Jerome Bruner was an influential American psychologist known for his theory of cognitive development and learning known as constructivism. Bruner believed that learning involves actively constructing knowledge through experiences. He proposed that knowledge is represented in three stages - enactive (action-based), iconic (image-based), and symbolic (language-based). Bruner's theory emphasizes using a concrete-pictorial-abstract approach to teaching mathematical concepts by progressing from physical manipulatives to visual representations to abstract symbols. This approach aims to help students fully understand concepts by connecting hands-on and visual experiences to abstract ideas.
“Concept Attainment ( indirect instruction strategy) Model” by Jerome Bruner. It also discuss on Descriptions of Bruner’s Concept Attainment Model. Merits, limitations and applications of Concept Attainment Model
“Concept Attainment ( indirect instruction strategy) Model” by Jerome Bruner. It also discuss on Descriptions of Bruner’s Concept Attainment Model. Merits, limitations and applications of Concept Attainment Model
Interpretation construction (icon) design modelThiyagu K
One major and popular instructional model based the constructivist approach is Interpretation Construction Model or ICON model which emphasizes on learners’ encounter with authentic issues in pair or groups, on constructing interpretation by the learners in groups, searching for information about the problems in groups and facing different interpretations about the problems in groups. In other words, it is group-based teaching-learning co-operative as well as collaborative approach which, as it is evident, lays emphasis and importance on the inclusive and all round socio-academic growth of the learners and also in way has drawn insights from the concept of Multiple Intelligences as propounded by the eminent cognitive scientist Gardner (1993). ICON Model, as Tsai, Chin-Chung. 2011 and other scholars in educational psychology argue, mainly rests on the principles such as observation in authentic activities (Understanding Zone), contextualizing prior knowledge and interpretation construction (Understanding Zone), cognitive conflict and apprenticeship (Understanding Zone), collaboration (Application Zone), multiple interpretations (Higher Order Thinking Skill zone), and multiple manifestations (Higher Order Thinking Skill zone).
TNTEU - B.Ed New Syllabus - Pedagogy of Mathematics - Semester 1 - Code BD1MA - Unit III Approaches for teaching - Bigge and Hunt Steps - Reflective Level of Teaching Advantages and Disadvantages - Conclusion
This presentation can give some idea about to understand different terminology like Information, Knowledge, Belief and Truth and also the concept different ways of Knowing
"Inductive & Deductive method" is one of the child centered approach. this PPT is useful for B.Ed, M.Ed and Dl.Ed students & also useful for teacher educators as a reference.
Meaning of interaction
Classroom inetraction(Characterstics, types and objectives)
Interaction Analysis
Classroom Interaction Analysis
Flanders Interaction Analysis
Advantages of FIACS
Limitations of FIACS
Interpretation Construction Design Model or more popularly ICON Model is a constructivist model of teaching learning. this is an innovation in the field of Educational Technology during the last decade of the last century, which came to be popular in the first decade of 21st century
TNTEU - B.Ed New Syllabus - Pedagogy of Mathematics - Semester 1 - Code BD1MA - Unit III Approaches for teaching - Herbartial Steps - Memory Level of Teaching Advantages and Disadvantages - Conclusion
This model guides teachers to go to the depth of the content. And helps students to attain new concepts. So the model has a great attribute on teaching -learning process.
It discuss about the Morrison teaching model in detail. It also discuss on understanding level of teaching - 1. Focus 2. Syntax and five types 3. Social system and 4. Support system in detail
Creative Reflection: The Critical Practice of Stepping Backchar booth
Reflective practice is the process of actively observing, understanding, and shaping pedagogy. Its associated skills include developing individual insight into the impact and practice of education through critical analysis, instructional design, theoretical grounding, and dialogue with peer educators. Also integral is gathering insight into the learner experience through meaningful assessment. Less often discussed is the role of creativity, experimentation, learner engagement, and the disruption of ingrained teaching habits and/or narratives; this keynote will explore strategies for cultivating a more holistic reflective practice in service of enriching and diversifying one’s teaching.
