Curricular
Metaphors
Bal Chandra
Luitel, Curtin University of Technology
Section
1: Metaphors
and shaping our teaching
“We
are concerned primarily with how people understand their experiences. We view
language as providing data that can lead to general principles of understanding.
The general principles involve whole system of concepts rather than individual
words or individual concepts. We have found that such principles are often
metaphoric in nature and involve understanding of one kind of experience in
terms of another.”
[Lakoff
& Johnson, 1980, p. 116]
Setting
the stage
I
was less aware of the pervasive role of metaphor in our day-to-day communication
and professional discourse although the term “metaphor” was not new to me.
After reading the great book metaphors
we live by and other articles about metaphors, I realized its importance in
our profession, particularly in the teaching field. One of my advantages as a
mathematics teacher is easy to realize the significant role of metaphors in
mathematics – a subject with full of metaphors. Similarly, when we are talking
about teaching method, we use a lot of metaphors to make understand the concept. In this light, I will present two major issues in this discourse: first,
I will seek to explore the concept of metaphors in our day-to-day communication
and in professional discourse; and I will discuss some prevailing teaching and
learning metaphors and their role in learning process.
Concept
of metaphors
The literal meaning of metaphor – a word or phrase used in an
imaginative way to describe something
(Wehmeier, 2000)
– is not so different from the interpretation of
dictionary makers and other students of meaning
(Lakoff & Johnson, 1980)
. However, this interpretation is limited because it does not
reflect the role of metaphors in our day-to-day communication and professional
discourse. Commonly speaking, metaphor is a way of expressing one experience in
terms of another. For instance, if we say teaching is journey, the two
different domains of experience are compared. We know teaching is different
experience from that of the journey. However, there are some similarities in
experiences that make these concepts comparable. In other words, we understand x
experience in terms of y metaphor, which can simply be interpreted as a
correspondence between target and source concept
(Lakoff & Johnson, 1980)
. For further discussion, I would like to raise a couple of
questions: Is metaphor only a matter of poetic imagination? What is the role of
metaphor in our day-to-day life? Let us discuss in the next paragraph.
If
we think about our everyday communication, we will find a number of metaphors. Argument
is war, time is money, life is journey, teaching is acting,
curriculum is conversation, and learning is constructing are all
metaphors we use in our usual communication. I have noted that education
minister usually says education is a gateway to success. We frequently
hear from professors as saying education is a catalyst. These examples
portray a pervasive nature of metaphors in our day-to-day activities.
Furthermore, on the one hand, the metaphorical expressions help understand the
worldview of others and on the other hand, it helps build our system of
understanding and knowledge. Consequently, the impact of thinking and
understanding is obvious in our action. Can we still say metaphors are only a
matter of poetic imagination? We cannot. They represent our thinking,
understanding and perception of concepts in the continuum of our normal
communication to professional discourse.
When
we compare one concept in terms of another, an inherent pattern of systematicity
of source concept is corresponded to make understand the target concept (Lakoff
& Johnson, 1980). For instance, when we are trying to conceptualise teaching
as acting we correspond such experience of acting (source concept)
that help understand teaching (target concept). For instance, rehearsal,
suitable dress, focus, eye contact may help someone understand teaching as
acting. My focus is that the systematicity of the metaphors and metaphorical
structure follow a pattern, which does not contradict to each other. For
instance, if we say learning is constructing then we will have the
following set of metaphorical concepts:
Your
construction is shaky.
For
better construction ideas must be blended.
Ideas
should be constructed in experiential level.
Connect
the ideas with the network.
Constructing
is connecting.
Threads
are the connections; nods are the concepts and web is the network.
When
we adopt a certain system of metaphorical concepts, consequently, it also
changes the subsequent parts of the system. If we say learning is constructing,
it does not follow learning is memorising. The notion of memorising is
very different from that of the constructing. What does happen if we say learning
is receiving? This metaphorical concept generates a number of other
metaphors like:
He has to bank my ideas.
He could not withdraw much enough.
I try to send my idea to her.
Putting in one’s head is difficult job.
Besides
understanding x in terms of y metaphor, there is another type of
metaphor, which may not be as obvious as the above mentioned, is known as
conduit metaphor. The notion of conduit metaphor is very simple that the ideas
are regarded as object, linguistic expressions (sentence, paragraph) are
container and communication is sending (Lakoff & Johnson, 1980).
