Maybe we will agree with the statement that as long as we are alive, then as long as we are still learning.

Especially for people who are still working as students, university students, prospective teachers,

or teachers themselves, of course the word learning is increasingly attached to everyday life.

We have basically done almost all learning theories, but often we are not aware that what we are

doing actually has a theory. Therefore, let’s try to understand the basis and concepts of

learning from Bruner’s theory.

Bruner’s theory itself is one of the theories that has had a significant impact on the field of education,

especially for learning mathematics. Then from the existence of this theory, his thinking

sparked discovery learning learning. Then, how did this learning theory succeed in developing

one of the latest learning models in this century? What are its contributions to learning in

mathematics? Everything will be explained in full below.

## Bruner’s biography

Jerome Seymour Bruner was born on October 1, 1915 in New York City. Bruner was born blind and

could not see until cataract surgery in infancy. He was a graduate of the Psychology study

program at Duke University in 1937. Next, Bruner also succeeded in obtaining his master’s degree in 1939 and

also a Ph.D in 1941 at Harvard University.

During World War II, Bruner served under General Eisenhower in the Psychological Warfare Supreme division

of the Allied Forces European Expeditionary Force. After the war ended, Bruner continued to

work at Harvard University in 1945. When he was working at Harvard, Brunei began to actively produce various

kinds of research on how a person thinks.

At that time, Bruner met with many psychologists at Harvard and many of them adhered to behaviorism which

views every behavior performed by humans as a response to a stimulus provided by their environment.

Even so, Bruner does not fully agree with the theory. Until finally he and Leopos

conducted a series of experiments which resulted in a new theory of perception called New Look.

The New Look reveals that perception is not something that happens immediately, as has been assumed in the

old theory. Vice versa, perception is a form of information processing and also interpretation

which involves choices. His view was that psychology itself should be concerned with how people

see and also interpret the world and how they respond to stimuli.

In 1960, Bruner and George Miller founded the center for cognitive research at Harvard University.

Both firmly believed that psychology should be concerned with cognitive processes that differ from

those of humans and the way thoughts are structured in logical syntax. This then spawned

Bruner’s prominent contribution, namely pioneering the school of cognitive psychology which gave impetus so

that education could pay attention to the importance of developing thinking.

Bruner’s

Learning Theory

Bruner provides more views on human cognitive development, how humans learn, or gain knowledge and

transform knowledge. The basic premise of this theory views humans as processors, thinkers, and

also creators of information. According to him, learning is an active process that allows

humans to discover new things beyond the information given to them. Bruner’s theory discusses

human learning activities that are not related to age and also the stage of development.

Bruner’s approach to learning is based on two assumptions, namely the first is that the acquisition of

knowledge is an interactive process, and the second assumption is that people construct their knowledge by

connecting incoming information with previously stored and obtained information. Bruner

explained about four educational themes. The first theme explains the importance of knowledge

structure, then the second theme is learning readiness, and the other theme emphasizes the value of

intuition in the educational process. The last theme is about motivation or the desire to learn

and the various ways available to teachers to stimulate this motivation.

## Discovery Learning

In his theory entitled “Learning Development Theory”, Bruner explains the learning process that uses mental

methods, namely individuals who learn to experience what they learn for themselves so that the process can

be recorded in their minds in their own way. Next, this one learning theory is adapted into a

discovery learning learning model that encourages students to learn independently by finding it for

themselves.

In discovery learning, students will learn through active involvement with various concepts and principles

in solving problems. Then the teacher will encourage students to gain experience by doing

activities that allow students to discover principles for themselves. This learning arouses

students’ curiosity, motivates students to continue working and also interact with the environment around

them to find answers.

## Bruner’s Learning Stages

The interaction that occurs between students and the environment will provide opportunities for them to

make discoveries. In connection with this physical experience, according to Bruner, in the

learning process, children will go through three stages, including:

### 1. Enactive Stage

At this stage, a person will know an aspect of reality without using thoughts or words and consists of

presenting past events through motor responses. In this way, a set of activities will be

carried out to achieve certain results. In other words, at this stage children will be directly

involved in manipulating or tinkering with an object. For example, we want to introduce the

concept of fractional numbers, so we can use an apple that is divided into two equal parts.

### 2. Iconic Stage

In this stage, presentation activities will be carried out based on internal thoughts, where knowledge is

presented through a series of pictures or graphics carried out by the child. It will also be

related to mental which is a picture of the objects it manipulates. Children will not directly

manipulate objects as students do in the enactive stage.

At this iconic stage, namely a stage of learning something knowledge where the knowledge is represented or

manifested in the form of visual images or visual imagery, images, or diagrams that describe concrete

activities or concrete conditions that exist in the enactive stage mentioned above in point a.

Language becomes more important here because it acts as a medium for thinking. Then,

someone will reach a transitional period and use iconic representations based on the sense of symbolic

representations based on abstract ways of thinking.

### 3. Symbolic Stage

In this stage, language is a symbolic archetype, where the child will manipulate symbols or symbols of

certain objects. Children are no longer attached to objects as they were at the previous stage.

