Inclusive and Supportive Education Congress
International
Special Education Conference
Inclusion: Celebrating Diversity?
1st - 4th August 2005. Glasgow, Scotland
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Inclusive and Supportive Education Congress 1st - 4th August 2005. Glasgow, Scotland |
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Assistant Piia Vilenius-Tuohimaa
University of Helsinki, Finland
piia.vilenius@helsinki.fi
In general, the research focusing on learning difficulties has been constrained to mainly consist of one background aspect at a time. The aspects usually arise from psychology, neuropsychology, linguistics etc. The sociocultural approach, however, combines the previously mentioned in a way that is also a quite useful in special educational interpretations. Sociocultural approach includes cultural institutions, linguistic mediation, the developing mind and social practices among the evident cultural aspect (Forman et. al, 1993).
Sociocultural approach today may be considered as an expansion to the Vygotskian activity theory research genre for its similar concepts of learning and the widely spread research that almost always includes Vygotsky’s theoretical and practical assumptions within the experiments and also in the research reports following. In this paper, also the British sociologist’s, Basil Bernstein’s, views are used in terms of discussing the role and effect of linguistic expression and linguistic abilities on children’s mathematical thinking. That is, mathematical learning difficulties may have their source in a very complex chain of events and competences other than for example the fact that the learning problems often are of a genetic origin. That chain might partly consist of social, motivational and language-based problems that end up as difficulties in solving different kinds of mathematical tasks.
The children’s task-orientation is an important aspect when mathematical competences are in question. Combined to the discussion about the linguistic expression, in my research project (Vilenius-Tuohimaa, 2005) there was a clear connection between children’s task-orientation and mathematical ability. When the concept of the motivation (or task-orientation) is considered to affect one’s linguistic abilities, the connection is less clear. But it has to be admitted that, one of the Bernstein’s theoretical assumptions is that also the family’s attitudes towards the school system, are reflected into one’s linguistic expression. That is: also task-orientation is partially socioculturally produced.
When this discussion about the usefulness and the holistic views of the sociocultural approach are combined to special educational reflections on mathematical learning difficulties, one important conclusion can be made: In addition of finding out the accurate area of one’s difficulty in learning mathematics and the organizing of a suitable part-time special educational plan for the pupil having problems, there should also at least be a consideration of the other factors such as possible problems understanding the school’s discourse, lack of motivation etc. behind the surfacing difficulties in order to produce really effective interventions.
Basil Bernstein developed a theory of linguistic elaboration in 1970’s. That abstract construct of the forms of language was divided into two language code types that were described as either restricted or elaborated according to how a person communicated (see Bernstein, 1973). According to the theory, a person who expresses her thoughts in a way that has a high level of content expectancy and when the form of the message is simple, stereotypical and grammatically inconsistent, the message may be considered as a sample of the restricted code type. Instead, the elaborated code type has been described as an analytical, flexible and a creative way of communicating. However, these classifications have been highly challenged (see Gumperz, 1972; Huspek, 1995) and the theory of the code types has been seen as structuralistic and deterministic (May & Harker, 1995), although Bernstein himself challenged this critique (Bernstein, 1995, p.5).
One important and relatively fresh view in the corrections aimed to this Bernstein’s dichotomous theory has been in revealing the reasonably understandable fact that despite one’s social background, a person actually acquires both the “code types” through the social action and communication in different contexts. When the codes are seen as altering ways to think and to communicate, the possibility to choose the appropriate way to express one’s thoughts in different situations and to solve problems by choosing the most efficient thinking strategy is the essential ability in question. Also, the capacity to choose correct strategies actually is the key to one’s development into an efficient knower and thinker in school and in community. (for further discussion, see also Cooper, 1998; Robinson, 2003.)
As a conclusive thought, it is more important to use the appropriate “code” according to a situation at hand than to primarily use only either the restricted or the elaborated code type whenever solving a problem – this is the most important addition to Bernstein’s view on communicational forms. Also Vilenius-Tuohimaa (2005) has realized that context in which the defining of the code type (or the level of the linguistic expression) is done, plays an important role also when the impact of the linguistic aspects to mathematical abilities is explored.
