Describe the nature and development of Mathematical thinking and numeracy process in children.
Mathematics, is one such subject which has a very deep impact on all the areas of life such as societal, personal as well as municipal. Hence being educated in the subject of mathematics is considered to be one of the most crucial part for development of opportunities for youth. However the most unfortunate part of this subject is that it is a struggling one for many and thereby they become unresponsive towards mathematics as they keep on facing hurdles with respect to engagement. As is discussed by the National Council of Teachers of Mathematics, the power of mathematics takes into account the capability of a person to discover, guess and reason rationally and further to this also build such ideas within mathematics and amongst other rational activity. There are various theoretical perspective of learning mathematics of which constructivism and behaviourism are two of them. The said essay discusses about and compares these two perspectives and also how in today’s world the way of teaching and learning mathematics has undergone a drastic change.
Mathematics is one subject which cannot be taught. Teachers have the role of stimulation within the children so as to aspire to learn the subject. It is a well known fact that students tend to learn mathematics only once they develop their own way of understanding the subject. A constructive perspective states that a teacher’s role is to ensure that a child learns about a particular subject by providing him/her with such a resource enriched surrounding through which they would guide a student’s learning. It has various features to offer such as it supports the idea that knowledge is not something that is achieved from the surrounding but something that is created uniquely by each child (Cey 2001). Children today develop new geometric awareness by reflecting on their material and psychological actions. Ideas are said to be constructed when kids incorporate them into their present knowledge base. It is the interpretations of the world that is important and they are formed by experiences. Thus learning of mathematics may be considered as a procedure of adapting to and organizing one’s quantitative world rather than digging out the ideas which already have been discovered by someone else in the past (Clements & Battista 2009). Mathematical skills and truths are basically formed by the culture around. Thereby, when a teacher asks the students to solve a particular problem in a specific manner, then they are actually putting a hurdle on their constructive thought process, thus curtailing and hampering the growth of the brain.
It is one of the best suited and most sought after perspective for learning mathematics in today’s world as it helps to serve two main goals. Firstly, children tend to develop such mathematical structures which are complex, abstract and powerful as compared to what they already possess. This helps them to handle such issues and problem which are complicated also in a number of ways. Secondly, the constructive theoretical perspective enables the children to become self-dependent, as well as self-motivated in their mathematical actions. They have a notion that mathematics is a solution to resoling various other problems. They are of the idea that it is the environment, experience as well as self exploration which helps to gain mathematical knowledge rather than being taught by the teacher as any other subject (Bhowmik 2014). Thus instead of giving weightage to only those ways and methods which are already spelt by eminent mathematicians, students try to develop their own unique ways of resolving problems. Thus the said perspective looks upon at the teachers as a guide and not a sage.
Another widely used theoretical perspective in the teaching and learning of mathematics is behaviourist theory. Behaviourism is a theory of learning that deliberates upon impartially apparent behaviours and does not take into account any self-governing activities of the mind. Thus the reactions which happen due to external surroundings, ultimately become habituated and the behaviour is then learned. Thus the said perspective emphasis upon teaching mathematics to students basis certain set methods, ways and formulas without allowing much of deviations, thereby hampering any kind of constructive development of the mind (Coz 2011). Thus it can be rightly said that the behavioural model promotes learning in the form of repeated and learned activities and actions.
However, many may prefer this traditional perspective, but even then the flaws it has makes the constructive perspective more logical and acceptable in case of mathematics. The said theory is not best suited to the particular subject as, constructivist instruction provides unsurpassed and paramount value to the growth and augmentation of a child’s personal arithmetical ideas. In contrast to the same, the behaviourist perspective gives weightage to only set and pre-defined arithmetical techniques, formulas and concepts. For example, even if most of the teachers are seen continuously utilising existing resources to initiate data, they use them only for an opening, whereas the main aim is to get the conceptual, figurative and recognized mathematics. Unfortunately this theory, unconsciously and involuntarily devalues the brain’s capacity to think logically and distinguish between the right and wrong (Kinder & Carnine, 1991). The students develop a feeling that their instinctive ideas and techniques are not associated to actual mathematics. But when it comes to constructive perspective, students are asked to find their own techniques for resolution of mathematical problems. They are asked to rack their brains and find a way out to the solution rather than just copying the other person’s method stereotypes. This does not mean that the teacher is not required. It simply means that the teacher is required in this kind of an approach as well but for guidance and not spelling out the technique of resolving a mathematical problem. A teacher following the former approach, offer specific tasks and activities and also provides the opportunities for conversation, guides the focus of the attention of children, thereby inconspicuously unswerving their learning. Hence it can be rightly said that behavioural perspective of learning and teaching mathematics fails to bring about reorganizations within students which is successfully done by the constructive approach.