Furthermore, according to the conduit metaphor, language contains meaning;
speakers and writers use linguistic expressions as containers to send meaning to
audiences; and, audiences take out the unchanged meaning from its container
(Eubanks, 2001)
. From the above discussion, it is clear that conduit
metaphor urges that words and sentences have meaning themselves. Some of the
examples are as follows:
He
extracted a lot of ideas from that book.
He
found the knowledge in a new book.
Your
words seem rather hollow.
That
movie/the book was filled with meaning.
There
was a lot of content in your idea.
This
was filled with meaning.
He
put a lot of meaning into this story.
The
poem was bursting with meaning.
Don't
force your meanings into the wrong words.
David
does not exactly overload his paragraphs with thought.
Try
to capture your good ideas in words.
There
are some ideas in the problems.
This
expression consists of more than one concept.
With
these examples, it is very difficult to realise the existence of any metaphor
and metaphorical concepts. However, the metaphorical structures like above are
very common to our day-to-day communication and professional discourse. In spite
of the criticism of its context independent nature, it gives the sense if
the
meaning is right there in the words
(Lakoff & Johnson, 1980)
.
Metaphors
are useful in developing understanding of concepts by corresponding the
different domains of experience. Furthermore, we also use the metaphors inside
the classroom to develop the understanding of concepts. Specifically, in
mathematics teaching I had used the different metaphors to develop learners’
conceptual understanding. For instance, I used to compare the Cartesian Plane (XY-
plane) with the soccer field, in which the centre could be understood as the origin
and the crossing lines could be regarded as the abscissa and ordinate.
Even in mathematics education, we frequently use the metaphor of street
mathematics to focus the role of contextualisation of mathematics learning.
The
notion of metaphor is not as limited as defined by the dictionary and the
students of meaning; instead, it is pervasive from our mundane details to
professional discourse. We think in terms metaphor, perceive through the system
of metaphor; build understanding through metaphorical concepts and communicate
effectively by the help of metaphor. However, we are less aware of its pervasive
nature in our thinking and action.
Teaching
and learning Metaphor
The notions of teaching and learning
are largely metaphorical. Furthermore, our practice of teaching is influenced by
the metaphors we used to represent the notions of student learning
(Dooley, 1998)
. Keeping this view in mind, I will discuss the role of
metaphors in shaping students’ learning taking such metaphorical concepts that
are prevailing in our normal conversation to scholarly discourse. For instance,
persuasion
(Murphy, 2001)
, facilitation,
acting
(Griggs, 2001)
, orchestrating, two-way street
(Dooley, 1998)
, scaffolding
(Englert, Berry, & Dunsmore, 2001)
are some contemporary metaphors concepts, used to portray
our teaching. Furthermore, I will seek to discuss the modernist, postmodernist
and constructivist metaphors in a view to examine their role in shaping student
learning.
One
of my colleagues used to say teaching as persuasion. The term “persuasion”
portrays sundry images, not all of which are positive. One of the positive
images includes that persuasion is not to mean learning as simply a series of
transmission. Most importantly, teaching
is persuasion portrays an image of learning as a process of changing
students’ conception, beliefs, and interests (Murphy, 2001). Furthermore, its
emphasis is on typical classroom that combines students’ ideas and feelings
along with that of the teacher. This metaphor also emphasizes that message can
play a vital role in developing students’ understanding. In my opinion, this
image may emphasize to count the success of teacher in terms of changing the
mind of his/her students. Furthermore,
this notion is more or less similar to one-way border crossing in which
teachers try to change students' understanding by imposing their idea
rather than incorporating students’ cultural, emotional and experiential
knowledge.
I had acquainted with teaching as
acting metaphor when I was a primary school teacher. I was perplexed with
this idea when one of my colleagues used to say I should be ready for acting.
He was trying to conceptualise teaching as acting: He could be acting in
front of his students as a mathematician of 17th century by
demonstrating his calibre in solving problem rather than providing with the
opportunity to the audience (learner) to comment his acting. In most of
the cases, the analogy of acting views learning as one-way communication: What
else to do with teaching! I am just acting. The epistemological link of
acting is with the dramatization and role-playing
(Griggs, 2001)
. I my view, this metaphor is more suitable for the teacher
educators rather than teachers. In my teacher training sessions, I had to act as
a model teacher, which helped them to understand the essential teaching
techniques.
