Chapter 5

Dynamic Assessment Of The Level Of Internalization Of Elementary School Children's Problem-Solving Activity

Boris Gindis and Yuriy V. Karpov

The advantages of dynamic assessment have been highlighted by a number of authors (see Haywood & Tzuriel, 1992; Lidz, 1997). The dynamic assessment procedure described in this chapter demonstrates another advantage of dynamic assessment: In contrast to static testing, this procedure makes it possible to evaluate qualitative cross-domain characteristics of human cognition.

The Cross-Domain Level Of Internalization Of The Child's Problem-Solving Activity: Concept And Criteria

Scholars who work within different theoretical perspectives are in agreement that internalization of children's problem solving is one of the most essential characteristics of their cognitive development (Bruner, 1964; Bruner, Olver & Greenfield, 1966; Galperin, 1966, 1969, 1957/1989; Piaget, 1952, 1947/1960; Zaporozhets 1978; Zaporozhets & Elkonin, 1964/1971). Although the understanding of internalization among these theorists may be different in certain details, its main aspect is described similarly as children's transition from one level of solving problems to the next. First, children are capable of solving problems only through real transformations of the situation and actual manipulations with objects. Then, they become capable of solving problems on the basis of operations with visual images. Finally, they come to the symbolic level of solving problems. In the remainder of this discussion, we use the term 'internalization' in this sense, designating the consecutive levels of internalization as visual-motor, visual-imagery, and symbolic.

Internalization of children's problem solving could refer to two types of phenomena. The first is internalization of a specific problem-solving process in the course of its acquisition by children. This can be illustrated by the following example. In the beginning, the child is capable of counting only at the visual- motor level (e.g. moving or touching the objects to be counted). After that, the child becomes capable of counting at the visual-imagery level (objects or their icons are counted by sight). Finally, the child becomes capable of counting at the symbolic level, dealing with abstract substitutes of real objects, that is, figures.

The second type of phenomenon to which the term internalization refers is the internalization of children's cross-domain level of problem-solving activity. Not only are specific problem-solving processes internalized in the course of their acquisition by children but, in the course of ontogenesis, children progress to increasingly higher levels of internalization of their problem-solving activity as a whole.

The problem of criteria for determining the cross-domain level of internalization of the child's problem-solving activity deserves a special discussion. What a static test is able to evaluate is the level of internalization at which the child has mastered a specific problem-solving process. For example, if we ask a child to solve a classification problem at the symbolic, visual-imagery, and visual-motor levels consecutively, the highest level at which the child is able to solve this problem will indicate the level of internalization at which that child has mastered the process of classification. However, the well-known phenomenon of horizontal decalages (a divergence of the levels of solving different problems by a child) makes it impossible to use the level at which the child is able to solve a specific problem as the criterion for determining the cross-domain level of internalization of that child's problem-solving activity. Indeed, how could we determine the cross-domain level of internalization of the child's problem-solving activity if she, for example, is able to count at the symbolic level, to classify objects of different shapes at the visual-imagery level, and to seriate different lengths at the visual- motor level? After all, even young children are capable of certain types of symbolic activity, and, as Piaget (1971) noted, even adults do not always solve problems at the symbolic level! Thus, static testing is not an appropriate method for the evaluation of the cross-domain level of internalization of the child's problem-solving activity.

Karpov (1982) suggested alternative criteria for the evaluation of this level, which rest on the assumption that this level reveals itself in the course of the child's learning new problem-solving processes. He hypothesized that there are two characteristics of the child's learning that are determined by the cross- domain level of internalization of the child's problem-solving activity and that, accordingly, these can be used as the criteria for determining this level. These characteristics are: (a) the highest level (symbolic, visual-imagery, or visual- motor) at which the child is able to understand the algorithm for a new problem-solving process; and (b) the highest level at which the child is able to perform a new problem-solving process after understanding its algorithm.

Experimental findings obtained in Karpov's research (Karpov, 1983, 1988, 1999; Karpov & Talyzina, 1985) and in independent replication studies (Khuntszyn, 1995; Le Van An, 1995) confirmed this hypothesis. The following is a brief discussion of these experimental findings.

The First Group of Findings

In a study with 46 six- to seven-year-old children (Karpov, 1983; Karpov, Talyzina, 1985), they were taught how to perform the process of analogical reasoning (e.g. a circle, a circle with a cross, a square), which was equally new to all of them. First, the child was taught the algorithm for the process of analogical reasoning at the symbolic level and then was asked to perform this process at the symbolic, visual-imagery, and visual-motor levels consecutively. If the child was unable to perform this process at any of the levels, he was taught the algorithm for this process at the visual-imagery level and was again asked to perform the process of analogical reasoning at the symbolic, visual- imagery, and visual-motor levels consecutively. If the child was still unable to perform this process at any of the levels, he was taught the algorithm for this process at the visual-motor level, and was again asked to perform the process of analogical reasoning at the symbolic, visual-imagery, and visual-motor levels consecutively.

