caRL RogErs

“The only person who is educated is the one who has learned how to learn - and change”

 

 “People are essentially trustworthy, that they have a vast potential for understanding themselves and resolving their own problems without direct intervention on the therapist’s part, and that they are capable of self-directed growth if they are involved in a specific kind of therapeutic relationship.”

 

“I have days when I think that educational institutions at all levels are doomed, and perhaps we would be well advised to bid them farewell---and let true learning begin to blossom outside the stifling hallowed halls.”

 

 

 

 

BRUNER & DISCOVERY LEARNING IN MATH

Discovery learning is an inquiry-based, constructivist learning theory that takes place in problem solving situations where the learner draws on his or her own past experience and existing knowledge to discover facts and relationships and new truths to be learned. 

Discovery learning encourages students to actively use their intuition, imagination, and creativity.

Bruner puts forward a learning theories that consists of three representational stages:-

a) Enactive stage (0-2years old) -------------> action
     > students who learn addition and subtraction using things, 
    e.g base ten blocks, woods, stone, beads etc
b) Iconic stage (2-4years old) ---------------> image
     > students use paper and pencil to solve problem. they are able to visualize image
     e.g solve 234+674
c) Symbol stage (5-7years old) ---------------> symbol
    > students are able to use symbol for abstract. 


According to Bruner, learning begins with an action that involves touching, emotion and manipulation.


THE PRINCIPLES OR THEOREMS OF LEARNING MATHEMATICS

construction principle

Better for a student to learn a new concept in mathematics is to construct his own presentation. The teacher presents examples and the students work with the examples until they discover the interrelationships.

e.g teacher introduce the concept of gradient by giving formula. teacher ask students what they found after discovering the formula. students should realize some basic characteristics about gradient :::::::::D--two parallel lines have same gradient

               :::::::::D--horizontal line has zero gradient

               :::::::::D--positive & negative gradient

  

notation principle

notation used in teaching should be suitable with intellectual development stage. For example, brackets should used when teaching primary school......

e.g 2+(3x5)=17        e.g use of ( X ) and ( . ) in multiplication 

contrast & variation principle

most of the mathematical concepts are easy to understand if they are compared with other concepts.

> multiplication & division

> differentiation & integration

> intersection set & union set 

connectivity principle  

every mathematical concept, principle and skill is connected to other concepts, principles & skills 

e.g concept of gradient  of a straight line

      - tangent of the curve at a certain point

      -derivative of dy/dx

      -continuous function

      -graphs of increasing & decreasing functions

 
                                                        
 

constructionism......(w9)

Seymour Papert defines that 

"The word constructionism is a mnemonic for two aspects of the theory of science education underlying this project. From constructivist theories of psychology we take a view of learning as a reconstruction rather than as a transmission of knowledge. Then we extend the idea of manipulative materials to the idea that learning is most effective when part of an activity the learner experiences as constructing a meaningful product."

CONSTRUCTIONISM

• learning occurs "most felicitously" when constructing a public artifact
• more about methods
• constructing i a good way to get mental constructions build
• learning by making or create something
• learning is most effective when the learner experiences as constructing a meaningful product 

Constructivism is deeper in its application, than could be conveyed by any such formula

Let students play around with things. Let them try to do something or taste it. 

For example, they make construction such as build sand castle or by using their toys. LEGO or puzzle.

Students will get satisfaction when they do their own construction.

BRING OUR INTROVERTED STUDENTS OUT OF THEIR SHELLS >make them become active learners<(literature review)

When we choose the teaching profession, we will be confronted with various students. Some of them easier to control and some beyond the control of teachers.


So, here we can use the learning theories to control our class. I think I want to use constructivism theory. The benefits of constructivist philosophies in the classroom are abundant. It is important for all teachers to be aware of constructivist philosophies in order to increase the learning ability of students in the classroom.

Even at the present time many students are exposed to the outside world, there is still a small number of students are still in their shell. They are quiet in class, just wait and getting on what they are asked to do. Moreover, they still avoid pushing themselves and feel them unnoticed. They are known as 'passive learners'.

For this kind of students, they actually miss out some skill “alternative curriculum”. Skills such as work with others or co-operation. Skills on how to involve in discussion and sharing ideas or forming of opinions. So, we are as the teachers should find the best way in order to bring the introverted students out of their shells.

One of the best ways to make them build their confidence and make them to become active learner is prepare some activities that required them to involve. 

Examples of the activities

Personalized learning

Introverted students become disaffected with a particular subject or teachers. They felt undervalued because they are not excellent in class. So, ask them to write a letter or an essay about themselves and something they like. Then, ask them about what they wrote. They will become more comfortable in class.

Think-pair-share

Besides that, introverted students not participate in class because most of them fear that what they said wrong, so they become quiet. Encourage the students to participate by giving them questions in class and let they think by themselves. Then ask them to share their ideas in pair or group. This activity relieves pressures on an individual student by making them all equal and allowing for thinking time.

Create class rules

Make a rule such that students should be expected to respect others when they are talking, listen to each other and treat each other as they would want to be treated. Other than that, do not allow any students rude or laughs at someone else.

In addition, to bring the introverted students out of their shell and make them become active learners, teachers need to use different learning style. Create more interactive and innovative activities to avoid students bored in class and make learning become enjoyable.

article:-
          http://www.helium.com/items/1985211-how-to-draw-out-introverted-students

p/s : menolong pelajar yang kurang berkemampuan untuk konstruk idea dan pengetahuan mereka dengan langkah-langkah yang mendorong mereka menjadi aktif "active learners". Mencuba cara yang termudah dan paling mudah untuk pelajar faham dan mempraktikkannya. Menyemai perasaan seronok dan teruja untuk belajar dalam setiap pelajar supaya mereka tidak lg terkongkong dalam dunia mereka sahaja. hal ini seterusnya meningkatkan minat mereka untuk belajar...:D

Constructivism in mathematics

Constructivism is based on perspective put forward by Jean Piaget in his theory of learning and theory of cognitive development but might not include some opinions, conceptions or assumptions in that theory.

Constructivism can be described as a learning process that explains how knowledge is acquired and structured in the mind of an individual.

School-based knowledge should not be transmitted from the teacher to the students in a complete form. Students need to construct the knowledge based on their experience and ability.

Constructivism can be applied in the learning of mathematics for students of various ages and level of ability. 

Mathematics instruction encourage and allow students to construct their own knowledge through problem solving, exploring and conjecturing.

Students should carry out activities through working in groups and learn to communicate each other.

Students should be given opportunity to construct their own knowledge and skill by connecting their previous experiences with future needs. Give them chance to develop their communicative and thinking skills.

In learning new concepts, a students need to construct his own knowledge by relating it to what he already knows.

Constructivism Learning

1.       Train students to be active learner
2.       Students create their own organising principle
3.       Gives students ownership of what they learn
4.       Concentrate on learning how to think and understand not only on rote memorisation
5.       Promotes social and communication skills