Orchestrating elicits teaching
as coordinating, arranging, planning and composing. The teacher can be
characterized as the orchestrator of learning for students. Specifically, the
orchestrator is one who helps them turn information into knowledge, rather than
one who is the supplier of knowledge
(Lewis, 1999)
. It includes strategies for planning, grouping, managing the
classroom, and promoting students for working collaboratively. Explicitly
speaking, teachers as orchestrator and teaching is orchestrating
implies that learning is sharing and constructing.
Teaching as two-way
street is another metaphor which I got from the paper Teaching as a two
way street: Discontinuities among metaphors, images and classroom realities
(Dooley, 1998)
. We often use this metaphor in another form as
teaching as exchange of ideas. Dooley (1998) focuses quoting a teacher’s voice
as saying “ I strongly believe that education is a two way street and that the
children give me things and I give them back and that I don’t have the
knowledge” (p.101). Furthermore, the two-way street is a valid metaphor that
emphasises to value the students’ idea as equally as that of the teacher.
Having this metaphor in mind, the teachers cannot be viewed as sole authority of
knowledge; rather they are eager to know about and interact with the other side
of the street. It is obvious that this metaphor portrays student-cantered
teaching and focuses on learner-generated construction and sharing process.
Scaffolding metaphor
(Englert et al., 2001)
comes from Vygotskian perspective. However, we use this term
frequently in our day-to-day communication. Basically, we use this metaphor
while constructing a supporting framework and remedial instruction for the
students. Scaffolding metaphor regards the learner as apprentice and learning as
supporting with structured strategies. This metaphor views that each learner has
unique characteristics that is to be dealt through individualised instruction
and regards the adult support (teaching) as a social process
(Confrey, 1995)
. The importance of scaffolding metaphor in mathematics
teaching and learning is noteworthy because mathematics learning is regarded as
constructing, embedding and making for up and top
(Kutzler, 1999)
. For instance, mathematics learning starts from simple
concepts in the beginning and approaches to the complex and composite conceptual
phase in the later which simply a process of making a scaffold. This metaphor
helps deal with the individual capacity of the learner through structured and
guided framework designed for his/her support. The learner is enabled by sharing
with the adult (teacher). However, this metaphor still regards the learner are
inferior to their teacher that rather provides a room for sharing.
I
would like to repeat that teaching and learning theories are metaphorical.
Furthermore, the continuum of faculty psychology and
constructivism is a trail of metaphors, which convey different notions of
learning process, and we incorporate those metaphors in our teaching. For
instance, the metaphors depicting the rational world portray non-eclectic, one
way, and objective image. In my observation, most of the teachers (especially,
mathematics teachers) of my country use these metaphors, as saying whatever they
teach is true; and mathematical knowledge is universal. It is obvious that
modernism regards learning as receiving, producing and transmitting and
preparing the learner for unilateral worldview. Consequently, such metaphors
hardly help foster the conceptual and connected understanding.
On the contrary, the postmodernist
metaphors are different from that of the modernist. For instance, eclecticism,
particularity, intersubjectivity, pluralism, irony, emotionality, aesthetics,
poetry, and spirituality are such metaphors to represent postmodernism
(Slattery, 1995)
. The postmodernist metaphors convey the message that
learning is a matter of subjectivity, which urges that the learning process must
address the local need. It focuses all round development of learners by adopting
cooperating approach rather than individual and coercive ones
(Slattery, 1995)
.
The constructivism embraces a set of
metaphors like construction, experiential level, network, schema,
representation, subjectivity, internalisation, accommodation, equilibration and
accommodation
(von Glasersfeld, 1995)
. The teacher with the constructivist metaphors perceives
learning as a matter of construction by virtue of experiential world.
Furthermore, tries to make contents more appealing to the learner (it is a
function of pedagogical content) by contextualising.
The image of constructivist teacher is like a collaborator who regards
teaching as two-way street. Obviously, the constructivist metaphor help foster
the conceptual understanding of learning.
