Chapter 4 in _Contexts for Learning_, Forman, Minnick, and Stone (eds.)
reviewed by Dewey Dykstra, Jr.
Introduction
This review of C, W, & Y's chapter focuses on particular significant issues
raised in the chapter as opposed to being a survey of everything in the
chapter. In what follows, after a very brief description of their project,
a case will be made that C, W, & Y offer a perspective of Vygotskian
notions which is based on a radical constructivist foundation. Their
perspective leads the authors to a different position with respect to
learning and teaching than that which seems typical of the literature of
the "Vygotskian community." This state of affairs supports the notion that
the differences between radical constructivism and Vygotskian theory do not
center on issues of individual vs. social.
(Note: It should be noted that the authors never use the expression
"radical constructivism" in the chapter. At least one of those with whom
they cite compatibility is von Glasersfeld, who not only uses the
expression, but whose works are usually cited as being the source of
specific defining descriptions of "radical constructivism." In so much as
is possible, the reader is cautioned against accepting or using substitute
descriptions of this philosophical position. Other definitions or notions
of constructivism are both incompatible with the author's statements and
their use can render both the chapter and this review unintelligible. It
is under these conditions that the writer of this review employs the
expression "radical constructivism" as descriptive of the position of the
authors.)
Their project:
C, W & Y set out to explore new instructional settings for mathematics in
second grade classes. Their intent was to induce and study changes in
mathematical understandings of the students. These new settings are
consistent with what can be described as "inquiry" mathematics as opposed
to more commonplace "school" mathematics. Their "inquiry" approach
operates without "the assumption that all the students should make certain
predetermined mathematical constructions when they completed and discussed
their solutions to particular instructional activities." (p. 93) Among
other things they sought to avoid the "social guessing games" that occur
"when teachers attempt to steer or funnel students to a procedure or answer
they have in mind all along," during which "the construction of
mathematical knowledge becomes an incidental by-product of the
interaction." (p. 93) They maintain that in the context of the mathematics
classroom "mathematics does not consist of timeless, ahistorical facts,
rules, or structures but is continually negotiated and institutionalized by
a community of knowers." (p. 112)
Reflexive relationships:
C, W, & Y discovered that their initial assumption that the broader system
in which the classroom was imbedded, the school and the school system,
would be flexible enough to accommodate these alternative instructional
settings essentially without influencing the project was unfounded.
Instead, at every level they experienced examples of dialectic
relationships between the cognitive activities of the participants and the
social settings in which the participants were immersed. The students'
notions of mathematics changed as a result of the social interaction
patterns in class, but these social interaction patterns changed as the
students' notions of what it is to do mathematics changed. The teachers'
notions about the processes of being a teacher in a mathematics classroom
changed as they interacted with the students learning mathematics, but
nature of their interactions with the students changed as a result of their
views of teaching mathematics changing. Features of the project were
influenced by the institutionally accepted assessment criteria for the
students' learning in mathematics and but the accepted view of the teaching
of mathematics in the school system seems to have changed in order to
accommodate the project and its expansion. In each case it seems that
neither did the social setting merely determine the cognitive changes nor
did the cognitive changes merely determine the social setting. Each
influenced the other. Affect was observed to have been a factor in both
the cognitive changes and the changes in social practices at every level.
These observations are consistent with Vygotskian theory. C, W, & Y state
that they find that ideas from the work of Vygotsky and Leont'ev inform
their own interpretation of their observations in the project.
Differences between C, W, & Y and Vygotskian literature:
C, W, & Y also point out certain differences which they see between
interpretations of Vygotski and Leont'ev in the literature and their own
view. For this reason, this chapter seems to differ in fundamental ways
from typical "Vygotskian" literature. Because C, W, & Y start from a
radical constructivist background, they do not view the meaning of any
social practice or of any piece of mathematics as existing independent of
the students and the teacher having constructed meanings for these social
practices or pieces of mathematics. Furthermore, they do not accept any
social conventions of school mathematics practice as pre-given. The
authors express themselves on this issue most clearly when they say:
on page 95:
"...we find ourselves in agreement with a basic tenet of Leont'ev's
activity theory...that an individual's psychological development is
profoundly influenced by his or her participation in particular forms of
social practice. We do, however, reject any analysis that takes a
particular social practice such as schooling or the mathematics education
of young children as pregiven."
on page 96:
"...we question [the] metaphor of either students or teachers being
embedded or included in a social practice. Such metaphors tend to reify
social practices, whereas we believe that they do not exist apart from and
are interactively constituted by the actions of actively interpreting
individuals. ...we are attempting to avoid any tendency that subordinates
the individual to the social and loses sight of the reflexive relation
between the two."
on page 100:
"Although they acknowledged that these practices evolve historically, there
is nonetheless a tendency to reify them when conducting psychological
analyses. For example, Vygotsky's (1934/1987) analysis of the dependence
of scientific concepts on school instruction takes as a given a classroom
scientific practice akin to what we have called the school mathematics
tradition. ...we wish to avoid the reification of these practices and,
instead, prefer the emphasize that a practice such as inquiry mathematics
is interactively constituted in the classroom and does not exist apart from
the activities of the individuals who participate in its constitution
(Maturana, 1980)."
