Innumeracy or "Why can't I understand my first-grader's homework?"

Innumeracy or “Why can’t I understand my first grader’s math homework?

Which one of these problems is correct?

1/5 + 2/5 = 3/10        

0.25 is > 0.5   

If there is a 50% chance of rain on Saturday and a 50% chance of rain on Sunday, What is the chance of rain on the weekend? Answer: 100%

Before we get to the answers, let me tell you that many students and adults will not be able to find the correct problem. Why? In a word – innumeracy.

Innumeracy is, according to Stanislas Dehaene, author of The Number Sense: How the Mind Creates Mathematics, “the analogue of illiteracy in the arithmetic domains.” In simple terms (those which I can understand), innumeracy is the thinking that causes problem solvers to jump to incorrect answers based on reasoning that is mathematical in appearance yet faulty – Whew!

Innumeracy causes us to jump to conclusions in math based on common misunderstandings. In the problems above, some assume that 1/5 + 2/5 = 3/10 because 1 + 2 = 3 and 5 + 5 = 10; 0.25 > 0.5 because 25 is greater than 5; 50% and 50% must add up to 100%. None of these are correct, yet we make these mistakes because they seem to fit the mathematical processes we have been taught. We don’t stop to see if the answers make sense, we just compute them.

         

How is innumeracy corrected? In a word: Reasonableness. Are the answers we are getting reasonable? Judging reasonableness takes real world knowledge.

         

When most of us were growing up, we were taught the processes of math: adding, subtracting, multiplying and dividing. We drilled until the answers became automatic. We practiced regrouping, reducing, and factoring. We got pretty good at following the formulas for doing math, but many of us didn’t understand why math works.

         

Today, things are different. I will be the first one to admit that many “new” math movements were a bunch of hokum (if you will forgive the technical term). Recently however, schools have been teaching children to understand not only what to do, but why to do it. They are teaching them to have number sense – to reason in math.

This boggles many adult minds – as witnessed by the many rants on Facebook about the lunacy of the new Common Core standards. Explaining those would take a book, but mathematical reasoning (there’s that word again) occurs when children understand what is behind math -- the nuts and bolts that build math.

In order for kids to do this, they need to be able to explore in math. They have to build models. They have to have real world examples to help them understand why 1/5 + 2/5 = 3/5 (that is one finger (which come in fifths) plus 2 fingers equals 3 fingers not ten), that they will feel cheated if they get 0.25 of a pizza rather than 0.50 and that 50% chance of rain on consecutive days does not guarantee a rainy weekend.

Kids have to get “down and dirty” with math, pull it apart and put it together again, get lost and retrace their steps, wallow in the unknown and figure it out for themselves. Parents, who insist that they learn it the “old” way, because it is simpler for the helping adults, are denying them the thrill of discovery as they look for their own paths to reasonableness.

         

Your first grader’s math homework may seem like Greek to you now, but your children will be bi-nummerative in math, knowing the new way and the “old” way, if you take some time to wander with them toward number sense. If you really get lost, call the teacher and ask her to give you, and the many other parents who are wandering with you, a few directions or host a class for parents. Most will be happy to help. And who knows, you may become more “nummerative” yourself.

Next time: Why is everybody screaming on Facebook?