Section
2: Curriculum
Portrayal
Introduction
The
term curriculum is not the same for all people. Even for a person, it is
different from one situation to another. Curriculum itself is a field: It is so
broad that it can be depicted differently for varying purposes. For instance,
policymakers can regard the curriculum as a matter of planning and goal setting
while the teachers can view it as a process. Moreover, curriculum can also be
regarded as a composer of such tradition that is ever changing and eliciting new
meaning within it
(Applebee, 1996)
. Generally, the image of
curriculum gives a glimpse of what should be taught, how should be taught and
why should be taught in a particular situation
(Beyer & Apple, 1998)
. Above all, this section deals
with the different curriculum metaphors and their role in student learning.
Curriculum
metaphors
The significant role of metaphor in
our professional discourse has already been discussed. Various curriculum
metaphors are used in order to portray its multifaceted image. Furthermore,
curriculum metaphors represent the developing image of curriculum from antiquity
to postmodern era. Among such curriculum metaphors, subject matter, programmed
activities, agenda for social reconstruction, cultural reproduction, discrete
task and concepts, intended learning outcomes, currere and experience will
critically be analysed in terms of their role in students’ all-round
development. Furthermore, modernist, postmodernist and constructivist metaphors
will also be discussed.
Curriculum as subject matter. This metaphor portrays a traditional
image of curriculum. Historically, the metaphor was common from Pythagorean
School to Plato’s Academy as the subject of teaching were trivium and quadrivium
(Eves, 1969)
. Specifically, this image
mirrors a type of curriculum, which receives the contents from the traditional
academic disciplines (Print, 1993), and makes them available to transmit the
learner. This metaphor represents
teachers thinking to depict curriculum as a litany of contents. Furthermore, the
process of curriculum development in most schools is also a subject base (Print,
1993), which tacitly regards the curriculum as a subject matter. Moreover, this
term has been embedded in people’s mind as synonymous with curriculum. Besides
the advantage of its simplicity in explaining the curriculum as a matter of
contents, school calendar (routine), list of textbooks and the like, it is the
narrow meaning of curriculum that does not address the pedagogical aspects. The
reflection of this curriculum inside the classroom is very traditional that does
not regard learning as a two-way street. Students creativity,
experiences, feeling and cognitive aspects are rarely addressed and
accommodated. So this notion of curriculum rather focuses the all-round
development of students.
Curriculum as programme of planned
activities. By this image of curriculum, student learning is regarded as a
planned programme, which is directed and executed by schools (Tyler, cited in
Print, 1993). A range of other definitions of curriculum regard it as planned
activities carried out by schools and institutions (Good, Rugg, Taba, Tanner
& Tanner, as cited in Clandinin & Connelly, 1988 & Eisner, Glatthorn,
Saylor & Lewis, Wheeler, as cited in Print, 1993). Specifically, written
documents – teacher guides, lesson plans, scope and sequence chart, and
curriculum implementation packages – are the examples of such curriculum
materials.
We
can specify its strength is to address the issue of pre-knowledge and
motivational factor, which are essential for learning activities. On the
contrary, this image of curriculum is more focused on peripheral notion of
learning that regards learning as a matter of activities. Therefore, there is no
attention to students’ internal development.
Curriculum as agenda for social
reconstruction. Social reconstructionists regard curriculum’s image as
agenda for social reconstruction. This image of curriculum challenges the
traditional curriculum because it merely helps maintain the status quo in the
society by supporting the elite culture. The emphasis of this metaphor is to
help reform the society and make it for all people (Print, 1993). The contents
of such curriculum are included from the societal needs, social issues, current
ideals and future aspirations. Furthermore, the environmental problems, racial
prejudice and ethnic cultures are taken as the areas of study.
The social reconstructionists view
learning as a process of critical analysis, deduction, information processing,
and inquiry. Furthermore, the focus of reconstructionists is on critically
oriented knowledge. With these characteristics, the learners are viewed as
potential agent for future social reconstruction and shaped the learning process
by making them reflective and critical. On the other hand, the
reconstructionists are criticised for introducing controversial issues in
education and insisting the learner to be biased for certain knowledge.
