Cece scored a 78 on her first math test. She scored an 84 on her second test. What is the percent increase, rounded to the nearest tenth, from Cece’s first score to her second score?
That’s a problem copied directly from the AIMS sample test. This is the topic I’m teaching now, and it is basically the bane of my existence. Last year, the kids never ever ever understood what I was trying to get them to do, and I thought maybe it was because I’d first introduced it with no voice. This year, I’m realizing that it is way more than that.
Start with the simple fact that plenty of functional adults would get this problem wrong. It’s perfectly common to say that Cece went up by 6%, to the point where I’ve started begging other teachers at school to STOP doing this when they talk about test scores with students. It’s also obnoxious because the change is 7.69%, which means a kid who stops calculating too early will get B instead of C. But that is actually not why this question kills us.
My first day of this unit was a simple introduction, where we calculated increases and decreases of 50%, 10%, and 20%. I started nice and low… 50% is the same as a half, so to calculate it we cut the number in half, and that’s the same as dividing by 2. Gentle and easy, right? Wrong. A startling majority of my kids were lost when I opened my mouth. They can’t calculate 50%. They don’t know how to split a number in half. They have to count by twos on their fingers to divide by two. Even once they’ve done that, they have no idea what that number means. They have no concept of percent or how it works. If I have $6 and increase by 50%, I should now have $56 because it says I increased by 50. If they do get far enough to calculate a 3, they’re then going to subtract it from $6 because they’re taking a 50-50 guess on whether to add or subtract on the word “increase”.
I can’t believe last year I thought the issue was me teaching it very quietly. The issue is the same issue that has been a theme through every concept my kids struggle with. The issue is that they have absolutely no understanding of parts of a whole. They think that 0.26 is bigger than 0.9 because 26 is bigger than 9. They can’t tell me how many fifths make one whole. They think that $6 + 50% is $56. They don’t know whether 1/4 or 7/8 is larger, they don’t know that 1/4 and 2/8 are the same, and they could definitely not explain why they’re the same. They can’t divide something in half. They just have no idea what all these things mean. No wonder they don’t understand why Cece’s score is 7.7% higher than last time.
I’m sorry that this entry sounds like I’m just trashing my kids. I love them and they often do a great job keeping up with 8th grade content. It’s just that 8th grade content doesn’t always have to involve parts of a whole, so I can see them excel by working around this deficit. Unfortunately, in percent change problems I am just getting slammed in the face by everything they don’t know. I walked around the classroom in horror, dreading talking to the next kid with a hand up because so many of them were just drawing an enormous blank on everything we were doing. It’s horrifying. How did this happen to so many of them?! How do I become the type of teacher who can get them to understand percent while still spending only four days on the topic?