Maarten K. van der Heijden

Center for the Study of Education and Instruction

University of Leiden - The Netherlands


'Approach behavior' is a 'fuzzy concept' that provides information on how students handle a (learning) task. In the paper, an holistic Vygotskian operational definition is developed for facilitating the objective description and measurement of approach behavior in its totality for different learning tasks. This operational definition is based upon (1) the three-part interactionmodel of action psychology, (2) diagnostic application of concepts used by Gal'perin. In the paper the emphasis is on the intellectual aspects of approach behavior. We discuss the function of the operational definition for the study of personality and learning.


Holism and empirical research
There seems to be an antithesis between empirical research and a holistic approach to personality and learning. Most empirical research on learning singles out one or a very few highly specific variables and is of a highly reductionistic character. Singley and Anderson (1998) conlude a discussion on prior knowledge and the subject conditions for transfer for instance as follows: "Taken to its logical conclusion, this point concerning prior knowledge puts cognitive psychologists in the quixotic position of not being able to say anything about current behavior without knowing the entire past intellectual history of subjects (Singley & Anderson, 1989, p. 267). We think that Vygotsky's idea of interiorisation can play a significant role here.

Vygotsky's legacy
During the past twenty years in Western Europe as well as in the United States there has been a growing interest in a psychological approach that diverges from the information-theoretical approach at several points. This so-called action psychology is a basically European approach rooted strongly in European philosophy (Van Oers, 1990; Van der Veer & Valsiner, 1991; Van Parreren & Carpay, 1972; Haenen, 1993). In Van der Heijden (1993) the above mentioned European Vygotskian approach is combined with the Anglo-American empirical-analytical tradition: (1) a general operational definition of the concept of approach behavior is worked out, (2) this operational definition is applied to the taskdomain of mental arithmetic (addition and subtraction up to 100), (3) diagnostic instruments are developed and individually administered with 174 elementary school pupils, and (4) the qualitative data are scored quantitatively, and several research questions are answered on the basis of a statistical analysis of the data.

In this paper the emphasis is on the theoretical and methodological aspects of the proposed general operational definition (section 2). We show how this general operational definition is worked out for the taskdomain of mental arithmetic and we discuss as an example some results of an empirical investigation in this taskdomain (section 3). In the last section (section 4) we discuss the function of our operational definition for the study of personality and learning.


'Approach' or 'approach behavior' is a 'fuzzy concept' that provides information on how students handle a learning task. The terms 'approach' and 'approach behavior' are used in information processing psychology as well as in action psychology (Van Parreren, 1951; Span, 1974; Veenman & Elshout, 1990). 'Approach' or 'approach behavior' refers to cognitive and metacognitive processes which take place when students are engaged in working on a problem. In this paper an holistic operational definition is developed for facilitating the objective description and measurement of approach behavior in general, i.e. in different learning tasks, for instance in mental arithmetic, spelling and reading. This operational definition is based upon the theoretical framework of action psychology. Action psychology, as we use the term here, will be understood as a psychological approach that studies all human attempts to deal meaningfully with material or mental objects in order to change them according to a certain goal. This psychological theory has been developed in Eastern Europe by Vygotsky, Luria, Leont'ev and Gal'perin, and in Western Europe by Lewin and Van Parreren (Lewin, 1926; 1935; 1942; Van Parreren & Carpay, 1972; Van Parreren, 1978; Van Oers, 1990). The influence of Vygotsky's legacy on our research on approach behavior can be summarized in two points:

In the next sections we successively go into these two points.

2.1 The three-part interactionmodel of action psychology
The interactionmodel of action psychology is a three-part model consisting of the components Situation, Person and Approach (see Figure 1). In the sixties the model has been worked out for classroom learning by Span (De Corte et al., 1974; Pennings et al., 1988). Witzlack (1977) and Witzlack et al. (1979) describe the model with respect to learning and assessment. We here give a short description of the models' three components in the first place. Next we shortly describe the model with respect to learning and development.

Component 1: Approach behavior
The model shows that, when a student is confronted with a task situation, a certain approach will result from the interaction between student personality and situation. At first glance, the model may appear trivial, but closer consideration reveals this not to be the case. Most cognitive-psychological interactionmodels contain only two components: person and situation (or environment). Models of information processing assume an essential distinction between internal (mental) and external aspects of human behavior. It is assumed that knowledge resides in symbolic structures in the head, and that mental processes consist in using, editing, and creating those symbolic structures (Greer & Verschaffel, 1990). Behavior is seen as the external result of internal productive mechanisms. The general model of behavior in action psychology on the contrary, is not dualistic but monistic: cognitive processes as well as behavior are of the same nature. Both are conceptualized as actions and can be interpreted as attempts to change material or mental objects (Van Oers, 1990). The three-part nature of the action-psychological model indicates that approach behavior is a separate category. Approach behavior neither belongs to the personality of a student, nor to the situation. Approach behavior (or more general human activity) - the middle member of the three-part model - forms the process through which the subject interacts with the surrounding world of objects (Leont'ev, 1979).1)

Component 2: Situation
Human activity does not take place in a vacuum but in a concrete socio- cultural and historical context. Within the situation-component we find the objectively (or in any case intersubjectively) demonstrable physical objects (i.e. people and things) with which the subject is acting, or perhaps better said, with which the subject is interacting.

