KATHRYN CRAWFORD

VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT IN

THE INFORMATION ERA

ABSTRACT. The paper exploresthe opportunitiesand challengesof learning and teaching

mathematics in the informationera from a Vygotskianperspective. A systemicapproach
is taken to an investigation of the ways in which informationtechnologieshave changed
the contexts for and forms of mathematicalactivity in society and the challengethat this
change presents to mathematicseducatorsat all levels.

INTRODUCTION

A Vygotskian view o f education in the information era

During his short life 1 Vygotsky (1962, 1978, 1986) made a substantial
contribution to psychology and our understanding of human development
in a social context. He challenged the positivist, empirical, behaviourist
psychology of his day, explored the limitations of information processing
models and sketched a more unified systemic view of human development
and consciousness with a socio-cultural ontogeny. More recently, edited
translations of his writing and that of his compatriots (e.g. James Wertsch,
1981, 1985, 1986) have made the ideas of Russian psychology accessible to
readers of English and have stimulated considerable interest and research.
Through the lens of Western culture, some of his ideas have been more
accessible than others. The unity of human cognition and situated action is
now widely accepted (e.g. Sternberg, 1985; Lave 1988; Lave and Wenger,
1990). Vygotsky's critique of psychological method has stimulated a great
deal of analysis as Western psychologists seek to interpret the implications
of his ideas (e.g. Foravsky, 1991; Kozulin, 1991; Newman and Holzman
1993; Van der Veer and Valsiner, 1991).
The notion of the "zone of proximal development" (ZPD) has been
of particular interest and has stimulated some research (a critical account
of some of this research is given by Newman, Grifffin and Cole, 1989,
and Newman and Holzman, 1993). In general, researchers have inter-
preted Vygotsky's concept in non dialectical terms that fit more closely
with the assumptions of a transmission model of learning, in which an

Educational Studies in Mathematics 31: 43-62, 1996.

9 1996 Kluwer Academic Publishers. Printed in the Netherlands.
44 KATHRYN CRAWFORD

expert "teaches" a novice, that underlie the social organisation of exist-

ing institutionalised settings. The focus of most research has been on the
opportunities of carefully structured dyadic interaction whereby a teacher
attempts to enhance each individual learner's development by providing
support for action beyond their individual capability. However, a more
dialectical view suggests that the awareness of teachers is also changed by
the experience of interaction with their students.
Vygotsky's view of human learning, and the developmental experience
of being and acting in a cultural context, challenges many of the epis-
temological beliefs and assumptions underlying educational practice. In
particular, it challenges traditional views of mathematics as value free,
objective and divorced from everyday personal concerns.
For Vygotsky the term "Activity" denotes personal or group involve-
ment, intent and commitment that is not reflected in the usual meanings
of the word in English. In his view the subjective and personal views of
individuals, their location in a context, and their knowledge derived from
past experience all shape their conceptions of needs and their interpreta-
tions of the purposes or goals of an activity. The needs and purposes of
people, their actions and the meanings that they attach to an activity, their
relationships with other people in the socio-cultural arena in which they
think, feel and act, and the presence of culturally significant artefacts, all
become important as determinants of multiple consciousnesses and evolv-
ing cognitive structures. They also determine individual interpretations of
the "reality" of the experience and their choices about later action. Eis-
er (1994: p. 109) bluntly articulates these questions in discussing recent
scientific views about the limits of objectivity:
What sense can we make of reality, if not in terms of our own experience? And if our
experiences are necessarily personal and selective, how can we make sense of anyone
else's, and come anywhere near sharing their reality?

Paradoxically, a Vygotskian view, while acknowledging the essential

subjectivity of all conscious experience, also shifts attention away from the
traditional psychological focus on descriptions of individual characteristics
or states and measures of performance towards a greater focus on maturing
pattems of change and the processes by which people are changed. The
focus is on the connections between people and the cultural context in
which they act and interact in shared experiences and communication
aimed at inter-subjectivity- a shared consciousness of culturally significant
phenomena mediated by the use of language and other symbolic tools.
Vygotsky worked in a time of enormous change in post revolutionary
Russia. That is perhaps one reason that his ideas are particularly relevant to
education in the information e r a - another time of rapid change in the con-
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 45

