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Performance characteristics of retarded and normal students on pattern recognition tasks
CONTEMPORARY
EDUCATIONAL
PSYCHOLOGY
2, 209-218
Performance Characteristics Normal Students on Pattern LES STERNBERG, MICHAEL Norrhern
(1977)
of Retarded and Recognition Tasks
H. EPSTEIN, AND DAN ADAMS Illinois
Universir?:
The purpose was to compare the performance of normal and educable mentally retarded children on pattern recognition tasks. Pattern recognition was assessed by the administration of 96 pattern tasks which measured the ability of children to find: (a) duplicate patterns and same elements as presented in model pattern sequences: (b) opposite patterns and same elements as presented in model pattern sequences; and (c) duplicate patterns but different elements than presented in model pattern sequences. The normal and mentally retarded children were matched on mental age derived from individual and group intelligence tests. Results indicated significant differences in performance measures between groups and various pattern tasks. The data support the suppositions that: (a) mentally retarded children and normal children show the same type of progression through the hierarchical arrangement of pattern tasks; and (b) mentally retarded children show a slower progression through the hierarchy than normal children when matched on mental age. Educational implications from this study are discussed.
The ability to recognize topological patterns is thought to play a crucial role in many cognitive functions (Patterson, 1953; Pinnter, Dragositz, & Kushner, 1944; Raven, 1956; Thurstone, 1938). Recently, pattern recognition has been related to the more specific conceptual areas of mathematics and language (Glennon & Alderman, Note 1; Sternberg, 1975a, b) as well as diagnostic and instructional procedures (Sternberg, 1975a,b). Extensive research has been conducted concerning the ability of children to copy and reverse specified orders of topological objects (i.e., colors and shapes). The results of observation and research (Copeland, 1970; Flavell, 1963; Piaget & Inhelder, 19.56)indicate that normal children can duplicate an order of objects between the ages of 4 and 5 (preoperational stage) and can display reversals between the ages of 6 and 7 (readiness level for the concrete operational period). Additional research has been conducted on the development of pattern recognition ability. Recognition of patterns (an order that has been repeated) as a developmental phenomenon has been investigated by Cromie (1971), McKillip (1970), and Sternberg and Larson (1976). Data from these investigations indicate a developmental hierarchy for normal children in their ability to recognize patterns. Cognitive growth in mentally retarded and normal children has been a topic of continuous research. A number of researchers have compared performance measures of retarded and normal children on various conAddress reprint requests to Les Sternberg, Illinois University, DeKalb, IL 601 IS.
Department
209 Copyright 0 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.
of Special Education,
Northern
210
STERNBERG,
EPSTEIN,
AND
ADAMS
ceptual tasks (Stephens, Note 2; Vitello, 1973; Woodward, 1963). The results indicate that mentally retarded children often display a developmental lag in acquiring certain concepts. The purpose of the present investigation was to answer two research questions related to pattern recognition ability: (a) Do educable mentally retarded children follow the same developmental hierarchy as normals on pattern recognition tasks? (b) Do educable mentally retarded children display acquisition on specific pattern tasks at the same time as do normal children of comparable mental age? METHOD
Subjects Children were selected from second-, third-, and fourth-grade regular education classrooms and primary and intermediate special education classrooms from a large metropolitan city school system in Illinois. Normal children were defined as those whose intelligence quotient fell within 1 SD of the population mean. Group intelligence tests were administered to this sample (SRA/PMA). Educable mentally retarded children were selected on the basis of an intelligence quotient falling below 1 SD below the mean. Individual intelligence tests were administered to this sample (Slosson, WISC, Stanford-Binet Form L-M). Seventy-five children were used in the investigation, 38 normal children and 37 mentally retarded children. Six groups were defined: (a) normal group 1 (N-l); (b) normal group 2 (N-2); (c) normal group 3 (N-3); (d) mentally retarded group 1 (MR-1); (e) mentally retarded group 2 (MR-2); and (f) mentally retarded group 3 (MR-3). These groups were delineated on adjusted mental age scores. Demographic data for the subjects are provided in Table 1. T tests were computed on mental age data to determine the independence of groups and no significant differences were found between the mean mental ages of the N-l and MR-1 groups, the N-2 and MR-2 groups, and the N-3 and MR-3 groups. All other comparisons between groups were significant (p < .05).
TABLE
1
MEANS AND STANDARD DEVIATIONS FOR CA, MA, AND IQ DATA BY GROUP N
CA (years)
MA (years)
IQ
MR-I
15
MR-2
11
MR-3
11
N-l
13
N-2
12
N-3
13
11.00 (SD = 82) 11.43 (SD = .71) 12.49 (SD = S6) 7.32 (SD = .28) 8.33 (SD = .28) 9.45 (SD = .24)
7.43 (SD = 29) 8.49 (SD = .25) 9.48 (SD = .46) 7.74 (SD = .60) 8.61 (SD = S9) 9.19 (SD = .71)
67.80 (SD = 4.60) 74.55 (SD = 4.85) 76.00 (SD = 3.52) 105.77 (SD = 6.91) 103.33 (SD = 6.17) 97.15 (SD = 6.08)
PERFORMANCE
CHARACTERISTICS
211
OF STUDENTS
lnstrumentation The components of pattern recognition were formulated from a model which was used to generate combinations of individual pattern tasks, stimulus dimensions, and patterns. An instrument based upon the model was used to measure pattern recognition ability (Sternberg, 1975b). The instrument was designed to evaluate different kinds of abstractions involved in the conceptualization of patterns. The following definitions, model, and procedure were used in an earlier investigation by the senior author (Stemberg & Larson, 1976). Pattern and pattern sequence. A pattern sequence was defined as two or more distinct elements (referred to as one repetend) repeated at least twice in the same order. A pattern was the abstract representation of the pattern sequence denoted by letters. For example, an ABAB pattern was a pattern sequence that was comprised of two repetends with two elements in each repetend (i.e., a shape pattern of the ABAB type would be; 0 0 q 0).