It is important to notice that the person is not reacting directly to the objectively given objects in a situation. The relevant objects in a situation on the contrary have a particular meaning or sense (Leont'ev, 1979) for the actor, and it is just this meaning that is determining activity. "Therefore, it is not any of the factors in themselves (if taken without reference to the child) which determines how they will influence the future course of his development, but the same factors refracted through the prism of the child's emotional experience [interpretation or appraisal]" (Vygotsky, 1994, p. 340, between brackets added by MvdH). In the model this refractioning- or appraisal-process is indicated by a lense.2)

Component 3: Person
Action psychology considers the actor as a goaldirected and partially rational being who actively tries to realize his or her goals, while orienting him or herselve on partially rationally grounded expectations (Van Parreren & Schouten- Van Parreren, 1981). In action psychology personality is conceived as a dynamic and layered phenomenon, in which rational and conscious actions build upon unconscious activity (Van Parreren, 1978). Personality can be characterized by relatively stable intellectual, motivational and emotional personality characteristics: the action potentialities or the action repertoire (Kossakowski et al., 1977; Van Parreren, 1988). Prior kwowledge can be considered an important part of this action repertoire. It is outside the scope of this paper to deal extensively with action-psychologically oriented theories of personality (Witzlack, 1977; Kossakowski et al., 1977; Asmolov, 1984; Smith, 1985; Schmidt, 1986; Trzebinski, 1985; Vorwerg, 1990; Van der Heijden, 1993).

Interaction, development, learning and interiorisation
Asmolov describes the relations between the three components with respect to development as follows: "the properties of the individual as organic preconditions for the development of the personality, the social environment as a condition for the development of the personality, and contradictions in the system of object- oriented activity as the driving force of the development of the personality" (Asmolov, 1984, p. 26). Vygotsky formulated the so-called interiorisation hypothesis about mental development: "Every function in the child's cultural development appears twice: first on the social level, between people (inter- psychological), and then inside the child (intrapsychological). This applies equally to voluntary attention, to logical memory, and to the formation of concepts. All the higher functions originate as actual relations between human individuals" (Vygotsky, 1978, p. 57; see also Valsiner, 1987).

Kossakowski & Lompscher describe the process of interiorisation with respect to approach behavior as a process of the formation of solid habits: "Wenn gleiche oder ähnliche Besonderheiten im Ablauf der psychischen Prozesse in der Tätigkeitsregulation wiederholt auftreten, verfestigen und verallgemeinern sie sich allmählich, d.h., sie werden für den Prozessverlauf bei dieser Persönlichkeit typisch und treten als individuell typische Fähigkeiten oder durch andere Verlaufsqualitäten psychischer Prozesse in unterschiedlichen Situationen mit hoher Wahrscheinlichkeit wieder auf. Man kann die Entwicklung aktueller psychischer Prozessqualitäten zu verfestigten Eigenschaften der Persönlichkeit in gewisser Weise auch als einem Vorgang der Interiorisation (Verinnerlichung) ursprünglich äusserer und äusserlich bedingter Tätigkeitsformen zu psychischen Verlaufsqualitäten charakterisieren" (Kossakowski & Lompscher, 1977, pp. 133-134).

From an action-psychological view learning is understood as a process of qualitative improvement of human actions as a result of both social intercourse with cultured others, and as a result of manipulations with culturally designed objects in a socio-historic environment (Van Oers, 1990; Tomic & Span, 1993).

2.2 Diagnostic application of the conceptual framework of Gal'perin
In this section we present the proposed general operational definition of 24 intellectual aspects of approach behavior. In section 4 below we will shortly discuss emotional and motivational aspects of approach behavior.

The intellectual aspects of approach behavior
According to action psychology, human activity consists of externally observable, practical actions as well as mental actions (Van Parreren & Carpay, 1972; Van Oers, 1990; Haenen, 1993). In order to describe the actions which make up approach behavior, we chose the conceptual framework used by the Russian educational psychologist P.J. Gal'perin who worked out the ideas of Vygotsky. Gal'perin's theory is by now well known thanks to various translations, introductory readers and summaries in different languages (Gal'perin, 1969; Van Parreren, 1978; Davydov & Andronov, 1981; Haenen, 1989; 1992; 1993).

Gal'perin makes a distinction in the first place between:

Secondly, Gal'perin distinguishes six properties or parameters for describing actions, namely:

As a seventh property we here add:

We can now describe the orienting, executive and control actions performed by a student in solving a problem in terms of the above-mentioned 7 properties of activity. This yields 21 indices for aspects of approach behavior.

