Fractions are hard. They are weird, they are strange, they are silly, and they are hard. But kids gotta learn ’em, so teachers gotta teach ’em. (Personally, I’d be happy if we just did everything in metric, but, alas, I imagine even kids in Australia have to learn fractions!) Which is why I have been working on fractions with my students for the past few weeks. I had my students take a test on fractions so I could see what they knew and what I still needed to work on.
The results were less than stellar.
Like I said, fractions are hard. Of course, it doesn’t help that the test usually offered no more than three problems on a related concept, so if the students missed one, they were already below the benchmark (80%) for demonstrating competency for a particular skill/concept. So we spent more time on fractions today.
I worked with small groups throughout the morning and afternoon while the rest of the class worked independently on practice and review. They wanted to know if they could work with partners, but I told them no, because I needed to be able to work with my groups without interruptions and distractions. I am glad I did this, because I was able to help a lot of students understand different concepts with fractions, such as how to show equivalency and how to compare fractions with different denominators.
I also learned that I have some students who want to solve all of their math problems mentally and so end up making silly mistakes. I keep telling them to write it down. I know that there are some people, like one of my older brothers, who can keep track of all the numbers and operations in their heads. These people can do mental math without making silly mistakes. But they are the exception, not the rule.
I’ve also discovered that the directions to “add or subtract” are interpreted by some students to do just that: add or subtract, regardless of what the operation sign says. I had to remind everyone in the class that they could not, in fact, choose to solve a problem involving fractions that are supposed to be subtracted by drawing a vertical line through the minus sign and then adding instead. (One student sheepishly hid his face when I said this, but he was not the only one in the class to have tried this creative strategy.)
And I’ve realised that I need to have my class spend a few minutes repeating this mantra over and over and over: “Don’t add the denominators!” After having them repeat this a few dozen times, I’ll draw a picture of 1/2 + 1/2 and have them see how the answer is 2/2 or 1, not 1/4. I’ve tried to teach this by showing that the denominator is the name (denomination) of the part, and it is similar to saying I have 3 dogs or 4 apples or 2 dollars. To wit: 3 dogs plus 3 dogs equals 6 dogs; likewise, 3 tenths plus 3 tenths equals 6 tenths.
Hopefully we’ll make some progress tomorrow!