The results of the study were as follows:

(a) The children showed differences regarding the highest level at which each of them was able to understand the algorithm for the process of analogical reasoning (the ability to perform this process at any level was used as an indicator that the child had understood the algorithm at the level at which it had been taught before). Ten of the 46 children performed this process after the algorithm had been taught to them at the symbolic level, twelve of the children - after this algorithm had been taught to them at the visual-imagery level, and 24 children - after the algorithm had been taught to them at the simplest, visual-motor level.

(b) The children differed regarding the highest level at which each of them was able to perform the process of analogical reasoning after understanding its algorithm. Eleven of the 46 children performed this process at the symbolic level, twelve children at the visual-imagery level, and 23 children at the visual- motor level.

(c) The highest level at which the child was able to understand the algorithm for the process of analogical reasoning was coincident with the highest level at which he or she was able to perform this process after understanding its algorithm. Having understood the algorithm at the symbolic level, nine of ten children performed the process at the symbolic level. Having understood the algorithm at the visual-imagery level, nine of twelve children performed the process at the visual-imagery level. Among the 24 children who were able to understand the algorithm only at the visual-motor level, 21 children performed the process at the visual-motor level. According to chi-square analysis, this coincidence was significant at p < 0.005 (X2 =>52.711, DF=4). It is important to note that even for those few cases where the child's level of understanding the algorithm for the process of analogical reasoning and the level of performing this process were different, these differences were always minimal (for example, the child was able to understand the algorithm at the visual-imagery level and then performed the process at the symbolic level).

The experimental findings described above were confirmed in the independent replication study of Le Van An (1995) with 40 six- to seven-year-old children. In another study, Le Van An (1995) used the experimental design described above to teach 41 six- to seven-year-old children another problem- solving process which was new to them: The process of identification of similarities among geometrical shapes. Children were taught how to compare complex figures (e.g. a small red circle, a small yellow square, and a small red square) and to identify what all of them had in common. The experimental findings of the study were similar to the findings presented above.

The Second Group of Findings

In a study with 32 six- to seven-year-old children (Karpov, 1983; Karpov & Talyzina, 1985) and in the replication study with 40 children of the same age group (Le Van An, 1995), they were taught how to perform two processes, which were equally new to all of them. The first was the process of analogical reasoning, and the second was the process of identification of similarities among geometrical shapes (both processes were described in the section The First Group of Findings). At the beginning, the children were taught the algorithms for these processes at the visual-motor level, and they were then asked to perform these processes at the symbolic, visual-imagery, and visual-motor levels consecutively.

The results of both studies indicated that after understanding the algorithm for a new problem-solving process some children were able to perform this process at the symbolic level, others at the visual-imagery level, and still others only at the visual-motor level. The comparison of the highest levels at which each child performed the two processes showed that these levels were the same for that child (according to chi-square analysis, in both studies this coincidence was significant at p < 0.005).

In another study with 72 six- to seven-year-old children (Karpov, 1999), they were taught to perform three problem-solving processes, which were equally new to all of these children.

The first was the process of analogical reasoning. The second was the process of associating a figure with a concept: Being given an artificial concept (e.g. 'Bik' is a square with a circle inside it') and a number of different figures (a square with a triangle, a triangle with a circle, a square with a circle, and so on), the child had to answer which of those figures belonged to this concept. The third process was designated as 'the process of excluding the third figure'. Presented with three figures (e.g. the first one - a small red square; the second one - a small red circle; the third one - a large red triangle), the child had to choose which figure differed the most from the other two. In the course of teaching the children each of these processes, they were first taught the algorithm for this process at the visual-motor level, and they were then asked to perform this process at the symbolic, visual-imagery, and visual-motor levels consecutively.

The results of the study were as follows: Having understood the algorithms for the three described processes, all 72 children managed to perform each of these processes at one of the levels (symbolic, visual-imagery, or visual-motor). The comparison of the highest levels at which each child performed the three processes showed that these levels were the same for that child in 85% of the cases. Even for those 15% of the cases where the levels of performing the three processes by the child were different, these differences were always minimal (for example, the child performed two processes at the symbolic level, and one at the visual-imagery level).