On the basis of a literature study regarding the approach behavior of students with learning problems (Van der Heijden, 1993), we here add the following two properties, namely:

Finally, we describe the actions performed by a student in terms of:

We can now describe the orienting, executive and control actions performed by a student in solving a problem in terms of the above-mentioned properties of activity. This description produces 24 indices for what we have called the intellectual aspects of approach behavior.

Diagnostic operationalization: process assessment and dynamic assessment
Vygotsky is often cited in connection with assessment of 'the zone of proximal development' or dynamic assessment (Schneider Lidz, 1987; Hamers et al., 1993). However Vygotsky propagated particularly a process approach (Wertsch, 1985; Van der Veer & Valsiner, XXX). In our research, in order to determine the various aspects of approach behavior, we use procedures taken from practical process assessment as well as dynamic assessment.

In process-assessment, or qualitative assessment, description of cognitive and metacognitive processes is emphasized in contrast to assessment of achievements in performance testing (Holowinsky, 1980; Meyers et al., 1985). Already in the twenties Lewin pleaded for using process-concepts rather than performance or achievement-concepts: "The danger of using performance-concepts ['Leistungsbegriffe' in German] can not be taken too seriously" (Lewin, 1926, p. 18, transl. MvdH; see also Lewin, 1935). Process-assessment in comparision with performance testing is characterized by a higher degree of relevance for instruction and remediation (Van der Heijden, 1993). Ysseldyke and Algozzine put in this respect: "Why is it that school personnel administer so many tests in order to make decisions about students? Is it because they learn so much about the students and how to teach them? Apparently, educational personnel believe so. We think, however, that there is much evidence to indicate that assessors learn very little about students from the students' performances on standardized tests" (Ysseldyke & Algozzine, 1982, p. 127).

In action-psychological oriented process assessment or qualitative assessment actions performed by a student in a concrete tasksituation are retrieved (or properly speaking re-constructed) by combining data originating from retrospection with data originating from behavior observation (Van Parreren, 1981). Combining data from these two different sources is often found in practical process- diagnostics, but rarely applied in scientific research. Process assessment is already in 1944 described by Cattell as interactive measurement (see figure 1) as opposed to normative measurement: "measurement in terms of the actual physical and biological effects of behavior, usually, in test situations, within a restricted framework defined by the test. It recognizes the onenes of the organism- environment and pays tribute to the oft-forgotten fact that a trait is never resident only in the organism but is a relation between the organism and the environment" (Catell, 1944, p. 293; italics MvdH). Catell continues: "interactive quantification is the queen of measurement" (ibid., p. 299).

In dynamic assessment, the student is helped or given instruction in order to determine the degree of independence of the student's activity: can a student who is unable to perform a certain activity spontaneously manage to do so when aided by an adult? Dynamic assessment can be regarded as the determination of 'the zone of proximal development' (Vygotsky, 1978).

Practical application
The above proposed general operational definition can be applied to different taskdomains, for instance arithmetic, reading and spelling. It depends on several factors which of the 24 aspects can factually be operationalized in practice. These factors are: (1) specific kind of tasks used, (2) level of progress of students in the taskdomain, and (3) specific diagnostic procedures that are applicated.


The above general operational definition of the concept of approach behavior was worked out for the task domain of mental addition and subtraction up to 100. This yielded the Leiden Diagnostic Arithmetic Approach Test (abbrevation: LDRT), a process-diagnostic instrument for assessing aspects of approach behavior in mental arithmetic. In mental arithmetic students actions are for a great deal abbrevated and automatic. With our test we were able to measure the following eight aspects of approach behavior:

  1. (1) Lack of attention
  2. (2) Orientation (handy arithmetic)
  3. (3) Solution procedures
  4. (4) Automatization
  5. (5) Flexibility
  6. (6) Insight
  7. (7) Consciousness
  8. (8) Control.
In addition, the LDRT produces two achievement-variables: a correct/incorrect score and a reaction time score.

We here give as an example a short description of our empirical study: a description of the instruments and especially a description of the operationalisations of the eight aspects of approach behavior, some information of the design and research questions and a summary of some of the results of our empirical investigation.

3.1 Leiden Diagnostic Arithmetic Approach Test
The Leiden Diagnostic Arithmetic Approach Test (Dutch abbrevation LDRT) (Van der Heijden, 1988a) is a standardized process-diagnostic instrument for assessing the above mentioned eight aspects of approach behavior in mental addition and subtraction up to 100. The test is administered individually and consists of two parts. Part A contains 30 mental arithmetic problems in formula form with two terms (for example: 34-18=?). Part B contains 18 problems with three terms (for example: 15+13-17=?). (See Van der Heijden, 1993 (p. 333) for a complete survey of the problems).