Stimuhs dimension. By definition, corresponding elements of each repetend were somehow the same (i.e., same color, same name, etc.) so that a pattern was formed. This was accomplished by choosing elements from a specific stimulus dimension. Elements of the same dimension shared a common property. A dimension then was this relevant stimulus property which defined the pattern sequence. An example of a possible dimension would be color. An ABAB pattern within the stimulus dimension of color would be a presentation of colored paper squares in the following order: red, blue, red, blue. Pattern task. A pattern task was a method to assess a child’s ability to recognize a pattern by identifying a pattern sequence that had the same or opposite pattern of a model pattern sequence. For example, using color, a red-blue-red-blue pattern sequence is the same as a green-yellow-green-yellow pattern sequence (both have the ABAB pattern). Model: Task stimulus dimension pattern. Four specific patterns were used in the study: (a) ABAB; (b) ABCABC; (c) AABAAB; and (d) ABBABB. Four stimulus dimensions which defined the pattern sequences were used: color, name, label, and category. A color pattern sequence was comprised of elements differing in color as the cue to the correct pattern sequence. Size and shape were held constant. A name pattern sequence was made up of elements that were different in many dimensions (multidimensionahty) and each repetend was an exact duplicate of the previous repetend. A label pattern involved elements that differed as to a specific attribute among an element-to-element correspondence (i.e., the A element in one repetend and the A element in another) but whose element-to-element name remained the same. A category pattern sequence was comprised of elements that differed as to the category that they represented. Examples of patterns, pattern sequences, and stimulus dimensions are shown in Fig. 1.
PATTERN
STIMULUS DIMENSION
ABAB
Color
ABCABC
SpecificName
c$j-&
AABAAB
Specific Label
,Y<’ ><.
ABBABB
Category
PATTERN SEQUENCE riiqiik~/RED
-$ f3M
cGi?Y+
hfy
/&PC
FIG. 1. Examples of patterns, stimulus dimensions, and pattern sequences.
212
STERNBERG,
EPSTEIN,
AND
ADAMS
Four different types of pattern tasks were employed in the investigation: (a) original learning (O.L.), where the correct choice pattern sequence is a duplicate in sequence and elements to the model pattern sequence; (b) reverse shift (REV), where the correct choice is the opposite pattern sequence to the model pattern sequence; (c) intradimensionai shift (I.D.), where the correct choice pattern sequence is the same pattern as the model but comprised of elements different from but in the same stimulus dimension as the model pattern sequence; and (d) extradimensional shift (E.D.), where the correct choice pattern sequence is the same pattern as the model but comprised of elements that are in a different stimulus dimension than the model pattern sequence. These terms were initially used in research involving discrimination learning transfer (Zeaman & House, 1963). Although this terminology generally refers to learning paradigms, in this study it refers to a description of shift conditions from a model pattern sequence display. Examples of pattern tasks, patterns, and pattern sequences are depicted in Fig. 2. Pattern recognition was assessed by 96 previously constructed tasks (Sternberg, 1975b). Each task was different in that all possible combinations of task, stimulus dimension, and pattern were tested. This was assured by a counterbalanced format in the design of the tasks. Counterbalancing in this case was done by categorically shifting each pattern per task and stimulus dimension. This produced four equivalent sets of 24 tasks each. Each subject was administered only one of the four task sets. Each model pattern sequence was comprised of two repetends representing a pattern defined by differing stimuli within a specific dimension. Each model was presented on an 8% x 1l-in. sheet of paper. Each of the four choice pattern sequences were also comprised of two repetends, one of the pattern sequences representing the same pattern as in the model (original learning, intradimensional shift, or extradimensional shift) or an opposite pattern MODEL
I
RED
pqEqi+
PATTERN TASK
PATTERN
O.L.
ABAB
/REDI/
REV
ABAB
/ BLUE 11 RED 11BLUE 1 RED
I.D. Shift
ABAB
1 GRN / 1 YEL I/ GRN 1
E.D. Shift kdor to label)
ABAB
O.L.
ABBABB
REV
AABAAB
I.D. Shit
ABBABB
E.D. Shift (name to color)
ABBABB
FIG.
PATTERN SEQUENCE
L--
2. Examples of pattern tasks, patterns, and pattern sequences.
PERFORMANCE
CHARACTERISTICS
OF STUDENTS
213
(reverse shift). The other three choices were also made up of the same number of elements as in the model and none represented a correct response if another question had been asked. All of the elements in the correct response were also used in the incorrect choices. They were simply aligned in a different sequence. All four choices were presented, one below the other on an 8% x 1l-in. sheet of paper. The correct pattern sequence was randomly assigned to one of four positions (first to fourth) in the first set of tasks so that an equal number of correct responses would be in each position. These correct positions were duplicated in each of the other three task sets.
Procedure Examiners presented a model pattern sequence on a desk in front of the subject and below this was placed a four-choice identification discrimination pattern sequence problem. Depending upon the question posed by the examiner (“Find the one that is lined up exactly like this one; find the one that is lined up backward to this one; find the one that is lined up most like this one”), the subject was asked to point to one of the choice pattern sequences which would be the correct response. After a response was given, the examiner scored either right or wrong on an evaluation sheet and proceeded to another item. The order of task presentation was identical for all subjects. Ordering was based upon prior research findings which indicated the hierarchy of difftculty of tasks as follows: original learning, reverse shift, intradimensional, and extradimensional (Stemberg & Larson, 1976). Dimensions within each of these pattern tasks were displayed in the following order: color, name, label, and category. Individual testing sessions lasted approximately 20 min.