Curriculum as cultural
reproduction. The curriculum metaphor is concerned with the notion of
transmission of culture from one generation to another. Furthermore, this image
comes from the view that regards curriculum as a reflection of culture. Looking
from this perspective, most of the curriculum has this image, which try to
prepare the youth for the culture of certain community, state and country.
This image of curriculum, however,
helps maintain the status quo by transmitting the culture of ruling class rather
than that of the oppressed. The schools are assumed as an agent of transmitting
the culture from one generation to another in a view to strengthen the elite
culture. This image of curriculum does not help develop critical thinking.
Curriculum as discrete tasks and
concepts.
Curriculum as discrete tasks and concepts is to represent a set of specified
skill focused curriculum. As we know, curricula set certain benchmarks and give
emphasis on specified skills for specific level. This image of this curriculum
includes mathematical algorithm, grammar rules, penmanship, legal writing,
operating software and the like.
The
role of the learner according to this curriculum image is like apprentice who
are guided by the adult to gain the certain skills. The skills are learnt with
highly structured rules in which the learners are expected to follow the
teacher. Teaching learning strategies are mostly practice, and drilling.
The educative role of this curriculum
is highly teacher centred. The notion of discrete skills, which the curriculum
image depicts, is quite limited that does not prepare the learner for the
changing world. Similarly, this curriculum image does not help develop wider
variety of concepts as interconnected knowledge, which is known as conceptual
knowledge; instead its focus is on the isolated and mechanical knowledge, which
may wipe out after a certain time.
Curriculum
as intended learning outcomes.
The notion of learning outcomes regards the intended outcomes as the ends
whereas the programmes and activities are just a means of achieving the goal of
curriculum. This image of curriculum serves curriculum as a process of goal
setting and drawing a pathway to culminate such goals. The outcomes are rather
expressed in the general term like understanding the value of mathematics;
instead, they are structured in a sequence with a focus on scope and grade band.
Today most curriculum frameworks including the Australian one have incorporated
this image (AEC Curriculum Corporation, 1991).
The
growing focus of curriculum as a realm of intentionality includes the following
advantages: outcomes have directional approach; the teacher and students can
determine their learning activities according to the situation; and learning
outcomes can be a basis for evaluating, accommodating and amending learning
programme according to the locale.
This
image, however, does not take account of the unintended learning outcomes, which
can also play the vital role in learning process. Similarly, it does not take
account of organisational and methodological effect that varies the outcome
attainment scale. So the comparability of the student performance
in terms of intended outcome becomes dubious.
Curriculum as currere.
Depicted
from the etymological meaning of curriculum as running of the race, this
image of curriculum focuses on reconceptualisation of one’s experience of
life. Furthermore, the curriculum image prefers the experiential perspective of
learning (Print, 1993). Explicitly citing, currere is all about the past that
comes to drive the present and direct the future of one’s professional and
personal life
(Connelly & Clandinin,
1988)
.
The image of curriculum regards the
learner as a source of experience and reflection of their experience is the
process of learning. The contents are among the experiences of the learners,
which they inquire from their past, construct for present and predict for their
future. The learners are expected to be reflective and the teacher as an
orchestrator for the reconceptualisation process. Furthermore, the
knowledge-in-action is another characteristic of this curriculum image.
The critics of this image concerned
with the impossibility of such situation because it regards highly subjective
knowledge while the learner are expected to learn objective one.
Curriculum
as experience.
This image of curriculum emphasizes that curriculum is a matter of experience
rather than the sets of activities. According to this image, curriculum has been
ever developing in means-ends continuum
(Schubert, 1986)
in which learners select
learning experience according to its significance in heir life. The image of
curriculum has also been interpreted as the experience of situation that
comprises of persons (teachers and students), things and process (Connelly &
Clandinin, 1988).
There are two distinct
characteristics of this curriculum metaphor: One deals with experience as means
and ends notion and the other deals with the notion of experience as
constructing and establishing connection from changing situation. The former
related to the perspective of John Dewey who opposes the notion of pre-planned
activity-cantered curriculum because such curriculum would neglect the
learners’ vital role in determining the learning process. The later takes into
account of whole situation as experience including persons, things and the
situation that regards curriculum as a process. Furthermore, while we talk about
experience, we should regard the knowledge in moral, emotional and aesthetic
dimension rather than only in temporal dimension (Connelly & Clandinin,
1988).