text of human development in many countries. Vygotsky's insistence on

non-absolute forms of consciousness seems less radical in an era of com-
puterised "virtual reality" for auditory, visual and, most recently, tactile
sensory domains. Mathematics, through information technology, is now
used increasingly to create the sensation of reality or to re-represent and
model information beyond sensory experience (e.g. in mathematical mod-
els in the physical and social sciences). Vygotsky's claims about the social
ontogeny of knowledge and cognitive structures also seem less radical in
an era where human activity in urban settings is increasingly circumscribed
by cultural artefacts and the creative symbolism of a consumer society.
Schools are constituted as a part of the wider cultural activity - they
form the culture and are formed by it. An interactive, systemic view of
learning in context acknowledges the multiple perspectives and actions
of the participants and the extent that such settings are constituted within
and influenced by the wider culture and the wider patterns of activity of
the time. That is, educational institutions are both a part of wider cultures
influencing the development of their populations and also have an identity
of their own which is defined by the wider culture. Figure 1. below sum-
marises the elements and influences and their connectedness for a teacher
(T) and a group of pupils (P1...n) in a mathematics class, in a school, in
a culture, during the information era. The experiences, perceptions, needs
and goals of each participant are influenced by many interacting factors.
These include each person's unique history of experience and awareness,
the more generally recognised characteristics of the era, the culture, the
ethos of the school environment, the role definitions of teachers and stu-
dents, the ways in which activity in a mathematics class is defined, and the
interactions between people in the immediate social context.
Mathematical knowledge also has a socio-cultural ontogeny. For math-
ematics educators, Vygotsky's cultural historical method of research - in
which attention is paid to the history of individual and group activity and
the socio-cultural context in which it occurs - provides a possible source
of insight about the tensions and inconsistencies emerging in mathematics
education. New forms of mathematical knowledge, constituted through
new forms of human activity using new tools, and changes in the ways
mathematics is used in technologically based societies, present challenges
to educators. They have a learning history from another era. In many cases,
they work in institutions with very stable forms of organisation that have
become somewhat isolated from the wider community. In the past, math-
ematics may have been an erudite activity of the academic elite - now,
particularly in its mechanised form, it is becoming a fundamental aspect
of organisation, creativity and opportunity at all levels of society.
46 KATHRYNCRAWFORD

information e r a s .

Fig. 1. Human development in school: a socio-cultural context.

Most people have learned mathematics in a form that is decontextu-

alised from the human activities that engendered it. Brousseau (1992: p.
22) uses the term "didactical transposition" to describe the shift in meaning
that occurs when knowledge is learned in contexts separate from where it
is generated and used in the wider community. He suggests that knowl-
edge is recontextualised in educational institutions but "...the restoration
of intelligible situations (recontextualisation) has as a price the shift in
meaning (didactical transposition)." That shift in meaning is experienced
by teachers of mathematics in both their own mathematical education and
in the ongoing context of their profession.
A Vygotskian view suggests a new set of questions for research in
mathematics education which reflect the fact that mathematical knowledge
increasingly shapes and is shaped by human activity and communication in
new technologically sophisticated contexts. In such a view, mathematics
learning becomes an integral and essential part of human development
and consciousness in an era at once fraught with ecological peril and new
opportunities for creativity and understanding on a global scale. Some of
the these questions are:
9 What is the nature of mathematical activity in the information era?
9 What is the history of mathematical activity for individuals and groups
in a culture - including teachers?
9 What is the effect of mathematical activity of various kinds on cog-
nitive development?
9 How is mathematics used in a culture? - by whom?
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 47

9 How do people experience mathematics - at school - at home - at

work?
9 What are the goals or purposes of mathematical activity in educational
settings? - in the wider community?
9 What needs and purposes are met by such activity? - For whom?
How?
9 What is the range of mathematical activity for different people work-
ing together in a particular setting?
9 What is the distribution of activity among people doing mathematics
in any setting?
9 What difference does the use of tools such as computers and calcula-
tors make to the quality of human activity and learning?
9 How are different learning experiences related to different forms of
mathematical knowledge and later dispositions to think and act math-
ematically?
9 What is the effect of computerisation and increased use of mathemat-
ics on the nature of knowledge and human activity in many fields?
A systemic view of human learning in a cultural context which now
includes the powerful cultural artefacts associated with information tech-
nology, suggests a view of mathematics education as a life long experience
inextricably connected to other forms of cultural activity including signif-
icant patterns of social interaction. The beginnings of these processes can
be seen in early childhood.