The Third Group of Findings

Ninety seven six- to seven-year-old children, to whom the process of analogical reasoning was equally new, were taught this process (Karpov, 1999). They were given the algorithm for this process at the visual-motor level and then asked to perform this process at the symbolic, visual-imagery, and visual-motor levels consecutively. As a result, 24 of the 97 children were able to perform this process at the symbolic level, 36 at the visual-imagery level, and 37 at the visual-motor level. We designated these three groups of children as 'the symbolic group', 'the visual-imagery group', and 'the visual-motor group'.

Ninety seven six- to seven-year-old children, to whom the process of analogical reasoning was equally new, were taught this process (Karpov, 1999). They were given the algorithm for this process at the visual-motor level and then asked to perform this process at the symbolic, visual-imagery, and visual-motor levels consecutively. As a result, 24 of the 97 children were able to perform this process at the symbolic level, 36 at the visual-imagery level, and 37 at the visual-motor level. We designated these three groups of children as 'the symbolic group', 'the visual-imagery group', and 'the visual-motor group'.

The next day, the children were given two transfer problems: (a) The child was presented the first, the second, and the fourth figures (for example, first - a triangle, second - a triangle with a cross on it, third - missing, fourth - a circle with a cross on it), and was asked what the third figure would look like; (b) The child was given 3 flowers (for example, first - a yellow tulip, second - a red tulip, third - a yellow rose), and was asked what the fourth flower would look like. Both problems were given to the child at the same level (symbolic, visual-imagery, or visual-motor) at which he or she had succeeded in performing the process of analogical reasoning the day before.

The results showed that 27 children solved both transfer problems, 41 children solved just one of the problems, and 29 children failed to solve either of the transfer problems. The highest performance in solving the transfer problems was demonstrated by 'the symbolic group', with median results by 'the visual-imagery group', and the lowest performance by 'the visual-motor group'. A one-way ANOVA revealed that the difference among the groups was statistically significant, F(2, 94)= 164.92, p < 0.01. The Extended Tukey Test showed that the statistically significant differences occurred between all 3 group mean-pairs beyond the 0.01 level.

The Fourth Group of Findings

Eleven six- to seven-year-old children, to whom the process of analogical reasoning was equally new, were taught this process (Karpov, 1988). They were given the algorithm for this process at the visual-motor level and then asked to perform this process at the symbolic, visual-imagery, and visual-motor levels consecutively. As a result, six children were able to perform this process at the symbolic level, three at the visual-imagery level, and two at the visual-motor level. Again, we designated these three groups of children as 'the symbolic group', 'the visual-imagery group', and 'the visual-motor group'.

After that, the children were trained in the phonetic analysis of words, which was equally new to all of them. When the training cycle had been completed, the child's change in ability to perform the phonetic analysis of words was assessed. The results showed that these changes were different for different groups of children. The greatest change was demonstrated by 'the symbolic group', an average change by 'the visual-imagery group', and the smallest change by 'the visual-motor group'. Computing a one-way ANOVA indicated that this difference was statistically significant, F(2,8) =45.24, p<0.01. The Extended Tukey Test, however, showed that the difference between the 'visual- imagery' and 'visual-motor' groups, while close to statistical significance, did not reach this level.

A similar experimental design was used in another study (Karpov, 1988) where 18 six- to seven-year-old children (three of them were shown to belong to 'the symbolic group', five - to 'the visual-imagery', and ten - to 'the visual- motor') were trained to build three projections of volumetric geometric bodies. After the training cycle had been completed, the child's change in ability to build three projections of volumetric geometric bodies was assessed. The results showed that these changes were different for different groups of children. The greatest change was demonstrated by 'the symbolic group', an average change by 'the visual-imagery group', and the smallest change by 'the visual-motor group'. Computing a one-way ANOVA indicated that this difference was statistically significant, F(2,15) = 23.75, p<0.01. The Extended Tukey Test showed that the statistically significant differences occurred between all 3 group mean-pairs (the difference between the 'visual-imagery' and 'visual-motor' group mean-pair was significant beyond the 0.05 level; the differences between the remaining group mean-pairs were significant beyond the 0.01 level).

Due to the small numbers of participants in both studies, their findings needed additional empirical support. Such support has been provided by the independent study of Khuntszyn' (1995) with 70 six- to nine-year-old children (34 of them were shown to belong to 'the symbolic group', 23 to 'the visual- imagery', and 13 to 'the visual-motor'). Her study demonstrated that whichever of these groups a child belonged to determined his or her success in learning different geometric concepts.