With this notion of curriculum, the
learners have a key role in curriculum process. The situation, in which they
act, is a consequence of their past and a background of the future. In other
words, their autobiography is very essential to mean the curriculum as a matter
of experience. The common notion of the experience is that it becomes rich when
learning progresses. So it helps shape the learner as a part of curriculum
process – planner, actor and reflector.
There are, however, some difficulties
in applying the curriculum as experience. Students’ involvement in planning
and selecting the learning experiences is very ideal. Similarly, they may not be
able to decide which is of their significance and which is not. The notion of
Connelly and Clandinin (1998) more or less is close to the notion of currere,
which may be difficult in applying the real situation, as it comprises of
diverse personal experience of learners and the teacher.
Curriculum
images and learners
So far we discuss some images of curriculum. There may be more other
images, which can view curriculum as conversation
(Applebee, 1996)
, as a matter of politics, as knowledge-in- action
(Applebee, 1996)
, as inquiry and the like. However, most images are
overlapping and implicit in many respects. For instance, when we talk about
curriculum as intended outcomes, we are also tacitly dealing with the image of
curriculum as a programme of planned activities. Similarly, the image of subject
matter or content is also inseparable from any of the images because we
experience the curriculum in terms of what we teach; how we teach; to whom we
teach; and even why we teach. Similarly, though the cultural reproduction and
social reconstruction are opposite, most curriculums should incorporate both
images aiming at reconstructing the society establishing new norms and values
and preserving important traditions. Looking at the curriculum image of currere
and experience, both metaphors are overlapping as their focus is on
reconceptualisation through experiences. However, both are very useful images of
transcending the learners’ all-round development.
We have traditions, which are very
difficult to give up. For the decades, we have been aware of transmissionism.
Our tradition of curriculum as knowledge-out-of-context should be replaced by
curriculum as knowledge-in-action. When we think of conversation, we take into
account the knowledge that makes sense. In my opinion, curriculum as
conversation can help all-round development of the learner by providing enriched
educational experiences and searching the value of knowledge from various
dimensions because conversation is a way of probing the existence of knowledge
of stillness and knowledge of silence (Elliot, cited in Slattery,
1995). Here, my focus is on both interpersonal and intrapersonal conversations,
which help revive our ignorance of the Word (Elliot, cited in Slattery,
1995).
Section 3: Curriculum
images in my classroom
Setting
the scene
It
was not my first class: I have taught six more years in junior classes and other
university classes. Specifically, I was a teacher trainer for in-service
teachers and tutor of the education students. I was interested to teach the
students of I. Sc. (intermediate
of science) level because my area of interest was pre-calculus
and introductory calculus, which were appealing to me because I could
teach those contents by relating with the real world.
I
have experienced more than one but implicit and overlapping curriculum images.
It was like a painting of mixed colour in which it is very difficult to separate
from one to another colour distinctly. Even without careful observation one
could not identify the basic colours that were mixed. This is my experience of
curriculum metaphors as a teacher. Similarly, the role of students’ metaphor
could also be vital in order to develop the learning process. In order to
discuss this issue, I would like to raise a couple of questions:
What is the role of students’ curriculum metaphor? What is the impact
of their curriculum metaphors in their learning? In my opinion students’
metaphor also play an important role in teaching learning process. I noticed
their apathy in learning mathematics when I started teaching. They just wanted
to be taught as if they could receive mathematics from me. I think they were
thinking of that sort of mathematics curriculum, which can help them to secure
good mark. What did the parents think of mathematics curriculum? In my
experience they portrayed mathematics curriculum as a difficult, dry and rude
but necessary to prepare their son and daughter for future. In this connection,
the following discussion will represent my curriculum images of that class.
Subject
matter or list of contents
One of the images of my curriculum
was a list of contents. For the students, the list was very important from their
examination point of view. The implied notion of learning, this curriculum image
holds, is a process of sending and receiving by students as the conduit metaphor
does. I realized that this image of curriculum created a fear among the students
because of its nature as unfamiliar, rude and dry mathematics rather than
applicable and contextual mathematics. It is a common practice in Nepal that the
primary image of mathematics curricula is a matter of content. It is because of
the process, adopted in designing mathematics curricula in school and tertiary
level: The experts select the content from the different textbook written by
foreign writer, which rarely match in Nepalese context. Consequently, these
questions are raised frequently: Does mathematics mean to represent only that is
written in the books? Who did write those books? Is there no influence of
culture, gender, emotion, experience, and feeling? Does this situation help
understand mathematics as a man-made subject?