RESULTS
Data were obtained relating to differential effects of stimulus dimensions, patterns, pattern tasks, and groups. Although the total data were analyzed, only the effects of the last two stated variables are reported. Data were analyzed using a Type I two-factor mixed design (Lindquist, 1956) which involves a two-way analysis of variance with one independent factor (group) and a repeated measure factor (pattern task). The dependent variable for the repeated measure factor was mean percentage correct scores. This dependent measure was used to make all pattern task scores comparable in that there were unequal task items for each pattern task type. Duncan’s Multiple-Range Test (a! level of .OS>was used to analyze simple effects. Table 2 summarizes the data. Significant differences were found to result from the main effect of group [F(5) = 6.399, p < .002] and from the main effect of pattern task [F(3) = 83.127, p < .OOOl]. No significant interaction was found [F(H) = .888, p < .58]. The significant main effect of group resulted from the significant difference in scores between the normal group 3 and mentally retarded group 1. The significant main effect of pattern task was due to the significant differences found between the original learning task and all other tasks, and the reverse shift task and all other tasks. No significant difference was found between the intradimensional and extradimensional shift tasks. Simple Main Effects
In terms of simple main effect of tasks within mentally retarded group 1
O.L. REV I.D. E.D. Mean percentage cross tasks
95.45 52.27 31.82 47.71
56.81
49.44
MR-2
83.33 45.00 36.67 32.76
MR-1
69.50
100.0 72.73 47.73 57.55
MR-3
64.26
90.38 67.31 51.92 47.42
N-l
70.31
95.83 72.92 54.17 58.31
N-2
TABLE 2 MEAN PERCENTAGE CORRECT SCORES OF EACH GROUP PER PATTERN TASK
93.33 64.33 46.33 50.87
98.08 78.85 55.77 65.36 74.51
Mean percentage cross groups
N-3
k
G
z
r;i z z! z m
F
E
s E z
PERFORMANCE
CHARACTERISTICS
OF STUDENTS
215
and normal group 1, it was found that the score of the original learning task was significantly higher than the score of all other tasks. However, for normal group 1, the score for the reverse shift task was significantly greater than the score of the extradimensional shift task. This simple main effect was not observed with mentally retarded group 1. Only for normal group 1 did the difference between the score of the reverse shift task in comparison to the score of the intradimensional shift task approach significance . An analysis of the simple main effect of tasks within mentally retarded group 2 shows basically the same arrangement of significant differences as in mentally retarded group 2 with one addition. The score for the reverse shift task was significantly higher than the score of the I.D. shift task. For normal group 2, the analysis of simple main effects produced the same arrangement of significant differences as was found in mentally retarded group 2. Mentally retarded group 3 and normal group 3 maintained the same arrangement of significant differences as was found in mentally retarded group 2 and normal group 2. There were no significant differences between any of the groups on the original learning task. On the reverse shift task, mentally retarded group 1 performance was significantly lower than all other groups except mentally retarded group 2. This latter group’s reverse shift score was significantly lower than the score of normal group 3. No significant differences were found between groups on the intradimensional shift task. For the extradimensional shift task the score of mentally retarded group 1 was significantly lower than the score of normal group 3, normal group 2, and mentally retarded group 3. DISCUSSION
The results of within-group comparisons provide an answer to the first research question. Mentally retarded group 2 and normal group 2 and mentally retarded group 3 and normal group 3 comparisons support the notion that mentally retarded and normal subjects follow the same developmental hierarchy through different pattern recognition tasks. The mentally retarded group 1 comparison does not violate this hypothesis. Indications are that the significant arrangement of pattern task scores as found in normal group 1 simply occur at a later time with the matched mentally retarded group. This is in support of Woodward’s (1963) study indicating that mentally retarded and normal children progress in a similar fashion on acquisition of cognitive concepts. Results of between-group comparisons provide a response to the second research question. The ability to reproduce a specific topological pattern is not usually displayed until a M.A. of 5 to 6 is attained (Sternberg & Larson, 1976)and since all the children in the study evidenced an M.A. of at least 7.43 years it was not surprising to find no significant differences
216
STERNBERG,
EPSTEIN,
AND
ADAMS
between groups on the original learning task. Since ability to reverse topological patterns is not displayed until the youngster has attained a mental age between 6 and 7 years (Stemberg & Larson, 1976), one would expect no significant differences in performance measures on the reverse shift task. However, this is not the case. The mean percentage correct score of normal group 1 is significantly greater than the mean percentage correct score of mentally retarded group 1 on the reverse shift task. Although there is no significant difference on the reverse shift task performance between normal group 2 and mentally retarded group 2, one can still see a considerable (yet nonsignificant) difference in mean percentage correct scores for these two groups. There appears, therefore, to be a developmental lag for mentally retarded subjects on reverse shift task performance when compared to normal subjects matched on mental age. When a comparison is made between mentally retarded group 3 and normal group 3, the mean percentage correct scores seem to coincide. This is not an unexpected finding in that both groups have attained adjusted mental age scores of at least 9.19 years. Although no significant differences are found between normal group 1 and mentally retarded group 1, normal group 2 and mentally retarded group 2, and normal group 3 and mentally retarded group 3 on the extradimensional