DOCUMENT RESUME EC 302 844 ED 368 099 Saccuzzo, Dennis P.; And Others AUTHOR Information-Processing in Gifted versus Nongifted TITLE African-American, Latino, Filipino, and White Children: Speeded versus Nonspeeded Paradigms. 94 PUB DATE R206A00569 CONTRACT 17p.; In: Saccuzzo, Dennis P.; And Others. NOTE Identifying Underrepresented Disadvantaged Gifted and Talented Children: A Multifaceted Approach. (Volumes 1 and 2); see EC 302 840. Information Research/Technical (143) Reports PUB TYPE Analyses (070) MF01/PC01 Plus Postage. EDRS PRICE Ability Identification; Aptitude Tests; *Cognitive DESCRIPTORS Processes; Comparative Analysis; Cultural Differences; Educational Diagnosis; Elementary Education; *Ethnic Groups; Evaluation Methods; Factor Analysis; *Gifted; *Intelligence Tests; Minority Group Children; *Reaction Time; Student Evaluation ABSTRACT Elementary students (N=160, grades 2-3 and 5-6) were evaluated in a battery of four information-processing tasks, including: Inspection Time, Reaction Time, Coincidence Timing, and certified Mental Counters (Working Memory). Half of the children were other half were selected from as gifted in a case study analysis; the non-gifted programs of the same school district. For each of the two main factors (giftedness and grade), equal numbers of participants African-American, Latino, were drawn from four ethnic backgrounds: Filipino, and White. Large differences on all four information-processing tasks appeared as a function of grade and membership in the gifted program. The sole significant relationship involving ethnic background was that gifted African-Americans showed the fastest reaction times and nongifted African-Americans the and slowest. Overall relationships between measures of processing intelligence quotient were modest. (PB) *********************************************************************** Reproductions supplied by EDRS ara the best that can be made from the original document. *********************************************************************** U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) eproduced as r organization received from the person originating it de to improve C Minor changes have been m reproduction Qualify ed in this docu Points of view of opinions sta resent official ment do not necessarily re OERI position or policy CHAPTER 4 African-American, Latino, Filipino, Information-Processing in Gifted Versus Nongifted Paradigms and White Children: Speeded Versus Nonspeeded Nancy E. Johnson, and Tracey L. Guertin Dennis P. Saccuzzo, San Diego State University Discretionary Grant Program, U.S. Funded by Grant #R206A00569, Jacob Javits to Dennis P. Saccuzzo, San Diego Department of Education. Direct requests for reprints San Diego, CA 92120-4913. State University, 6363 Alvarado Court, Suite 103, for providing the battery of tasks and The authors wish to thank Gerald Larson also express their appreciation to the San for valuable input into this study. The authors Education (GATE) Administrator David Diego City Schools, to Gifted and Talented Will Boggess, Marcia Dome, Eva Hermanson, and to the following school psychologists: Sy, and Daniel Williams. Jarosz, Dimaris Michalek, Lorraine Rouse, Ben addressed to Dennis P. Saccuzzo, Correspondence concerning this article should be San Diego Clinical Training Program, 6363 Joint San Diego State/University of California, California 92120-4913 (Telephone: 619-594-2844 / Alvarado Court, Suite 103, San Diego, [email protected]). FAX: 619-594-6780 / e-mail: @ 1994 wr.,: en permission from the authors. Do not reproduce in any form without express k 2 Abstract battery of four One hundred and sixty children were evaluated in a paradigm), information-processing tasks: Inspection Time (backward masking (Working Memory). Reaction Tune, Coincidence Timing, and Mental Counters study analysis; half were Half of the children were certified as gifted in a case district. Within each selected from the nongifted program in the same school in the 2nd-3rd grade, half in the 5th- group (gifted vs. nongifted), half were (giftedness and grade), 6th grade. Finally, for each of the two main factors ethnic backgrounds: there were an equal number of children from four large differences African-American, Latino, Filipino, and White. There were tasks as a function of grade and on all four information-processing interaction occurred membership in the gifted program. Only one significant showed the involving ethnic background, in which giftca African-Americans Regression analysis fastest RT's and nongifted African-Americans the slowest. Inspection Time, revealed that measures of speed of processing, particularly and membership in the gifted program. were the primary correlates of both IQ of processing and Overall, however, the relationship between the measures discussed. IQ were modest. Implications of these findings are 3 104 Filipino, and White Nongifted African-American, Latino, Information-Processing in Gifted vs. Paradigms Children: Speeded vs. Nonspeeded children from diverse backgrounds nontraditional method of selecting A relatively little-used abilities (Grinder, 1985; Sternberg, the analysis of information-processing for gifted programs involves styles subcultures in the U. S. foster different (1986) noted, "If different 1981). As Horowitz and O'Brien identify and it should be possible to of information processing, then of thinking on different strategies of information-processing may population" (p. 1148). Alternately, measures describe these for each of selecting for giftedness. provide an unbiased method of three main approaches identified information-processing as one Wagner and Sternberg (1984) which uses traditional the psychometric approach, intelligence. The other two were to the concept of cognitive based on Piaget's theory of Piagetian approach, which is standardized tests, and the in researchers attempt to analyze responses information-processing approach, development. In the information-processing begins them. For example, processes that underlie terms of the basic component stored or held in a short-term storage or stimulation. This input is then initially with input of external The results of this analysis are analytical processes are performed. working memory system while where new incoming information systems, such as long-term memory, subsequently transferred to other can be made. knowledge so that an appropriate response one's present store of can be compared to problems. able to learn and to solve information processors are better Theoretically, faster or more efficient efficiency with view that the speed or literature have supported the Indeed, reviews of an extensive related to one's processes is highly small number of basic cognitive which an individual can execute a and Raven Wechsler Intelligence Scales of intelligence such as the performance on psychometric tests Vernon, 1987; Larson & Rimland, 1984; 1982; Jensen & Reed, 1990; Progressive Matrices Test (Jensen, Vernon, Nador, & Kantor, 1985). approach have been advanced. of the.information-processing Thus far, two main variations skills, such or executive complex processes"metacomponential" Sternberg's (1981) theory emphasizes Sternberg's theory selection, and solution monitoring. recognition, process selection, strategy as problem inferences to new domains, apply previously made to make inferences and stresses the role of the ability storage information from long-term memory encoding and retrieval of and of learning skills such as standard and widely approach presently lacks a Although promising, this (Sternberg & Davidson, 1983). skills are In addition, many of the the various stages of processing. accepted set of tasks to evaluate disadvantaged them less suitable in selecting ability, which may make highly dependent on verbal children. to in the present study, attempts approach, the one evaluated A second information-processing tasks through the use performance on more complex that theoretically underlies tap into a basic ability speed of information- 1982, 1987) that evaluate tasks (Hunt, 1978; Jensen, of elementary cognitive encode and manipulate faster in their ability to this view, gifted children are processing. According to this speed of knowledge. Consistent with retrieve and analyze existing environmental input and to of visual and (1986) found that several measures Larson, and Rimland processing theory, Saccuzzo, skills and required complex problem solving which contained little or no auditory speed of processing, variance instructions) shared significant common the ability to understand minimal language skills (only degree of intellectual content that did contain a high standardized psychometric tests with conventional solving. and involved complex problem differences in speed and individual relationship between processing Empirical support for a uncertainty to which a manipulate the level of reaction time studies that intelligence has come from 1990; Lunneborg, 1978; 1979; Jensen & Reed, 1979; Jensen & Munro, subject must respond (Jensen, time, slope of reaction such as median reaction Vernon, 1981). Using parameters Smith & Stanley, 1983; deviations of reaction time intraindividual standard number of bits, and time as a function of the 1 105 4 I 41W retarded persons and those of reported large differences between performance, investigators have students (Jensen 1980; 1982). vocational-college students and university normal IQ, as well as between the correlation between of the literature, Jensen (1982) estimated Based on his own findings and a survey and -.4. The correlations vary differences on IQ tests to be between -.3 reaction time and individual (Lunneborg, 1978). widely across samples; however between speed of processing have found support for a relationship A number of investigators and Jensen (1985), for example, Overtoom-Corsmit, 1986). Cohn, Carlson, and giftedness (Span & their speed of information- fundamentally from average children in found that gifted children differed compared a group of "bright- time paradigm. Cohn et al. (1985) processing as evaluated in a reaction of comparable age who were of academically gifted children average" 7th-grade children to a group significant group