Interpretation construction (icon) design modelThiyagu K
One major and popular instructional model based the constructivist approach is Interpretation Construction Model or ICON model which emphasizes on learners’ encounter with authentic issues in pair or groups, on constructing interpretation by the learners in groups, searching for information about the problems in groups and facing different interpretations about the problems in groups. In other words, it is group-based teaching-learning co-operative as well as collaborative approach which, as it is evident, lays emphasis and importance on the inclusive and all round socio-academic growth of the learners and also in way has drawn insights from the concept of Multiple Intelligences as propounded by the eminent cognitive scientist Gardner (1993). ICON Model, as Tsai, Chin-Chung. 2011 and other scholars in educational psychology argue, mainly rests on the principles such as observation in authentic activities (Understanding Zone), contextualizing prior knowledge and interpretation construction (Understanding Zone), cognitive conflict and apprenticeship (Understanding Zone), collaboration (Application Zone), multiple interpretations (Higher Order Thinking Skill zone), and multiple manifestations (Higher Order Thinking Skill zone).
TNTEU - B.Ed New Syllabus - Pedagogy of Mathematics - Semester 1 - Code BD1MA - Unit III Approaches for teaching - Bigge and Hunt Steps - Reflective Level of Teaching Advantages and Disadvantages - Conclusion
This presentation can give some idea about to understand different terminology like Information, Knowledge, Belief and Truth and also the concept different ways of Knowing
"Inductive & Deductive method" is one of the child centered approach. this PPT is useful for B.Ed, M.Ed and Dl.Ed students & also useful for teacher educators as a reference.
Meaning of interaction
Classroom inetraction(Characterstics, types and objectives)
Interaction Analysis
Classroom Interaction Analysis
Flanders Interaction Analysis
Advantages of FIACS
Limitations of FIACS
Interpretation Construction Design Model or more popularly ICON Model is a constructivist model of teaching learning. this is an innovation in the field of Educational Technology during the last decade of the last century, which came to be popular in the first decade of 21st century
TNTEU - B.Ed New Syllabus - Pedagogy of Mathematics - Semester 1 - Code BD1MA - Unit III Approaches for teaching - Herbartial Steps - Memory Level of Teaching Advantages and Disadvantages - Conclusion
This model guides teachers to go to the depth of the content. And helps students to attain new concepts. So the model has a great attribute on teaching -learning process.
It discuss about the Morrison teaching model in detail. It also discuss on understanding level of teaching - 1. Focus 2. Syntax and five types 3. Social system and 4. Support system in detail
Creative Reflection: The Critical Practice of Stepping Backchar booth
Reflective practice is the process of actively observing, understanding, and shaping pedagogy. Its associated skills include developing individual insight into the impact and practice of education through critical analysis, instructional design, theoretical grounding, and dialogue with peer educators. Also integral is gathering insight into the learner experience through meaningful assessment. Less often discussed is the role of creativity, experimentation, learner engagement, and the disruption of ingrained teaching habits and/or narratives; this keynote will explore strategies for cultivating a more holistic reflective practice in service of enriching and diversifying one’s teaching.
Keynote for SCIL event at UC Irvine - EXPERI(M)ENT(I)AL: Developing Process-oriented, User-focused Methodologies in the Library. See http://guides.lib.uci.edu/experi-m-ent-i-al/home
Light is a very common topic to make a presentation on.
i hope my ppt will help you all.
If you need more help, follow me on Google Plus : bobbysz182@gmail.com.
Or follow me on twitter.
Jennifer Chess, Communications & Marketing Librarian; Lori Mullooly, Events and Programming Librarian; Lisa Gomez, Exhibition Librarian; U.S. Military Academy Library, West Point, NY (FTE: 4,400)
Big Talk From Small Libraries 2024
February 23, 2024
http://nlcblogs.nebraska.gov/bigtalk
The proof is in: There's no scientific basis that learning styles or Meyers-Briggs personality types exist. So much of what educators have based adult learning design on is flawed, so what kind of new educational paradigm is needed?