In the light of this image, I had
some conflict with me as a traditional teacher and progressive (I would not say
modern) teacher. As a traditional teacher, I tried to force myself to adopt
ditto what was mentioned in the so-called textbook: specifically, in order to
define mathematical terms, concepts and to generate the rules and principles.
This usually gives an authoritarian image of the teacher. Moreover, when we talk
about textbook and even prescribe it for teaching, this image of curriculum
hardly takes into account of the learner’s experience. As a progressive
teacher, I tried to discard the traditional way perceiving mathematics as a more
formal and structurally written from.
Could this image have positive role
in strengthening the learners? I have thought one advantage could be that they
were aware of what they would be taught during that academic year. However, this
image of curriculum did not take account of the learners’ experience and was
best for the philosophy of learning as a reproduction rather than
construction.
Programme
of planned activities
Mix
of currere and experience
As
the class progressed, I was trying to develop the curriculum from my
perspective. The process was similar to Connelly and Clandinin’s (1988)
“Cycles and Rhythms in the Stephanie’s Classroom” (p.159). Consequently,
the process was influencing their learning process: They started to see new
examples, problems and new approach of solving problems. When I assigned them to
comment of what they learn in a particular topic, they asked, if I would ask
that sort of question for their test. There was a conflicting image of
mathematics curriculum: As a teacher, I was trying to make mathematics
curriculum as a matter of running of the race in which teacher and
students construct their mathematics whereas the students were developing their
notion of mathematics as a running of the race of someone else –
mathematicians’ teachers’ and scientists’. However, a conflict between
teacher and students’ currere was apparent within this image. The students’ currere
was the backwash of their previous learning styles and impetus of the
contemporary society.
The
notion of currere as I incorporated in my curriculum helped them develop the
understanding of mathematics rather than learning the isolated skills. As the
curriculum comprised of pre-calculus contents, the students had to develop the
understanding of the concept of “function”. Function, oh a big idea! It is
one of the difficult concepts to make understand the students. We need more
metaphors that come from street mathematics and learner’s experience.
Conflicts appeared in my classroom at that time when they asked to write a
definition, which they would memorize for their test. I did it but again I
assigned them to bring the examples of injective, surjective and
bijective functions from outside the classroom. They brought various
examples: Some were real world examples and the others were pseudo-real world
examples.
My aim through this curriculum was to
reconceptualise the notion of mathematics learning. Furthermore,
reconceptualisation is a process of sharing through which the learner develops a
greater understanding of the subject matter
(Print, 1993)
. With reconceptualisation, students could see the value of
mathematics in their life: not only from utilitarian perspective but also from
the aesthetic, emotional and spiritual perspectives.
The notion of currere and experience
helped develop greater understanding of
what they learned. I noticed that the scale of reconceptualisation of
student is not similar with that of the teacher. Even it is different from
student to student. This sometimes became a problem of understanding of what the
teacher was trying to communicate and what the students were trying to perceive.
Open
and hidden curriculum
The
notion of open curriculum – also known as overt curriculum (Print, 1993) –
is to represent the curriculum that can previously be planned and intended. In
my context, the open curriculum comprised of teaching objectives, contents and
activities.
For me, the open curriculum was a
means of establishing context of what to teach, how to teach, and to some extent
why to teach. While the objectives
reflected contents explicitly or implicitly, I had to think about the approach
of carrying out the learning process. Furthermore, I had to select metaphors for
making meaningful learning. These all reflected a need of planned activities,
which could help me to direct the learning programme.
Under this curriculum image, the
educative relationship between my student and me was like consumers- distributor
relationship. Moreover, they thought they had to consume what I intended them to
learn. My plan was like a store and they were receiving from the store,
just like receiving and banking the ideas for their exams because the intents
were the hallmarks for their exam. Their banking capacity was judged according
to the withdrawn knowledge from the store.
