Cognitive Learning

"Again he has made the same mistakes in mathematics test in class as he did last week. He did not understand a simple formula of Area of rectangle. Sometimes he divides length with width, sometimes he sum up both to get area. He is more focused on playing Roblox, Candy Crush and other video games.” 

The complaint about my son by his mother made me think seriously about his learning capacity. How a kid who is good at playing video games is not able to understand a simple mathematics formula!! ??

I decided  to teach him like a primary school teacher. 

After 15 minutes, he was able to solve the problems mentioned as exercise in the book perfectly. I felt myself proud to be a good teacher as he has memorized the formula exactly and multiplying the length and width perfectly.

Suddenly he asked me a series of questions:

·       What is the difference between Length and Width?

·       Why we do addition to get perimeter?

·       Why we do multiplication to get area?

For a moment I was speechless and struck dumb as I was not expecting these questions. These questions were a strong proof of my failure to teach a kid about a simple mathematics concept. On the other hand, I was glad that he raised the questions at least. Kids should be encouraged to raise the questions. More they will ask the questions, they will be well-educated.

I just replied him “My dear, I will answer you all these questions later. Let us first go to market to buy a rope needed to hang washed clothes to dry.”

I deliberately made an urgent situation to go to market which is located at few minutes’ drive from home. We arrived there and asked for rope from shopkeeper. Shopkeeper asked “How much length of rope we need?”

Now the situation was interesting. He was looking towards me to respond to shopkeeper. On the contrary I asked him “How much length of the rope we will need?”

He innocently replied “I do not know”.  

I replied in a serious and helpless tone that “Even I do not know. We need a measuring tape to measure it first. Then we will be back to buy exact length of rope.”

He agreed with me and we went back to home with measuring tape.

To cut the story short, at the end of the day, the kid calculated the area of every room of home, all flat rectangular surfaces like tables, cupboards, sofa, chairs etc etc by measuring the length and width. He was conceptually cleared about the area, perimeter, length and width when he found the usability and application of the mathematical formula of area and perimeter in real life.  I am pretty sure that he will never do the mistakes to calculate the area and perimeter now.

Sort of the same situation I have experienced during teaching at somewhere in some department of some university during delivering a lecture about Geodesy and Surveying subject to Post Graduation Students. I asked students a simple question.

“How we will calculate distance between two points having coordinates (x₁,y₁) and (x₂,y₂) ?”

The answer is simply the distance formula.

Almost all the students were aware about the formula and answered correctly.

I asked them further consecutive questions:

   

·       Why we use the difference of x ordinates and y ordinates in the formula?

·       Why we square the differences?

·       Why we take the square root?

Surprisingly, no one could answer satisfactory.

The question is related to the basic analytical geometry and is included in the curriculum of High School mathematics.  The post graduation students answered the first question correctly but could not answer consequent three questions because they were not conceptually taught about the formula. They relied on the memorization of the formulas to answer the question in the exam.

Sort of similar situations I have witnessed during interviewing the science and engineering graduates (even post graduates) for job. The candidates have high grades and GPA but lack in conceptual understanding of subjects related with mathematics and geometry.

The prime reason for this inadequacy is our education system which revolves around the grades and procedural knowledge. The exercises mentioned at the end of the chapter in book or the problems created by the teacher in class are considered as the only problems. Rather such situations should be posed by teachers which make the learning so interesting, engaging and intellectually stimulating. The teaching methods should not be limited to procedures only rather the mathematical and geometrical formulas & theorems should be demonstrated as strongly related with the situations outside of classroom i-e real physical world. That’s the cognitive learning which make students realize the “Why” behind a topic or theory and how it fits into the real life.