The answer lies in the findings of neuroscientists who show that not only can engagement enhance adult learning, it can aid retention and application. But that depends on how you craft your education design and engagement strategy. This presentation shows you how to use the latest scientific findings on how the brain works and apply it to your educational programs.
For more education about meeting/education design, visit: http://planyourmeetings.com. Find an event near you at http://planyourmeetings.com/events.
W R I T T E N E X E RC I S E # 1 O N E I S A S T O .docxjessiehampson
W R I T T E N E X E RC I S E # 1
“ O N E I S A S T O N I S H E D I N T H E S T U D Y O F H I S T O RY A T T H E R E C U R R E N C E O F T H E I D E A T H A T
E V I L M U S T B E F O R G O T T E N , D I S T O R T E D , S K I M M E D OV E R . W E M U S T N O T R E M E M B E R T H A T
DA N I E L W E B S T E R G O T D R U N K B U T O N LY R E M E M B E R T H A T H E W A S A S P L E N D I D
C O N S T I T U T I O N A L L A W Y E R . W E M U S T F O R G E T T H A T G E O R G E W A H I N G T O N W A S A S L AV E
O W N E R … A N D S I M P L Y R E M E M B E R T H E T H I N G S W E R E G A R D A S C R E D I TA B L E A N D I N S P I R I N G .
T H E D I F F I C U L T Y, O F C O U R S E , W I T H T H I S P H I L O S O P H Y I S T H A T H I S T O RY L O S E S I T S VA L U E A S
A N I N C E N T I V E A N D E X A M P L E ; I T PA I N T S P E R F E C T M E N A N D N O B L E N A T I O N S , B U T I T D O E S
N O T T E L L T H E T R U T H . ”
~ W. E . B . D U B O I S ( B L A C K R E C O N S T R U C T I O N )
What is history? Why should we study history? Within the context of our stories
concerning Christopher Columbus, Native Americans, the Pilgrims, or slavery,
discuss how historians (Zinn and Loewen) have dealt with the above issues
specifically. How have history textbooks begun to complicate our histories even
further? With regard to the above topics, how have your readings and studies in
this class differed from the ways in which these topics have been portrayed (all the
way back to elementary school) to you in previous classes? In the quote above,
W.E.B. DuBois suggests that in our studies of history, when we skim over the bad
parts, our histories begin to lose their value as “incentive and example.” What
does he mean by this? What are the far-reaching consequences of the ways in
which so many of us have been taught history?
“ H I S T O R Y I S F I C T I O N , E XC E P T F O R T H E PA R T S T H A T I L I K E , W H I C H A R E , O F C O U R S E , T R U E . ”
~ J I M C O R D E R
U N I T E D S T A T E S H I S T O R Y
A M Y B E L L
DIREC TIONS
1) Your response to the question must be typed—twelve point font, double-spaced,
one-inch margins. In writing your answer, please do not exceed five pages.
2) In your response, use only your assig ned text(s), the instructor’s handouts, or
class notes taken from discussions. Do not use additional library or internet
sources.
3) Your generalizations must be supported by direct citations from the text, class
notes, or instructor’s handouts.
4) Citations should be made in MLA format. For class notes or presentations, you
might use: (60’s handout) or (class notes).
Note: You must cite parenthetically throughout your narrative. Please follow this format. There
should be ma ...
Busy? We all have the same amount of time, 168 hours per week. Yet some of us are in a state of flow, while others are managing overwhelm. We feel stress when the way we spend our time is misaligned with our values. This slide deck will help you get back in control, so you can spend your precious time doing what you love most.