The hidden curriculum – known as
covert
(Print, 1993)
and de facto
(Sambell & McDowell, 1998)
curriculum – exists because of culture of schooling
(Schubert, 1986)
. Hidden curriculum is the form of all unintended and
unnoticed activities, which can also contribute to profound learning
(Schubert, 1986)
. Furthermore, this notion of curriculum appears in the
implementation level. So, the persons, things and processes
(Connelly & Clandinin, 1988)
are responsible for such curriculum rather than the
curriculum designer. The literature on hidden curriculum regards it as an
indispensable aspect of teaching learning process
(Connelly & Clandinin, 1988; Print, 1993)
.
The hidden curriculum was apparent in
my teaching. Specifically, I had been trying to use such examples, activities
and techniques that could communicate a hidden message of mathematics as a
fun. It was implicit and unintended curricular message for the students of
that level. Similarly, I used to solve some model problems and they used to
follow me: Here, the hidden message was to follow my style of solving
mathematical problem rather than that of the other teachers. I did not say
directly, but unknowingly, I followed my style while checking and marking their
assignment. Similarly, asking questions to the brilliant students used to convey
a hidden message that the student, who was asked, was praised. Unknowingly, it
used to happen that my experience-generated beliefs and conceptions
(Liyod, 1998)
of mathematical concepts communicated as if they were true
mathematical knowledge for them.
Talking about educative relationship, I have realized that the image of
hidden curriculum had had both negative and positive impact on student learning.
Explicitly speaking, the hidden curriculum had conveyed the message of supremacy
of the teacher, which helped view the teacher as an ultimate authority of
knowledge. On the contrary, the hidden message of mathematics as a fun
could help develop a positive attitude towards mathematics. My conceptions of
mathematical knowledge gained through experience, which also mirrored my
worldview, had a significant influence in their learning.
References
AEC
Curriculum Corporation. (1991). A National Statement on Mathematics for
Australian Schools. Australian Education Council and Curriculum Corporation:
Carlton, Victoria.
Applebee, A. N. (1996). Curriculum as
conversation. Chicago: The University of Chicago Press.
Beyer,
L. E., & Apple, M. W. (1998). Values and the politics in the curriculum. In
L. E. Beyer & M. W. Apple (Eds.), The
Curriculum: Problem, politics and possibilities. Albany: Sate University of
New York Press.
Confrey,
J. (1995). How compatible are radical constructivism, sociocultural approaches,
and social constructivism. In J. Gale (Ed.), Constructivism
and Education. Broadway, Hillsdale: Lawrence Erlbaum Associates, Publishers.
Connelly,
F. M., & Clandinin, D. J. (1988). Teachers
as curriculum planners: Narratives of experience. New York: Teachers College
Press.
Dooley,
C. (1998). Teaching as two-way street: Discontinuities among metaphors, images,
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P. (2001). Understanding metaphors for writing: In defence of the conduit
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H. (1969). An introduction to the history
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T. (2001). Teaching as acting: Considering as epistemology and its use in
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B. (1999, Aug 3 1999). The algebraic
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Lakoff,
G., & Johnson, M. (1980). Metaphors we
live by. Chicago: University of Chicago Press.
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A. C. (1999). Washington Commentary: Looking Back, Looking Ahead. Phi Delta Kappan, 80(8), 563.
Liyod,
G. W. (1998). Supporting innovation: The impact of a teacher's conceptions of
functions on his implementation of a reform curriculum. Journal
for Research in Mathematics Education, 29(3), 248-.
Murphy,
P. K. (2001). Teaching as persuasion. Theory
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Print,
M. (1993). Curriculum development and
design. St. Leonards: Allen & Unwin Pty Ltd.
Sambell,
K., & McDowell, L. (1998). The construction of the hidden curriculum:
Messages and meaning in the assessment of student learning. Assessment
and Evaluation in Higher Education, 23(4), 391-402.
Schubert,
W. H. (1986). Curriculum: Perspective,
Paradigm, and Possibility. New York: Macmillan Publishing Company.
Slattery,
P. (1995). Curriculum Development in the
Postmodern Era. New York: Garland Publisher.
von Glasersfeld,
E. (1995). Radical Constructivism.
London: The Falmer Press.
Wehmeier,
S. (Ed.). (2000). Oxford Advanced
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