I was speaking with a friend that teaches adults preparing for their GED’s. They were describing the moans and groans heard as the teacher announced they would begin to review fractions. It reminded me how many of my middle grade students hate fractions and love decimals. There is something very reassuring about decimals to students in grades 6-8, and possibly even older.
I have a theory about why fractions are so hated among this crowd. These theories have no research to back them up, so I hope that readers out there will feel free to call me to the mat on this. First lets do a little comparison between fractions and decimals.
So the ways in which decimals are better than fractions are the addition, subtraction, and comparison (by which I mean being able to compare the magnitude of numbers). I would say this is at the heart of my middle school student’s love of decimals. These are the operations which students feel most confident with. In fact, I would venture to say that students often don’t really feel the “know” a fraction. If they must give answer they like to give a decimal. Students love to give answers like 3.291098094. At this point the reason for this is almost beyond my grasp.
I will say of the three areas I think that comparison is the most important. I believe that this is because each student has a sort of internal measuring tape. They feel they know a number when they know where it goes on the measuring tape. It can be difficult for a student to place with a degree of certainty 4/13 on such a mental measuring tape.
How do we help students feel more comfortable with fractions? I propose the following steps:
➢ Emphasize fraction’s strengths. They solve division problems easily 3 divided by 23 is 3/23 for example. They can be multiplied easily. A good example is .125 * .75 is 3/32. Division too.
➢ Help student to understand the meaning of fraction in many different ways. As rates, as ratios, as the solution to division problems. As a number with a unit e.g., 3 eighths. Eighths can be thought of as a unit, like feet or inches. This is why we must have a common denominator to add.
➢ Help students find ways to estimate the size of fractions. This may help them place the answer on their mental number line. For example, 4/13 is a little smaller than 4/12 = 1/3 so 4/13 is just a little smaller than one-third.
➢ Help students understand through pictures and a variety of situations why multiplying fractions can lead to smaller numbers and division can lead to bigger ones. This should include a thorough discussion of the meanings of multiplication and division. Too often students just see these as ways to make numbers bigger and smaller.
It really is an interesting question. Why do students dislike fractions so? Fractions predate decimals by a good 600 years. I often wish I could watch a middle school math class prior to Simon Stevin to see what the kids were bitching about then.