shift task, it is of interest to note the mean percentage correct scores of these groups. It seems as if mentally retarded group 2 and normal group 1 performed in a near equivalent manner on the extradimensional shift tasks. Mentally retarded group 3 and normal group 2 also displayed near equivalence. Both mentally retarded groups have significantly higher mental ages than the comparable normal groups. Again, these comparisons support the hypothesis of a developmental lag for mentally retarded children on pattern recognition task performance when compared to normal children matched on mental age. The results suggest that mentally retarded and normal children follow the same developmental hierarchy on pattern recognition tasks. However, mentally retarded children show slower development through this hierarchy than normal children matched on mental age. This supports the research findings of Woodward (1963), Vitello (1973), and Stephens (Note 2) concerning retardate-normal comparisons on acquisition of other conceptual tasks. Although one might conclude from this study that the results merely indicate once again that mentally retarded individuals are mentally retarded, other important finding must be realized. A critical deficiency remains in conclusions reached by prior research concerning mentally retarded-normal comparisons. To posit a developmental lag of mentally retarded children in concept development does not necessarily lead to any useful ameliorative implications. Wechsler (1972) states that mental age is
PERFORMANCE
CHARACTERISTICS
OF STUDENTS
217
a poor determinant of attained cognitive stage. It is the hypothesis of the present investigators that mentally retarded children display specific behavioral cognitive competencies later than normal children. It is further suggested that mentally retarded children will asymptote at lower behavioral cognitive competency levels than normal children. It is hoped that these factors would lead future researchers focusing on retardatenormal comparisons to use behavioral attainment rather than mental age attainment or other norm-referenced measures for appropriate matching purposes and to use these behaviors diagnostically for predictions of possible subsequent cognitive accomplishments. The findings from this study have direct implications to education of exceptional children, in general, and to mentally retarded children, in particular. Although developed to provide an assessment of a child’s ability, the diagnostic tests traditionally given to exceptional children present global data rather than specific or functional information regarding a child’s cognitive or academic behavior. The problems inherent with these tests have been fully discussed elsewhere (Haring & Ridgway, 1967; Keogh, 1971, 1972; Sternberg & Larson, 1976; Ysseldyke, 1973) and one clear message emerges: the need to identify viable alternative forms of assessment. One alternative is to use instruments which measure specific cognitive styles and which are behavior-referenced, rather than normreferenced. The instrument used in the present study presents cognitive tasks that are behaviorally stated and sequential in development, and that indicate a child’s level of cognitive functioning. A child’s performance on these tasks could conceivably provide a diagnostic statement that could be used to program remediation activities. Thus, future research with specific cognitive tasks needs to verify the relationship between task performance and prescriptive utility. REFERENCES COPELAND, R. W. How children learn mathematics. New York: Macmillan, 1970. CROMIE, R. Ci. The ontogeny of linear patterns among young normal children in an econom-
area. Unpublished doctoral dissertation, University of Connecticut, 1971. FLAVELL, J. The developmental psycho1og.y of Jean Piaget. New York: Van Nostrand Reinhold, 1963. HARING, N., & RIDGWAY, R. Early identification of children with learning disabilities. ically disadvantaged
Exceptional
Children,
1967, 33, 387-395.
B. K. A compensatory model for psychoeducational evaluation of children with learning disorders. Journal of Learning Disabilities, 1971, 4, 544-548. KEOGH, B. K. Psychological evaluation of exceptional children: Old hang-ups and new directions. Journal of School Psychology, 1972, 10, 141-145. LINDQUIST, E. Design and analysis of experiments in psychology und education. Boston: Houghton-Mifflin, 1956. MCKILLIP, W. D. Developing and evaluating putterns. Atlanta: University of Georgia. 1970. KEOGH,
218
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EPSTEIN,
AND
ADAMS
PATTERSON, C. H. The Wechsler-Be/hue
scales: A guide for counselors. Springfield, IL: Charles C Thomas, 1953. PIAGET, J., & INHELDER, B. The chi/d’s conception of space. London: Routledge and Kegan Paul, 1956. PINTNER, R., DRAGOSITZ, A., & KUSHNER, R. Supplementary guide for the revised Stanford-Binet scale. Stanford, CA: Stanford University Press, 1944. RAVEN, J. Coloured progressive matrices. London: L. K. Lewis, 1956. STERNBERG, L., & LARSON, P. The development of pattern recognition ability in children. Contemporary Educational Psychology, 1976, 1, 146-156. STERNBERG, L. Pattern recognition training: A key to mathematics and language skill development. Teaching Exceptional Children, Winter, 1975(a). STERNBERG, L. PRSZ: Pattern recognition skills inventory. Northbrook, IL: Hubbard Scientific Company, 1975(b). THURSTONE, L. L. Primary mental abilities. Chicago: University of Chicago Press, 1938. VITELLO, S. Facilitation of class inclusion among mentally retarded children. American Journal of Mental Dejiciency, 1973, 78, l%-162. WECHSLER, D. Wechsler InteUigence Scale for Children. New York: The Psychological Corp., 1972. WOODWARD, M. The application of Piaget’s theory to research in mental deficiency. In N.R. Ellis (Ed.), Handbook of mental deficiency. New York: McGraw-Hill, 1963. YSSELDYKE, J. Diagnostic-prescriptive teaching: The search for aptitude treatment interactions. In L. Mann & D. Sabatino (Eds.), Thejirst review ofspecial education. Philadelphia: Buttonwood Farms, 1973. Pp. 5-32. ZEAMAN, D., & HOUSE, B. The role of attention in retardate discrimination learning. In N.R. Ellis (Ed.), Handbook of mental deficiency. New York: McGraw-Hill, 1963. Pp. 159223.