differences were mathematics and science. Large and taking college-level courses in information-processing. reaction-time measures of speed of found on each of nine elementary information-processing, also has the study of speed of visual A second line of investigation, complex cognitive tasks. In processing speed and performance on supported a relationship between briefly exposed "target" stimulus, subject makes a discrimination for a the typical visual paradigm, the The left of central fixation is longer. lines presented to the right and such as identifying which of two line non-informational mask ( e.g., a uniform by a spatially overlapping target stimulus is followed masking An extensive literature on the the lines of the target stimulus). that completely superimposes impulse provided by the target is duration that the informational task itself reveals that it limits the 1980). Speed of processing, system (Felsten & Wasserman, available for processing in the central nervous by either Nettelbeck, & Willson, 1972), is estimated it is usually called (Vickers, or "Inspection Tune" as the minimum duration needed duration of the target and estimating systematically varying the exposure 1976), or by keeping the stimulus Nettlebeck, 1977; Nettelbeck & Lally, for criterion accuracy (Lally & mask (Saccuzzo, Kerr, Marcus, & interval between the target and duration constant and varying the 1983). Brown, 1979; Saccuzzo & Marcus, mentally retarded statistically significant difference between Numerous studies have reported a in a backward masking individuals in inspection time as evaluated and non-retarded (average IQ) of the stimulus, method of spite of wide variations in the nature paradigm. Such differences occur in speed (Saccuzzo & Michael, technique used to estimate visual processing stimulus presentation, and The general finding is a direct clear-cut developmental differences. 1984). There are, moreover, (Blake, 1974; Liss & Haith, well as mental age and performance relationship between chronological as relationship between degrees Finally, the evidence supports a significant 1970; Saccuzzo et al., 1979). of the relationship remains processing speed; however, the magnitude of normal intelligence and visual Nettelbeck, 1982). controversial (Mackintosh, 1981; on the astonishing -.92 correlation between scores Though an early study reported an Inspection Tune (Nettelbeck & Adult Intelligence Scale (WAIS) and Performance Scale of the Wechsler significant, relationship between investigators found a less spectacular, but Lally, 1976), most subsequent -.45. These positive findings have with a median correlation of about Inspection Tune and intelligence, sizes (usually no more than 25 methodological groundssmall sample been criticized, however, on inflates the correlation due to the retarded persons, which greatly subjects); the inclusion of mentally size; and analyses based only on performance relative to the sample extremely disparate range of Nettelbeck, inflate correlations (Irwin, 1984; which, again, is well-known to extreme scoring subjects, 1982). work in the area. Nettelbeck's at his own and others' Nettelbeck (1982) took a careful look Tune. between intelligence and Inspection small but consistent association analysis revealed a relatively intelligence between Inspection Time and modest but significant correlations Irwin (1984) similarly found relationship provided an estimate of -.50 as the recently, Nettlebeck (1987) test performance. More subsequently confirmed by Kranzler intelligence. This estimate was between Inspection Time (IT) and literature review and meta-analytic meta-analysis. Based on an extensive and Jensen (1989) in a general measures of IQ, the IT- estimated that for adults, with procedures, Kranzier and Jensen and effects of artifactual sources of error, about -.54 after correction for the intelligence correlation is 106 gifted work is needed to determine if these promising findings, more -.30 prior to correction. Despite be so tasks, and whether they can from nongifted children on IT children can be distinguished distinguished in an unbiased manner. of information processing. examine racial differences in speed A few studies have attempted to 9-year-old compared 350 black South African Lynn and Holmshaw (1990) In a reaction time study, slower While the black children had children on 12 reaction time tests. children with 239 white British also tremendous IQ differences than the white children, there were decision times and greater variability to the first percentile and was children's mean Raven IQ corresponded between the groups. The black in the 56th percentile, with an The white children, by contrast, were equivalent to an IQ of about 65. lower in IQ than is generally the black sample in this study was equivalent Raven IQ of 102. Because white generalizability to American black and results have little, if any, found for U.S. samples, these populations. (1972) is similarly limited. Bosco in a backward masking paradigm A study of racial differences school children. There were clear first- arid sixth-grade black and white compared