Okay, we do have to differentiate between mindless drill & kill and what really makes kids better at math - focused practice, error correction, and repetition of correct processes. Just as hacking around on a soccer field doesn't help the team nearly as well as a directed practice, endless pages of addition problems aren't useful in developing math skills.
Do ten at a time until you get them right. Examine the work, identify errors and don't repeat them .... which sounds like what Common Core asks math teachers to do and what math teachers have been doing for a long time.
This all sounds like what you've been doing, unless you have Curriculum coordinators like mine who denigrate practice as "drill and Kill. We should have the kids do critical thinking", as if critical thinking and error analysis were two different things.
"Healthy children start making that switch between counting to what’s called fact retrieval when they’re 8 to 9 years old, when they’re still working on fundamental addition and subtraction. How well kids make that shift to memory-based problem-solving is known to predict their ultimate math achievement. Those who fall behind “are impairing or slowing down their math learning later on,” Mann Koepke said.So, those teachers who insist that the kids should have a calculator and an internet connection so they can look it all up are really doing a job on their kids.
It turns out that adults don’t use their memory-crunching hippocampus in the same way. Instead of using a lot of effort, retrieving six plus four equals 10 from long-term storage was almost automatic, Menon said. In other words, over time the brain became increasingly efficient at retrieving facts. Think of it like a bumpy, grassy field, NIH’s Mann Koepke explained. Walk over the same spot enough and a smooth, grass-free path forms, making it easier to get from start to end. If your brain doesn’t have to work as hard on simple math, it has more working memory free to process the teacher’s brand-new lesson on more complex math. source.So the next time someone says that elementary students should have a calculator, that "you can look that up" and "all we need is to teach them information retrieval skills", remind them that the brain needs to have some basic facts to work with before it can handle more complex tasks.
Currently, the argument point brought up here is the Japanese education system, which has been moving away from drill and practice and turning to the higher-order thinking that reformers here in the States are always going on about.
Remember, however, that a typical Japanese high school teacher does NOT have to do as much of this preparatory drill and skills practice ... because of the ubiquitous "jukus" - after-school academies that nearly every Japanese student attends to make sure that he/she has a shot at higher education.What do the "jukus" do? Drill. Basic skills. Practice, practice, practice. Because it works.
Here's a description of one of these "cram schools":
"This school broadcasts lectures to its 800 satellite schools all over Japan and supports students via telephone, fax and the Internet. Students can take math training menu and other drills on the Internet through a service called Toshin Home Lesson. They can choose from one series of lectures to a whole package."
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