on page 104:
"It is, of course, possible to analyze this interaction in terms of the
teacher scaffolding the children's activity. However, such an analysis
would tend to lose sight of the influence of the classroom mathematics
tradition and downplay both the children's interpretive activity and their
active contributions to the interaction. It is for this reason that we
prefer to emphasize that the teacher and children together constitute a
novel form of joint mathematical activity while simultaneously
acknowledging the institutionalized power imbalance between the teacher and
children."
on page 105:
"Following Vygotsky (1933/1976), one can in fact argue that the children
created a zone of proximal development for themselves... Such a view
emphasizes that children's social realities are relative to their levels of
development and stands in stark contrast to characterization of development
as the transfer of transmission of culturally developed modes of thinking
from those who know to those who do not."
on page 105:
"...what counts as science and as rationality cannot be specified in terms
of a historical criterion. Instead, scientific knowledge and the
encompassing research tradition are continually reconstructed together,
with each informing the other."
on page 110:
"...qualitative differences in the emerging mathematical entities reflected
and were reflected in qualitative differences in classroom mathematics.
Once again, we stress that the students were not simply embedded in
differing mathematical activity systems. Rather, they participated in the
constitution [of] differing systems ... and thus in the constitution of the
social situations of their development. ... By characterizing the situation
in this way, we once again question the tendency to reify social activity
systems and instead emphasize the reflexive relation between the individual
and the social."
on page 111:
"Such observations again emphasize the children's active contributions to
the interactions in which they participated, a point that tends to be
overlooked if one focuses on the teacher and regards her as scaffolding
children to higher levels of performance."
The assertiveness, specificity, clarity and number of such quotations in
the chapter attest to the significance of this aspect of their position as
a difference from what they see in the literature.
On the nature of social and mathematical/cognitive knowledge:
Further evidence of a radical constructivist "take" by the authors is
evident in their treatment of the nature of knowledge. This is seen in
their discussion of "shared" knowledge of social norms where they say on
page 106:
"...the most that can be said when interactions precede smoothly is that
the teacher's and the children's beliefs fit in that each acted in
accordance with the other's expectations... Situations in which social
norms were renegotiated occurred when there was a lack of fit--when either
the teacher's or a child's expectations were not fulfilled."
In typical radical constructivist fashion, they also treat "shared"
mathematical knowledge in the same fashion as "shared" social knowledge,
seen in the following from page 113:
"From the cognitive perspective, their conceptions of place value
numeration were not shared but, instead, fit sufficiently for them to talk
about mathematics without becoming aware of discrepancies in their
mathematical interpretations. In short, they individually constructed
conceptualizations that were adequate for the purpose of coordinating their
mathematical activity with that of others as they completed tasks and
engaged in collaborative mathematical activity."
These two examples of the author's views on the nature of social and
mathematical knowledge seem to make the expression "taken-as-shared"
particularly appropriate, superior to the term "shared," in reference to
mathematical knowledge and social practices and their meaning. In both
cases the notion of "fit" of the knowledge is used in the same fashion as
von Glasersfeld has in describing the radical constructivist position on
the nature of knowledge. In the first quotation from p. 106 about social
knowledge the notion of change in social practices and their meaning being
driven by failure of fit or by "breaches" in social norms is described.
This is analogous to radical constructivist descriptions of changes in
knowledge and would be a logical extension of the quote from page 113.
Vygotskian "scientific knowledge":
The authors only use the expression "scientific knowledge" once (see the
quote above, the second one from page 105). They specifically refer to
"scientific knowledge" as being "continually reconstructed." While one
might still interpret C, W, & Y's isolated statement to refer to
"organized, academic, disciplinary knowledge" or "school knowledge," it is
hard, if not impossible, to see how they could mean this in the context of
the chapter as a whole. It is the case that radical constructivism is
founded on the notion that _all_ meaning or understanding merely fits
experience, that it is constructed by the holder of that meaning or
understanding is a _by-product_ of this fundamental tenet. (One could make
a case here that the term "constructivism" is a potentially mis-leading
label for this philosophical point-of-view.) In the context of C, W, & Y's
examples, it is hard now to see how Vygotskian positions on the reflexive
relationship between the learner's development and the learner's social
environment and on what is called scientific knowledge are logically
compatible.
In summary:
C, W, & Y found it essential to view their initial goal of understand
children's mathematical learning in the context of reflexive relationships
between individual and social, between cognitive, social and affective
knowledge, between teachers and students, between the classroom and its
broader social setting, a notion consistent with Vygotski and Leont'ev. At
the same time their basic radical constructivist foundation leads them to
be independent of the notion that particular social norms or mathematical
knowledge exists independently of the action of the teacher and students.
As a result the authors are able to view these important reflexive
relationships as truly reflexive. At the same time, this has led the
authors to note important differences between their understanding of their
observations and certain representations typically found in Vygotskian
literature.
Comments and suggestions concerning this review are welcome.
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Dewey I. Dykstra, Jr. Phone: (208)385-3105
Professor of Physics Dept: (208)385-3775
Department of Physics/SN318 Fax: (208)385-4330
Boise State University dykstrad who-is-at varney.idbsu.edu
1910 University Drive Boise Highlanders
Boise, ID 83725-1570 novice piper
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