Thinking about Teaching: Mindfulness and Metacognition as Pedagogychar booth
In meditation and psychology, “mindfulness” promotes reflective self-awareness, whereas in educational theory metacognition encourages “thinking about thinking” to enhance critical reflection, engagement, and information retention. This interactive presentation investigates mindful and metacognitive approaches to teaching and learning. Learn ideas for incorporating related strategies into the physical/digital classroom.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
1. Jerome
Bruner
C O N S T R U C T I V I S T T H E O R Y-
C O N C E P T F O R M AT I O N
2. Biography
Jerome Seymour Bruner (October 1, 1915 – June 5,
2016) was an American psychologist who made
significant contributions to human cognitive
psychology and cognitive learning theory in
educational psychology. Bruner was a senior
research fellow at the New York University School
of Law. He received a BA in 1937 from Duke
University and a PhD from Harvard University in
1941. He taught and did research at Harvard
University, the University of Oxford, and New York
University. A Review of General Psychology survey,
published in 2002, ranked Bruner as the 28th most
cited psychologist of the 20th century.
3. BRUNER’S CONSTRUCTVIST
THEORY.
Cognitive Structure
Learning Theory
Bruner believes that the essence of
learning is that one connects the
similar things and organizes them
into meaningful structures, and
learning is the organization and
reorganization of cognitive
structures. Knowledge learning is
to form the knowledge structure of
all subjects in the minds of
students.
Bruner is one of the pioneers of
cognitive psychology in the United
States, which began through his
own early research on sensation
and perception as being active,
rather than passive processes.
Like Ausubel (and other cognitive
psychologists), Bruner sees the
learner as an active agent;
emphasizing the importance of
existing schemata in guiding
learning.
4. Bruner’s Theory Continued
Bruner argues that students should discern for themselves the structure of subject content –
discovering the links and relationships between different facts, concepts and theories (rather than
the teacher simply telling them).
Bruner (1966) hypothesized that the usual course of intellectual development moves through three
stages: enactive, iconic, and symbolic, in that order. However, unlike Piaget’s stages, Bruner did
not contend that these stages were necessarily age-dependent, or invariant.
Piaget and, to an extent, Ausubel, contended that the child must be ready, or made ready, for the
subject matter. But Bruner contends just the opposite. According to his theory, the fundamental
principles of any subject can be taught at any age, provided the material is converted to a form
(and stage) appropriate to the child.
5. Principles of Bruner’s Theory
• Instruction must be concerned with the experiences and contexts that make the student willing and
able to learn (readiness).
• Instruction must be structured so that it can be easily grasped by the student (spiral organization).
• Instruction should be designed to facilitate extrapolation and or fill in the gaps (going beyond the
information given).
6. For Example:
• The concept of prime numbers appears to be more readily grasped when the child, through
construction, discovers that certain handfuls of beans cannot be laid out in completed rows and
columns. Such quantities have either to be laid out in a single file or in an incomplete row-column
design in which there is always one extra or one too few to fill the pattern. These patterns, the child
learns, happen to be called prime. It is easy for the child to go from this step to the recognition
that a multiple table , so called, is a record sheet of quantities in completed multiple rows and
columns. Here is factoring, multiplication and primes in a construction that can be visualized.
7. Spiraling According to Bruner
• The spiral approach to curriculum has three key principles that sum up the approach nicely. The
three principles are:
1. Cyclical: Students should return to the same topic several times throughout their school career;
2. Increasing Depth: Each time a student returns to the topic it should be learned at a deeper level
and explore more complexity;
3. Prior Knowledge: A student’s prior knowledge should be utilized when a topic is returned to so
that they build from their foundations rather than starting anew.
8. Spiraling Used In Mathematics
• In mathematics, we often return to the same content repeatedly but add complexity each time.
• For example, your teacher may first cover simple fractions, then more complex fractions, and then
start getting you to add and subtract fractions.
• Rather than focusing on fractions for an entire year, your school will spread fraction classes out
over the course of many years.
• Each time you return to fractions, your teacher will assess how well you retained previous
information, and then help you build upon that prior knowledge.