Discussion

The studies revealed two qualitative characteristics of the child's learning: (a) the highest level (symbolic, visual-imagery, or visual-motor) at which the child was able to understand the algorithm for a new problem-solving process; and (b) the highest level at which the child was able to perform a new problem- solving process after understanding its algorithm. These characteristics were coincident and stable for each child and were related to that child's cross- domain ability to learn and transfer new knowledge. Thus, Karpov's (1982) hypothesis was confirmed. Accordingly, he suggested using these characteristics of learning as the criteria for determining the cross-domain level of internalization of the child's problem-solving activity (Karpov, 1983, 1999).

The Cross-Domain Level Of Internalization Of The Child's Problem-Solving Activity: The Dynamic Assessment Procedure

Several dynamic assessment procedures have been designed with respect to the above criteria for determining the cross-domain level of internalization of the child's problem-solving activity (Karpov, 1983, 1999; Karpov & Talyzina, 1985). The following is a description of one of these procedures, which is built around teaching elementary school children the process of analogical reasoning.

Pretest

The goal of the pretest is to find out whether the child is able to perform the process of analogical reasoning at the simplest, visual-motor level. The child is shown three figures under ordinal numbers, and five supplementary shapes (the figures and the shapes are cut out of construction paper) (Fig. 1).

The child is then asked to use the supplementary shapes to make Fig. #4 in such a way that it would differ from Fig. #3 in the same way that Fig. #2 differs from Fig. #1. The following is a detailed description of the format of the pretest.

Evaluator: Do you like to solve problems? Let me show you a problem. The first piece will be like this (placing a square under #1). What is this called?

Child: -----.

Evaluator: Correct, a square. And the second piece will look like this (placing a square with a circle on top of it under #2). Let us call this: 'a square with a circle'. And our third piece will look like this (placing a triangle under #3). What is this called?

Child: -----.

Evaluator:: Correct, a triangle. And the fourth piece is missing (pointing to the empty spot under #4). Let us use these shapes (pointing at the supplementary shapes) to make the fourth piece so that it will differ from piece #3 in the same way that piece #2 differs from piece #1 (pointing at each of these pieces consecutively). What is the difference between piece #1 and piece #2?

Child: -----.

Evaluator: That is right, piece #1 is a square, and piece #2 is a square with a circle on top of it (lifting the circle up a bit). So, the second piece differs from the first piece by a circle. Now try to use these shapes (pointing at the supplementary shapes) to make the fourth piece so that it will differ from piece #3 in the same way that piece #2 differs from piece #1 (pointing at each of these pieces consecutively).

The Dynamic Assessment Procedure

The goal of the dynamic assessment procedure is to find the highest level (symbolic, visual-imagery, or visual-motor) at which the child is able to perform the process of analogical reasoning after understanding its algorithm. The procedure includes four steps.

Step 1. The child is taught the algorithm for the process of analogical reasoning. The experimental material used in the explanation is the same as the pretest material (see Fig. 1). The following is a detailed description of the teaching procedure.

Evaluator: Let me teach you how to solve these problems. Please, listen carefully. We must use these shapes (pointing at the supplementary shapes) to make the fourth piece so that it will differ from piece #3 in the same way that piece #2 differs from piece #1 (pointing at each of the figures consecutively). First, tell me what the third piece is, what do we call it?

Child: -----.

Evaluator: Correct, a triangle. So, the fourth piece should be a triangle too (placing a triangle from the supplementary shapes under #4). Is the fourth piece like the third one?

Child: -----.

Evaluator: Correct, the fourth one is a triangle, and the third one is a triangle. They are the same. And what should the fourth piece be?

Child: -----.

Evaluator: Correct, the fourth piece should differ from piece #3 in the same way that piece #2 differs from piece #1 (pointing at each of the pieces consecutively). Look here, what is the difference between pieces #1 and #2 (lifting the circle up a bit)?

Child: -----.

Evaluator: Correct, a circle. Look, the first is a square, and the second is a square with a circle on it. So, the second is different from the first by a circle (pointing at each of the pieces consecutively). So, the fourth should be different from the third by a circle (placing a circle from the supplementary shapes on top of the triangle under #4). Now, the fourth piece differs from the third by a circle, and the second differs from the first by a circle. So, we solved the problem! The fourth piece differs from piece #3 in the same way that piece #2 differs from piece #1. Did you understand how to solve these problems?

Child: -----.

If the child has not understood the algorithm, which will rarely happen, Step #1 should be repeated; otherwise, Step #2 of the dynamic assessment is started.

