Why Is Everybody Screaming on Facebook?

Why is everybody screaming on Facebook?

Or, How I learned to stop worrying and love the Common Core

One of my all-time favorite rants on Facebook concerns the new Common Core standards. First, a disclaimer, I am not an expert on the Common Core, but I did teach the math that these folks are screaming about, so I feel that I have a right to offer an educated opinion.

The offending math problem looks like this: 32–12 =? Every adult in the nation says, “Well that’s easy. Subtract 2 from 2 and 1 from 3. The answer is 20.” Then they show the way second grade students are taught to solve the problem: Here’s the solution shown.

12+3=15;

15+5=20;

20+10=30;

30+2 = 32

Add 3+5+10+2=20 so 32–12 again equals 20.

Facebook friends scream that this is insane. Their method is much easier. It sure does look simpler, doesn’t it? Obviously, the Common Core method is ridiculous. But when asked why their way works, many adults might not be able to explain.

Let’s put it another way. Suppose you buy a cappuccino that costs $5.33. You have a five and a one. You give them to the barista and count on him giving you the right change. You are expecting two pennies, a nickel, a dime and a half-dollar (2+5+10+50=67 cents). Hmm, seems like you just made the same kind of calculation in your head. Probably none of us would sit down with a piece of paper and subtract with all that regrouping.

This is common sense to us, but not to kids. We learn this as we develop number sense. The new process that freaks everyone out makes much more sense when explained this way. And, surprise, surprise, the offending method is NOT proscribed by the Common Core. It is just common sense.

         

Try the same process of counting up using an equation where you would have to regroup (the bane of many students’ lives).

Let’s say, 41–23=?

So 23+7 =30;

30+10 =40;

40+1 =41.

7+10+1=18 -- the very same answer found with adults will find with the much more complicated regrouping process. Kids don’t tear their hair out, and as an added bonus, they learn that addition and subtraction are complementary processes.

To go back to the original scream-invoking equation (32-12=20): How many remember that 3-1 is really 30-10? This concept often gets lost when we just do the process. How about a really hard problem, like 2,000-899=? What a lot of regrouping! Numbers might get lost in the shuffle when solvers jump from place to place. But add this simple step: subtract one from each number.

2,000-1=1,999

899-1=898

This changes the equation to 1,999-898=1,101.

It gets a lot simpler and surprise, surprise, the answer is the same. Get out the calculator and check.

         

These are just two of the ways which are shown to students for solving problems. They are also taught the “old” process as yet another way to think about math. They then choose the way that makes sense to them -- and when kids get to choose, they LOVE math. Do you?

         

So you do it your way and the kids will do it theirs and we will all get the right change, find the right answer, and enjoy a refreshing drink at the well of math. Take a deep breath, think about it, and please, don’t shout at me on Facebook.

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?