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ABSTRACT
The increase in the flow of information in the field of sciences requires the improvement of technologies that serve
to master it, and the introduction of new technologies. Learning materials consist of variables, characters, etc.
However, mastering educational materials is not just learning symbols, but most importantly, being able to apply
knowledge in everyday life. And abstract educational materials are very important in mastering science. This article
explores the pedagogical possibilities of introducing the CPA (Concrete-Pictorial-Abstract) approach to primary
education. Based on the analysis, it became clear that the CPA (Concrete-Pictorial-Abstract) approach has not been
thoroughly studied by local scientists and its possibilities have not been analyzed.
KEYWORDS
Cognitive, enactive, figurative, symbolic, concrete, visual, abstract.
INTRODUCTION
It is known that misconceptions can cause great
problems for students in later topics. Conceptual
understanding should be considered as knowledge
that students should acquire from the beginning of
learning science. This is especially true when working
with complex materials, involving multiple actions at
the same time, or with plot issues. As a result, students
face difficulties in solving problems.
After the above, we should understand that making it
easier for students to work with more complex,
especially non-standard problems, will reduce the
number of errors in working with concepts. Properly
approached exercises help students to think logically,
identify patterns, draw conclusions, make arguments,
and solve new and unfamiliar issues.
Research Article
PEDAGOGICAL POSSIBILITIES OF IMPLEMENTING THE CPA (CONCRETE-
PICTORIAL-ABSTRACT) APPROACH
Submission Date:
February 11, 2024,
Accepted Date:
February 16, 2024,
Published Date:
February 21, 2024
Crossref doi:
https://doi.org/10.37547/ijp/Volume04Issue02-13
Ruzikulova Nigora Shuxratovna
Doctor Of Philosophy In Educational Sciences (Phd), Associate Professor, The Doctoral Student Of Tashkent
State Pedagogical University Named After Nizami (Dsc), Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ijp
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 04 Issue 02-2024
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International Journal of Pedagogics
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Publisher:
Oscar Publishing Services
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LITERATURE ANALYSIS AND METHODS
The concrete-visual-abstract approach (CPA) based on
J. Bruner's concept of enactive, figurative and symbolic
expression methods is a technology promoted by the
Ministry of Education of Singapore since the early
1980s [14].
One of the educational concepts proposed by J.Bruner
in the book "Toward a Theory of Instruction" [8] is
"concrete (lat. concretus - real existing, clear, clear,
marked [21]) (vital)- visual-abstract)" is a concept of
expression
methods. This concept
lays
the
groundwork for a number of educational practices, all
of which have significant tripartite similarities with
J.Bruner's model.
The algorithm of J. Bruner's model consists of the
"concrete-visual-abstract" (CPA) sequence. The CPA
sequence has been shown to be particularly effective
for struggling students in mathematics [9].
In particular, the "concrete" link in the sequence of
CPA is the use of a real object ((r. subject - thing, object)
any material thing that exists outside of our
consciousness [21]) that can be felt through the sense
organs. serves as a theoretical basis for [23].
Fuchs and Hollenback [5] also advocated the use of the
CPA sequence to teach students about ordinal
numbers, geometry, and fractions.
In the practice of teaching mathematics in Singapore,
J. Bruner's enactive-image-symbolic concept is based
on the "concrete-visual-abstract" (CPA) approach. The
CPA approach, which emerged in the 1980s, is the main
educational strategy promoted by the Singapore
Ministry of Education. This is evidenced by its regular
mention in official educational documents, including
the curriculum introduced in 2013 [13]:
Again, the CPA approach involves learning by "doing."
It is particularly effective for teaching mathematical
concepts and skills at the elementary and intermediate
levels, and in some cases at the advanced levels.
Students use manipulatives (manipulation (lat.
manipulus - hand movement)) to create meaning and
concepts in the exercise of learning and mastering
mathematical
concepts
and
skills.
can
use
communicative influence [22] or other resources that
lead to the activation of states (emotions, attitudes,
stereotypes). Based on specific manipulatives and
experience, students reveal abstract mathematical
concepts or results. During training, students clearly
and communicate and share their perspectives using
visual expressions.The teacher's role is to guide
students through concrete, visual, and abstract levels
of understanding while providing appropriate support
and feedback. is the role of a mediator" (Ministry of
Education, 2012, p. 23, emphases added) [13].