REFERENCE
NOTES
1. GLENNON, V. J., & ALDERMAN, D. The ontogeny of linear tesselations in one variable among young children. Storm, CT: University of Connecticut, 1970. (Mimeographed) 2. SrEPna~s, W. A Piagetian approach to arithmetic for the mentally retarded. Paper presented at the International Meeting of the Council for Exceptional Children, Miami, April 1971.
EDUCATIONAL
PSYCHOLOGY
2, 209-218
Performance Characteristics Normal Students on Pattern LES STERNBERG, MICHAEL Norrhern
(1977)
of Retarded and Recognition Tasks
H. EPSTEIN, AND DAN ADAMS Illinois
Universir?:
The purpose was to compare the performance of normal and educable mentally retarded children on pattern recognition tasks. Pattern recognition was assessed by the administration of 96 pattern tasks which measured the ability of children to find: (a) duplicate patterns and same elements as presented in model pattern sequences: (b) opposite patterns and same elements as presented in model pattern sequences; and (c) duplicate patterns but different elements than presented in model pattern sequences. The normal and mentally retarded children were matched on mental age derived from individual and group intelligence tests. Results indicated significant differences in performance measures between groups and various pattern tasks. The data support the suppositions that: (a) mentally retarded children and normal children show the same type of progression through the hierarchical arrangement of pattern tasks; and (b) mentally retarded children show a slower progression through the hierarchy than normal children when matched on mental age. Educational implications from this study are discussed.
The ability to recognize topological patterns is thought to play a crucial role in many cognitive functions (Patterson, 1953; Pinnter, Dragositz, & Kushner, 1944; Raven, 1956; Thurstone, 1938). Recently, pattern recognition has been related to the more specific conceptual areas of mathematics and language (Glennon & Alderman, Note 1; Sternberg, 1975a, b) as well as diagnostic and instructional procedures (Sternberg, 1975a,b). Extensive research has been conducted concerning the ability of children to copy and reverse specified orders of topological objects (i.e., colors and shapes). The results of observation and research (Copeland, 1970; Flavell, 1963; Piaget & Inhelder, 19.56)indicate that normal children can duplicate an order of objects between the ages of 4 and 5 (preoperational stage) and can display reversals between the ages of 6 and 7 (readiness level for the concrete operational period). Additional research has been conducted on the development of pattern recognition ability. Recognition of patterns (an order that has been repeated) as a developmental phenomenon has been investigated by Cromie (1971), McKillip (1970), and Sternberg and Larson (1976). Data from these investigations indicate a developmental hierarchy for normal children in their ability to recognize patterns. Cognitive growth in mentally retarded and normal children has been a topic of continuous research. A number of researchers have compared performance measures of retarded and normal children on various conAddress reprint requests to Les Sternberg, Illinois University, DeKalb, IL 601 IS.
Department
209 Copyright 0 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.
of Special Education,
Northern
210
STERNBERG,
EPSTEIN,
AND
ADAMS
ceptual tasks (Stephens, Note 2; Vitello, 1973; Woodward, 1963). The results indicate that mentally retarded children often display a developmental lag in acquiring certain concepts. The purpose of the present investigation was to answer two research questions related to pattern recognition ability: (a) Do educable mentally retarded children follow the same developmental hierarchy as normals on pattern recognition tasks? (b) Do educable mentally retarded children display acquisition on specific pattern tasks at the same time as do normal children of comparable mental age? METHOD
Subjects Children were selected from second-, third-, and fourth-grade regular education classrooms and primary and intermediate special education classrooms from a large metropolitan city school system in Illinois. Normal children were defined as those whose intelligence quotient fell within 1 SD of the population mean. Group intelligence tests were administered to this sample (SRA/PMA). Educable mentally retarded children were selected on the basis of an intelligence quotient falling below 1 SD below the mean. Individual intelligence tests were administered to this sample (Slosson, WISC, Stanford-Binet Form L-M). Seventy-five children were used in the investigation, 38 normal children and 37 mentally retarded children. Six groups were defined: (a) normal group 1 (N-l); (b) normal group 2 (N-2); (c) normal group 3 (N-3); (d) mentally retarded group 1 (MR-1); (e) mentally retarded group 2 (MR-2); and (f) mentally retarded group 3 (MR-3). These groups were delineated on adjusted mental age scores. Demographic data for the subjects are provided in Table 1. T tests were computed on mental age data to determine the independence of groups and no significant differences were found between the mean mental ages of the N-l and MR-1 groups, the N-2 and MR-2 groups, and the N-3 and MR-3 groups. All other comparisons between groups were significant (p < .05).
TABLE
1
MEANS AND STANDARD DEVIATIONS FOR CA, MA, AND IQ DATA BY GROUP N
CA (years)
MA (years)
IQ
MR-I
15
MR-2
11
MR-3
11
N-l
13
N-2
12
N-3
13
11.00 (SD = 82) 11.43 (SD = .71) 12.49 (SD = S6) 7.32 (SD = .28) 8.33 (SD = .28) 9.45 (SD = .24)
7.43 (SD = 29) 8.49 (SD = .25) 9.48 (SD = .46) 7.74 (SD = .60) 8.61 (SD = S9) 9.19 (SD = .71)
67.80 (SD = 4.60) 74.55 (SD = 4.85) 76.00 (SD = 3.52) 105.77 (SD = 6.91) 103.33 (SD = 6.17) 97.15 (SD = 6.08)
PERFORMANCE
CHARACTERISTICS
211
OF STUDENTS
lnstrumentation The components of pattern recognition were formulated from a model which was used to generate combinations of individual pattern tasks, stimulus dimensions, and patterns. An instrument based upon the model was used to measure pattern recognition ability (Sternberg, 1975b). The instrument was designed to evaluate different kinds of abstractions involved in the conceptualization of patterns. The following definitions, model, and procedure were used in an earlier investigation by the senior author (Stemberg & Larson, 1976). Pattern and pattern sequence. A pattern sequence was defined as two or more distinct elements (referred to as one repetend) repeated at least twice in the same order. A pattern was the abstract representation of the pattern sequence denoted by letters. For example, an ABAB pattern was a pattern sequence that was comprised of two repetends with two elements in each repetend (i.e., a shape pattern of the ABAB type would be; 0 0 q 0).
