Constructivism is both a theory of construction of knowledge and learning philosophy. Its proponents include Piaget, Vygotsky and Glaserfeld. The constructivist approach is new trend in teaching of mathematics by many enthusiastic pedagogues and teachers in many countries. Constructivist pedagogy does not consist of a single teaching strategy. Instead, it has several features that should be attended to simultaneously in a classroom. It has been asserted that for a successful constructivist strategy the teaching has not only to be student centered and the teacher a mere facilitator, but the teacher has the added responsibility to create a conducive classroom environment. Research has established that constructive methods of mathematics teaching have been much more successful than the traditional methods. Constructivism is a theory of knowledge i.e., epistemology and a theory of learning. It is not a particular pedagogy. Constructivists believe that human beings are active information receivers. They use their existing experience to construct understanding that makes sense to them. Humans assimilate and accommodate new knowledge and build their own understanding knowledge is viewed as personal an subjective. Reality resides in the mind of each person. Learning is based on the previous experience and knowledge. Thus, multiple interpretations of an event are possible and multiple answers to a question are source of creativity in learners. It is held by constructivists that learner need time to reflect on their experiences in relation to what they already know. After some time, they reach consensus about what specific experience means to them.
Constructivism views learning as a process of constructing meaningful representations of external reality through experiences. Construction of internal representation of knowledge is depends on the degree to which learners integrate new idea with the previous one.
It is significant to note that in constructivist view knowledge constructing takes place in working memory. How the teacher has constructed the content and the activities as well for guiding the learner’s construction of idea is a key component in this context.
CONSTRUCTIVISM IS AN EPISTEMOLOGICAL VIEW OF LEARNING RATHER THAN TEACHING
Students’ previous knowledge and their active participation in problem solving and critical thinking all play a vital role in the formation of knowledge. One of the most important goals of constructivism is to develop students’ “critical thinking skills”, which is possible only in a conducive learning environment in the class. The teacher may have to improvise the day’s lesson or change the sequence of activities, depending on the needs of the students or due to any other unexpected development. Such flexibility is said to be a valuable quality of a positive learning environment. The following are the some of the important features of a constructivist learning environment:
- Learners are encouraged to become active presenter than passive listeners.
- Learning environment should encourage interpersonal discussion and dialogue.
- Learners should be challenged by ideas and problems that generate inner cognitive conflicts.
Constructivist learning environment emphasize authentic tasks in a meaningful context rather than abstract instruction out of context. The classroom climate of constructivist approach gives an importance to construction of knowledge rather than the reproduction of knowledge
The complexity of the real world is establishes through multiple representations. Students should be given sufficient time for reflection for constructing relationship and for discussion.
MATHEMATICS CLASSROOM AND CONSTRUCTIVISM
There is no single constructivist strategy for instruction in the class. Different pedagogies and researches have highlighted various elements in varying degrees for the benefit of classroom instructors. Even so, there are several common themes which can be described here. Education is a student-centered process and the teacher is only facilitator. Learning depends on shared and imbibe experience with peers and teachers. Collaboration and cooperation is a major teaching method. Students actively explore and use hands on experience. The constructivist views knowledge as being formulated in a social context. It is an active social process. Learners cannot construct understanding alone; they do it collaboratively through interactions. Learning is an active process hence the learner should be encouraged for imagination and intuitive learning.
To solve the problem in the hand the “thinking” should be focused so in constructivist learning ‘thinking’ effectively is focused to greater extent. The ‘Understanding’ is another objective followed the knowledge construction. So proper understanding of knowledge is leads to correct thinking hence understanding should be clear. In metcognition the learners’ thinks of his/her own thinking style that is purposeful thoughtfulness. A motivated and thinking learner tries to check his errors and tries to find why he failed in his earlier attempt. Such a learner’s knowledge would be deep and durable. As Yager says, “one only knows something if one can explain it”(Yager, 1999). One the other hand, a novice learner does not check for quality in his work and thus he fails to make amends to his earlier errors.
THE CONSTRUCTIVIST MATHEMATI CS CLASSROOM AND ROLE OF TEACHER
Towards the higher goals: Mathematicas content teaching is the narrower goal as compare to creating mathematical learning environments.
The content areas of mathematics addressed in our schools do offer a solid foundation, while there can be disputes over what gets taught at which grade and over the level of detail included in a specific theme, there is broad agreement that the content areas (arithmetic, algebra, geometry, mensuration, trigonometry, data analysis) cover essential ground.
What can be leveled as a major criticism against our extant curriculum and pedagogy is its failure with regard to mathematical processes. We mean a whole range of processes here: formal problem solving, use of heuristics, estimation and approximation, optimization, use of patterns, visualization, representation, reasoning and proof, making connections, mathematical communication. Giving importance to these processes constitutes the difference between doing mathematics and swallowing mathematics, between mathematisation of thinking and memorizing formulas, between trival mathematics and important mathematics, between working towards traditional teaching and constructivism teaching.
