I overheard a student asking, “Why do we have to learn percentages?” It is important to be aware of the students, to listen to them, and to respond. When we respond to their questions and displays of interest, we get better educational results.

 

To deal with this, I started by asking the very simple question,

 

“What percentage of the students are boys?”

 

They replied, “50%”.

 

“This seems right,” I responded.

 

I then asked, “What percentage of girls are blonde?”

 

One girl popped up and said, “Do you mean natural blonde or all blondes?”

 

“Let’s say natural blondes,” I replied. “This means if we have 100 girls, how many are natural blonde?”

 

The important thing about statistics is to use whole numbers, i.e., frequencies, not decimal fractions, in order to make it more meaningful.

 

“About 15 girls.”

 

“Okay. This means that 15% of the girls are natural blondes. Now how many girls are blonde, natural or not?”

 

“About 40%.”

 

“Good. Now how many blonde girls are natural blonde? If we have 100 girls, 15 are natural blonde, and 40 are blonde. The number of natural blondes out of all blondes is 15/40.

 

They started figuring. I said to make it faster, as the bell was going to ring, try to double numerator and denominator. We get 30/80. If we make numerator and denominator a little larger, so that the denominator is 100, the numerator will also be larger. Say 40. It means that 40% of blonde girls are natural blonde. This means that 60% of the blonde girls color their hair.

 

We now see the importance of percentages. We now discovered how many girls are not natural blonde.

 

I then asked the girl who popped the question of natural or not whether she is natural. She said she was. Well, she is special, one of the few blonde girls who are natural. Now she feels good. Now the children got the point of the need for percentages.

 

When we talk about something meaningful and important to them, such as hair color, their interest and attention increases.

 

Again, when we talk about percentages, such as 40% of the blonde girls are natural blonde, we do not give them the picture that 0.40 blonde girls are natural, but that 40 girls out of 100 blonde girls are natural. It is hard to think of 0.40 girls, as opposed to 40 girls.

 

Adults also get confused with percentages. Frequencies, which are whole numbers, are much easier to comprehend than decimal fractions. If the adult finds a concept confusing, the student certainly will be confused. We should try to minimize confusion by using whole numbers.

 

As a general rule, we have to examine ourselves, and if we find something the least bit confusing, we must think it through carefully and plan how to present it.