Constructivism in Mathematics

Constructivism in learning mathematics is one of the fundamental theoretical aspects that serve the purpose of disseminating the mathematical learning to the children. Students are required to develop their styles of understanding of the mathematical concepts for effective learning of the course and the applications contained in. A key aspect of the constructivism based learning the subject is decomposition of the mainstream subject into different developmental steps and then learning the concept following a Piagetian theory of knowledge. Constructivism believes that the focus should not be on the content rather it should be on the way how people learn the subject. It believes that the mathematics knowledge results from people forming models in response to the questions and challenges that arise when practically engaged in understanding the math problems and environments (Fosnot, 2013).

Constructivism considers problem-solving as the heart of learning, thinking, and development of the human beings. As children or people actively involved in problem-solving they develop constructs and based on the consequences of their actions and from reflections they get from the previous experiences will develop their own approach towards understanding new concepts. The constructivisitic attitude does have routes from the biological evolution and the adaptive functionality of cognition. Piaget et al postulated that the learning in the children and human beings will be form through the adaptation of the information assimilation and accommodation of the same (Ackermann, 2001).

Learning mathematics with constructivist approach is the ultimate theme of the essay and the supporting views and the facts are provided in the essay. Constructivism as well behavioristic theories are normally used for formulating the learning procedures. However for teaching mathematics constructivist ideology based learning is more significant. Like constructivist ideology behavioristic ideology believes that the learning do from the interactions of the learner with the environment, without interfering anything that is going on inside the learner. It is just based on the application of the methods of science to the study of human learning. Behavioristic approach just focus on the issues like situation, behavior and the consequences of the behavior, it does not focus on any issue beyond this. Hence constructivist approach is selected as right ideology for learning mathematics in this discussion. Constructivist believes that the knowledge is acquired by the person’s construction of himself or herself in the given environment. Hence his inner response constructs play a key role in his learning approach. The following parts of discussion focus on constructivism and its key features in the context of learning mathematics (Kolb, 2014).

Mathematics is a unique subject; frankly speaking there is no other subject like mathematics. It is not possible to teach mathematics through conventional means and it is not possible to teach mathematics by any teacher through all the traditional methods. An effective mathematics teacher is the one, who can actually stimulate the students to learn mathematics. There are research based findings actually seconding the concept that the students can only learn mathematics if they have all their own mental construction of the concepts and only if they have their own understanding the concepts of the mathematics. The only way possible to create, construct and discover mathematics is by constructivist approach. This is possible by stimulating the student intuition of exploration, explanation and justification of the solution strategies to mathematical tasks(Draper,2002). Constructivism is the best fit in this direction; since it is the best tool that works on to enhance the mathematical power in students. Mathematical power is the ability of the students to logically reason, conjecture as well effectively communicate mathematics.

Active engagement is the key for learning mathematics. There are several theories that actually support the view expressed by Constructivism. The learning skills develop in human beings through the social interactions with more knowledgeable persons. This human learning actually presupposes a specific social nature and the process by which children grown into the intellectual life of those around them. Interaction is the key to develop proximal developments in the human beings (Steaffie, 2013).

Traditionally play is proved to be vehicle of thought and it’s considered to be critical element in early childhood education and pedagogy. Play in early childhood can be used to promote the mathematical concepts, ideas and explorations. Educators can customise the plays that do promote the needed mathematical concepts and the ideas. Play will not actually guarantee the mathematical development, however they will provide rich possibilities of mathematical development. Play has capabilities to promote the natural curiosity in children. Play naturally do consist the attributes of fund and there is no limits for creativity than can be fused into the play. Mathematics learning through the application of play actually makes people believe that it is a social activity and it is relevant to everyday lives of children (Singer, 2006).