The problems of the LDRT are classified according to three criteria:

  1. (I) four types of problems with two terms: addition and subtraction with and without carrying over
  2. (II) three types of problems with two terms classified according to degree of difficulty (empirical criterion based on the answers given: more than 80% correct / between 65% and 75% correct / less than 60% correct)
  3. (III) eight types of so-called 'handy-arithmetic problems' with two as well as three terms that allowed effective strategy choice (for example: 18+14+2=? / 15+17-15=?).
The child is asked to read aloud a problem, to compute the answer, and to say the answer and to write it down. On the basis of behavior observation and standardized retrospection-questioning scores are produced for eight aspects of approach behavior in mental arithmetic. The LDRT instruction manual contains standardized retrospection- questioning rules, helping algorithms and fixed observation criteria, and the scoring manual contains fixed scoring rules. Approximately 40 raw scores are collected for one problem. In our study, approximately 300.000 data were fed into the computer. In order to create the approach-variables a phase of data- reduction, data-modification and data-aggregation (on all problems of the two parts of the test as well as on several problems of the same type) was necessary (see Van der Heijden, 1993). Below we will present a rather general description of the eight approach-variables as well as the two achievement-variables in mental addition and subtraction up to 100.

Achievement-variables and approach-variables
The LDRT produces two achievement-variables in the first place: a correct/incorrect score (based on the first given answer) and a reaction time score (based on the time needed for computation). The internal consistency (Cronbach's alpha) of these LDRT achievement-variables (on 30 and on 18 items) is .85 to .94 (N=174).

Secondly the qualitative retrospection-protocols are scored quantitatively. This results in several variables for eight aspects of approach behavior in mental arithmetic:

1. Lack of attention
In the LDRT, addition and subtraction problems are presented in random order. A student exhibits lack of attention if he or she, while reading aloud the problems, makes mistakes in (1) the sign (plus instead of minus or the reverse) and/or (2) the numbers (for example reading 52 instead of 25). Lack of attention is also diagnosed if a student makes mistakes in the writing down of the answers (for example writing 36 but saying 63). On the basis of the results on the prior knowledge test for the LDRT (see above) number errors were divided into errors due to lack of prior knowledge or errors due to lack of attention (i.e. mistakes).

2. Orientation (handy arithmetic)
The goal of orientational activity is to survey the situation and the possibilities for action in it. Gal'perin uses the terms 'insight' and 'skill' here: "It is clear that the differences in one and the same action with different children arise from differences in insight in the action and from differences in the skill to execute the action in different situations. 'Insight' and 'skill' are the subjective descriptions of the two most important parts of the objective action that is executed by the child. We name the one part, that we briefly indicate with the term 'insight', the orientational part, because of the objective function of this part in the action as a whole. ... The second part of the objective action consists of the execution itself" (Gal'perin, 1972, transl. MvdH).

In the LDRT the degree of orientation is defined on the basis of the degree to which handy arithmetic problems are solved in a handy instead of a standard fashion. The handy approach is based on a 0/1 scoring of the retrospection-protocols. Some examples are given below.

Problem          Handy approach
18+14+2=?        student restructures problem (does first
15+17-15=?       student does first 15-15=0

Verschaffel et al. (1992) demonstrated the validity of retrospection with these 'clever strategies' by using eye movements in combination with retrospective data.

By applying stepwise structured help with students that did not display the handy approach spontaneously, scores for the degree of independence of the handy approach were ascertained as well (zone of proximal development). Van der Heijden (1993, pp. 330-332; 1994) describes the procedures for help as used.

3. Solution procedures
For the nature of the task specific operations (executive actions) the retrospection- protocols are analysed with respect to the applied solution procedures (Klein & Beishuizen, 1994). Here, two main procedures are widely in use: the so called decomposition strategy or split-procedure '1010' (15+13=? as (1) 10+10=20 / (2) 5+3=8 / (3) 20+8=28) and the whole number strategy or jump-procedure 'N10' (15+13=? as (1) 15+10=25 / (2) 25+3=28). The LDRT scoring manual gives detailed scoring instructions for these two main procedures as well as some others.

4. Automatization
The retrospection- and observation-protocols are scored (0/1-scoring) on the following process-aspects of automatization of component actions, based on the theory of P.J. Gal'perin (see section 1.2). Following Gal'perin the process of automatization is characterized by a increasing degree of abbrevation as well as level of the activity:

  1. (1) Degree of abbrevation (from high to low):
  2. (2) Counting-level (from high to low):
On the basis of the raw scores of (1) and (2) an automatization composite score is computed and aggregated over the problems (see Van der Heijden, 1993, p. 338). This automatization composite score indicates the degree of automatization.

5. Flexibility
Flexibility is defined as the use of a different approach with different problems or problemtypes in order to raise computational efficiency. From previous research (Van der Heijden & Beishuizen, 1986; Beishuizen, 1993) it appeared that some students use the above mentioned two solution procedures in a flexibel way dependent on the type of problem at hand: 1010-procedure with addition problems and N10-procedure with subtraction problems. Probably this is due to the fact that with subtraction the 1010-procedure causes a higher load on working memory and increases the risk for errors, especially with subtraction problems with carrying (41-39=? as 40-30=10 / 9-1=8 / 10+8=18). On the basis of an analysis of the retrospection-protocols a flexibility-of-procedures variable is defined as the degree in which students use the 1010-procedre for addition and the N10- procedure for subtraction problems.