Although CPA is now well-known within the
Singaporean mathematics education community (and
even beyond), it is extremely difficult to find scholarly
work in the literature regarding its theoretical roots
and practical application in the classroom. The study
examines the origins of CPA technology and its impact
on science curriculum development and teaching.
It is known that the recommended approach is to first
start with more concrete teaching methods for
elementary students, and then gradually replace
images with formal mathematical symbols or shapes to
acquire the necessary knowledge. important in
mastering. For example, this is the teaching strategy
recommended by Ketterlin-Geller, Chard and Fien [10].
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is important in the effectiveness of the education of
students with disabilities.
In a new study using the CPA sequence for some
elementary students with low math achievement,
Flores [4] found that students improved fluency and
increased confidence in performing arithmetic
calculations.
emphasizes
what
they
have
demonstrated. In addition, a number of other studies
have reported that the use of CPA has had a positive
effect on students who have difficulties in mastering
fractions [2], word problems [18]. Therefore, using the
CPA approach to teach mathematical concepts,
especially at the elementary level, has been proven to
be effective.
Despite similarities with other methods of determining
the sequence of training, some features of the CPA
approach are unique.
A number of authors [3] believed that the theoretical
roots of the CPA approach belong to J. Bruner's
"enactive", "image" and "symbolic" concepts.
It should be noted that views on enactivism have been
reflected in a number of studies. The concept of active
cognition (active cognition) or activity (enactivism) is
considered as a new form of constructivism in
epistemology, which includes the problems of mind
and div, subject and object of cognition, cognition
and life, living organism and environment, reality and
virtuality. the traditional solution is obtained [26].
J. Bruner began by clearly defining the parameters to
which such a theory must conform:
- determining methods of helping students to develop
"tendency to learn";
- determining the ways of creating an approximate
amount of knowledge for students;
- determining the most effective sequence of
presentation of educational materials;
- defining rubrics.
The enactive-image-symbol concept played a role in
the second and third parameters to a certain extent.
In the second paragraph about the structure of
knowledge, J. Bruner introduced enactive-image-
symbolic "methods of expression" [8].
Any knowledge ... can be expressed in three ways:
with a set of actions suitable for achieving a certain
result (active expression);
with a set of brief images or graphics that represent
the concept without fully describing it (figurative
representation);
(symbolic) representation by a set of symbolic or
logical sentences derived from a system of symbols
regulated by formative and transformative rules or
laws" [8].
J. Bruner did not mean internal mental operations; on
the contrary, he paid attention to external expressions
of knowledge. According to him, knowledge can be
embodied in action, visual image or symbolic language.
J. Bruner was a supporter of expressing the concept in
every way [8].
The scope of his educational theory is, firstly, related to
the amount of information needed to process
expressions in understanding basic knowledge; the
second is related to the potential of the student to
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acquire deeper or domain-specific concepts. J.Bruner
proposed methods of expressing mathematical ideas
that teachers can bring into the classroom and how
they can make decisions about the realistic forms they
can take to teach students using these methods.
According to J.Bruner, if it is true that the normal
course of intellectual development moves from
enactive to symbolic representation of the world, then
the optimal sequence in education can develop in the
same direction [8].
It is well known that step-by-step movement provides
comprehensive learning, with particular emphasis on
the gradual development of symbols in a symbolic
system in alternating stages and overlapping ways.
Ultimately, the goal of the CPA (Concrete-Pictorial-
Abstract) approach is to get students to freely use
symbols and abstract concepts. In fact, if students
work only in enactive and figurative ways, if they
cannot work with symbols and abstract concepts, they
will not be able to master the material sufficiently.
Because, like other researchers [17], it should be noted
that working freely in the field of symbols is the
essence of mathematics. It is known that, in practice,
in many cases when working with symbolic (symbolic)
expressions, the previous stages are omitted, or in an
accelerated case, the transition to this stage is
observed. If the students have achieved the ability to
work with the symbol system, the first two steps can
be skipped. But if the learner fails to achieve the goal
of solving the problem of symbolic transformations,
there is a danger that he will not have figurative
thinking on which to rely” (8; p. 49).