It can therefore be rightly said that learning and teaching of mathematics is no more restricted towards application of preset formulas and methods but rather full of creativity and construction of ideas as well. It has been almost thirty years wherein constructivism has been ruling the learning theory of mathematics as student engagement is of utmost importance for ensuring that the subject is liked by the student and the interest is developed (Attard 2015). Mathematics is one such subject which helps in the development of logical reasoning skills. Self concept in mathematics is the road to success in this subject and also personal life. There has been a significant shift from the rehearsal methodology of teaching mathematics to that of engaging pedagogy which is more fun and creative in nature (Klinger 2015).
In this world of globalisation, deep rooted understanding of logics is a must which cannot be learnt via certain techniques but can use them learnt through experience and constructive development of ideas. Mathematics is one such subject which demands development of such skills which would help the students solve such issues and problems which may otherwise not be possible via certain preset formulas, simply because of their ability to learn the subject by application of various models. The engaging pedagogy, unlike the behaviourist theoretical perspective, calls for the teachers to use such a method which would encourage the students to build upon each others ideas and perspectives and to discuss about the problem amongst themselves till such an extent that they have been able to develop a shared understanding of a concept (Long 2011). By getting away the age old method of teacher opening the book, mathematics has become more of a playful subject wherein students are made to be a part of the classroom and thereby forced to construct new ways of resolving problems (Cresswell 2016). This shift has led to involvement and development of interest of many students towards this subject which otherwise was being lost. Students were lacking the space to think and re-think until the problem was resolved and thus this method helped mathematical engagement.
Thereby on a concluding note, with reference to mathematics learning and teaching for those students who are anti-maths, the age old method has to be left as the said disengaging predagogy has many deficiencies which has a direct negative implication on them towards the subject. Student engagement gives way to development of self-confidence, self-efficiency as well as personality of a student. They are made to feel a part of the subject and the fact that their ideas are also given weightage helps them develop greater interest towards learning that subject. Constructivism has changed the outlook of teaching and learning of mathematics greatly wherein students are guided by their teachers who no more emphasise upon only application of stereotypes formulas, but welcome ideas and solutions to a problem in various ways. Lastly, students found it authorizing to be able to show their efforts and to have the occasion to rationalize their selections in an atmosphere where everyone is respected and appreciated for the efforts being put in. Those who were disengaged also showed interest and were inclined towards application of engaging predagogy which involved fun, playful and creative ways and means of learning.
Attard,C. (2015). Engaging teachers to engage students with mathematics : Building teacher capacity through sustained professional development. Retrieved from https://www.westernsydney.edu.au/__data/assets/pdf_file/0006/864168/Engaging_Teachers_to_Engage_Students_with_Mathematics-Final_Report_for_web.pdf
Bhowmik,M. (2014). Constructivism approach in mathematics teaching and assessment of mathematical understanding. Retrieved from https://basicresearchjournals.org/education/pdf/Monoranjan.pdf
Cey,T. (2001). Moving towards Constructivist Classrooms. Retrieved from https://etad.usask.ca/802papers/ceyt/ceyt.htm
Cox,M.W. (2011). The Effects of Behaviorist And Constructivist Instruction On Student Performance In College- Level Remedial Mathematics. Retrieved from https://oaktrust.library.tamu.edu/bitstream/handle/1969.1/ETD-TAMU-2011-08-9920/COX-DISSERTATION.pdf
Clements,D.H. & Battista,M.T. (2009). Constructivist Learning and Teaching. Retrieved from file:///C:/Users/E-ZONE/Downloads/751_chapter.pdf
Cresswell,J. (2016). Disengagement, Pedagogical Eros and (the undoing of?) Dialogic pedagogy. Dialogic Pedagogy: AN International Online Journal. 4. 27-46. Retrieved from file:///C:/Users/E-ZONE/Downloads/182-722-2-PB.pdf
Kinder,D. & Carnine,D. (1991). Direct Instruction: What it is and what it is becoming. Journal of Behavioral Education. 1, 193-213
Klinger,C.M. (2015). Behaviorism, cognitivism, constructivism or connectivism ? Tackling mathematics anxiety with ‘isms’ for a digital age. Retrieved from https://www.alm-online.net/images/ALM/proceedings/alm16/Articles/15klinger.pdf
Long,A.M. (2011). Engaging and Disengaging : a Qualitative Study of Middle School Girls and Mathematics. Retrieved from https://scholarworks.uvm.edu/cgi/viewcontent.cgi?article=1139&context=graddis
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