. 53 1. 01 . 3721 G x C x T 1 . 00 .00 .9919 . 26 . 08 . 7853 G x P x T 1 17. 01 .91 . 3436 . 29 . 08 . 7744 G x V x T 1 17. 35 .93 . 4004 . 54 . 15 . 8580 G x P x V x T 2 6. 93 .37 .6913 1. 90 . 54 . 5856 E r r o r s 56 18.64 3. 51 36 APPENDIX D UNIVARIATE ANALYSIS OF VARIANCE OF T H E NUMBER OF T O T A L ERRORS AND T H E RATIO OF CRITERION TEST ERRORS TO NUMERICAL ERRORS MADE ON T H E C O M P L E X - R U L E TASK (N = 84) Criterion Measure Number of Total E r r o r Ratio of Two Kinds of E r r o r Source of Variation d.f. Mean Square F P K. Mean Square F P< Grand Mean 1 4429.75 421.41 . 0001 42. 92 458.78 . 0001 Grade 4 vs. (5 and 6)(G) 1 344.05 32. 73 . 0001 . 00 . 00 .9740 Visual Cue vs Verbal-only (C) 1 9.45 .90 . 3473 . 02 : .25 . 6165 Pointing vs. No PointingCP) 1 78. 12 7.43 . 0086 1.46 15. 57 . 0003 Visual Cues (V) 2 1. 50 . 14 . 8674 . 03 . 37 . 6952 P x V 2 13. 17 1. 25 . 2937 .09 1.01 . 3702 C-Rule vs. I-Rule (T) 1 3. 05 .29 . 5925 . 01 . 09 . 7588 G x C 1 1. 05 . 10 . 7532 . 15 1. 62 . 2083 G x P 1 7. 35 . 70 .4067 . 10 1. 12 . 2940 G x V 2 22.39 2!. 13 . 1284 . 19 2. 00 . 1453 G x P x V 2 . 39 . 04 . 9638 . 13 1. 38 . 2612 G x T 1 1. 7j> .. 16 . 6900 .01 . 10 . 7503 C x T 1 27. 16 2. 58 .1136 . 00 . 06 .8127 P x T 1 . 12 . 01 .9136 . 01 . 08 . 7847 V x T 2 23. 17 2. 20 .1199 .15 1. 61 . 2090 P x V x T 2 6. 17 .59 . 5596 . 07 . 80 .4539 G x C x T 1 1. 05 . 10 . 7532 . 06 . 70 .4076 G x P x T 1 3. 12 . 30 . 5878 . 06 . 59 .4446 G x V x T 1 3. 72 . 35 . 7034 . 24 2. 57 . 0854 G x P x V x T 2 13. 17 1. 25 . 2937 .09 .92 .4039 E r r o r s 56 10.51 .09 

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