Stimuhs dimension. By definition, corresponding elements of each repetend were somehow the same (i.e., same color, same name, etc.) so that a pattern was formed. This was accomplished by choosing elements from a specific stimulus dimension. Elements of the same dimension shared a common property. A dimension then was this relevant stimulus property which defined the pattern sequence. An example of a possible dimension would be color. An ABAB pattern within the stimulus dimension of color would be a presentation of colored paper squares in the following order: red, blue, red, blue. Pattern task. A pattern task was a method to assess a child’s ability to recognize a pattern by identifying a pattern sequence that had the same or opposite pattern of a model pattern sequence. For example, using color, a red-blue-red-blue pattern sequence is the same as a green-yellow-green-yellow pattern sequence (both have the ABAB pattern). Model: Task stimulus dimension pattern. Four specific patterns were used in the study: (a) ABAB; (b) ABCABC; (c) AABAAB; and (d) ABBABB. Four stimulus dimensions which defined the pattern sequences were used: color, name, label, and category. A color pattern sequence was comprised of elements differing in color as the cue to the correct pattern sequence. Size and shape were held constant. A name pattern sequence was made up of elements that were different in many dimensions (multidimensionahty) and each repetend was an exact duplicate of the previous repetend. A label pattern involved elements that differed as to a specific attribute among an element-to-element correspondence (i.e., the A element in one repetend and the A element in another) but whose element-to-element name remained the same. A category pattern sequence was comprised of elements that differed as to the category that they represented. Examples of patterns, pattern sequences, and stimulus dimensions are shown in Fig. 1.
PATTERN
STIMULUS DIMENSION
ABAB
Color
ABCABC
SpecificName
c$j-&
AABAAB
Specific Label
,Y<’ ><.
ABBABB
Category
PATTERN SEQUENCE riiqiik~/RED
-$ f3M
cGi?Y+
hfy
/&PC
FIG. 1. Examples of patterns, stimulus dimensions, and pattern sequences.
212
STERNBERG,
EPSTEIN,
AND
ADAMS
Four different types of pattern tasks were employed in the investigation: (a) original learning (O.L.), where the correct choice pattern sequence is a duplicate in sequence and elements to the model pattern sequence; (b) reverse shift (REV), where the correct choice is the opposite pattern sequence to the model pattern sequence; (c) intradimensionai shift (I.D.), where the correct choice pattern sequence is the same pattern as the model but comprised of elements different from but in the same stimulus dimension as the model pattern sequence; and (d) extradimensional shift (E.D.), where the correct choice pattern sequence is the same pattern as the model but comprised of elements that are in a different stimulus dimension than the model pattern sequence. These terms were initially used in research involving discrimination learning transfer (Zeaman & House, 1963). Although this terminology generally refers to learning paradigms, in this study it refers to a description of shift conditions from a model pattern sequence display. Examples of pattern tasks, patterns, and pattern sequences are depicted in Fig. 2. Pattern recognition was assessed by 96 previously constructed tasks (Sternberg, 1975b). Each task was different in that all possible combinations of task, stimulus dimension, and pattern were tested. This was assured by a counterbalanced format in the design of the tasks. Counterbalancing in this case was done by categorically shifting each pattern per task and stimulus dimension. This produced four equivalent sets of 24 tasks each. Each subject was administered only one of the four task sets. Each model pattern sequence was comprised of two repetends representing a pattern defined by differing stimuli within a specific dimension. Each model was presented on an 8% x 1l-in. sheet of paper. Each of the four choice pattern sequences were also comprised of two repetends, one of the pattern sequences representing the same pattern as in the model (original learning, intradimensional shift, or extradimensional shift) or an opposite pattern MODEL
I
RED
pqEqi+
PATTERN TASK
PATTERN
O.L.
ABAB
/REDI/
REV
ABAB
/ BLUE 11 RED 11BLUE 1 RED
I.D. Shift
ABAB
1 GRN / 1 YEL I/ GRN 1
E.D. Shift kdor to label)
ABAB
O.L.
ABBABB
REV
AABAAB
I.D. Shit
ABBABB
E.D. Shift (name to color)
ABBABB
FIG.
PATTERN SEQUENCE
L--
2. Examples of pattern tasks, patterns, and pattern sequences.
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(reverse shift). The other three choices were also made up of the same number of elements as in the model and none represented a correct response if another question had been asked. All of the elements in the correct response were also used in the incorrect choices. They were simply aligned in a different sequence. All four choices were presented, one below the other on an 8% x 1l-in. sheet of paper. The correct pattern sequence was randomly assigned to one of four positions (first to fourth) in the first set of tasks so that an equal number of correct responses would be in each position. These correct positions were duplicated in each of the other three task sets.
Procedure Examiners presented a model pattern sequence on a desk in front of the subject and below this was placed a four-choice identification discrimination pattern sequence problem. Depending upon the question posed by the examiner (“Find the one that is lined up exactly like this one; find the one that is lined up backward to this one; find the one that is lined up most like this one”), the subject was asked to point to one of the choice pattern sequences which would be the correct response. After a response was given, the examiner scored either right or wrong on an evaluation sheet and proceeded to another item. The order of task presentation was identical for all subjects. Ordering was based upon prior research findings which indicated the hierarchy of difftculty of tasks as follows: original learning, reverse shift, intradimensional, and extradimensional (Stemberg & Larson, 1976). Dimensions within each of these pattern tasks were displayed in the following order: color, name, label, and category. Individual testing sessions lasted approximately 20 min.
