Thinking Mathematically - K Bhanumoorthy

 

THINKING

“To think is easy. To act is difficult. To act as one thinks is the most difficult of all.” 

                                               ---- Johann Wolfgang Von Goethe.

 Introduction: 

Let me write about thinking. Think means as per dictionary, it means use your mind to form ideas, solve problems, imagine, cogitate, ruminate, ponder, consider, reflect, so on. There are various ways of thinking. I would like to discuss (restricted to mathematics). Thinking could be creative, analytical, critical, concrete, abstract, divergent, convergent, lateral. The way one approaches problems and solutions relies more on how the brain manages processes information rather than the facts presented.

I. Creative thinking: This way of thinking allows anyone to generate new ideas, a new design is formulated to get the required results. There is involvement, artistic, original, being resourceful. Students shall be able to frame own questions, open ended approach in solving problems. It’s matter of divergent skills. Self-imposed conditions are removed. I mean to say overcome fixation.

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An example: a question of this kind. 

I) Find two numbers where the sum is 9, the difference is 2. Ans: 3.5, 5.5.

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ii) There are 3 boys, 3 girls. They are standing in a line. How many students are there? Everyone knows there are 6 students in total. The question can be modified. In how many ways the students can stand in a line. (ans.4x3x2x1= 24 ways). If they are arranged in a line with condition no students of same gender stand together. How many ways can be arranged?  Then the answer is 2x2x2= 8ways.

iii) The volume of a tank is given as 30 Sq m. what could be different measurements? 

One answer is 3m, 2m,5m.

II. Analytical Thinking: This is detailed study. This is very much required in mathematics. Analytical thinking simplifies mathematics learning, especially in proving theorems. Mathematic is language of pattern. Concept in mathematics requires analytical thinking.

Source -  Image 1:- Analytical Thinking Skills for Problem Solving – IspatGuru 

Source - Image 2 :- Analytical Thinking & Problem Solving - SEMINAR BAGUS (seminar-bagus.com)

Example: When we increase the perimeter of a rectangle, does the area increase?

1)      Length 6cm, breadth 4cm. Then Area is 6x4 = 24 sq cm. Perimeter is 2(6+4) 20 cm.

2)      l =8cm, b =3cm, A = 24 sq cm, Perimeter is 2(8+3) 22 cm. Many other possibilities are there.

 We can conclude when we increase the perimeter of rectangle, the area does not increase.

III. Critical thinking: This is an important factor, in solving mathematics problems. It is an ability to analyse the given data and then proceed, to find solution. This kind of thinking we do require in one’s personal life and professional life also. This kind of thinking strengthens an individual to identify the sources and to draw the

Image Source:- CRITICAL THINKING SKILLS. 1. Analytical Part of critical thinking… | by Zaini Mirza | Medium

conclusions. Helps in Mathematics worksheets, puzzles, multiple choice questions, matching questions so on.

Examples: i) An electrical engineer evaluate materials suitable for particular job. Ii) A manager of a company / shop analyses customer feedback for better customer service.

      ii) What do the 4 animals in common? Cat, fox, squirrel, mouse. (Ans: tail.)

      iii) Find the odd man out? Tea, Diesel, coffee, apple juice. (Ans: diesel)

 

                                               ----- be continued

By - K Bhanumoorthy