The social ontogeny of mathematical development in early childhood

Computers provide a new context for children's activity with different
opportunities for and constraints on the development of cognitive struc-
tures. Educational tools such as paper, pencils, paints and computers,
according to Vygotsky, are cultural artefacts. They have a socio-cultural
ontogeny and their significance for individual or group patterns of devel-
opment depends on how they are culturally defined, the social context in
which they are encountered, and the ways in which they are used. Booth
(1984) has described how spontaneous pattern making of young children
with paint and paper follows the edge of the paper (usually rectangular).
The cognitive structures that are formed through individual and group
activity with computers are also influenced by the features of a compu-
tational environment and the socio-cultural context in which the activity
occurs. In an information era, computational environments influence chil-
dren at an early age.
A study of pre-school children's use of Logo (Crawford, 1988) provides
an illustration of the social ontogeny of knowledge and the tensions and
48 KATHRYN CRAWFORD

opportunities for learning that are created by a new context for mathe-
matical exploration. The study forms a part of a larger study of the social
context of mathematics learning for young children. The children (N=25)
attended an informal pre-school setting twice a week in which they were
encouraged to choose from a range of activities, which included explo-
ration of a modified form of Logo, for a period of twelve weeks. At the
beginning of the program the children's ages ranged from 54--60 months.
Gender differences in skills and expectations were already evident in the
group - boys spent more time with block building, puzzles and gross motor
activity, girls spent more time playing with dolls, negotiating, chatting and
creating detailed drawings. For this group and their teacher this was an
initial introduction to a computer. Some children's parents used computers
at home or at work.
The time spent on the computer was described as "drawing on TV"
in an effort to associate the activity with other cultural experiences of
free expression and exploration. This definition, or sign in Vygotsky's
terms, caused initial tensions and contradictions because the teacher and
other adults had quite different expectations of computing activities. Initial
plans to have the activity closely supervised by an adult were abandoned
because the adult felt a need to instruct the children according to their
more formal expectations of programming and to "help" children "do it
correctly". Girls in particular responded to this social context with help
seeking and dependent learning behaviour - boys lost interest and moved
off to another activity.
The program was modified. After the introduction of basic commands
the children were told to seek help as they needed it and encouraged to
explore the new medium freely with less close supervision by an adult.
Activities were observed and records were kept for each child of the time
spent, knowledge of commands, planning, discussion and whether the child
initiated or followed ideas. With the exception of one child, all the children
chose to spend time on the activity at least once a week.
In the initial weeks the children generally followed a pattern of activities
which included:

9 random and impulsive experimentation with commands (Logo scrib-

ble).
9 Purposeful investigation of the two aspects of the medium that were
most different from paper and pencil. The children played "hide the
turtle" and attempted to predict where the turtle was after using com-
mands. They also explored the wraparound effect by continuously
using the F (fd 10) command.
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 49

9 A gradually increasing focus on control of direction. Horizontal and

vertical lines were the first indication of this stage. The terms quickly
became part of the children's vocabulary as they discussed what was
happening on the screen.

The public nature of the screen meant that new ideas and things to do
were open to scrutiny by other children and "spread" through the group
very rapidly. No matter who was "playing" with the computer, other chil-
dren came to see what was happening and later tried out new ideas for
themselves. The new context was defined socially in terms of related expe-
riences with other cultural artefacts and the reactions of members of the
group including adults. Notions of left and right, horizontal, vertical dis-
tance and direction were useful in the Logo environment. They were also
greeted very positively by adults in the context and by the children's par-
ents. The phenomena were socially meaningful and the language signs to
describe them and the ability to recognise and name them quickly became
important in the wider social context as well as in the computer context.
The children had gained early access to ideas and cognitive structures that
are not usually established at pre-school. The new knowledge not only
empowered them in the Logo medium but also in their social relationships.
Adults responded positively to their new knowledge and ideas.
After four weeks, the children's conceptions of the social and techno-
logical possibilities of the Logo environment were extended. They were
given a session in which they played at using the same commands to "con-
trol" a turtle-robot on the floor. They were initially startled and delighted
to find that the same commands could be used with the robot. They spon-
taneously built the turtle-robot a house and some shops to visit and moved
it about in a much more planned way in their imaginary suburb. They soon
tired of the robot's slow movement and returned to the computer screen.
However, the robot-turtle activity had involved co-operative building and
playing where planning was an important element. Back on the computer
screen there was a substantial change in the form of their activities.