RESULTS
Data were obtained relating to differential effects of stimulus dimensions, patterns, pattern tasks, and groups. Although the total data were analyzed, only the effects of the last two stated variables are reported. Data were analyzed using a Type I two-factor mixed design (Lindquist, 1956) which involves a two-way analysis of variance with one independent factor (group) and a repeated measure factor (pattern task). The dependent variable for the repeated measure factor was mean percentage correct scores. This dependent measure was used to make all pattern task scores comparable in that there were unequal task items for each pattern task type. Duncan’s Multiple-Range Test (a! level of .OS>was used to analyze simple effects. Table 2 summarizes the data. Significant differences were found to result from the main effect of group [F(5) = 6.399, p < .002] and from the main effect of pattern task [F(3) = 83.127, p < .OOOl]. No significant interaction was found [F(H) = .888, p < .58]. The significant main effect of group resulted from the significant difference in scores between the normal group 3 and mentally retarded group 1. The significant main effect of pattern task was due to the significant differences found between the original learning task and all other tasks, and the reverse shift task and all other tasks. No significant difference was found between the intradimensional and extradimensional shift tasks. Simple Main Effects
In terms of simple main effect of tasks within mentally retarded group 1
O.L. REV I.D. E.D. Mean percentage cross tasks
95.45 52.27 31.82 47.71
56.81
49.44
MR-2
83.33 45.00 36.67 32.76
MR-1
69.50
100.0 72.73 47.73 57.55
MR-3
64.26
90.38 67.31 51.92 47.42
N-l
70.31
95.83 72.92 54.17 58.31
N-2
TABLE 2 MEAN PERCENTAGE CORRECT SCORES OF EACH GROUP PER PATTERN TASK
93.33 64.33 46.33 50.87
98.08 78.85 55.77 65.36 74.51
Mean percentage cross groups
N-3
k
G
z
r;i z z! z m
F
E
s E z
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and normal group 1, it was found that the score of the original learning task was significantly higher than the score of all other tasks. However, for normal group 1, the score for the reverse shift task was significantly greater than the score of the extradimensional shift task. This simple main effect was not observed with mentally retarded group 1. Only for normal group 1 did the difference between the score of the reverse shift task in comparison to the score of the intradimensional shift task approach significance . An analysis of the simple main effect of tasks within mentally retarded group 2 shows basically the same arrangement of significant differences as in mentally retarded group 2 with one addition. The score for the reverse shift task was significantly higher than the score of the I.D. shift task. For normal group 2, the analysis of simple main effects produced the same arrangement of significant differences as was found in mentally retarded group 2. Mentally retarded group 3 and normal group 3 maintained the same arrangement of significant differences as was found in mentally retarded group 2 and normal group 2. There were no significant differences between any of the groups on the original learning task. On the reverse shift task, mentally retarded group 1 performance was significantly lower than all other groups except mentally retarded group 2. This latter group’s reverse shift score was significantly lower than the score of normal group 3. No significant differences were found between groups on the intradimensional shift task. For the extradimensional shift task the score of mentally retarded group 1 was significantly lower than the score of normal group 3, normal group 2, and mentally retarded group 3. DISCUSSION
The results of within-group comparisons provide an answer to the first research question. Mentally retarded group 2 and normal group 2 and mentally retarded group 3 and normal group 3 comparisons support the notion that mentally retarded and normal subjects follow the same developmental hierarchy through different pattern recognition tasks. The mentally retarded group 1 comparison does not violate this hypothesis. Indications are that the significant arrangement of pattern task scores as found in normal group 1 simply occur at a later time with the matched mentally retarded group. This is in support of Woodward’s (1963) study indicating that mentally retarded and normal children progress in a similar fashion on acquisition of cognitive concepts. Results of between-group comparisons provide a response to the second research question. The ability to reproduce a specific topological pattern is not usually displayed until a M.A. of 5 to 6 is attained (Sternberg & Larson, 1976)and since all the children in the study evidenced an M.A. of at least 7.43 years it was not surprising to find no significant differences
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between groups on the original learning task. Since ability to reverse topological patterns is not displayed until the youngster has attained a mental age between 6 and 7 years (Stemberg & Larson, 1976), one would expect no significant differences in performance measures on the reverse shift task. However, this is not the case. The mean percentage correct score of normal group 1 is significantly greater than the mean percentage correct score of mentally retarded group 1 on the reverse shift task. Although there is no significant difference on the reverse shift task performance between normal group 2 and mentally retarded group 2, one can still see a considerable (yet nonsignificant) difference in mean percentage correct scores for these two groups. There appears, therefore, to be a developmental lag for mentally retarded subjects on reverse shift task performance when compared to normal subjects matched on mental age. When a comparison is made between mentally retarded group 3 and normal group 3, the mean percentage correct scores seem to coincide. This is not an unexpected finding in that both groups have attained adjusted mental age scores of at least 9.19 years. Although no significant differences are found between normal group 1 and mentally retarded group 1, normal group 2 and mentally retarded group 2, and normal group 3 and mentally retarded group 3 on the extradimensional shift task, it is of interest to note the mean percentage correct scores of these groups. It seems as if mentally retarded group 2 and normal group 1 performed