the performance of and selected from a suburban area, between the whites, who were differences in socioeconomic status background were Since race and socioeconomic selected from the inner city. the blacks, who were umesolved. relationship between race and IT was confounded, the issue of the relatively have focused on speed, with information-processing and intelligence To date, studics of behavior. also underlie intelligent information-processing tasks that might little attention given to other two subjects to respond at the instant timing (CT), a task that requires One such task is coincidence (Dunham, 1977; Poulton, 1950). objects intersect or "coincide" Poulton, timing (Dorfman, 1977; traced the history of coincidence Smith and McPhee (1987) relates to McPhee noted, coincidence timing Purvis, 1981). As Smith and 1950; Thomas, Gallagher, & object on a conveyor belt, and and off escalators, picking up an such everyday tasks as stepping on In more coincide with a gap in traffic. of lanes on the freeway will predicting when one's changing to in predicting where to aim a spear timing also had survival value, as primitive societies, coincidence integrate attend to changing conditions, timing tasks require subjects to hit a moving animal. Coincidence 1987). future event (Smith & McPhee, that information to predict a informEtion over time, and use determine if a correlation exists the first published attempt to Smith and McPhee conducted Progressive Matrices Test, and evaluated by the Standard Raven between psychometric intelligence, as 56 males and females administered a 10 minute CT task to task. These investigators a coincidence timing key at the very Subjects were required to press a high" socioeconomic status. of "high" to "moderate to significant negative stationary line. There was a touched (coincided with) a moment a moving target addition, there task and Raven scores. In number of errors on the CT correlation (-.294) between the (consistency of intrasubject standard deviation correlation (-.359) between was a significant negative performance) and Raven scores. adds a and coincidence timing the correlation between Raven scores As Larson (1989) noted, intelligence and information- between psychometric the well-known correlation new dimension to does not require time, coincidence timing previous tasks such as reaction processing tasks in that, unlike for adding to the Thus, the task has potential attention and estimation. speed of processing, but rather underlie, related to, and perhaps content that may be simple tasks devoid of intellectual range of relatively Smith and McPhee's Raven. Larson (1989) confirmed problem solving such as the tests involving complex intelligence, as measured task and psychometric relationship between the CT finding of a significant To date, however, of 127 male Navy recruits. Qualifying Test (AFQT), in a group by the Armed Forces children, or distinguish gifted and nongifted coincidence timing task can it has yet to be determined if a differences in this skill. whether there are ethnic performance on variable might underlie Larson (1989) is whether some A question raised by according to Larson, such common variable, and coincidence timing. One reaction time, inspection time, problem solving. As Larson cognitive work space for memorythe hypothetical may be working cognitive tasks and bridge between simple provides a theoretical (1989) noted, working memory 107 6 and/or fidelity" (p. 366). In the such as "representational agility psychometric tests, based on concepts hypothesis through of Larson's theoretical bridge attempted to provide a direct test present study, we mental counters (Larson, 1986). task of working memory called the use of a microcomputerized Method Subjects: school psychologist were compared to a been certified as gifted by a Eighty children who had and nongifted) of these two samples (gifted nongifted children. For each matched sample of eighty Each of the four 5th- to 6th-grade children. 3rd-grade children and forty there were forty 2nd- to 10 White Filipino, 10 Latino/Hispanic, and had 10 African-American, 10 subgroups of forty children and gifted children on the basis of age, race, children were matched to the children. The nongifted school district. Procedure: school psychologist in a individually for each child by a Giftedness was determined teachers, recommendations by parents or This analysis considered comprehensive case study analysis. of risk factors including tests scores, and the presence checklist, achievement, standardized a behavior environments. second language, and negative cultural differences, English as a economic disadvantage, Choice follows: Inspection Time (IT), battery of microcomputerized tests as Each child was given a presented Mental Counters (MC). These tests were Coincidence Timing (CO, and Reaction Time (CRT), keyboard. The tests white monitor and standard microcomputer with a black and on an IBM PC/XT hour. lasted approximately one in one session, which in counterbalanced order were administered and their second session. All subjects, standard Raven in a