9 There was more collaboration and discussion

9 Closed curves of various kinds began to appear and there was much
discussion of ways to make shapes of various kinds.
9 Planned filling of the available space occurred. For boys this involved
use of geometric patterns - for girls, detailed representation of people
and events.

The experience with the turtle-robot had re-contextualised the computer

activity in association with other cultural knowledge and activities.
 50 KATHRYNCRAWFORD

By the end of the study there were no substantial differences, between

boys and girls, in either enthusiasm for or competence in the Logo medium.
However, the gender differences in social experience and expectations, that
were generally evident at the beginning of the program, were reflected in
the expressed goals and needs of children and thus in their interpretation
of the meaning and potential uses of the new cultural artefact after a few
weeks. Boys were most interested in translation and rotation of shapes and
the repetition of procedures - t h e y were fascinated with the pattern making
that was possible. The girls were more interested in representing people
and events. They were frustrated that the L and R commands (Lt 30, Rt 30)
were cumbersome and were interested in more precise ways to form angles.
Both groups were able to articulate the mathematical ideas underlying these
needs in ways normally expected of much older children.
For the children, the meaning and purposes of the computer activities
were defined through the lens of their existing cultural consciousness.
The "drawing on TV" activity was initially associated with expressive
and creative activities. The use of the robot-turtle extended the children's
view of the possibilities through association with planning, rule making and
exploratory activities in play. The personal dispositions and the knowledge
of culturally approved meanings constituted through these activities were
a far cry from the forms of mathematical knowledge constituted through
the more intellectually limited and less personally meaningful imitation
and memorisation of techniques in early mathematical activities at school.
The results of the project suggest that, for young children, exploration of
and playing with a mathetic artefact in an informal educational setting had
a positive effect on their development of and inclination to talk about and
use mathematical knowledge.

Human Development in Educational Settings: History, Activity and

Change
Vygotsky wrote about Activity in general terms to describe the person-
al and voluntary engagement of people in context - the ways in which
they subjectively perceive their needs and the possibilities of a situation
and choose actions to reach personally meaningful goals. As mentioned
above, in translations of Vygotsky's writings, the Russian word translat-
ed as "activity" denotes levels of personal involvement, meaningfullness
and intent that is not conveyed in English. His compatriots developed the
notion of Activity (eg Leont'ev, 1981; Davydov et al., 1983; Davydov and
Radzikhovskii, 1985, Semenov 1978) and made a clear distinction between
conscious actions and relatively unconscious and automated operations.
An action involves conscious behaviour that is stimulated by a need subor-
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 51

dinated to a goal. An operation is an action that is transformed as a means

of obtaining a result under given conditions. Operations are habits and
automated procedures that are carded out without conscious intellectual
effort. Both actions and operations form part of any Activity by groups or
individuals. Luria (1973) developed a theory of brain function in a social
context and was influenced by Vygotsky's ideas. My own early research,
(Crawford, 1986a, 1986b) investigated the relationships between cogni-
tive abilities (based on psychometric tests drawing on the work of Luria),
social experience and mathematical problem solving. The results support-
ed the notion of an activity relationship between socio-historical factors,
cognitive processes, subjective perceptions of roles, needs and goals, and
mathematical problem solving.
The study raised serious questions about the limits of student activity
during traditional mathematics instruction within traditionally organised
schools. In particular, it suggested that traditional forms of instruction were
effective in establishing student abilities to implement standard mathemat-
ical techniques - or operations. However, students in the sample showed
almost no spontaneous disposition to personally engage with mathematical
tasks - Activity. They were inexperienced and unskilled in interpreting the
meaning of mathematical information, defining a problem, selecting strate-
gies, and evaluating the results of problem solving efforts. That is, they
were inexperienced in mathematical actions. When students were prompt-
ed to undertake such activities many lacked the conceptual framework in
mathematics to "make sense of" non-standard problems.
More recently, a study of first year university students (Crawford et al.,
1993) found that more than eighty percent of the sample studied viewed
mathematics as a set of rote learned rules and techniques and approached
mathematics learning in a fragmented fashion with the intent to reproduce,
using paper and pencil, axioms and standard techniques for examination.
That is, the majority of the most successful students of mathematics, at
the end of their school experience, viewed mathematics as a series of
operations - techniques and rules to be implemented.
The conceptions of mathematics and student orientations to mathemat-
ical tasks that are revealed in the above studies were not the intention of
curriculum experts and educational administrators. They are the results
of the informal learning with a socio-cultural ontogeny in the particular
characteristics of the mathematical Activity in schools. In most parts of the
world, curriculum documents now state the importance of active learning,
problem solving, modelling, investigation and communication in math-
ematics. However, in Australia at least, there is evidence that, in many
schools, the ways in which mathematics is taught has changed very little in
52 KATHRYN CRAWFORD