Step 2. The child is asked to perform the process of analogical reasoning at the symbolic level. The following is a detailed description of Step #2.

Evaluator: Now, I will give you the same problem, but this time there will be no pieces on the table. I will tell you what the first, the second, and the third pieces are, you will remember them and tell me what the fourth piece is. Remember, the fourth piece should differ from piece #3 in the same way that piece #2 differs from piece #1. Listen carefully! The first piece is a circle, the second - a circle with a cross, and the third - a square. What is the first piece? The second? The third? .The second? The third?. The first? (until the evaluator is sure that the child has memorized all the figures; if the child has forgotten the name of a figure, the evaluator repeats it). Now think and tell me what the fourth piece should be?

Child: -----.

If the child's answer is correct (square with a cross), Step #2 is repeated with a different set of figures. If the answer is correct again the conclusion is made that the child is at the symbolic level of problem-solving activity, and the assessment is finished. If the child fails to solve the problem, Step #3 of the dynamic assessment is started.

Step 3.

The child is asked to perform the process of analogical reasoning at the visual-imagery level. The experimental material is presented in the form of a card with figures drawn on it (Fig. 2). The following is a detailed description of Step 3:

Evaluator: Let me give you the same problem, but this time with pictures (the evaluator presents the card shown in Fig. 2). You can see three pieces here. The first one is. . .? (pointing)

Child: -----.

Evaluator: Correct, a circle. The second.. ? (pointing)

Child: -----.

Evaluator: Correct, a circle with a star. The third? (pointing)

Child: -----.

Child: -----.

If the child's answer is correct (triangle with a star), Step #3 is repeated with another set of figures drawn on a card. If the answer is correct again - the conclusion is made that the child is at the visual-imagery level of problem-solving activity, and the assessment is finished. If the child fails to solve the problem, Step #4 of the dynamic assessment is started. The child is asked to perform the process of analogical reasoning at the visual-motor level. The experimental material is analogous to the one used in the course of the Pretest and Step #1: Three figures under ordinal numbers, and five supplementary shapes (the figures and the shapes are cut out of construction paper) (Fig. 3). The following is a detailed description of Step #4,

Step 4:

Evaluator: Let me give you the same problem, but this time with cut-out pieces. The first piece will look like this (placing a triangle under #1). What is this called?

Child: -----.

Evaluator: Correct, And the second piece will look like this (placing a triangle with a ~ cross on top of it under #2), What is this called?

Child: -----.

Evaluator: Correct. And the third piece will look like this (placing a circle under #3). What is this called?

Child: -----.

Evaluator: Correct. And the fourth piece is missing (pointing to the empty spot under #4). Now think and make the fourth piece of these shapes (pointing at the supplementary shapes).

Child: -----.

If the child has solved the problem (has placed a circle from the supplementary shapes under #4, and placed a cross on top of the circle), Step #4 is repeated with a different set of figures. If the child has succeeded again - the conclusion is made that the child is at the visual-motor level of problem-solving activity, and the assessment is finished. If the child fails to solve the problem, which would rarely happen unless the evaluator made an error in the course of the teaching phase of the procedure, the dynamic assessment procedure should be repeated.

Case Study Of Elaine, A 7 Year-2 Month-Old Girl

Description of the Case and Assessment Results

Elaine was referred for a psychological evaluation due to significant learning problems presumably related to her 'immature' behavior and limited cognitive abilities. She is currently a student in a regular first grade receiving supportive services (occupational therapy and speech/language therapy). According to her classroom teacher, Elaine's school performance is erratic and her educational gains are inconsistent. Neurological examination revealed no significant abnormalities except for ADHD symptoms and some minor delays in the areas of gross-motor and language.

The educational evaluation, including classroom observation, found her academic skills to be erratic and appropriate to the kindergarten level at best, with difficulties in following directions and working independently. In terms of her particular skills (knowledge of colors, shapes, body parts, etc.; under- standing of social situations and people/object functioning; ability to discriminate among object, e.g. first/last, big/bigger/the biggest, etc.) she showed inconsistency, demonstrating such skills on one occasion and not on the next. At times she puzzled the examiner by performing well on relatively difficult tasks and failing on much easier ones. At times, Elaine tended to answer in a tangential manner, and on a few occasions her responses had little relationship to the questions asked. Poor relatedness, a high level of distractibility, and immature social skills were cited as characteristics of this child. Both a speech/language evaluation and an occupational therapy evaluation indicated her eligibility for remediation services due to moderate to significant delays in her language and fine-motor skills.