Bernstein’s emphasis was, that the family’s social status has a very important role in mediating the ability to understand and express academic discourse, which also can be interpreted as the “school’s“ expectation for the pupils’ understanding and using the elaborated code type. In other words, Bernstein claimed that there is something in the family’s role system as well as in the way that the family members communicate and act with each other that reflects and reproduces the social status of the family and therefore affects the child’s capacity to interact and to effectively learn at school.
However, it is hard and impossible even, to classify people into two categories according to how they express their thoughts: that is why many of the research projects that follow the Bernstein’s theory have been modified to be less restricted when the research participants’ structures of linguistic expression are classified (see for example Hautamäki, 1982; Thorlindsson, 1987). The modification has been done, for example, either by using the points a person gets from the given task as a continuum (Thorlindsson, 1987) or by using a three-scale point system in which the level of one’s elaboration in speech is assessed. The interpretation of the scale is then, that the higher the score a person gets the more elaborated his speech is (Hautamäki, 1982, see also Vilenius-Tuohimaa, 2005 for comparison).
The framework of the code types has also been discovered to be an attempt to produce a sociological ability theory (Nash, 2001). Actually, the concept of the linguistic elaboration is very useful in trying and to indicate the nature-nurture effect in learning in terms of the sociocultural interpretations. Language is the most important tool of mediating and acquiring of knowledge in schools. That is where Vygotsky’s theory of the connection between thought and language is needed.
Vygotsky (1982) defines learning as a concept-organizing and restructuring process that is fuelled by the communication and action between pupils, for example. It is important to notice that different forms of communication do not exist only in schools and in classrooms but they also take place in social circles outside school. Nash (2001) realizes that Bernstein and Vygotsky have interpreted the level of learning in a similar way: through the social acquisition of language and also the social formulation of concept structures (and thinking processes). The gist of Vygotsky’s theory is the school’s requirement of the pupils’ acquisition of the abstract thinking ability and the effective use of cognitive and cultural tools that make the acquisition possible. Bernstein’s theory, in addition, includes the social class as a possible producer of difficulties understanding and using academic / scientific discourse in schools.
Also Cooper (1998, 512) has stated that if a pupil mainly uses thinking strategy comparable to restricted code type, it might produce results that only are based on concrete actions and concepts regardless of what the nature of the original problem is. More clearly said, the expected thinking and acting in school usually is a question of choosing the most efficient path instead of repeatedly constructing answers by using a certain problem solving strategy (see also Cooper, 2002).
It is important to notice the effect that the children’s differing sociocultural backgrounds have on their capacity to understand the school’s discourse (Daniels, 2001). In the research project reported here, the analyses were drawn from the parental educational level’s point of view. However, it is as important to realize that Bernstein’s theory cannot be straightforwardly interpreted in Finland in its’ whole because of mismatch of the structure of the Finnish society. That is why some theoretical and interpretational alterations have always been made whenever the Bernsteinian aspects have been used.
Although most of the studies carried out in Bernstein’s sense are qualitative (more precisely discourse analytical, respectively) of their nature, it is possible to use his theoretical framework in quantitative explorations, as well (see also Thorlindsson, 1987). The research (N = 67 primary school children from Finland) lasted two school years and included four testing sessions in autumn 2001 – spring 2002 but the results discussed here consist of a pathway model constructed from the first and the last testing session.
The focus of the research project was to explore, how the connections lie between the parent’s educational level, children’s linguistic expression (a test constructed following Bernstein’s empirical explorations as well as his code type theory), task-orientation (a part of learning motivation, measured with a questionnaire given to the class teachers) and mathematical skills (three different tests that focus on number concept, mental number line processing and number ratio processing) during the two-year period. The theoretical background - an essential part of any research project based on pathway modeling - consisted of Vygotskian, Bernsteinian and Piagetian considerations. Although the Bernsteinian research often focuses on working class and middle class comparisons, this study concentrated on estimating the parents’ high educations impact on the children’s linguistic expression, motivation and mathematical skills.
In the research, some between-genders analyses (Anova’s and t-tests) were made. In those explorations, there were not such phenomenal differences between genders or new findings that they should at all be discussed here, respectively. The results part is constrained to consist of the participants as a whole group (N = 67).