Constructivism will prompt the students to formulate their own way of making questions, it will let the students interpret their own perception of the situation, they will express the learning their own way. It does encourage group works and will help problem solving in teams as well. Constructivism is all about learning how to learn the concept and applying the same for problem solving. Students are no more considered some sort of blank states on whom the knowledge is heed. Rather they are considered as the instances who develop their own knowledge of the situation and works out ways of solving them. There is lot of scope for applying concrete materials, sensory motor experiences and met language through creative playlets for developing the needed learning experiences for children in mathematics. Value of play and met cognition will cultivate in students an awareness and capabilities to think divergently and will help them learn and apply the mathematical knowledge to the things around. Play based learning has capabilities to let the students engage in activities and methods that has potential to develop mathematical knowledge and skills in practice and working mathematics and to use the same for communicating their understandings(Beg,2015).

As per the policy statement on numeracy education in children, several mathematical organizations have briefed that the being numerate possesses the capabilities to use mathematics effectively to meet the general demands of life at home, in paid work as well in the community and civic life. Numeracy skills in 21^st century focused on the following aspects of the learning, mathematical, contextual and strategic skills. All these skills should be blended in right form and in right proportion to meet the practical requirements. The mathematical process and numerating process is supposed to meet the above requirements in the 21^st century. The new generation children in school can accept the techniques only when they are meaningful and possess real value and sense to them. Even though the children in school level will not be having the enlightment of what they will be using at the university level and thereafter, the basic view of the people at the university level towards mathematics is that they feel they need only instrumental education (Sarama, 2009). However school level mathematical learning is more about the developing the concepts and constructs to take up more challenging learnings in the future to come. It might be right attitude to cultivate the school mathematics learning to possess the inclination to include statistics, computer codes, algebra in the main stream process. Each one of these mathematical skill can be rightly induced to the children through constructivist instruments of learning. They indeed will provide a right platform for children to develop all the needed knowledge base for the future requirements (Gilakanj, 2013).

The write up has focused on two types of theories of learning behavioristic as well as constructivist approaches. The constructivist approach focus on the way inner feelings and response of the human beings results in developing the key traits in understanding solutions to the problems. Active engagement in creative plays and related strategies is considered as right tool for developing the skills of mathematical power in children. Considering the significance of mathematical process and numeracy, the 21^st century children should be exposed to the constructivist learning methods of active involvement based learning, more focus on integrating the concepts with the game play, the integration process should be highly creative, more and more emphasis should be provided to the hands on activities, there should be more interaction between the school children, the environment and other stake holders, emphasis more on the building the capabilities and the constructs rather than the actual problem solution(Clarke,2009). Hence Learning mathematics is to be introspected for radical change in the teaching approach and constructivism should be employed for the total revision of the current practice and trends in teaching mathematics for school children. Inactive and recitation based learning methods are obsolete and cannot be used further.

References

Troelstra, A. S., & Van Dalen, D. (2014). Constructivism in mathematics (Vol. 2). Elsevier.

Fosnot, C. T. (2013). Constructivism: Theory, perspectives, and practice. Teachers College Press.

Steffe, L. P., & Wood, T. (Eds.). (2013). Transforming children's mathematics education: International perspectives. Routledge.

Gilakjani, A. P., Lai-Mei, L., & Ismail, H. N. (2013). Teachers' use of technology and constructivism. International Journal of Modern Education and Computer Science, 5(4), 49.

Liu, C. C., & Ju, I. (2010). Evolution of constructivism. Contemporary issues in education research, 3(4), 63.

Hennessey, M. N., Higley, K., & Chesnut, S. R. (2012). Persuasive pedagogy: A new paradigm for mathematics education. Educational Psychology Review, 24(2), 187-204.

Begg, A. (2015). Constructivism: An overview and some implications.

Clarke, B., Grevholm, B., & Millman, R. (2009). Tasks in primary mathematics teacher education. New York: Springer.

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.

Kolb, D. A. (2014). Experiential learning: Experience as the source of learning and development. FT press.

Ackermann, E. (2001). Piaget’s constructivism, Papert’s constructionism: What’s the difference. Future of learning group publication, 5(3), 438.

Draper, R. J. (2002). School mathematics reform, constructivism, and literacy: A case for literacy instruction in the reform-oriented math classroom. Journal of Adolescent & Adult Literacy, 45(6), 520-529.

Singer, D. G., Golinkoff, R. M., & Hirsh-Pasek, K. (2006). Play= Learning: How play motivates and enhances children's cognitive and social-emotional growth. Oxford University Press.