In school mathematics, certainly emphasis does need to be attached to factual idea, procedural fluency and conceptual understanding. New idea is to be constructed from experience and prior knowledge using conceptual elements. However, invariably emphasis on procedure gains ascendancy at the cost of conceptual understanding as well as construction of idea based on experience. This can be seen as a central cause for the fear of mathematics in children.
On the other side, the emphasis on exploratory problem solving, activities and the processes referred to above constitute learning environments that invite participation, engage children and offer a sense of success. Transforming our classrooms into constructivism based approach paradigm and designing mathematics curricula that enable such a transformation is to be accorded the highest priority. i.e.,
- Mathematics that people use,
- Use of technology i.e., technology innovation and learning.
A teacher is not a ultimate. He does not lecture. He is a facilitator or mentor. He helps the learner. The facilitator has to create proper environment in the class so that the students are motivated, challenged and think deeply to arrive at his own conclusion.
As a facilitator, the teacher has to support the learners to becoming effective thinkers. The facilitator and the learners, both learn from each other. Students should be encouraged to arrive at their own version of truth and then compare it with that of the instructor as well as with that of their peer. Teachers have only to observe in the beginning of a session and assess the progress. They should pose questions to create right environment. They should intervene if any ‘conflict’ arises or if the process of learning is going astray. An important task for a constructivist mathematics teacher is to create a “learning friendly environment” which facilitates students thinking and motivate them to explore. An authentic planning environment is obtained if real-life complexities and a real-world situation is simulated. A mathematics teacher creates congenial learning environment when learning goals are negotiated through consensus and discuss with students.
Direct instructions are not appropriate. Learning should take place by “active involvement of the students by doing”, by generating their own ideas. In a well-planned classroom environment students learn how to learn. Learning is like a spiral. Students reflect on their previous experience and integrate new experience.
The constructivist environment in a mathematics classroom will be created by adopting the following:
Provide experience with the knowledge construction process
The teacher presents a topic to the learners and guide them to explore the topic through experimentation. The learners are encouraged to construct a research question and teacher helps them to answer the research question constructed by them through scaffolding.
Experience in and appreciation for multiple perspectives
All learners are different to each other in their way of thinking and so the need arises to look at a problem from multiple perspectives and provide the opportunities to learners to experiment and discuss their alternative ways of thinking. Here, the students are encouraged to work in groups. Finally, all the groups can share their opinions on the topic with each other.
Provide social and emotional learning
The social and emotional aspects of learning will be taught to the students in an integrated manner. The five aspects of social and emotional learning which could be covered in the teaching are as follows: self-awareness, managing feelings, motivation, empathy and social skills.
Use multiple modes of representation
The multiple modes of representation also assist the goal of experiencing multiple perspectives. Use of multiple media to enrich the learning environment provides the learners to view the topic being discussed in the class from multiple dimensions.
The teacher should prepare a list of media available and supporting the topic. The teacher should also decide the use of media in supporting the authentic nature of the task.
A combination of the following learning strategies can be used by the mathematics teachers to create constructivist learning environment
- Use of multimedia/teaching aids
- supporting system
- Case studies
- Role playing
- Group discussions/Group activities (reciprocal Learning).
- Deep interrogation.
- Project based learning
- Use of learning strategies for social and emotional learning of students.
Teachers can use various strategies to promote and strengthen “think about their thinking”. Eggen.P and Kauchak. D (2007) have suggested the following strategies for the purpose.
- Teachers should posses some provocative questions to students and also encourage them to frame their own questions on the problem at hand.
- PQ4R strategy: PQ4R is an acronym for Preview, Questions, Read, Reflect, Recite and Review.
- IDEAL strategy: IDEAL is an acronym for Identify, Define, Explore, Act and Look.
- KWL strategy: Teachers should teach the students to be aware of 1). What they already Know, 2). What they want to Learn, and 3). What they have eventually Learnt.
So from the above discussion, constructivism based paradigm shift in teaching-learning process (i.e., in mathematics classroom).
- Objectivist learning theory Constructivist learning theory.
- Teacher centered Student centered
- Teacher as expert, information
Giver Teacher as facilitator, guide, coach
- Teacher as knowledge transmitter Learner as knowledge constructor
- Teacher in control Learner in control
- Focus on whole class room teaching Focus on individual and group learning.
In the NCF 2005 and 2009 it is clearly mentioned that the consrstructivism approach is the best strategy over the behaviouristic approach. The childcenterd education is the new paradigm shift in education ,so it will be perfectly fulfilled by constructivism based approach. The teacher training in this regard is must other wise this pedagogic approach will be get failed. Off course it consume time so patience will be play the key role in the success of adaptation of constructivism to teach Mathematics in the classrooms.
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