The psychological evaluation found her functioning within the borderline range of general cognitive ability on the Stanford-Binet, IV (Composite score of 74 + /-4). There was no significant discrepancy between her verbal and non- verbal skills: Most of her scores were within the borderline range with the Short Memory subtest score the lowest. It was observed that Elaine had difficulty in responding to isolated (context-reduced) questions and in matching isolated geometrical patterns. She performed somewhat better when asked to replicate designs with a set of blocks or when answering 'context-embedded' verbal questions.

Similar to her performance in the course of the educational evaluation, Elaine demonstrated a high level of inconsistency within each of the Stanford-Binet sub-tests, being able to perform a task and then failing on a similar and easier task. Often, she would answer questions without thinking them over, demonstrating impulsive behavior and a high level of distractibility. Therefore, the school psychologist questioned the extent to which Elaine's standardized test performance reflected her actual cognitive potential as opposed to reflecting her impulsivity and distractibility. The dynamic assessment procedure described earlier was recommended for the evaluation of Elaine's level of cognitive development.

In the course of the Pretest, Elaine failed to perform the process of analogical reasoning at the simplest visual-motor level, demonstrating impulsive disorganized actions and the lack of any applied systematic mental strategy. The assessment proceeded to Step #1, where Elaine was taught the algorithm for the process of analogical reasoning.

At the beginning of Step #1, she had difficulty concentrating on the evaluator's explanation, stating she was 'tired' and 'bored' with this 'baby stuff'. It took the evaluator some effort to direct her attention to his explanation and the manipulation of the figures that accompanied the explanation. Elaine finally became engaged and began answering the evaluator's questions. Eventually it was concluded that Elaine now understood the algorithm for the process of analogical reasoning, and Step #2 of the dynamic assessment procedure was started.

At the beginning of Step #2, Elaine had obvious difficulty memorizing the figures in the analogical-reasoning problem. The evaluator had to repeat their names several times until he was sure that Elaine had remembered them. When subsequently asked to name the fourth figure, she gave the wrong answer. The conclusion was made that she was not able to perform the process of analogical reasoning at the symbolic level, and Step #3 of the dynamic assessment procedure was started.

At Step #3, Elaine accurately named all three figures in the picture and paused for a while (which was not typical for her). Then she confidently and correctly identified the fourth figure. She was given a similar assignment with another set of figures, and again gave the correct answer with visible ease. It was concluded that Elaine was able to perform the process of analogical reasoning at the visual-imagery level, and, accordingly, was at the visual- imagery level of problem-solving activity.

Analysis of the Case and Suggested Remedial Intervention

The results of the dynamic assessment procedure indicate that Elaine is at the visual-imagery level of problem-solving activity. As has been demonstrated in several studies (Karpov, 1988; Khuntszyn, 1995), this level of functioning is developmentally appropriate for elementary school students, making it possible for them to learn successfully. What are the reasons then for Elaine's poor performance at school, as well as for her low scores during the educational and psychological assessments? The data from Elaine's evaluations interpreted in light of her performance during the dynamic assessment procedure make it possible to suggest that the major reasons for her poor performance are her impulsivity, high distractibility, and difficulty with following directions. Such a conclusion is supported by ADHD symptoms found in the course of Elaine's neurological examination.

All the described shortcomings of Elaine's performance deal with a poor level of development of the processes of self-regulation (self-planning, self- monitoring, self-checking, and self-evaluating) that are designated in contemporary psychological literature as metacognitive (executive) processes (see, e.g. Borkowski & Kurtz, 1987; Brown, 1987; Brown, Bransford, Ferrara & Campione, 1983; Brown & DeLoache, 1978; Flavell, 1976; Kluwe, 1987). Therefore, it may be concluded that intervention with Elaine should be directed towards the development of self-regulation.

Efficient ways of undertaking such intervention have been identified in a number of Vygotsky (1978, 1981, 1983, 1934/1986) based studies (for reviews of these studies see Braten, 1992; Berk & Winsler, 1995). Summarizing their findings, remediation of children's self-regulation should proceed through the following steps.

At the beginning, the teacher involves the child in the course of joint activity and takes the major responsibility for regulating their shared performance. The child's responsibility is to perform the actions. Using external speech, the teacher plans the sequence of actions to be performed, monitors the process of performance, and evaluates its results. By doing this, the teacher is not only regulating the child's performance, but is also modeling verbal tools for self- regulation.

Gradually, the teacher passes more and more responsibility for regulation of their joint performance to the child, at the same time encouraging the child to use the verbal tools for self-regulation that were previously modeled by the teacher for planning, monitoring, and evaluating their performance. It is important that the child is asked to use these tools in the form of external speech, talking to himself or herself aloud while performing the task (so-called private speech).