separate, Subjects were administered a school their participation. Nevertheless, one written informed consent for parents, provided voluntary receive the children (11 gifted) did not administration of the Raven; 18 district refused to allow the described below. information-processing battery are for each task in the Raven. The specific parameters the non-adaptive procedure based on The inspection time (IT) task was a Inspection Time (IT). described in detail by and Larson (1987) and Rim land (1984) and Saccuzzo methods of Larson and unequal length (17.5 of two horizontal lines of A target stimulus consisting Larson and Saccuzzo (1989). Tne two lines appeared of the computer monitor. briefly presented in the center mm and 14.3 mm) was left on a random basis. the longer appearing right or left of central fixation, with to the right and of a single visual noise mask, consisting of the target, a backward Immediately following termination known presented. The mask is superimposed spatially on the target, was horizontal line that completely (Felsten system by the target to the central nervous of the sensory signal delivered to limit the duration stimulus durations: of five completely randomized Targets were presented at one & Wasserman, 1980). refresh cycles on the video corresponded to 1, 2, 4, 6, and 9 150.3 msec, which 16.7, 33.4, 66.8, 102.2, and subject's task was to for a total of 50 trials. The trials per stimulus duration, monitor. There were 10 is longer, by pressing of the two lines of the target discrimination, indicating which make a forced-choice instructions, examples, The task began with a set of the microcomputer keyboard. one of two keys on visual feedback Subjects were given computer-generated to the test proper. and pracfice to criterion prior on their performance. time task, for a 1,3, and 5 choice reaction Paradigm). A Hick paradigm Choice Reaction Time (Hick used to evaluate choice Larson and Saccuzzo (1989), was Saccuzzo et al. (1986) and as described by the bottom of the of lights was presented at A horizontal arrangement reaction time performance. order of presentation 5-choice conditions, with presented with 1-,3-, and monitor. All subjects were Subjects responded used as stimulus lights. on the monitor were completely randomized. Open squares forefinger rested lightly on illuminated. The subject's bar as soon as a square was by pressing the space has shown involved. Previous research essentially no movement time the space bar, so that there was reaction time tasks involving effective as more traditional reaction time task is as due that this "no movement" minimizing errors that occur has the advantage of Saccuzzo, Larson, 1987), and movement (Kostas, subject In this procedure, the movement time paradigm. pressing two keys in the to the necessity of After a random period of five line drawn squares. which there are one, three, or views the monitor on 7 108 is defined as the number the squares is illuminated. Reaction time time from 1.5 to 2.5 seconds, one of is illuminated) of the stimulus (i.e., where one of the stimulus squares of milliseconds between the onset the space bar. and the instant the subject presses used by Larson (1989), liming task was identical to that Coincidence Timing. The Coincidence each of three conditions, the by Smith and McPhee (1987). For based on the description provided moment that a horizontally bar on the computer keyboard at the exact subject's task was to press the space Condition 1 consisted of a dot that line in the middle of the monitor. moving dot crossed a vertical second, with random delays in the line at the speed of 0.10 meters per moved in a straight horizontal speed of 0.15 meters per second. In identical to Condition 1 but at a starting time. Condition 2 was delay and speed of 0.10 meters random (jagged), with a random Condition 3, the path of the dot was 0.13 dot from orgin to crossing the line was distance traversed by the moving per second. The total meters. trial consisted of a cycle in 30 trials at each condition. Each As in Larson (1989), there were the dot crossed the centerline the screen, then right to left so that which the dot moved left to right across related to the type of skills that such as coincidence timing may be twice. Finally, since skill in tasks 1983), each of the 160 children such as Nintendo (Salthouse & Prill, children develop playing video games they spend playing video games the number of hours per week that in the study were asked to estimate tasks. implementation of the information-processing in a self-report procedure prior to subjects are asked to Counters(MC) task (Larson, 1986), Mental Counters (MC). In the Mental rapidly and in random order. The independent "counters" that change keep track of the values of three values that change rapidly. hold, revise, and store three counter task requires subjects to simultaneously (three side-by-side horizontal represented as dashes on the video monitor The counters themselves are (0.25 (0,0,0). When a small target The initial counter values are zero dashes in the center of the screen). counter must be adjusted of