According to J.Bruner, although it is important for
students to be able to work in the system of symbols,
the method of symbolic representation is not
necessarily "superior" to the figurative method in all
mathematical situations. For example, in a problem-
solving context, visual representation of a concept can
be a good alternative to problem-solving. This implies
that the inability to switch to another method limits the
student's ability to solve problems; exposure to other
methods allows students to "return". This can be
interpreted as follows: if the learner learns only in a
symbolic way, he will not be able to use this method
effectively, causing him to "return" to restore the
meaning of symbols in the symbolic way. If there are
no stages of conscious learning (enactive-figurative) in
other ways of expression, it will not be possible to
"return"; Movement through the three modes of
learning reflects "the course of normal intellectual
development" [8].
It is not necessary to use all three steps unless there are
potentially powerful resources for solving the
problems explored in other methods. In this case, it is
possible to consider an alternative teaching direction
for students, bypassing the initial methods.
The CPA approach takes into account the differences
between students and serves as an important
empirical approach to the introduction of science ideas
and methods. Due to its theoretical foundations and
ease of use in education, this approach is considered
effective enough.
There is a similar correspondence between Singapore's
"concrete-visual-abstract" model and J. Bruner's
"enactive-image-symbolic" concept. In the CPA
(Concrete-Pictorial-Abstract) approach, the formal
interpretation of "concrete" is not limited to "specific
manipulatives" but also to "concrete experience".
J.Bruner's "enactive-image-symbolic" concept is
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explained as enactive consists of activities with
appropriate manipulatives. Thus, the views on
"concrete" largely correspond to J. Bruner's views on
"enactive". Also, the concept of "abstract" is
conceptually close to the linguistic-symbolic meaning
of J.Bruner's concept of "symbolic" [13].
Another source of information on understanding these
terms can be found in the Singapore Mathematics
Textbooks commissioned by the Singapore Ministry of
Education. The CPA approach is included in these
textbooks.
The Elementary Mathematics Textbook Project, led by
Dr. Ho Teck Hong, aims to use effective approaches in
teacher training and professional development, and to
develop teaching materials for teaching and learning
mathematics in elementary education. The "concrete-
visual-abstract" approach to educational materials in
primary education projects is promoted [11].
We reviewed primary education textbooks. A typical
chapter introduction in these textbooks comes in the
following order: a "real-life" situation that provides
context for the featured situation or problem (e.g., the
problem of dividing a pie), a visual representation of
the situation or other related problem (e.g.,
representing pies in circles) and abstraction from visual
forms to symbolic form (for example, working with
numerical fractions). Thus, there is a sequence that
exactly repeats the steps of CPA. However, the
"concrete" things presented in the textbooks seem to
deviate from J.Bruner's original concept of activity and
take the form of a simple description of activity. In
other words, the authors of the textbooks tried to
extend the "concrete" to him not only the activity, but
also this activity.
A distinction has been made between the concept of
"concrete" used in projects on teaching mathematics
in primary education in the early 1980s and in the
curricula introduced in 2013. In this case, the concept of
"concrete" corresponds to the concept of J.Bruner.
According to the analysis, an important change in the
1990s was the shift from teaching to learning. In
addition to educational manuals, a wide range of
educational manipulatives was introduced. The
teacher's role is to shape the learning experience of
the respective student, including concrete experiences
to support learning. Concrete experience can include
educational activities, real-life contexts, or the ability
to use manipulatives. Analysis of the Singapore
Ministry of Education's CPA curriculum in recent years
shows that CPA as an educational strategy was first
introduced only in 1980 due to the results of projects
on teaching mathematics in primary education.
introduced. The original source was identified in the
1990 curriculum. In it, the CPA approach was officially
approved as a recommended approach for teaching in
junior high school classes [13].
However, there is one feature that differs from
J.Bruner: "concrete", "visual" and "abstract" are
described as "levels of understanding" in Singapore
Ministry of Education documents. J. Bruner lists them
as stages, not as "levels". The word "stages" used by
J.Bruner refers to a sequence of teaching over time
rather than "levels of understanding". It is known that
the external forms of information expression depend
on the internal psychological activity of students.
Associating this with student competence is a very
important step. Psychological process (as an activity)
includes not only one level of mental activity in the
conditions of problem solving, but also complex
adaptive activity with various forms of expression.
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According to researchers, students who are able to
work freely in the abstraction method have mental
capabilities that allow them to solve more complex
tasks.
Hence, cognitive psychologist Jerome Bruner believes
that the goal of education should be intellectual
development or development, not learning, teaching,
or memorizing facts and information. In his research,
he distinguished three stages of his cognitive concept.
