What Happens When We Don't Understand Fractions.

There have been events throughout recent years that show most people do not have a good unstanding of fractions.  By that I mean that they do not grasp the differences between one-third and one-fourth or five eights and six ninths.  Many ended up with the idea that the larger the number in the denominator, the larger the number which as we know is not really true.

If you look back to when the A & W restaurants tried to take on McDonalds by offering their own burger deal.  They decided to offer a larger one-third pound burger which was bigger, tasted so much better in blind taste tests,  and cost less.  In other words, they offered a better deal than McDonalds but people didn't go for it because they didn't understand that one-third is bigger than one-fourth. People thought that one-third was less than one-fourth because three is less than four.

Another example comes from the 1980's when the game Dungeons and Dragons became popular.  A they spread across the country that players of Dungeons and Dragons were more likely to commit murder or suicide due to a few cases.  This happened during the time when the United States was undergoing a panic about Satan and his influence and it even made the news show "60 minutes". Unfortunately, no one took the time to actually look at the numbers of players who committed murder or suicide versus the total number of people who played the game.

One person researched the numbers and over a five year period, only about 28 players either committed murder or suicide out of the 3 million or more teenagers who played the game.  In order for the fear to be true, the numerator should have been at 360. or more based on the normal number of teen suicides back in the 1980's.  So in reality, the people who played Dungeons and Dragons were less likely to commit suicide than the regular teen age population.

Now if you look at a test given to more than 20,000 eighth graders about 40 years ago, only about 24 percent were able to answer questions on fractions correctly.  Since then, the number of students who showed they understood fractions only increased to 27 percent.  Not much of an increase.  It has been discovered that how well a fifth grader understands fractions and can use them can be used to predict how well they will learn algebra and what they achieve in high school mathematics.  By the time a student gets into high school math, they will be facing more problems and formulas containing fractions. In fact, a lack of knowledge of fractions can impede students learning high school math and can make it difficult to do certain jobs once they are out of high school.

Furthermore, when students learn fractions in elementary school, they often have trouble intrinsically with being about to use what they've learned.  For instance, when they multiply fractions, they have to multiply the numerators and then the denominators but in adding or subtracting fractions, they cannot do that. This and other things makes it difficult for students to learn to use fractions challenging.  

The second thing that makes it more difficult is that teachers often find it difficult to explain why problems are done a certain way.  For instance, many teachers are unable to provide an explanation for why we turn a fraction division problem into a multiplication problem with the reciprocal. It's even difficult to provide a visual to show fractional division.

So when these same students become adults, they carry the same lack of understanding with them so when they see things like the A & W third pounder, they have no idea it is a bigger hamburger.  Humans have a tendency to not look at the full picture when deciding if a situation is really bad or good. Instead, humans rely on a cognitive framework to make quick decisions.  This process is called heuristics and for the most part it works but when it fails, it fails horribly. 

Let me know what you think, I'd love to hear.  Have a great weekend.