At the same step of the remedial intervention, the child is involved in the course of joint activity with a less capable peer and is given responsibility for regulating this activity. The teacher encourages the child to use the verbal tools for self-regulation for planning, monitoring, and evaluating the children's joint performance, correcting the child if necessary.

Finally, the child is given individual assignments and is encouraged to use private speech for self-regulation of the performance. As the child becomes more proficient in self-regulation, private speech reduces until the child develops self-regulation of performance by the use of inner speech.

Analysis of Elaine's case makes it possible to suggest that the described remedial intervention could be highly beneficial for her.

Case Study Of Carol, An 8-Year-Old Girl

Description of the Case and Assessment Results

Carol was referred for psychological evaluation due to learning problems at school. Her teacher expressed concern about an apparent mismatch between Carol's current academic skills (particularly in reading and spelling) and her second grade school curriculum. For example, Carol was unable to read most of the words on her spelling list; her spelling was invariably faulty. According to her teacher, Carol had been consistently asked to perform at a level that was 'beyond her intellectual capability' which it was thought resulted in difficulties with her attention and task perseverance.

In the classroom, Carol showed increased distractible behavior, lack of awareness of appropriate routines, and poor recall of instructions. In reading, Carol was functioning at a 'readiness' level, still struggling with letter recognition, sound-symbol association, and phonemic awareness. In dealing with print, either of letters or numbers, she did not appreciate the importance of order, and would at times confuse the direction in which she was proceeding.

On a measure of general cognitive functioning (Stanford-Binet, IV) that compared her intellectual abilities with her age group, an estimation of Carol's functioning placed her in the range of low average to average. There was a statistically significant difference between her scores on verbal/quantitative measures compared with nonverbal, more perceptually-dependent tasks: Verbal Reasoning 93 (Average), Quantitative Reasoning 106 (Average), Abstract! Visual Reasoning 80 (Low Average), Short-Term Memory 88 (Low Average). As the school psychologist observed, Carol was less comfortable with subtests that involved spatial orientation and/or placement and sequential ordering. It was suggested that such difficulties might have implications for reading. At the same time, Carol's overall test results were within the 'normal' (average) range; in fact, the Stanford-Binet indicated no cognitive deficiencies that might explain her poor level of school performance. To get more insight into Carol's level of cognitive functioning, the dynamic assessment procedure described earlier was recommended.

In the course of the Pretest, Carol willingly agreed 'to solve a problem'. She succeeded in solving the first problem correctly, leaving at the same time the impression that her success was just 'a good guess'. This impression was confirmed by her failure to solve a similar problem with a different set of figures, and as a result the dynamic assessment procedure was begun.

At Step #1 of the procedure, Carol seemed very involved. She listened very attentively to the evaluator's explanations and carefully watched his manipulation of the figures. Sometimes, however, she was reluctant to answer orally the evaluator's questions, limiting herself to gesturing (pointing, nodding, etc.). She apparently understood the algorithm for the process of analogical reasoning, and Step #2 of the dynamic assessment procedure was started.

At the beginning of Step #2, Carol memorized very easily the first three figures of the analogical reasoning problem. However, when asked to name the fourth figure, she gave the wrong answer. It was concluded that she was not able to perform the process of analogical reasoning at the symbolic level, and Step #3 of the procedure was started.

At Step #3, Carol confidently and accurately named all three figures in the picture, but was not able to identify the fourth figure. It was concluded that she was not able to perform the process of analogical reasoning at the visual- imagery level, and Step #4 of the dynamic assessment procedure was started.

When asked at Step #4 to make the fourth figure from the supplementary shapes, Carol paused briefly to think and then performed the task confidently and correctly. She was given a similar task with another set of figures, and again she made the fourth figure correctly and without hesitation. It was concluded that Carol was able to perform the process of analogical reasoning at the visual-motor level, and, accordingly, was at the visual-motor level of problem-solving activity.

Analysis of the Case and Suggested Remedial Intervention

As has been shown, standardized assessment of Carol did not reveal a delay in her cognitive development. These data alone can not explain the reasons for Carol's serious learning problems at school. The picture, however, becomes much clearer when one considers Carol's results on the dynamic assessment procedure. These indicate that Carol is at the visual-motor level of development of problem-solving activity, whereas the developmentally appropriate level of functioning for children of her age group is visual-imagery (Karpov, 1988; Khuntszyn, 1995). Thus, unless the teacher's explanations and students' learning are supported by manipulatory actions, which could rarely be expected in the second grade of a contemporary American school, Carol will inevitably have difficulties in acquiring new knowledge.

