Now that I’m basically home-schooling my daughter due to The Lockdown, I’m realizing how ridiculous math textbooks and workbooks are. Who writes these things / creates these problem sets? Today’s homework assignment had these nuggets in it:
“Kelly subtracted 2.3 from 20 and got 17.7. Explain why this answer is reasonable.”
The obvious answer is “because it is correct.” But that would get the student zero points. The expected (I assume) answer is about number sense / estimation, e.g., “If I subtract 2 from 20 I get 18, but I have to subtract a little bit more, and 17.7 is a little bit less than 18, so 17.7 is a reasonable answer.” Now my issue with this problem is that the actual arithmetic is so simple that it is arguably easier to do just do it than it is to go the estimation route. The problem sets the students up for failure, and undercuts the point of the unit: that estimation is a valuable tool. A better problem would have used numbers with more digits to hint that the students were supposed to estimate the result instead of calculating it, and to show that estimation saves time and effort.
“At a local swim meet, the second-place swimmer of the 100-m freestyle had a time of 9.33 sec. …”
This one made me laugh out loud, and I’m not even a sports fan who follows swimming. But even I know that swimming is a lot slower than running, and upon checking, I found that the world record for the 100m freestyle is 46.91 seconds. Who was competing in this “local swim meet?” Aquaman? My issue here is that the problem creator failed to understand the reason for using this type of word problem: reinforcing the important notion that math is important in the real world. But by choosing these laughable numbers, the creator not only undercut that notion, but created exactly the opposite impression in the students: that math has no relationship to the real world.
And from today’s section of the textbook, this table:
| Location | Rainfall amount in a typical year (in inches) |
| Macon, GA | 45 |
| Boise, ID | 12.19 |
| Caribou, ME | 37.44 |
| Springfield, MO | 44.97 |
Followed by this question: “What is the typical yearly rainfall for all four cities?” The book expects 139.6 inches as the answer, but that answer makes no sense. Rainfall amounts measured in inches can not be added up between multiple locations, because they are ratios, specifically volume of rain per area. How is that supposed to work? Stacking the four cities on top of each other? As in the previous example, this problem undercuts the goal of showing that math has a relationship to the real world. These students, being in fifth grade, wouldn’t necessarily realize the issue with this problem, but it really makes me think whether the person creating this example has advanced beyond fifth grade. Or, even worse, if that person is actively trying to create the impression that math is just some numbers game that happens in a vacuum. If so, good job.
My daughter was actually stumped by this last one, having no idea what the book meant by “typical yearly rainfall for all four cities,” and I had to explain to her that the question makes no sense, and reassure her that math is important, even if the math textbook goes out of its way to teach the students that math is frustrating, incomprehensible, and has no point. Again, good job, textbook writers.
In violation of Betteridge’s Law, I will answer the question posed in this post’s headline with a resounding “YES!“
Amen to you…. I gave up trying to understand and teach my son, common-core math. He was frustrated by all of the stupidity; I finally showed him all of my shortcuts, and how I learned it as a child. He asked me, “why isn’t our school teaching us math your way?”
Completely agree there! I’ve come across many examples like the one you’re describing and is totally frustrating for the kids and makes us parents roll our eyes at the teacher (because they don’t explain why the textbooks are poorly worded).
To add to your list are: Jimmy is painting his 2″ x 5″ bedroom with 3″ high walls. How much paint does he need? And the farmer putting a fence around his 15 x 40 mm field… Math textbooks are not written by teachers. I don’t know who does, but examples like this are everywhere and funny in the best case (if your kid sees the absurdity) to infuriating (if your kid is a stickler for getting it right).
Cheers!
Further, we also squander opportunities to use that math to develop a rough-quantitative understanding of the physical world. Quite a few marine mammals can do 10 m/s in water. Low order 100 m/s requires leaping through air. Humans can manage low order 10 m/s with high-tech fins and suits, but are mostly order 1 m/s. Global average annual rainfall is 100 cm, deserts are < 25 cm, and rainforests > 250 cm – pretty, no?
But “hate math” as the failure mechanism? Consider a popular intro physics text, which for many years and revisions, had an ideal gas law chapter problem, with numbers describing solid argon. The official answer was not, of course, “ideal gas approximations apply poorly to solids”. Answers like that aren’t a thing. But did the authors, checkers, and decade-worth of professors and instructors and students, all “hate math”?
A problem takes minutes to create. And a great variety of textbooks and workbooks exist. So did you happen to provide your child and their class with better problems or books? Is “hate math” a good characterization of why not? Likely not. If it were easy… various things would need to be different for it to be easy.
“Who writes these things / creates these problem sets?” I don’t know in general, but at least sometimes, math textbook problems are farmed out by large publishers to independent contractors, including teachers. With long lists of rules, like “don’t use dinosaurs”. And sometimes even “numbers should make sense”.
So yes, math and science education content is a dumpster fire. But that mass of dysfunction and regrettable incentives is a enormous collaborative multi-decade project encompassing everyone from science research funders to parents. We’ve been having this conversation for at least three quarters of a century. Perhaps XR and personalized instruction will help us escape. But unless we’re clear on what needs to change, how much of it will end up being merely the usual wretchedness, now in 3D?
Glancing at this again, perhaps “The book expects 139.6 inches as the answer” is the problem? Combined annual rainfall, with these semi-arid, midwest, south- and north- east cities, isn’t far from national and global average. Perhaps this was a reasonable question about averages, that was regrettably repurposed for addition?