the past 20 years (see Speedy, 1989). Papert (1994: p. 2) notes that: " I n the
wake of the startling growth in science and technology in our recent past,
some areas of human activity have undergone a megachange ..... School is
a notable example of an area that has not."
Educational policy reflects the learning needs of students entering the
information era. Educational practice still reflects nineteenth century ideas
of mathematics education in which culturally approved knowledge and
operational skills are passed from an expert to a novice. Too often, in
schools, "active learning" is interpreted as more "work" under greater
pressure of time, "on task" behaviour and conformity to extended teach-
er expectations. "Problem solving" is an extra thing to teach - teachers
select the "problems" and evaluate the solutions. A transition to an empha-
sis on personally meaningful mathematical Activity for students would
require a radical transformation of cultural definitions of "teacher" and
"student", their roles and the relationships between them, the organisa-
tion and resourcing of educational institutions and stronger connections
between educational settings and other cultural activity.
In cultural historical terms we have operationalised schooling in ways
that were appropriate in a former era. The traditional notions of expertise
and authority are still implicit in teacher education and the organisation
of educational institutions at all levels. Shared cultural conceptions about
mathematics and how it is learned stem from shared experiences of math-
ematical activity in school and university - in countries where schooling
is compulsory, almost everyone learns mathematics at school.
There are generational and organisational tensions and inconsisten-
cies between the new opportunities for human development and historical
notions of learning and teaching in all fields. Nowhere are these tensions
and inconsistencies more evident than in mathematics education. This is
because the new technologies have both changed the nature of and oppor-
tunities for human mathematical activity in fundamental ways and also
widened the use and influence of mathematical information at all levels of
society.

Cultural Historical Tensions: Schools and Information Technology

We know that schools are slow to change. The introduction of exploratory

activities using Lego-Logo materials to a group of twelve year olds in a
traditional girls school (Crawford, 1992b) provides a situation calculated
to highlight the tensions between historically based stable forms of edu-
cational practice, gendered experiences of mathematics and technology
(Walkerdine, I988; Crawford, Groundwater-Smith and Milan, 1990), and
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 53

the fundamental challenges and opportunities for new forms of activity

and development that are presented by information technology.
The school environment, in Vygotsky's terms, formed a micro-culture
which formed and was formed by all members of the educational commu-
nity. All staff at the school were aware of the parents' conservative beliefs
about child rearing, schooling and work. Discipline, conformity to commu-
nity expectations and values, and order were highly valued. Uniforms were
worn by all students. Observations of the classrooms consistently revealed
a highly teacher-centred mode of classroom organisation where neatness,
accurate reproduction of demonstrated procedures and orderly predictable
behaviour were highly valued. The girls generally worked alone. "Cheat-
ing" by getting help from a friend was discouraged and all peer interaction
was closely scrutinised. Most communication - indeed most relationships
during lessons - were restrained to those between the teacher and each
individual child. Paper and pencil tests and percentage marks for achieve-
ment were the only forms of assessment and reporting in mathematics.
Teachers expressed a transmission model of learning mathematics. They
talked of "covering the content" and ensuring that the students had learned
"the basics" - mostly well automated arithmetic computation procedures.
For the students, "school work" was defined in terms of following instruc-
tions precisely and doing what was required. Figure 2. below presents a
simplified diagram of the major aspects of the social interaction in the
characteristic setting of classrooms in the school.
Vygotsky's notion of the "zone of proximal development" (ZPD) has
generally been interpreted by Western psychologists as an individual char-
acteristic constituted within a particular activity in context. However, from
a more systemic view, these common patterns of communication and inter-
action also defined the nature and dimensions of a shared ZPD for students
in mathematics classes - t h e possibilities and probabilities of mathematical
activity and development. In general, formal instruction was communicat-
ed from the teacher to the students. Most staff assumed that their needs,
goals and intentions in a lesson were shared by the students. Little attention
was paid to the personal experience of the students - to their individual
needs and goals - to the subjective meaning of the experience for each
learner. The students understood their role as "finding out what she wants"
, memorising and practicing with an intent to accurately reproduce the
culturally approved information and procedures. Some students demon-
strated their competence by answering questions in class "discussions".
Most remained silent.
At the beginning of the project it was clear that in such a context,
exploratory "playing with computers and lego blocks" was marginal to
54 KATHRYNCRAWFORD