6. Insight
Insight is defined by Gal'perin as the degree to which actions are based on the relevant and essential properties of the situation at hand. The approach-variable insight is based on an analysis of the protocol with respect to the kinds of errors made. It is beyond the scope of this chapter to deal extensively with the analysis of errors of the LDRT (see Van der Heijden, 1993, pp. 80-82). However insight errors are defined as errors that are repeated when the child is asked to solve a problem with a wrong answer again. Counting errors, and errors due to wrong automatizations are excluded from the definition.

7. Consciousness
In action psychology the concept of consciousness takes a central position: "With the exeption of the concept of 'activity' itself, consciousness is the most important category of activity theory" (Kaptelinin, 1992, p. 45). The degree of consciousness of a student's activity is defined as the degree to which a student is able to account for his or her actions, mainly in a verbal manner. There are different aspects of activity that students can more or less account for (Asmolov, 1981). The LDRT produces three approach-variables for this aspect of approach behavior.

A variable consciousness verbalisation of executive actions is based on a quantitative judgement of the quality of the verbal retrospection protocol. How well the student is able to account for his or her computational actions is diagnosed on the basis of a scoring of several aspects of the protocol:

Secondly a variable consciousness of a correct or incorrect answer is based on a comparision of the students given answers with the students judgements of their answers as correct or incorrect.

In the third place the students are questionned about the kind of errors they made. On this basis a variable consciousness of type of errors is defined as an indication of the degree to which the students are able to say something about this aspect of their computational activity.

In our study the above three consciousness-variables are treated separately and a single composite score indicating 'consciousness' is computed as well.

8. Control
During the administration of the LDRT several opportunities are given to the students to correct their answers. A control-variable is based on the occurence of corrective actions during the test administration.

The reliability of the LDRT approach-variables was investigated in two ways:3)

(1) By a separate generalizability study in which the LDRT was administered two times with one student by two assessors. Assessor 1 interacted actively with the student (and made a protocol) and assessor 2 only made the protocol passively. The roles of assessor 1 and 2 were alternated.

(2) By analysis of assessor effects in this study (N=174), which was conducted by 7 assessors.

Both reliability studies revealed no significant assessor effects (Van der Heijden, 1993, pp. 150-151).

Validity of the approach-variables was investigated on the basis of correlational analyses between LDRT approach-variables and respectively (1) LDRT-achievement variables, (2) the two mathematics achievements tests, (3) the indices for verbal and non-verbal intelligence (see section 3.2). The results of these analyses show a satisfying convergent and discriminant validity (Van der Heijden, 1993). Correlations with the schoolnotes suggest ecological validity as well.

3.2 Other instruments
Two Dutch standardized general mathematics achievement tests were taken by the students (GSO: Kema & Kema-van Leggelo, 1987; TTR: De Vos, 1987). In addition a standardized vocabulary test (indication for verbal intelligence) (GSO: Kema & Kema-van Leggelo, 1987) and Raven's Coloured Progressive Matrices (Van Bon, 1986) were administered. These instruments have satisfying reliabilities.

Schoolnotes for mathematics were obtained from the teachers. Also a measure of the educational and occupational background of the parents (SES indication) was obtained (Van Westerlaak et al., 1975).

In addition a instrument was developed by the author in order to measure the prior knowledge needed for computation of the problems of the LDRT:

Prior knowledge test for the LDRT
In action psychology knowledge is conceived as action-potentialities resident in the individual (i.e. in the person-component of the three-part model). The prior knowledge test for the LDRT produces two scores for general prior knowledge necessary for mental arithmetic up to 100:

  1. (1) reading and writing numbers, and
  2. (2) knowledge of the place value system.
In addition, this test produces three scores for specific preconditions for handy arithmetic.

The results on reliability (Van der Heijden, 1993, p. 130-131) of the prior knowledge scores express a satisfying reliability.

3.3 Design, population, research questions and statistical analyses
Our research can be considered as descriptive. The in sections 3.1 and 3.2 mentioned instruments were administered with 174 elementary school students at the end of second grade. The sample consisted of 93 boys and 81 girls. The mean age of the students was 8 years and 3 months (SD: 5 months; min.: 7 years and 8 months; max.: 9 years and 7 months). The 174 pupils were from 8 schoolclasses. In 4 classes a traditional mathematics method was used and 4 classes used a modern method. The boys and girls were equally divided among the schoolclasses. Although no attempt was made to provide a representative sampling, the average level of arithmetic achievements in our group did not differ from the general population of second grade students in the Netherlands (Van der Heijden, 1993, pp. 122-126). Every student was individually interviewed during about three hours.