Another point about CPA is that there are various
ambiguities regarding the terms "concrete" and
"abstract". Part of this uncertainty is due to the
different definitions of these terms in different
theories. In some studies, for example J.Bruner, the
"abstract" stage can be defined not as the concept of
working in the system of symbols, but as the final result
of the process of abstraction by comparison of
similarities [24]. An additional complication lies in the
subjective nature of what is considered concrete or
abstract. Therefore, one of the results of these
ambiguities and subjectivities in science teaching,
particularly mathematics teaching, is that what is
considered "concrete", "visual" and "abstract" for a
given div of knowledge is not universal. ; teachers
must tailor methods to the needs of their students. For
this purpose, the characteristics of expressions
provided by J.Bruner remain a useful guide.
You can also find scientific studies on the use of the
CPA approach in classes [13]. In particular, the details
of the application of the CPA approach in teaching
mathematics are described in the works of Long, Tap,
Tap, Thilagam, Karen, Quik, Tan [14]. At first, they
discussed the difficulties that their students, who are
behind the indicated results, face when they encounter
mathematical manipulations. According to teachers,
students make a lot of mistakes when performing
symbolic manipulations. Thus, their goal was to
develop lessons that would help students understand
the meaning of the algebra they were learning.
Research based on the CPA approach aims to help
students start with concrete mathematical concepts
and then gradually connect them with symbolic form
during lessons.
In the CPA approach, by providing the child with
multiple representations of the same general idea
expressed in a common symbol, the learner is helped
to move from concrete sensory properties of the
concept to abstract properties. In some cases, there is
a "fading" period (or phase) during the "transition".
Many researchers have also discussed this fading
process [6, 7, 12].
We can refer to the scientific research of a number of
researchers about this process [19]. For example,
studies have investigated the positive effect of fading
on the transfer efficiency of group theory students
[20].
The duration of the fading process varies from student
to student. It is important to give motivational tasks in
this process.
In the CPA approach, it is desirable to use the general
features of the teaching model to guide the entire
process based on the steps proposed by Lewis [16],
Stepanek, Appel, Leong, Mangan, and Mitchell [25]:
identify the difficulties students face and so on. setting
goals, developing an activity plan; conduct additional
discussions; conduct the lesson.
It is known that teachers feel a lack of time when they
try to pass the curriculum within the time allotted in
the lesson schedule [1, 15]. When working regularly
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with limited time to cover topics, there is a natural
tendency to shift to basic skills to teach each topic in
the most effective way. This leads to rapid
convergence with the rules and formulas that students
need to master, and also means abandoning other
ways of expressing information and moving directly to
the "abstract" stage. However, this often leads to
students not paying attention to understanding the
learning material. Therefore, it provides a basis for
using the CPA approach.
RESULT
Despite understanding that direct teaching of arbitrary
rules jeopardizes the thoroughness of students'
mastery of basic mathematical concepts, the problem
of lack of time is so strong that teachers often They do
not use time-consuming approaches and technologies.
Therefore, any realistic attempt to implement a CPA
approach must take these issues into account.
It should be emphasized that when introducing the
CPA approach, it is important to start with the
development of training programs that create
conditions for its use. At the same time, it is impossible
to implement the CPA approach for the entire
curriculum. Depending on the capabilities of the CPA
approach sequence, it can be used in a specific
sequence of lessons. The CPA approach may not be
suitable for teaching some subjects. The main focus
should then be on sections where the sequence of the
CPA approach is appropriate.
CONCLUSION
Developing a CPA strategy over several lessons allows
for a smooth transition from one stage to the next. The
duration of several lessons allows students the
freedom of time to move on to the next method of
expression when they feel ready. "Intensification" of
the CPA approach in a certain period, for example,
within one lesson, does not allow to achieve the
expected results; on the other hand, extending the
duration of the CPA to a longer period makes it
unrealistic in terms of meeting the time frames of the
training schedule.
Thus, beginning with the development of continuity
boundaries is also useful in terms of teacher
development. Practicing teachers can be involved in
the process. Thus, teachers do not see themselves as
mere "end users" of CPA-based development; on the
contrary, by actively participating in the development
of duration limits and sequences of teaching materials,
they will not only have the opportunity to develop a
critical interpretation of the CPA approach, but also
contribute to clarifying its use in practical teaching in
the classroom.
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