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Allan Gulinao
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Constructivism is a theory of learning and an approach to education that lays emphasis on the ways that people create meaning of the world through a series of individual constructs. The constructivist approach views learning as an active process of constructing meaning  which is greatly influenced by the learners accumulated experiences and understandings. As an active process the learner continuously revise past learning and “reconstruct” concepts as they interact daily with environment.
Constructivism is anchored on the assumption that “the absorption or assimilation of knowledge is somewhat personal and therefore no two learners can build up the same meaning out of one situation.” Knowledge therefore is the result of the learners own construction of reality.
Constructivism learning theory is a philosophy which enhances students' logical and conceptual growth. The underlying concept within the constructivism learning theory is the role which experiences-or connections with the adjoining atmosphere-play in student education. Constructivism is the theory that people construct their own understanding and knowledge of the world, through experiencing things and reflecting on those experiences.
The constructivism learning theory argues that people produce knowledge and form meaning based upon their experiences. Two of the key concepts within the constructivism learning theory which create the construction of an individual's new knowledge are accommodation and assimilation. Assimilating causes an individual to incorporate new experiences into the old experiences. This causes the individual to develop new outlooks, rethink what were once misunderstandings, and evaluate what is important, ultimately altering their perceptions. Accommodation, on the other hand, is reframing the world and new experiences into the mental capacity already present. Individuals conceive a particular fashion in which the world operates. When things do not operate within that context, they must accommodate and reframing the expectations with the outcomes.
The role of teachers is very important within the constructivism learning theory. Instead of giving a lecture the teachers in this theory function as facilitators whose role is to aid the student when it comes to their own understanding. This takes away focus from the teacher and lecture and puts it upon the student and their learning. Instead of telling, the teacher must begin asking. Instead of answering questions that only align with their curriculum, the facilitator in this case must make it so that the student comes to the conclusions on their own instead of being told. Constructivism modifies the role of the teacher so that teachers help students to construct knowledge rather than reproduce a series of facts. 
The constructivist teacher provides tools such as problem-solving and inquiry-based learning activities so that students can formulate and test their ideas, draw conclusions and inferences, and convey their knowledge in a collaborative learning environment.

In a constructivist classroom, learning is 
• Constructed: Students come to learning situations with already formulated knowledge, ideas, and understandings. Students will integrate new experiences and interpretations to construct their own personal meaning with this previous knowledge.
• Active: The student is the person who creates new understanding for her/himself. The teacher guides knowledge, but allows the students to experiment, manipulate objects, ask questions and try things that don't work. Students also help set their own goals and means of assessment.
• Reflective: Teachers should create opportunities for students to question and reflect on their own learning processes, either privately or in group discussions. The teacher should also create activities that lead the student to reflect on his or her prior knowledge and experiences. 
• Collaborative: The constructivist classroom relies heavily on collaboration among students because students learn about learning not only from themselves, but also from their peers. When students together review and reflect on their learning processes, they can pick up strategies and methods from one another.
• Inquiry- or Problem-Based: The main activity in a constructivist classroom is solving problems. Students use inquiry methods to ask questions, investigate a topic, and use a variety of resources to find solutions and answers. 
• Evolving: Students have knowledge that they may later see as incorrect, or insufficient to explain new experiences. As students explore a topic or problem, they draw conclusions, and, as exploration continues, they revisit those conclusions and modify them to support new knowledge or experiences. 

What is Constructivism?
"Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to 'transfer' mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept."
It's not surprising that constructivism has a strong voice in the current dialogue on math education. Many are concerned about the success - or lack of success - of math education. Constructivism cuts a nice path between the main ideas that have influenced how math has been taught: the concept of math as facts to be transmitted to the student, and the view that some people have it and some people don't, where the educator's task is to figure out how "smart" students are and choose the right tasks for them to perform. Questions remain, however, about whether these offer rich information for developing different ways of teaching. And what's to be done for the students who aren't succeeding?
In contrast, constructivism focuses our attention on how people learn. It suggests that math knowledge results from people forming models in response to the questions and challenges that come from actively engaging math problems and environments - not from simply taking in information, nor as merely the blossoming of an innate gift. The challenge in teaching is to create experiences that engage the student and support his or her own explanation, evaluation, communication, and application of the mathematical models needed to make sense of these experiences.
What Is Constructivism?
Most traditional mathematics instruction and curricula are based on thetransmission, or absorption, view of teaching and learning. In this view, students passively "absorb" mathematical structures invented by others and recorded in texts or known by authoritative adults. Teaching consists of transmitting sets of established facts, skills, and concepts to students.
Constructivism offers a sharp contrast to this view. Its basic tenets -- which are embraced to a greater or lesser extent by different proponents -- are the following:
1. Knowledge is actively created or invented by the child, not passively received from the environment. This idea can be illustrated by the Piagetian position that mathematical ideas are made by children, not found like a pebble or accepted from others like a gift (Sinclair, in Steffe and Cob 1988). For example, the idea "four" cannot be directly detected by a child's senses. It is a relation that the child superimposes on a set of objects. This relation is constructed by the child by reflecting on actions performed on numerous sets of objects, such as contrasting the counting of sets having four units with the counting of sets having three and five units. 
2. Although a teacher may have demonstrated and numerically labeled many sets of objects for the student, the mental entity "four" can be created only by the student's thought. In other words, students do not "discover" the way the world works like Columbus found a new continent. Rather they invent new ways of thinking about the world.
3. Children create new mathematical knowledge by reflecting on their physical and mental actions. Ideas are constructed or made meaningful when children integrate them into their existing structures of knowledge.
4. No one true reality exists, only individual interpretations of the world. These interpretations are shaped by experience and social interactions. Thus, learning mathematics should be thought of as a process of adapting to and organizing one's quantitative world, not discovering preexisting ideas imposed by others. (This tenet is perhaps the most controversial.)
5. Learning is a social process in which children grow into the intellectual life of those around them (Burner 1986). Mathematical ideas and truths, both in use and in meaning, are cooperatively established by the members of a culture. Thus, the constructivist classroom is seen as a culture in which students are involved not only in discovery and invention but in a social discourse involving explanation, negotiation, sharing, and evaluation.
6. When a teacher demands that students use set mathematical methods, the sense-making activity of students is seriously curtailed. Students tend to mimic the methods by rote so that they can appear to achieve the teacher's goals. Their beliefs about the nature of mathematics change from viewing mathematics as sense making to viewing it as learning set procedures that make little sense.
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