Because we in the first instance did not want to make assumptions about the approach variables higher than on a ordinal level we did nonparametrical analyses in the first place. However comparing nonparametrical results with results of parametrical analyses did not lead to different interpretations. The following statistical analyses were executed in order to answer questions about the following subjects.

Consistency of approach behavior
The following domain-specific consistency questions were investigated:

In order to answer these questions we did Nonlinear Principal Components Analysis (SPSS-procedures HOMALS and PRINCALS) as well as nonparametric analysis of variance (Friedman ANOVA; see Siegel & Castellan, 1988). In addition we compared Kendall's W computed on the original data-matrix with Kendall's W computed on the transposed data-matrix (see ibid.), and we also computed Cronbach's alpha.

Relationships between approach, achievements and intelligence
Relationships between approach-variables, achievement-variables and intelligence were investigated by correlational analyses (Spearman's rank order correlations, Pearsons product moment correlations, as well as partial correlations). Especially we were interested in the question to what degree both LDRT-achievement variables could be predicted by the approach-variables together. This question was analysed by nonlinear canonic correlation analysis (SPSS-procedure CANALS) as well as regression analysis. In Van der Heijden (1993) the regression results are presented.

Structure of approach behavior
The bivariate interrelationships between the approach-variables were investigated by correlational analyses. The multivariate relationships of the approach-variables were explored by Nonlinear Principal Components Analysis (SPSS-procedure PRINCALS).

Determinants of handy arithmetic
A previous study (Van der Heijden, 1988b) revealed that the majority of students approach handy arithmetic problems in a standard fashion. In order to get some more information about possible determinants of this deficiency in the handy approach we included in this study (1) measurement of some specific preconditions for handy arithmetic (see section 3.2: test for prior knowledge), and (2) measurement of the degree of independence (zone of proximal development) of the handy approach (orientation).

Gender differences
Gender differences were explored by analysis of variance with and without covariates. Possible gender differences in prior knowledge, intelligence, age and socio-economic status were excluded as explanation for the gender differences en LDRT-approach en achievement variables. The question wether differences in achievement between boys and girls could be explained by differences in approach was investigated by analysis of variance on the LDRT achievement- variables with the LDRT approach-variables as covariates.

3.4 Main conclusions of the empirical study
Detailed results of the above mentioned analyses are described in Van der Heijden (1993). The main conclusions of our study are briefly summarized below.

Consistency of approach behavior in mental arithmetic

The opposite is found in only one aspect of approach behavior for one specific problem type.

In Van der Heijden (1993) we contend that the high degree of consistency found here can be interpreted as inflexibility: Students tend to use the same solution methods regardless of the type of problem at hand. On the basis of our results, we demonstrate that this type of inflexibility is linked to relatively low achievements in mental arithmetic, while, on the other hand, a flexible approach is linked to relatively higher achievements.

Arithmetic approach, arithmetic skills and intelligence

Central aspects: consciousness - control - automatization
From the principal components analyses on the approach-variables is concluded:

The importance of consciousness and control (metacognition) for mental arithmetic using formula problems with which students have relatively much experience is particularly striking. On the whole, little attention has been paid to these aspects of approach behavior in scientific research into mental addition and subtraction. In Van der Heijden (1993) these research results are discussed against the background of theories regarding consciousness, automatization, metacognition, control and metacontrol (Shiffrin & Schneider, 1977; Brown, 1979; Flavell, 1979; Leont'ev, 1979; Baars, 1988; Van Haneghan & Baker, 1989 ; Kaptelinin, 1992).

Handy arithmetic, orientation and the functioning of knowledge
These results are in accordance with an observation made by Gal'perin (original publication from 1941): "for though a system may exist, one may nonetheless be unable to use it. And that is the crux of the matter: a system may be used or not" (Gal'perin, 1979, p. 91). The conclusion must alas be drawn that the students' education has not led to the habit of first analyzing a problem before beginning the calculations: a 'mathematical attitude' or 'disposition to higher order thinking' (Resnick, 1987) is conspicuously absent here. At this point Resnick remarks: "people have thinking abilities that they do not necessarily use. (...) This possibility puts the question of higher order skill teaching in a new light. It suggests that the task for those who would raise the level of intellectual performance of children is not just to teach them new cognitive processes, but to get them to use those processes widely and deeply" (Resnick, 1987, p. 433).

Gender differences
As to differences between male and female students, the results confirmed the following pattern:

In Van der Heijden (1993) the above results are discussed against the background of research into gender differences in arithmetic and mathematics achievement (cf. Friedman, 1989). There, a number of socio-cultural, motivational and emotional factors are propounded in explanation of gender differences found here (Fennema, 1985; 1989; Lester et al., 1989; Tavecchio et al., 1991). The above results offer points of departure for decreasing gender differences in arithmetic achievement by means of teaching a more adequate approach behavior. And if our hypothetical explanation for the gender differences found here is supported in future investigations, mathematics instruction has not only to deal with intellective factors but with non-intellective factors such as self-confidence and fear of failure as well (Van der Heijden, submitted for publication).