parent clients.
Fig. 2. Patternsof interactionin traditionalclassrooms.

the "real" purposes of the curriculum. A "computer club" was formed so

that students could choose to extend the range of their activity through
use technological materials after school in a less formal setting. An aim
of the project was to investigate learning through creative construction,
exploration and collaborative problem solving. Figure 3. below illustrates
the different patterns of social interaction that were fostered as the students
were encouraged to work collaboratively in groups to actively engage with
the materials and take greater responsibility for problem solving and self
evaluation. Note the stronger connections with the context outside the
school, and the materials at hand, and the reduced focus on teacher student
interaction.
The girls in the computer project had no experience of independent or
collaborative activity in school. Despite the fact that the computer activi-
ties were available after normal school lessons, they were initially almost
paralysed with anxiety about the discontinuity between the usual teacher
direction and suggestions that they might like to plan a project for them-
selves. The response of the girls to the new setting was in marked contrast
to the response of the younger children with no experience of learning in
school. They expressed coneem about "making mistakes". Probe questions
revealed that a "mistake" was "not doing what the teacher wants". It also
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 55

K~

Fig. 3. Social interaction for collaborative learning in groups.

became clear that their mathematics curriculum in which they had "done
lots of work on three dimensional shapes", and their informal experiences
of cultural activity outside school had left them with neither the language
nor the spatial knowledge needed to build models with the lego material.
They initially had difficulty naming the new materials and discussing their
projects. There was much muddled talk of "thingies" and "whatsits". One
student wrote in her diary after a session in which her group had attempted
to build a simple four wheeled vehicle:
We made a snow machine thing with small and big wheels.., we had trouble working and
trying to move the darn thing.., it was hard!

They all had many examples of applications of information technology

in their homes, but until the project started they had not paid any attention to
them orthe logic of how they worked. They were also very inexperienced in
model building. They suggested that model building and technology were
things that concerned their fathers and brothers. Their school experience
of "doing" 3D shapes geometry and gears in science had not equipped
them for using such knowledge with actual blocks, gears and machines.
Actually selecting bricks of appropriate length and width was a challenge
for many. One group had real difficulty deciding where to attach a light
sensor to a simple vehicle so that it could detect a black line on the floor.
For a long time the sensor was pointing forwards.
56 KATHRYN CRAWFORD

In the informal setting of the computer club, the girls' confidence grad-
ually grew. As they "played" with the new artefacts, their ownership and
personal involvement in their building projects grew, and their efforts
were recognised and supported by project staff. Another journal entry by
the same child later in the project indicates the changes in attitude, per-
sonal commitment and involvement in an Activity. It also suggests a more
integrated and relational understanding of the elements of the problem.
She wrote:

I worked with Nadine and our project was a tower with a flashing light and three gears with
a smaller gear that go faster and a bigger gear that goes slower. This tower had a helicopter
like top and if it had no gears to make it go slower, it would spin off..., which happened
last week ..... Our new thing we did was to make gears..., to make the helicopter (top) not
fly off. It was fabulous that we made gears. I feel fabulous and proud that we made this
creation.