At this stage, children are able to use notation without dependence on real objects.

At the symbolic stage, learning is represented in the form of abstract symbols, namely arbitrary

symbols that are used based on the agreement of people in the field concerned, be they verbal symbols, for

example words, letters or sentences, mathematical symbols, or abstract symbols that are other.

For example, in studying the addition of two whole numbers, learning will occur optimally if students learn

this from the start using concrete objects, for example combining 3 marbles with 2 marbles and after that

counting the number of marbles. These are the reactive stages.

Then, learning activities are continued by using pictures or diagrams that represent the 3 marbles and the

2 marbles combined, then counting the number of marbles altogether, by using the picture or diagram or the

second stage, which is iconic. The students can do the addition by using the visual image of

the marbles. Then in the next stage, namely the symbolic stage, students can add the two

numbers by using number symbols, namely: 3 + 2 = 5.

We can accept the steps given by Bruner in simple logical learning. Where the introduction of

learning starts from the simplest or real things, then reaches the abstract things. Maybe we

can apply this concept in our daily learning process.

## Bruner Mathematics Learning

Bruner is one of the educational leaders who is engaged in mathematics as the material being tested.

According to him, learning mathematics will be more successful if the teaching process is directed

at the concepts and structures made in the subject matter being taught, in addition to the related

relationships between concepts and structures. By getting to know the concepts and structures

included in the material being discussed, children will later understand the material they have to

master.

According to Bruner, there are four principles regarding how to learn and teach mathematics which are

called postulates or theorems. Theorems or theorems related to learning mathematics according

to Bruner and also Kenvey based on their experiments and experiences include:

### 1. The Argument of Compilation

The argument for the arrangement says that students will always have the ability to master definitions,

theorems, concepts, and also other mathematical abilities. Therefore, the best way for students

to start learning concepts and principles in mathematics is to construct the concepts and principles they

are learning themselves.

### 2. Notational Proof

The notational theorem says that the mathematical notation used must be adapted to the child’s level of mental

development, namely enactive, iconic, and symbolic.

### 3. The argument for contrast and

diversity or variation

The argument for contrast and also diversity says that a concept must be contrasted with other concepts and

must be presented with various examples. For example, to be able to understand the concept of

the number 2, students will be given activities to make groups of objects that have 2 members. In addition,

they will also be given activities to make groups of objects that do not have 2 members. Then, they can also

choose which group belongs group of 2 objects and which group is not a group of 2 objects.

### 4. The Attribution Proposition

The argument for this association says that one mathematical concept has a close relationship with other

mathematical concepts, both in terms of content and in terms of the use of formulas. For

example, the formula for the area of a rectangle is a prerequisite material for the invention of the

formula for the area of a parallelogram derived from the formula for a rectangle.

## Learning Methods in Bruner’s Theory

Bruner’s theory says that students should learn by participating actively with concepts and principles.

So that later they will be encouraged to gain experience and conduct experiments that will allow

them to discover the various principles themselves. The knowledge gained by this discovery

learning method shows several positive impacts, including:

1. The knowledge will last a long time or can be remembered in other ways.

2. Discovery learning

outcomes have a better transfer effect compared to other learning outcomes. In other words,

concepts and principles that are made into one’s cognitive property are easier to apply to new

conditions.

3. Overall discovery learning will enhance students’ reasoning

and ability to think freely. Specifically, discovery learning will train students’

cognitive skills to find and solve problems without help from others.

Then it was argued, that discovery learning would arouse students’ curiosity, provide motivation to work

continuously until they found answers. Moreover, the approach can teach skills, solve problems

without help from others, and also require students to analyze and also manipulate information, not just

receive it.

The structure of the field of study, especially given by the basic concepts and principles of the field of

study. If a student has mastered the basic structure, it will be easier for them to learn other

subject matter in the same field of study. In addition, they will also find it easier to

remember new meaningful material, which they can use to see connections that are essential in that field of

study. That way, they can understand things in detail.

## Bruner’s Theory of Instruction in Bruner’s

Learning Theory

In Bruner’s theory, pure discovery learning takes time. Therefore, in his book entitled “The

Relevance of Education (1971), Bruner suggested that the use of discovery learning would only be applied to

certain limits, namely by directing it to the structure of the field of study. In this section,

it will also be discussed how teaching or instruction is carried out in accordance with the theory put

forward regarding learning. According to Bruner, a theory of instruction should include:

1. Optimal experience for students to want and be able to learn.

2. Structuring knowledge for optimal

understanding.

3. Details of the order in which the subject matter is presented

optimally.

4. The form and also the provision of reinforments.

## The Optimal Experience For Students

Who Will and Can Learn

According to Bruner’s Theory, learning and problem solving depend on alternative investigations.

Therefore, teaching or instruction must expedite and regulate alternative investigations, from the

student’s point of view. This alternative probe requires activation, orientation, and

maintenance. In other words, this alternative investigation requires something to get started.

Once initiated, the condition must be maintained or maintained. Then guarded so as not

to lose direction.

This is an explanation of what Bruner’s theory is and the various stages that must be passed.

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