In this paper we presented a holistic operationalisation of the concept op approach behavior based on: (1) the three-part interaction-model of action psychology, (2) the conceptual framework of Gal'perin, and (3) practical process assessment and dynamic assessment procedures. We presented as an example some results of an empirical study in the domain of mental arithmetic. In this section we want to discuss the function of the proposed operational definition for the study of personality and learning in the following four points: (1) domainspecific research, (2) extension of our model with non-intellective factors, (3) cross-situational consistency of approach behavior, and (4) relevance for instruction and remediation of learning problems.

To begin with we discuss a possible objection against our approach: the atomistic or elementaristic character of the proposed operationalisation. It may be contented that our approach is violating the meaningful character of activity by 'counting actions' with certain properties and doing statistical analyses on these separate elements. We would like to answer this objection in the following way: In the first place our approach presupposes that meaningful wholes of activity are analysed, for instance the solution of a mathematical problem, the reading of a text etc. It is important that the task situation (as well as the duration of time of the units of analysis) is precisely described and consists of a meaningful piece of activity (Tolman, 1932). Secondly our smallest units of analysis (or elements of our analysis) consists of the actions that are part of a meaningful activity. The aspects of approach behavior have to be considered as sides of this phenomenon that can be distinguished (or constructed) by the observer. In the third place we think that the results of our statistical analyses (see section 3) indicate that meaningful results can be obtained.

Domainspecific research
Most empirical research in the field of learning is highly reductionistic, i.e. using but one of the approach variables for instance automatization or conscious awareness or control. It is inpossible to gain insight in the relationships between different aspects of approach behavior and their relation with achievement by way of these reductionistic studies. In addition we think that reductionistic approaches lead to overemphasis on one factor as the decisive one for learning and instruction depending on the fashion of the time and the choice of individual researchers.

Our empirical study produced reliable and valid data and our study produced some interesting results in the field of mental addition and subtraction up to 100. So application of our approach to other fields (i.e. reading and spelling) may be fruitful as well.

In addition the proposed operationalisation facilitates research into the relationships between the structure of psychological processes (approach behavior) and psychoneurological activity of the brain (Luria, 1973; Eccles, 1994).

Motivational and emotional aspects of approach behavior
It is by now rather widely recognized that in research on learning intellective as well as non-intellective variables are of influence (McLeod & Adams, 1989; Boekaerts, 1991; McLeod, 1990). One of the characteristics of human activity is that it is not dispassionate and disinterested. In action psychology the individual is not seen as a rational processor of information but as an emotional involved goal directed being (Van Parreren, 1981). The intellective aspects of approach behavior that we described in this paper can easily be complemented with non-intellective aspects such as motivation, emotion and personal sense. In action psychology motivation is mainly conceptualised as a description of the goals a student tries to pursuit. Already in 1942 Lewin writes: "All intellectual processes are deeply affected by the goals of the individual" (Lewin, 1942, p. 238). In action psychology emotions are conceived as having mainly an evaluative as well as a heuristic function (Tikhomirov & Vinogradov, 1975; Van Parreren, 1989). Gal'perin includes an emotional/volitional valuation (appraisal) in the orienting activity: "The orienting activity in its broad range - from perception to thinking - is not restricted to intellectual functions. Needs as well as emotion and volition not only require orientation, but are psychologically speaking nothing else than different forms of the orienting activity of the subject" (Gal'perin, 1980, p. 113).

At the moment we are working out the motivational and emotional aspects of approach behavior on the basis of motivation theory (Heckhausen, 1980) and emotion theory (Frijda, 1986). This opens up possibilities to study the relationships between the intellective and the non-intellective aspects of approach behavior and to test for example the following hypothesis: "emotional insecurety ... is the basic cause of most educational disabilities and learning failures, which are not due to mental defect" (McCarthy, 1948; cited in Wechsler, 1950, p. 84).

However much work has to be done to work out theoretically as well as instrumentally these non-intellective aspects of approach behavior.

Cross-situational consistency of approach behavior
Our general operational definition of approach behavior is now being worked out for other task domains as well (i.e. in reading and spelling). This facilitates future research into the as yet unsolved issue of cross- situational consistency of approach behavior across different learning task domains (Alexander & Judy, 1988; Ennis, 1989; Perkins & Salomon, 1989; Van der Heijden, 1993).