in a near equivalent manner on the extradimensional shift tasks. Mentally retarded group 3 and normal group 2 also displayed near equivalence. Both mentally retarded groups have significantly higher mental ages than the comparable normal groups. Again, these comparisons support the hypothesis of a developmental lag for mentally retarded children on pattern recognition task performance when compared to normal children matched on mental age. The results suggest that mentally retarded and normal children follow the same developmental hierarchy on pattern recognition tasks. However, mentally retarded children show slower development through this hierarchy than normal children matched on mental age. This supports the research findings of Woodward (1963), Vitello (1973), and Stephens (Note 2) concerning retardate-normal comparisons on acquisition of other conceptual tasks. Although one might conclude from this study that the results merely indicate once again that mentally retarded individuals are mentally retarded, other important finding must be realized. A critical deficiency remains in conclusions reached by prior research concerning mentally retarded-normal comparisons. To posit a developmental lag of mentally retarded children in concept development does not necessarily lead to any useful ameliorative implications. Wechsler (1972) states that mental age is
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a poor determinant of attained cognitive stage. It is the hypothesis of the present investigators that mentally retarded children display specific behavioral cognitive competencies later than normal children. It is further suggested that mentally retarded children will asymptote at lower behavioral cognitive competency levels than normal children. It is hoped that these factors would lead future researchers focusing on retardatenormal comparisons to use behavioral attainment rather than mental age attainment or other norm-referenced measures for appropriate matching purposes and to use these behaviors diagnostically for predictions of possible subsequent cognitive accomplishments. The findings from this study have direct implications to education of exceptional children, in general, and to mentally retarded children, in particular. Although developed to provide an assessment of a child’s ability, the diagnostic tests traditionally given to exceptional children present global data rather than specific or functional information regarding a child’s cognitive or academic behavior. The problems inherent with these tests have been fully discussed elsewhere (Haring & Ridgway, 1967; Keogh, 1971, 1972; Sternberg & Larson, 1976; Ysseldyke, 1973) and one clear message emerges: the need to identify viable alternative forms of assessment. One alternative is to use instruments which measure specific cognitive styles and which are behavior-referenced, rather than normreferenced. The instrument used in the present study presents cognitive tasks that are behaviorally stated and sequential in development, and that indicate a child’s level of cognitive functioning. A child’s performance on these tasks could conceivably provide a diagnostic statement that could be used to program remediation activities. Thus, future research with specific cognitive tasks needs to verify the relationship between task performance and prescriptive utility. REFERENCES COPELAND, R. W. How children learn mathematics. New York: Macmillan, 1970. CROMIE, R. Ci. The ontogeny of linear patterns among young normal children in an econom-
area. Unpublished doctoral dissertation, University of Connecticut, 1971. FLAVELL, J. The developmental psycho1og.y of Jean Piaget. New York: Van Nostrand Reinhold, 1963. HARING, N., & RIDGWAY, R. Early identification of children with learning disabilities. ically disadvantaged
Exceptional
Children,
1967, 33, 387-395.
B. K. A compensatory model for psychoeducational evaluation of children with learning disorders. Journal of Learning Disabilities, 1971, 4, 544-548. KEOGH, B. K. Psychological evaluation of exceptional children: Old hang-ups and new directions. Journal of School Psychology, 1972, 10, 141-145. LINDQUIST, E. Design and analysis of experiments in psychology und education. Boston: Houghton-Mifflin, 1956. MCKILLIP, W. D. Developing and evaluating putterns. Atlanta: University of Georgia. 1970. KEOGH,
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PATTERSON, C. H. The Wechsler-Be/hue
scales: A guide for counselors. Springfield, IL: Charles C Thomas, 1953. PIAGET, J., & INHELDER, B. The chi/d’s conception of space. London: Routledge and Kegan Paul, 1956. PINTNER, R., DRAGOSITZ, A., & KUSHNER, R. Supplementary guide for the revised Stanford-Binet scale. Stanford, CA: Stanford University Press, 1944. RAVEN, J. Coloured progressive matrices. London: L. K. Lewis, 1956. STERNBERG, L., & LARSON, P. The development of pattern recognition ability in children. Contemporary Educational Psychology, 1976, 1, 146-156. STERNBERG, L. Pattern recognition training: A key to mathematics and language skill development. Teaching Exceptional Children, Winter, 1975(a). STERNBERG, L. PRSZ: Pattern recognition skills inventory. Northbrook, IL: Hubbard Scientific Company, 1975(b). THURSTONE, L. L. Primary mental abilities. Chicago: University of Chicago Press, 1938. VITELLO, S. Facilitation of class inclusion among mentally retarded children. American Journal of Mental Dejiciency, 1973, 78, l%-162. WECHSLER, D. Wechsler InteUigence Scale for Children. New York: The Psychological Corp., 1972. WOODWARD, M. The application of Piaget’s theory to research in mental deficiency. In N.R. Ellis (Ed.), Handbook of mental deficiency. New York: McGraw-Hill, 1963. YSSELDYKE, J. Diagnostic-prescriptive teaching: The search for aptitude treatment interactions. In L. Mann & D. Sabatino (Eds.), Thejirst review ofspecial education. Philadelphia: Buttonwood Farms, 1973. Pp. 5-32. ZEAMAN, D., & HOUSE, B. The role of attention in retardate discrimination learning. In N.R. Ellis (Ed.), Handbook of mental deficiency. New York: McGraw-Hill, 1963. Pp. 159223.
REFERENCE
NOTES
1. GLENNON, V. J., & ALDERMAN, D. The ontogeny of linear tesselations in one variable among young children. Storm, CT: University of Connecticut, 1970. (Mimeographed) 2. SrEPna~s, W. A Piagetian approach to arithmetic for the mentally retarded. Paper presented at the International Meeting of the Council for Exceptional Children, Miami, April 1971.