As mentioned before, mathematical abilities of the children were assessed by using tests that mainly measure constructs of the number sense thinking strategies (see Dehaene, 1997) or the number concept. Number line processing or the number ratio processing was also a central skill measured by the tests. The teacher’s assessed the level of the children’s task-orientation. They filled in a Likert-scale questionnaire with propositions about how the children concentrate in class during mathematics sessions, how they express their enthusiasm in different kinds of mathematical learning situations etc.
It has been shown in previous research projects that the linguistic expression is hard to be measured in Bernsteinian sense. However, a test was constructed according to Bernstein’s theory and Hautamäki’s (1982) research. The linguistic expression was assessed in imaginary context. The children were shown a story-forming series of pictures (five pictures).
The story is about a girl getting to sleep at night. His mother and father come to say goodnight. When the father turns the lights off, the girl thinks she sees a ghost in the room. She shouts and the father comes. The “ghost” proves to be a chair with clothes on it. When the child had finished telling the story, the researcher pointed a picture where the girl realizes what the ghost actually is.
Then a question was asked: “What is the girl saying in that picture”? If the child would answer: “I don’t know” or nothing, the researcher asked: “What COULD the girl be saying”? The questions are constructed based on Bernstein’s (1973) assumptions of certain children that have to be linguistically encouraged to use their imagination.
The scale was from 0 to 15 points and it was possible to get either 0 points or 1 point from each part, except for two last parts which were three-point scaled from 0 to 2, 0 indicating no answer or “I don’t know”, 1 indicating non-logical answer and 2 indicating right answer, see more precisely from next page (Diagram 1.)
Diag. 1. Linguistic expression’s assessment frame
Part Scale
- Grammatically correct language / everyday language 1 / 0
- Logical / unlogical story structure 1 / 0
- Story focuses into processes / into things 1 / 0
- The number of verbs above average / under average* 1 / 0
- Colourful story / shallowness of the story 1 / 0
- Consistent tenses / inconsistent tenses 1 / 0
- Adverbs / Adjectives in story / no adverbs / adjectives 1 / 0
- Rich vocabulary / stereotypical vocabulary 1 / 0
- Grammatically correct / incorrect implications to persons ** 1 / 0
- Notifies all the people from the pictures / only notifies some 1 / 0
- Notifies things and objects / talks only about what is happening 1 / 0
- Explicitness / implicitness of the story*** 1 / 0
- Implications to motivations, emotions / no motiv.,emot. 1 / 0
logical answer. 0 / 1 / 2
unlogical answer / logical answer 0 / 1 / 2
* The average amount of verbs was separately calculated in each storytelling time. For example, the amount (mean) of the verbs in the first testing session (autumn 2000) was 7 other, than be-verbs. If there was >7 verbs in the story, the child got one point. If there were <7 verbs, there were no points given.
** There are correct implications to persons: for exemple he, her, his, not ”IT”.
***An explicit story is analytical by nature. Implicitness means that the story is descriptive and based only on the pictures.
The Pathway Model: Accounting for mathematical skills through the parents’ educational level, children’s linguistic expression and task-orientation
The model was constructed by using the parents’ educational level’s direct effect to estimate the other variables only in year 2000 (the first testing session). This was done because the research project’s theoretical framework does not include an assumption concerning the parent’s educational level’s effects strengthening or generally altering later. That is, the point when the children have just started their school path is considered to be of essence. The education-variable was dichotomous where 0 indicated non-academic education and 1 indicated academic education of the parents.
The linguistic expression was classified into three categories 1 indicating restricted code type, 2 indicating “varying” code type and finally 3 indicating elaborated code type.
According to the goodness-of-fit estimates, the theory and the data are sufficiently consistent: χ 2 = 16.247 (12), p = .18., IFI = .95 (>.90) and RMSEA = .07. According to the model (see Figure 1, standardized β:s included, see Appendix 1 for standardized residuals and B: s with probability estimates), there are a few interesting findings:
2) The mother’s education’s connection to children’s linguistic expression is stronger than the father’s.
3) The father’s educational level is more strongly connected to children’s task-orientation but the effect is very weak.
