Ashu Threja: Creating Constructive Environments in Mathematics Classrooms

8/3/2019 Ashu Threja: Creating Constructive Environments in Mathematics Classrooms

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CREATING CONSTRUCTIVE ENVIRONMENTS

IN MATHEMATICS CLASSROOMS

Ashu Threja

Miranda House

University of Delhi


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Objectives

There is a kind of teaching that can be

legitimately called constructivist teaching in

mathematics

The constructive environment can be created

in mathematics classroom


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Tenets of constructivism in

Mathematics education

Knowledge is actively created or invented by thechild, not passively received from theenvironment

Children create new mathematical knowledge byreflecting on their physical and mental actions

Learning mathematics should thought of as aprocess of adapting to and organizing one'squantitative world, not discovering pre-existingideas imposed by others


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Cont..

Learning is a social process in which children

grow into the intellectual life of those

around them (Bruner 1986)

Students view mathematics as sense making

as compared to viewing it as learning setprocedures


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Strategies to create constructive

environments in Mathematicsclassroom


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PlacingTasks In Meaningful Context

EXAMPLE:Learners encouraged to construct

the concept of half by means of the contextual

situation via story requiring the monkey to

distribute chapatti equally between two cats.


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EXAMPLE : Learners presented contextual situation related with distribution of sweets to

construct meaning of fractions as parts of whole and equivalence of fractions


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ENCOURAGING CONSTRUCTIONS BY POSING PROBLEMS WITH MORE THAN ONE

ANSWER


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EMPLOYING A STYLE OF TEACHING THAT FOCUS ON PROCESSESS RATHER THAN ON

PRODUCT


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ENCOURAGING CONSTRUCTIONS BY DISCUSSIONS OF SOLVED TASK


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PATH SETTING IN REALISTIC

SITUATIONS


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MAKING CONSTRUCTIONS WHEN

LEARNING MATHEMATICS BY

CONTRASTING


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ENCOURAGING AND DEVELOPING

THEIR OWN STRATEGIES


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EMPLOYING DIFFERENT MODES OF

REPRESENTATION AND REQUIRING CHILDREN TO

MAKE THEIR OWN REPRESENTATIONS: I have a problem. I am thinking about.I: Please do come up with.S: But what if it was 1 and 1I: Like this 1/1? OR like 4/4 OR 6/6S: Puts a circle like other children.I: Okay.Another Student: Just fill in all.Another Student: Yeah its one piece.I: Remember what a fraction tells us.S: (Interrupts), but its whole thing.I: So how can we fill in?

S: Whole thing.


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EMPLOY INSTRUCTIONAL STRATEGIES WHICHENCOURAGE REFLECTION


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FINDINGS

The researcher and her B.El.Ed interns who have employed the above strategies based on thetenets of Constructivism have observed:

It empowers us the mathematics teachers to understand how children come to know and createmathematics.

It asserts that constructivist notion that an act of cognition involves action, perception, reflectionand expression is a useful model for teachers who wish to create lessons which have potential toinvoke meaningful learning experiences for learners.

Despite the intended goals of teacher, students construct mathematics based on their ownstructures, and they can still arrive at incomplete or profound understandings unanticipated bythe teacher.

In a constructivist environment knowledge and understanding is built by the students based ontheir personal knowledge and the teacher needs to observe carefully the understanding displayedby his or her students and provide opportunities for validation, together with provocative andinnovative challenges for them. However, it is a students response to the situation rather thanthe nature of situation which determines the students pathway to understanding.

In a constructivist environment the assumption of different understandings and different levels of

understanding leads a teacher not merely to look for simple answers to routine questions but toallow for and seek and even be surprised by the different mathematical understandings shown bythe students.


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REFERENCES:

*Bauersfeld, H. (1992) Classroom Cultures: From a Social Constructivist perspective. EducationalStudies in Mathematics, 23,pp 467-481

*Clements, H.Douglous &Battista, T. Micheal (1990) Constructivist Learning and Teaching,Arithmetic Teacher,pp 34-37

*Grayson, H.Wheatley (1992) .The role of reflection in mathematics learning.Educatonal Studiesin mathematics, 23, pp 529-541

*Kamii, Constance (1982) Encouraging Thinking in Mathematics. Phi Delta Kappan 64, pp247-251 *Lockhead, J .Knocking Down the Building Blocks of Learning : Constructivism and the venture in

S. Atkinson (Ed.)1992 Mathematics with Reason: The Emergent Approach to PrimaryMathematics, Hodder and Stoughton, London

*NCERT Grade 4 Mathematics Book Titled Mathemagic4 based on NCF05 recommendations.

*NCERT Grade 5 Mathematics Book Titled Mathemagic4 based on NCF05 recommendations

*Pirie,S. ,Kiren,T.,1992 Creating Constructivist Environments and Constructing CreativeMathematics. Educational Studies in Mathematics 23 pp505-528

*Threja ,Ashu .2008 Teaching Mathematics at Elementary Level Based on ConstructivistPerspective ; M.Phil Dissertation submitted to the Department of Education ,DU

*Whitbread.(1995)Emergent Mathematics or How to Help Young Children Become ConfidentMathematicians in Julia Anghileri(Ed.) Childrens mathematical thinking in the primary years.Perspective on Childrens learning.

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Ashu Threja: Creating Constructive Environments in Mathematics Classrooms