The blocks were associated with self directed play activities by the
teaching staff. However, the programming activities were seen as part of
the "real curriculum". Thus as the project evolved, the social characteris-
tics of the setting - the shared ZPD - for learning through building with the
blocks involved problem definition, argument, strategic decision making,
risk taking and experimentation and self evaluation in a collaborative peer
group. In contrast, when it came to developing programs for their models
a more teacher directed instructional setting evolved around programming
activities. The girls were "helped" with programming solutions. Conse-
quently, in this domain, the range of their activity was reduced in terms of
personal involvement and cognitive activities.
The differences in personal ownership and awareness, associated with
experiences of qualitatively different forms of Activity in the two aspects
of the social context, were clearly reflected in the diaries that were kept
by each student - their subjective reality of the project. All of the diaries
contain initial typed instructions for Logo programming pasted in. These
are followed by increasingly enthusiastic reports about what they have
learned from building with their models - details of difficulties - joyful
exclamations about the resolutions achieved. Few diary entries mention
programming problems or their resolution. Follow up interviews revealed
that whereas the model building was their own and enjoyable, the pro-
gramming was "real work" and not their own. They could not write about
it because "they could not understand the teacher's solutions". The block
activities had become part of their consciousness, the programming gen-
erally had not.
This project clearly illustrates the tensions between traditional forms of
educational practice with traditional educational technologies and the new
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 57

forms of cultural activity associated with the creative possibilities of new

and complex technological systems.
First, the students' experience of their role as actors, during teacher-
centred instruction in paper and pencil geometrical activities, resulted
in knowledge about how to reproduce a series of culturally approved
procedures and axioms and knowledge of the cultural symbols to denote
shapes of various kinds. This narrow range of operational activity did not
result in knowledge that was part of each student's own consciousness and
a basis for creative problem solving. Second, creativity and exploration
demand a setting in which the explorer/creator/learner is able to own the
project, grapple with it, and take responsibility for the outcomes of the
activity. In schools, such a context implies radical rearrangement of the
power relationships between teachers, administrators and students and of
traditional forms of social organisation.

Teachers' knowledge and information technology

It is little wonder that the majority of successful students enter univer-
sity with a view of mathematics as a set of axioms and techniques that
must be learned by rote and reproduced on demand - that is their school
experience of mathematics. The conceptions of mathematics and how it
is learned, of first year students at university level, have been mentioned
above. The social ontogeny of such conceptions and their relationship to
the quality of mathematical experience in school is evident from the dis-
cussion in the above section. The transmission model of learning is more
strongly represented at high school level, reinforced by the measurement
needs of matriculation examiners, and persists strongly at university level.
Academics are experts in their field. The usual university forms of course
delivery reinforce the model of learning the culturally approved knowledge
from experts.
However, the new technological tools make possible new forms of aca-
demic activity that are changing the nature of the knowledge arid expertise
of people working in universities. This change is most evident in math-
ematics, and the physical sciences. New knowledge generation is now
possible as mathematical models are tested and abstract concepts repre-
sented within computational environments. However, an equally radical
change in the nature of knowledge generation has also occurred in the
humanities and in most professional fields (Fugita, 1993). In archaeology,
for example, computer based models and data organisation and new dating
techniques have revolutionised research processes. As yet, there is little
indication of similar changes in the ways in which universities present
courses at undergraduate level. Thus, in universities also, the nature and
 58 KATHRYNCRAWFORD

meaning of knowledge generated in one form of Activity, through research

and creative theorising, is changed or transposed as academics "transmit"
information to undergraduate students, in a different social context, about
other people's discoveries and techniques.
In education, a growing body of expertise is emerging as researchers
grapple with the design and use of technologically based learning contexts.
These changes are placing substantial pressure on staff at university level to
update their expertise and rethink old conceptions of knowing, teaching and
learning. To the extent that information technology has enhanced our pow-
ers of data organisation and analysis, the traditional place of mathematical
activity in a university micro-culture has been changed. For example, some
conceptual understanding of statistics, and in particular an understanding
of non-linear, multilevel relationships is needed in most professional and
academic fields. The pressure for change is not merely to teach more math-
ematics to more students in more fields, but to prepare students through
experience of a new sort of mathematical Activity that has investigation
and problem resolution as its goal and in which the operations are tech-
nologically supported. For those mathematics departments engaged in the
development of new courses of this kind, there are tensions and chal-
lenges associated with the cultural history of mathematical activity of both
academics and students.
The education of mathematics teachers at all levels now needs to involve
learning to use information technology effectively as an educational aid.
For teacher educators that will also mean learning to guide student-teachers
in a social context that fosters a greater depth in intellectual, emotional
and enactive involvement and responsibility. This is required because in
the new forms of mathematical activity, in the wider culture, people use
mathematics in a social context and their mathematical actions to meet
their personal and political needs and goals are operationally supported by
powerful information technologies. Mathematics educators now need to
be able to create a range of new learning environments that foster Activity
rather than merely operational techniques in order to meet new societal
needs for informed and critical use of mathematics in all fields. Some of
these settings may involve information technologies but such culturally
potent artefacts are not a prerequisite for changes in the intellectual depth
and social and personal relevance of mathematics education, merely a
reason for such changes.
Recent research (Crawford, 1992a in press) suggests that the experi-
ences of creating and changing learning contexts, with or without the use of
new technologies, is also a powerful learning activity. From a Vygotskian
point of view, the Activity of reproducing a set lesson, using a text book as
 VYGOTSKIAN APPROACHES IN HUMAN DEVELOPMENT 59