One of the as yet unresolved fundamental issues in learning as well as in personality psychology is the person/situation controversy: to what extent is behavior determined by personality characteristics, by the properties of situations, or by person/situation interactions? A related, and sensitive issue in assessment is whether, when dealing with a student with learning problems, one should set up and test diagnostic hypotheses regarding personality traits relevant to learning (such as intelligence and cognitive style), or situation characteristics (such as the didactic method used) or interactions between the two (Sundberg, 1977). In the classic psychometric approach, judgments regarding students' personality traits are based on the administration of standardized psychological tests. In the (more modern) behavioral approach to assessment, the tendency is to limit oneself to situation specific judgments based on direct observation of a given learning behavior (Shapiro, 1987). The two approaches, viewed theoretically, are at odds with one another and do not do justice to the variety and complexity of the phenomena. On the one hand are students whose action repertoire reveals fundamental shortcomings. Such students demonstrate an adverse approach to all sorts of school tasks; that is, they have an inadequate work attitude that is more or less interiorised in their personality. On the other hand, however, are children who merely demonstrate domain specific deficiencies in one or a few subjects.

In Van der Heijden (1993), an initial impetus is given to what we have called a process-consistency approach to personality. Conclusion of a certain personality characteristic is based on determining the degree of consistency of approach behavior across different learning tasks. This diagnostic decission procedure is, as it were, diametrically opposed to the reasoning in which behavior in a given classroom situation is predicted on the basis of a psychometric test score.

If we have determined that Sylvia demonstrates a great deal of consciousness in approaching an arithmetic task, a reading task, and a spelling task, then we may state that Sylvia's personality is characterized by a high degree of consciousness.

If we have diagnosed a lack of insight in Karl's approach to an arithmetic task, a reading task, and a spelling task, then we may state that Karl's personality is characterized by a lack of insight.

If Erica demonstrates a lack of attention in approach behavior with regard to all sorts of arithmetic problems, but works intently at other learning tasks, then we may state that a lack of attention does not typify Erica's personality but, rather, that the lack of attention is situation specific: it remains confined to one task domain, namely arithmetic.

Determining the degree of consistency of approach behavior (or speaking with Vygotsky the degree of interiorisation) is important in diagnosing learning problems because the more different learning task domains there are in which a student demonstrates the same inadequate approach, the less a plan of treatment can restrict itself to task specific subject deficiencies. In such instances, diagnostic hypotheses must also be formulated and tested regarding the fundamental shortcomings in the action repertoire and their possible causes.

The proposed process-consistency approach makes use of common processes in various learning tasks in order to describe aspects of the personality structure. Cattell indicates a similar approach when stating: "The objective location and measurement of common processes (...) is practically unrepresented in psychological research at the present time. (...) Despite this methodological neglect it is obvious that processes, for example, typical processes of learning (...) are important structures. They are structures in the sense of recurrent patterns of behavior, but even less than traits are they to be considered as definable entirely in the individual. They are joint structures in the individual and his physical environment" (Cattell, 1979, p.33). In the same vein, Bem states in the framework of the person/situation controversy: "Our fundamental scientific task is to convert observations of particular persons behaving in particular ways in particular situations into assertions that certain kinds of persons will behave in certain kinds of ways in certain kinds of situations, that is, to construct triple typologies or equivalence classes - of persons, of behaviors, and of situations - and to fashion theories of personality that relate these equivalence classes to one another" (Bem, 1983, p. 566). The process-consistency approach suggested here reveals similarities to the 'act frequency approach to personality' propagated by Buss and Craik within the psychology of personality (Buss & Craik, 1986).

A number of conceptual, methodological, instrumental and empirical conditions must be met in order to conduct research into the cross-situational consistency of approach behavior across different learning task domains (Van der Heijden, 1993).

Instruction and remediation of learning problems
Our holistic operationalisation can serve as an 'overarching theory' (Schön, 1983) for process assessment in different learning task domains. Our approach is directly relevant for instruction because the conceptual framework of Gal'perin that we use diagnostically makes up also the instructional theory as developed by Gal'perin: the theory of the stepwise formation of mental actions (Haenen, 1993). Gal'perin's instructional theory has proven especially fruitful for students with learning problems (Lompscher, 1972; Van Parreren & Carpay, 1972; Gal'perin, 1974; Rollet, 1987; Koning, 1988). But in the Vygotskian tradition there are also different approaches to instruction (Davydov, 1982; 1993; Carpay, 1993).

In practical work with children with learning problems holism is a conditio sine qua non because one always deals with the total personality of the child, including his or her history. Many remediation programms for children with learning problems exclusively focus on the exucutive aspects of approach behavior neglecting orientation, consciousness and control, and also neglecting the motivational and emotional aspects. A holistic approach is also important because in remediation one has to base a programm on the weaknesses as well as on the strengths of the child (Vygotsky, 1993).


1) From an epistemological point of view Toulmin puts forward in a comparable line of reasoning that the idea that mental life or the 'psyche' resides in our heads has turned out to be incorrect. And that we don't realize enough that mental life stems from practical live that we have internalised in one way or another (Toulmin cited in Kayzer, 1993 p. 262 and 276).

2) So the concept of 'situation' we use here has not to be confounded with the concept of 'situation' used by Lewin. Lewin's concept of 'situation' includes the subjective appraisals of the individual (Stadler, 1989).

3) In terms of test-reliability the high degree of consistency (see section 3.4) can be interpreted as a satisfying reliability as well.

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