4) Task-orientation is statistically significantly connected to mathematical skills.
5) Linguistic expression is very weakly connected to mathematical skills and in addition, the path has a negative estimate.
5) Task-orientation as well as the linguistic expression is quite stabile in the two-year period. Mathematical skills are not statistically significantly connected but that is partly caused by the variation of the tests used in different testing sessions.
The most interesting result here is, that Basil Bernstein’s theory of linguistic elaboration proved to be empirically challenging once again. However, the weak connection between the children’s linguistic expression and mathematical skills can partly be interpreted through the fact that the imaginary (storytelling-) context probably was not the best choice when trying and to demonstrate the connection between linguistic and mathematical thought processes. If the assessment would have been made in mathematics class, for example, the effect between the two important variables could have been stronger.
There were not very strong connections between the parent’s educational level, children’s linguistic expression, motivation and mathematics. However, the important finding was that there are different kinds of effects between the mothers and fathers to their children’s different abilities. The fathers’ high education’s positive effect on children’s mathematical skills was stronger than the mother’s effect but the mothers’ high education seems to positively affect the children’s linguistic expression’s level.
Motivational level’s (task-orientation) connection to mathematical skills is evident. That is, the more orientated the teacher assessed the pupil to be, the better the pupil achieved in the mathematics tests.
An overall effect of the model is 24 % (28 % if all the modification index alterations would have been executed). The sample size is very small and it would be interesting to see how the results would change when the sample size gets bigger.
Bernstein is one of the world’s most used theoreticians in the sociological field even today although the quantitative adjustments on his theory of linguistic elaboration have not been very successful (Edwards, 1987; Robinson, 1978; Thorlindsson; 1987). Still, according to this research project discussed here, it has to be admitted that, the linguistic expression’s level measured in code type theory’s sense is not connected to mathematical skills and that the parent’s high educational level by itself is not a sufficient independent variable when their effects on children’s motivation, linguistic or mathematical skills are estimated.
Although the level of children’s linguistic expression was not very strongly connected to mathematical skills, there are some interpretations that should be made of the negative connection between the two variables. First, the negative connection was partly caused for the nature of the mathematics tests. The tests used in the research project were not highly comparable to mathematical processing that includes linguistic forms of thought. Instead, the tasks included “number sense strategies” that are universal and non-linguistic processes in mathematical reasoning. Secondly, there was only one context the level of the children’s linguistic expression was defined in. If there had been additional contexts such as classroom discourse situations in mathematics class and informal language-use situations, a broader conception of the children’s code type would have been possible.
However, even though the linguistic expression did not prove to have a high effect on children’s mathematical abilities, it is evident that one part of children’s problems in mathematical problem solving is caused by difficulties in choosing the appropriate thinking strategy or the lack of “everyday”-estimating and thinking abilities crucially needed in several mathematical tasks (See also Cooper, 1998; Cooper, 2002). That is why extra effort on enhancing the children’s capacity to concentrate on tasks and to be motivated in mathematical problem solving situations is a very important key to better learning.
This discussion leads to the conclusion that the special educational knowledge school’s special teachers have should be used to primarily reveal the thinking strategy behind pupil’s answers in different mathematical tasks, not leaving out the motivational surveying and acting according to the results of it, of course. Then the possible problems rising from the cycle formed by the lack of motivation and of the repetitive choosing of wrong thinking strategies in certain tasks may be corrected instead of concentrating on helping the pupil mainly at the level of the procedural aspects of solving the tasks at hand.
Bernstein, B. (1973) Class, Codes and Control. Vol 1:Theoretical studies towards a sociology of language. London: Routledge & Kegan Paul.
Bernstein, B. (1995) Code Theory and Its Positioning: a case study in misrecognition. British Journal of Sociology of Education , 16 (1), pp. 3–20.
Cooper, B. (1998) Using Bernstein and Bourdieu to understand children’s difficulties with “realistic” mathematics testing: and exploratory study. International Journal of Qualitative Studies in Education, 11 (4), pp. 511–533.
Cooper, B. & Harries, T. (2002) Children’s responses to contrasting “realistic” mathematics problems: Just how realistic are children ready to be? Educational Studies in Mathematics , 49, pp. 1–23.