a source of information and using well automated teaching strategies in the

usual way involves little conscious intellectual activity for the teacher-
the process involves operations within an assumed conceptual framework.
On the other hand, experience in creating a new learning context in a class-
room, experimenting with and refining strategies to foster new kinds of
learning activity among students, representing mathematical information in
new ways, changing the nature of mathematical activity, and being respon-
sible for an evaluative account of the resulting learning and development
requires intense personal involvement. Personal strengths and weaknesses
and personal needs and goals are important. For most student-teachers at
university such new requirements are a challenge. One such student wrote
the following account in her journal at the beginning of the semester:
During the first tutorial I noticed that many people began to feel threatened .... It was
apparent that students did not feel comfortable with a view of mathematics education that
took the power away from them. People view the role of teaching as a powerful one and
beginning teachers feel most comfortable with this power. Perhaps it is because this mirrors
our own experience at school.

Such purposeful Activity by student-teachers involves problem defini-

tion, interpretation, strategic thinking and evaluation in and of the kind of
fluid and changeable social context in which teachers work. It results in a
well developed rationale for decision making about the design of learning
experiences and a disposition to creative approaches to enhancing student
involvement in meaningful mathematical activity through investigation
and problem solving, A journal entry by the same student-teacher at the
end of the semester illustrates the impact of the experience and her recog-
nition of the more active involvement by school children that has been
facilitated by changes in teaching practice. Note in the two entries the pat-
tern of initial confusion and lack of involvement and later commitment to
the processes and a more dynamic and dialectic understanding of teaching
and learning as part of a single interactive process:
This last session in school was a very positive experience for both students and teachers...
At this stage, they (the students) knew exactly what information they wanted to present on
their posters. There was less in-group fighting when teachers were not present... During this
session little intervention was required. They worked very diligently and it was obvious
that their co-operative group skills had vastly improved... It was wonderful for us to be part
of this change. [Italics added]

Opportunities to represent mathematical ideas in new ways, whether or

not information technologies are part of the context, deepens mathematical
understanding. All student-teachers reported the need to grapple with and
extend their mathematical concepts. In addition, learning to create new
contexts for mathematical learning in technological settings provides a
motivating problem base for student-teachers to develop skills in ways that
60 KATHRYNCRAWFORD

they see as relevant. Most importantly, during such an experience student-

teachers have a new glimpse of themselves as one powerful element in a
whole system of collective activity in which the history of each person,
their existing knowledge and their intellectual, enactive and emotional
involvement, and individual conceptions of the goals of the activity and of
personal needs are all part of the learning experience.

1. CONCLUSIONS

Vygotsky's systemic view of human development and consciousness medi-

ated through action in a cultural context was formed in another era of social
change. In the present era, another time of rapid change in the nature and
purpose of human activity, his insights may be valuable as a lens though
which to view modern dilemmas and challenges.
Now that we have built machines to carry out the forms of mathemati-
cal technique that have dominated the curriculum at all levels, it is time to
reconsider the traditional narrow operational focus of students' mathemat-
ical activities. Now that information is stored on data bases and standard
techniques are carried out by machines, it is particularly inappropriate that
the "zone of proximal development" in mathematics classrooms still ori-
ents students towards, imitation, memorisation and practicing techniques
with the intent to reproduce them in obedience to authority figures and
without any reference to their personal needs and goals.
The full mathematical potential of information technology will only be
fulfilled when the social ontogeny of "school mathematics" is recognised
and the socio-cultural context of mathematical development, in educational
institutions, is changed in ways which recognise the new tools and the new
ways in which mathematical knowledge is made and used through human
activities.

NOTES

1 Lev Vygotsky lived from 1896 until 1934.

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