9. Three Stages
of Bruner’s
Theory
ENACTIVE REPRESENTATION
(ACTION-BASED)
ICONIC REPRESENTATION
(IMAGE-BASED)
SYMBOLIC REPRESENTATION
(LANGUAGE-BASED)
10. Enactive
Representatio
n
(action-based)
I N T H E E N A C T I V E M O D E ,
K N O W L E D G E I S S T O R E D P R I M A R I L Y
I N T H E F O R M O F M O T O R
R E S P O N S E S . T H I S M O D E I S U S E D
W I T H I N T H E F I R S T Y E A R O F L I F E
( C O R R E S P O N D I N G W I T H P I A G E T ’ S
S E N S O R I M O T O R S T A G E )
T H I N K I N G I S B A S E D E N T I R E L Y
O N P H Y S I C A L A C T I O N S , A N D
I N F A N T S L E A R N B Y D O I N G , R A T H E R
T H A N B Y I N T E R N A L
R E P R E S E N T A T I O N ( O R T H I N K I N G ) .
I T I N V O L V E S E N C O D I N G P H Y S I C A L
A C T I O N - B A S E D I N F O R M A T I O N A N D
S T O R I N G I T I N O U R M E M O R Y . F O R
E X A M P L E , I N T H E F O R M O F
M O V E M E N T A S M U S C L E M E M O R Y , A
B A B Y M I G H T R E M E M B E R T H E
A C T I O N O F S H A K I N G A R A T T L E .
11. The Enactive
Stage In
Mathematics
I n t h e e n a c t i v e m o d e , t h e c o n c e p t i s r e p r e s e n t e d t h r o u g h t h e l e a r n e r s
a c t i n g o n c o n c r e t e , p h y s i c a l o b j e c t s . F o r a l g e b r a , t h e c o n c e p t o f a n
u n k n o w n q u a n t i t y c a n b e r e p r e s e n t e d b y a b a g o r b o x o f a n u n k n o w n
n u m b e r o f c o u n t e r s .
T h e t e a c h e r c a n a s k q u e s t i o n s s u c h a s “ W h a t h a p p e n s i f t h r e e
c o u n t e r s a r e p l a c e d i n t h e b a g ? W h a t i f o n e c o u n t e r i s t a k e n o u t ?
W h a t i f t h e r e a r e t e n b o x e s w i t h t h e s a m e n u m b e r o f c o u n t e r s i n
e a c h ? ”
A v a r i a b l e c a n b e r e p r e s e n t e d a s a c h a n g i n g l e n g t h , f o r e x a m p l e ,
l e a r n e r s c a n m e a s u r e t h e l e n g t h o f a p e a s t r e e a s i t g r o w s .
12. Iconic
Representatio
n
(image-
based)
•I N F O R M AT I O N I S L E A R N E D
A S S E N S O R Y I M A G E S
( I C O N S ) , U S U A L LY V I S U A L
O N E S , L I K E P I C T U R E S I N
T H E M I N D . F O R S O M E , T H I S
I S C O N S C I O U S ; O T H E R S
S AY T H E Y D O N ’ T
E X P E R I E N C E I T.
•T H I S M AY E X P L A I N W H Y,
W H E N W E A R E L E A R N I N G A
N E W S U B J E C T, D I A G R A M S
O R I L L U S T R AT I O N S A R E
O F T E N H E L P F U L T O
A C C O M PA N Y T H E V E R B A L
I N F O R M AT I O N .
•T H I N K I N G I S A L S O B A S E D
O N U S I N G O T H E R M E N TA L
I M A G E S ( I C O N S ) , S U C H A S
H E A R I N G , S M E L L O R
T O U C H .
13. The Iconic
Mode in
Mathematic
s
IN TH E IC ON IC MOD E, A PIC TU R E
ILLU STR ATES TH E U N K N OW N
QU A N TITY TH E PIC TU R E TA K ES ITS
MEA N IN G FR OM TH E LEA R N ER ’S
PR EVIOU S EN A C TIVE EXPER IEN C ES.
14. The Symbolic
Representatio
n
• T H I S D E V E L O P S L A S T . I N T H E S Y M B O L I C
S T A G E , K N O W L E D G E I S S T O R E D P R I M A R I L Y A S
L A N G U A G E , M A T H E M A T I C A L S Y M B O L S , O R I N
O T H E R S Y M B O L S Y S T E M S .
