Fear of Fractions

I came across this comic in my Google Reader a few days ago.

Fear of Fractions (I hope this link works, now.)

http://xwhy.comicgenesis.com/d/20090204.html

Why does the slightest mention of fractions send students’ brains running off in all directions?

The first day of the semester, my Algebra II class started Chapter 8, rational expressions — just a fancy mathematical way of saying “fractions”, sort of. We reached adding and subtracting rational expressions, and wow, it was like pulling teeth!

Anyhow, rational expressions with polynomial numerators and denominators versus regular numerical fractions, students still seem to be more afraid of the numerical fractions. I makes no sense to me.  Actually, maybe it does make a bit of sense.

When you ask a student, “I have 16 apples and gave you half of them. How many did I give you?”, they can actually answer that question. But rephrase it to say, “Sixteen times one half,” and you’ll get all sorts of answers.

What does that tell me? It tells me that people probably understand the concept of what a fraction represents, but can’t quickly make the connection with the numerical representation that we actually call a fraction.

Now let’s think about why. Calculators use decimals. Money uses decimals. Almost all mental math that we do, we think about in base 10. Now what if I asked you to add 10 + 15, but in base 16. What would you do? Well, if you are like most people, you would probably convert to base 10, add the two numbers, then convert back to base 16. A lot of work for something that looks as simple, yet deceiving, as 10 + 15. Now if I told you to add 4A + A3D, the problem is not as deceivingly easy as 10+15. It actually looks like it takes more work, students who know how to solve the problem are not intimidated.

The same thing goes for fractions. Add 1/4 + 2/3. It looks simple enough — integers less than 10, all positive numbers, and we’re just adding for god’s sake! But we all know that it takes more than just adding. In a way, it’s even more work than adding two numbers in base 16. It’s as if we have two numbers, each written in different bases — not exactly, but sort of. And as deceivingly easy as it may seem, there is so much extra work involved in order to write both fractions with a common denominator.

Now, as much as we teach and re-teach fractions, students seem to never get it! Well, I take that back. They do get it… when you teach it. Then, they appear in a problem a week later, and they are back at square one, again. Do the students not know how to work with fractions? No, I don’t believe that’s the case.

I believe the students inability to perform the math mentally, even though it though it looks easy, is the problem.  Something you realize when you start teaching: If you give students a really easy problem or question and they can’t solve or answer it quickly, they tend to give up and their minds shut down.

I learned about the concept of a student’s affective filter while in the credential program. If a student feels threatened, they hold keep a high affective filter, which makes it very difficult for them to think and learn. On the other hand, if a student feels safe and unthreatened, they tend to have a much lower affective filter, and have a much better chance of learning and thinking critically.

So when students continue to see fractions in problems and they can’t solve these “simple” problems quickly, their affective filters spike, forcing their brains to shut down. This continues, and the students end up training themselves to give up whenever they see fractions.

Now this is just a theory. Obviously, I haven’t done any research, nor do I believe it explains everyone’s issue with fractions. But let’s assume this is true. My next question is, how do I get around it? The way I see it, I have two options:

(1) find a way to help students get over their fears and just take the extra time to do the work when fractions appear, or

(2) drill fraction concepts and skills so hard into the students heads, that they really CAN do the work mentally.