This interpretation of the reasons for Carol's problems makes it also possible to explain obvious differences between the characteristics of her performance in class as reported by the teacher (difficulty with attention, high distractibility, and poor recall of instruction), and the characteristics of her performance during the dynamic assessment procedure (good attention, an ability to concentrate on a task, and a willingness and ability to follow instructions). Of course, these differences may partly reflect the fact that almost any child would demonstrate higher attention and lower levels of distractible behavior in the one-to-one situation of psychological evaluation as compared with classroom learning. It could be suggested, however, that an additional factor that contributes to the deficiencies of Carol's classroom performance is her difficulty with learning without supportive manipulatory actions. Such a suggestion is consistent with the teacher's explanation of the deficiencies of Carol's classroom performance as a result of making her perform 'beyond her intellectual capability'. Thus, if asked to perform at her characteristic visual- motor level of problem solving, as she did in the course of the dynamic assessment procedure, Carol may be less likely to demonstrate such problems with self-regulation. The major recommendations for Carol is that her learning at school should be 'exteriorized' as much as possible. That means that both the teacher's explanation and Carol's learning should be initially supported by manipulations with objects or their substitutes. For example, given Carol's difficulties with phonemic awareness, a program such as Elkonin's (1976) could be recommended. This involves teaching the child to construct the phonetic models of different words through repeating the given word several times, every time stressing one of the sounds within the word and fixing this sound by putting a special chip on the table.

For example, the child is given for the phonetic analysis the word 'dog'. She repeats this word for the first time, stressing the first sound ('dddog'), and fixing the sound 'd' by putting a chip on the table. Then she repeats the word for the second time, stressing the second sound ('dooog'), and fixing the sound '0' by putting the second chip on the table. After that she repeats the word for the third time, stressing the third sound ('doggg'), and fixing the sound 'g' by putting the third chip on the table. Thus, the child has constructed the phonetic model of the word to be analyzed. When asked how many sounds the word 'dog' has, the child counts the chips on the table to arrive at the correct answer.

It was shown that the use of this procedure leads to a step-by-step internalization of the process of the phonetic analysis of words, until the child develops the ability to perform this analysis internally, neither stressing the sounds nor using the chips. Similar procedures for teaching elementary school students in different subject areas are described in Bodrova and Leong (1996).

In addition to making it possible for Carol to be successful in acquiring new knowledge, the use of the aforementioned instructional procedures could be advantageous for her in another respect. The most essential component of all these procedures is children's work with models of, and substitutes for, different processes and events. There is some evidence that these experiences may be instrumental in children's transition from the visual-motor level of problem-solving activity to the visual-imagery level (Elkonin, 1978; Poddyakov, 1977; Zaporozhets, 1978). To be sure, Carol's learning would benefit from this transition.

Conclusion: Comparative Analysis Of The Two Cases

Both Elaine and Carol were referred for evaluation due to significant learning problems, but the analysis of their two cases shows that the reasons for Elaine and Carol's poor learning at school and the recommended approaches to remedial intervention are not the same.

Whereas standardized assessment of Elaine's functioning could lead to a conclusion of poor cognitive development, the results of her dynamic assessment do not support such a position. These results indicate that Elaine is  at the visual-imagery level of problem-solving activity, which is developmentally appropriate for her age group. The data obtained from Elaine's psychological and educational evaluations interpreted in light of her performance during the dynamic assessment procedure and the results of her neurological examination make it possible to suggest that a major reason for her poor performance is poorly developed self-regulation. An efficient approach to remediate Elaine's self-regulation has been recommended.

The opposite situation pertains in the case of Carol, where standardized assessment did not indicate delayed cognitive development. The dynamic assessment procedure, however, did reveal such a delay: Carol is at the visual- motor level of development of problem-solving activity, whereas the developmentally appropriate level of functioning for children of her age is visual-imagery. Accordingly, Carol will have serious difficulties in acquiring new knowledge unless the teacher's explanations and her learning are supported by manipulatory actions. The recommendations have been formulated regarding instructional procedures that will make Carol's learning much more successful, and that may be beneficial for her transition to the visual- imagery level of problem-solving activity.

As Lidz (1991) noted, 'To merely describe the child's performance does not allow us to draw conclusions or to derive recommendations' (p.24). Assessment information should make it possible to reveal the reasons for the child's poor functioning, as well as to recommend efficient remediations. As was shown for the presented cases, the described dynamic assessment procedure meets these requirements.

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