• T H I S M O D E I S A C Q U I R E D A R O U N D S I X T O S E V E N
Y E A R S O L D ( C O R R E S P O N D I N G T O P I A G E T ’ S
C O N C R E T E O P E R A T I O N A L S T A G E ) .
• I N T H E S Y M B O L I C S T A G E , K N O W L E D G E I S
S T O R E D P R I M A R I L Y A S W O R D S , M A T H E M A T I C A L
S Y M B O L S , O R O T H E R S Y M B O L S Y S T E M S , S U C H A S
M U S I C .
• S Y M B O L S A R E F L E X I B L E I N T H A T T H E Y C A N B E
M A N I P U L A T E D , O R D E R E D , C L A S S I F I E D , E T C . S O
T H E U S E R I S N ’ T C O N S T R A I N E D B Y A C T I O N S O R
I M A G E S ( W H I C H H A V E A F I X E D R E L A T I O N T O
T H A T W H I C H T H E Y R E P R E S E N T ) .
• A C C O R D I N G T O B R U N E R ’ S T A X O N O M Y , T H E S E
D I F F E R F R O M I C O N S I N T H A T S Y M B O L S A R E
“ A R B I T R A R Y . ” F O R E X A M P L E , T H E W O R D
“ B E A U T Y ” I S A N A R B I T R A R Y D E S I G N A T I O N F O R
T H E I D E A O F B E A U T Y I N T H A T T H E W O R D
I T S E L F I S N O M O R E I N H E R E N T L Y B E A U T I F U L
T H A N A N Y O T H E R W O R D .
15. The Symbolic Mode in
Mathematics
• In the symbolic mode, the concept is represented in an abstract or a conventional way. Bruner
considers words (such as ‘five’, ‘add’ or ‘tin’) to be symbolic in the same way as conventional
letters and signs are (e.g. 5, + or t).
• FOR EXAMPLE
When students learn the knowledge of squares, they do not grasp the concept and nature of squares in isolation,
instead link the knowledge of squares to other geometric knowledge, such as quadrilaterals, parallelograms,
rectangles, diamonds, and so on. And they conclude the new knowledge into the original knowledge structure, so
as to form and perfect the quadrilateral knowledge structure diagram constantly in the mind.
16. The CPA Approach of Bruner’s
Theory
The CPA approach, that is the CONCRETE, PICTORAL and ABSTRACT approach lies at the
heart of Mathematics.
It enables a natural and supportive progression for learners as they develop their
understanding and skills in math. For example, in exploring equivalent fractions with
students you can begin with multi-link cubes, then progress to the pictorial problems in the
book and then on to questions with no visuals provided except numbers and the necessary
mathematical symbols. This will result in a fully embedded understanding of the concepts
throughout the classroom.
17. Concrete Stage
• Concrete is the “doing” stage. During this stage, students use concrete objects to model problems.
Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem,
the CPA approach brings concepts to life by allowing children to experience and handle physical
(concrete) objects. With the CPA framework, every abstract concept is first introduced using
physical, interactive concrete materials.
• For example, if a problem involves adding pieces of fruit, children can first handle the actual fruit.
From there, they can progress to handling abstract counters or cubes which represent the fruit.
18. Pictorial (Representational)
Stage
• Pictorial is the “seeing” stage. Here, visual representations of concrete objects are used to model
problems. This stage encourages children to make a mental connection between the physical
object they just handled and the abstract pictures, diagrams or models that represent the objects
from the problem.
• Building or drawing a model makes it easier for children to grasp difficult abstract concepts (for
example, fractions). Simply put, it helps students visualize abstract problems and make them more
accessible.
19. Abstract Stage
• Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Students
will not progress to this stage until they have demonstrated that they have a solid understanding of
the concrete and pictorial stages of the problem. The abstract stage involves the teacher
introducing abstract concepts (for example, mathematical symbols). Children are introduced to the
concept at a symbolic level, using only numbers, notation, and mathematical symbols (for example,
+, –, x, /) to indicate addition, multiplication, or division.