the three dashes, the corresponding inch, hollow box) appears above one corresponding counter below one of the three dashes, the by adding one. When the target appears number of targets and the rate of The test items vary both in the must be adjusted by subtracting one. presentation (0.633 seconds and there were two different rates of presentation. In the present study Order of changed 8 times. that the values of the initial counters 1.42 seconds), and 8 targets, such subjects were given instructions, counterbalanced. Prior to the test proper, presentation of speeds was The maximum and minimum (three consecutive correct responses). examples, and practice to criterion subject's task was to select, from among +3 and -3, respectively. The counter values varied between the Selection was made by pressing final values for the three counters. four choices, the correct list of the test proper. during practice, and not during keyboard. Feedback was given only proper key on the Results Video Games. such as Nintendo were week spent playing video games Data for self-reported hours per ANOVA. The only significant nongifted) X 4(Ethnic Background) evaluated in a 2(GATE: gifted vs that the gifted .042. This result revealed GATE, F(1,152) = 4.208, p < finding was a maM effect for than the nongifted week (about half) playing video games children spent significantly less time per did if prior practice at such tasks 6.04 hours, respectively. Thus, children, with means of 3.82 hours vs much nongifted children, since they spent have been far in favor of the make a difference, it would of hours ethnic differences in the number video games. Notably, there were no more time playing spent playing these games. 109 8 Raven. 111 Table 1 shows the Raven scores for gifted vs nongifted children as a function of ethnic background. The table shows the average Raven Z scores based on the U.S. smoothed norms provided by Raven et al (1986). These data were subjected to a 2(GATE) X 2(Grade) X 4(Ethnic Background) ANOVA. As might be expected, there was a significant main effect, F(1,135) = 42.69, p < .001, for Gifted (M = 1.11, SD = .92) vs Nongifted(M = .02, SD = 1.0) children. The only other significant finding was a GATE X Ethnic Background interaction, F(3,135) = 3.58, p < .05. Newman-Keuls post hoc multiple comparison tests of this difference revealed the gifted White, African-American, and Filipino children did not differ significantly among themselves and all three of these groups were significantly higher than the gifted Latino children and each of the four nongifted groups, none of whom differed significantly among themselves. It should be noted, however, that of the 11 gifted children who did not receive 111 Raven, 6 were in the Latino group. The absence of these children may have artificially lowered the overall mean for the Latino children. Table 1. Raven Z-Scores as a Function of Ethnic Background for Gifted versus Nongifted Children 111 Filipino African-American Latino/Hispanic White Gifted Nongifted Nongifted Gifted Gifted Nongifted Gifted Nongifted 111 0.16 1.09 -0.38 1.34 0.36 M 0.01 1.36 0.51 0.92 0.58 0.95 0.79 1.31 0.78 0.81 1.17 SD For each of the four information-processsing variables, all F values, significance levels, means, and standard deviations are presented in Table 2 to conserve space. Whereas Grade reflects differences between 5th and 6th versus 2nd and 3rd graders, GATE reflects differences between Gifted versus 111 Nongifted children, and Condition reflects the condition under study, such as Stimulus Duration, Choices, and Fast vs. Slow. IP 9 110 Table 2 Summary of significant findings SD Level df A4 Significant Effects Inspection Time 13.19 66.17 5th - 6th Grade 1/140 36.73*** Main Effect: Grade 2nd 3rd Grade 14.68 57.50 14.62 63.78 Gifted 1/140 7.84** Main Effect: GATE 15.01 59.83 Nongifted 10.7 52 Duration 1 4/560 80.12*** Main Effect: 13.4 57 Duration 2 Stimulus Duration 15.7 57 Duration 3 17.2 68 Duration 4 18.3 74 Duration 5 4/560 8.73*** Grade X Inspection Time 4/560 3.76** GATE X Inspection Time Reaction Time (msec) 5th 6th Grade 90.55 383 1/135 56.83*** Main Effect: Grade 133.47 564 2nd - 3rd Grade 113.75 422 Gifted 1/135 6.21* Main Effect: GATE 139.70 467 Nongifted 117.71 384 One Choice 2/278 141.99*** Main Effect: Choices 127.01 454 Three Choices 479 142.0U Five Choices 2/278 4.17* Grade X Choices 2/278 5.08** GATE X Choices 323* 3/139 GATE X Ethnicity Coincidence Timing (Errors) 7.51 5th - 6th Grade 18.34 1/140 36.27*** Main Effect: Grade 17.87 29.16 2nd - 3rd Grade 8.89 19.80 Gifted 1 /140 19.95*** Main Effect: GATE 18.01 27.73 Nongifted 11.39 16.95 Slow, NonVariable 2/280 94.76*** Main Effect: Condition 14.69 2.5.18 Fast, NonVariable 18.21 29.32 Random 2/280 3.75* Grade X Condition 2/280 3.58* GATE X Condition Mental Counters 4.11 10.84 5th - 6th Grade 1/112 48.00*** Main Effect: Grade 3.76 6.46 2nd - 3rd Grade 4.34 9.68 Gifted 1/112 7.08** Main Effect: GATE 4.59 8.34 Nongifted 5.07 10.17 66.00*** Slow 1/112 Main Effect: Condition 3.95 7.87 Fast 8.99** 1/112 Grade X Condition 1/112 6.41** GATE X Condition *p< .05 ** p < .01 p .001 1 0