Mathematical creativity

Mathematical  creativity

           

             The ability to transcend traditional ideas, roles, patterns, relationship or the like and to create meaningful   new ideas forms, methods, interpretations etc. Creativity is a dynamic property of the human mind that can be enhanced and should be valued.  It can be either strengthened or deteriorated there for, it is important to study creativity and determined it characteristics. Nature of mathematics provides a suitable platform for creativity.

             Chamberlin moon (2005) defined creativity in mathematics as an unusual ability to generate novel and useful solutions to simulated or real applied problems using mathematical modeling.

             Leikin (2009) defines mathematical creativity as a dynamic property of the human mind that can be improved and appreciated

Laycock (1970) described mathematical creativity as an ability to analyses a given problems from deferent prospective, see pattern, deference and similarity, generate multiple ideas and choose a proper mothered to deal with un familiar mathematical situations.

Some researchers have made distinction between definition of mathematical creativity at the professional level and the school level; some researchers believe that creativity in mathematics generally associated with problem solving or problem posing (Chamberlin and Moon, 2005). Sreraman (2006) proposed that at the professional mathematical creativity can be defined that

·         The ability to produce original work that significantly extends the bogy of knowledge

·         The ability to open up avenues of new questions for other mathematicians

·         The process that result in unusual (novel) and insightful solutions to given problems 

·         The formulations of ne questions or possibilities that allow an old problem to be regarded from a new angle

Development of mathematical creativity

Ervynck (1991) considers three stages for development of mathematical creativity. Firstly, ”preliminary technical stage “ : this stage consists of application of practical or technical procedures in mathematics without person knowing what mathematics support them. In other word, the user is not aware of why it works empirically one may  have seen bricklayers who use a plummet for constructing a wale throe expressing this presses but they do not know the mathematics behind it. This preliminary stage is a part of modern mathematical teaching learning theories.

 Secondly, ”algorithmic activity teach” : this is the stage in which procedures in mathematics are applied to perform mathematical technique. For instance, the concepts of group ring etc.  are concepts in mind of algebraists which are interiorized so that they used them without reflecting on them.

Last stage,” creative activity”: in this stage the person make a none- algorithmic decision. The decision which could not be made with algorithmic procedures  this decision is in a manner which seems  to signified an underline sprout of concept formation.

Cultivating creativity

Creativity in mathematics classroom is not just about what pupils do but also what we do as teachers. So we think about the following three things in mind.

·         How we present content

·         How we model good practice

·         How we encourage our students to be creative

Creative ways to teach mathematics are given below.

1.      Use dramatizations

2.       Use children’s group

3.      Use children’s play

4.      Use stories

5.      Use children’s natural creativity

6.      Use children’s problem solving abilities 

7.      Use technology

Characteristics of mathematical creativity

1.      It is universal

2.      It produces something new or novel

3.      Originality of idea’s and expressions

4.      Adaptability and sense of adventure

5.      It has wide scope

6.      It is adventures and open thinking

7.      It creates self respect and self discipline among children

8.      It rests more on divergent thinking than on divergent thinking

9.       It is inmate as well as acquired

10.  It is ability to transfer learning to a new situation  

Stages in mathematical creativity  

  

Wallas (1926) described the processed as four stages

1.      Preparation

2.      Incubation

3.      Illumination

4.      Verification

Levels of creativity

            According to the level theory developed by I. A Taylor (1975) creativity may be described as existing at five levels in an ascending hierarchy

1.      Expressive level

2.      Productive level

3.      Discovery level

4.      Innovative level

5.      Emergency level

(1) Expressive creativity, in which originality and quality of product is unimportant;

 (2)  Technical or Productive :  This is concerned with skill rather than  novelty;

 (3)  Inventive : This  form consists mainly of ingenuity  leading to the production of a  novel

and appropriate product;

 (4)  Innovative :  This brings further  development to an established body of meaning;

 (5) Emergentive : The final and most complex  form of creativity.  It is individualistic and  results in highly generative insights.

Role of the teacher

           

How to develop mathematical creativity

1.      Freedom to respond

2.      opportunity for ego involvement

3.      encouraging originality and flexibility

4.      removal of hesitation and fear

5.      providing  appropriate opportunities  for creative expression

6.      developing a healthy habits among children

7.      using creative resources of the community

8.      avoidance of blocks to creative thinking

9.      proper organization of curriculum

10.  reform in the evaluation system

11.  use of special techniques for fostering creativity