Daniels, H. (2001) Vygotsky and Pedagogy. London: Routledge.
Dehaene, S. (1997) The Number Sense: How the Mind Creates Mathematics? New York: Oxford University Press.
Edwards, A. D. (1987) Language codes and classroom practice. Oxford Review of Education, 13 (3), pp. 237–247.
Forman, N., Minick, C.A. & Stone (Eds) Contexts for Learning: Sociocultural dynamics in children’s development . Oxford: Oxford University Press.
Gumperz, J. J. (1972) Sociolinguistics and communication in small groups. In J. B. Pride & J. Holmes (Eds) Sociolinguistics. England: Penguin Books.
Hautamäki, A. (1982) Activity environment, social class and voluntary learning. An interpretation of Vygotsky’s concepts. Joensuun korkeakoulun julkaisuja A 22. Doctoral Thesis.
Huspek, M. 1995. Oppositional versus reproductive codes: a response to Basil Bernsteins ‘Rejoinder to Michael Huspek’. British Journal of Sociology, (46), 1.
May, S. & Harker, R. (1995) Code Theory and its Positioning: a case study in misrecognition. British Journal of Sociology of Education, 16 (1), pp. 3–20.
Nash, R. (2001) Class, ‘Ability’ and Attainment: a problem for the sociology of education. British Journal of Sociology of Education, 22 (2), pp. 189– 203.
Robinson, W. P. (1978) Language Management in Education: the Australian context. Sydney: Allen and Unwin.
Robinson, W. P. (2003) Language in Social Worlds. Oxford: Blackwell Publishers.
Thorlindsson, T. (1987) Bernstein’s Sociolinguistics. An Empirical Test in Iceland. Social Forces, 65 (3), pp. 695–704.
Vygotsky, L. S. (1982) Ajattelu ja Kieli. [Thought and Language]. Espoo: Weilin + Göös.
Manuscript under evaluation:
Vilenius-Tuohimaa, P. (2005) Vanhempien koulutustaso, lapsen kielellinen ilmaisu ja
tehtäväorientaatio matemaattisten taitojen selittäjinä koulutien alussa. [Accounting
for mathematical skills through parent’s educational level, children’s linguistic
expression and task-orientation at the beginning of the school path.] Helsingin
yliopisto: Soveltavan kasvatustieteen laitos. Erityispedagogiikka.
Väitöskirjakäsikirjoitus. [Doctoral Thesis Manuscript].
Appendix 1.
Diag. 2 The unstandardized regression effects (B) and probability estimates (p)
Path
B
p
Father’s educ – Linguistic Expr 2000 -.12 .514
Mother’s educ – Linguistic Expr 2000 .23 .295
Father’s educ – Task-orientation 2000 .16 .482
Mother’s educ – Task-orientation 2000 -.13 .634
Father’s educ – Mathematics 2000 1.43 .184
Mother’s educ –Mathematics 2000 .59 .650
Task-orientation 2000 – Linguistic expr 2000 .14 .170
Task-orientation 2000 – Mathematics 2000 1.20 .045
Task-orientation 2000 – Task-orientation 2002 .35 .000
Task-orientation 2002 – Mathematics 2002 4.40 .000
Task-orientation 2002 - Linguistic expr 2002 .06 .587
Linguistic expr 2000 – Mathematics 2000 -.23 .749
Linguistic expr 2000 – Linguistic expr 2002 .27 .007
Linguistic expr 2002 – Mathematics 2002 -1.24 .337
Mathematics 2000 – Mathematics 2002 .33 .092
Diag. 3 Standardised residuals for the pathway model
1. 2. 3. 4. 5. 6. 7. 8.
1. Mother’s educ .00
2. Father’s educ .00 .00
3. Task-orientation (2000) .00 .00 .00
4. Linguistic expr (2000) .00 .00 .00 .00
5. Task-orientation (2002) 1.10 1.01 .00 1.12 .00
6. Linguistic expr (2002) 1.03 .59 -.20 .07 .36 .03
7. Math (2000) .00 .00 .00 .00 2.31 .62 .00
8. Math (2002) .86 -.32 .39 1.06 .38 .27 .90 .24
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