Here’s a novel idea …
Bring back math memorization … at the Algebra 1 level!
No — I’ not suggesting that we ask students to memorize the times tables from the 12s to the 20s.
Nix on that because it is NOT critical information for algebra students to have. So it would not serve the greater purpose of these students.
But I am suggesting that we require students to memorize a handful of facts that will make
their algebra experience considerably less painful.
For starters, let’s require students to memorize a limited set of exponential powers for small integers.
Initial proposal: students memorize all powers of 2 from 2^0 through 2^10.
On the benefit side. Consider how much easier it would be for students to simplify √ (32) if they knew that 2^5 = 32.
They just figure like this:
= √ (2^5) [this step done in a flash, instead of the typical half-minute]
= √ (2^4) (2^1)
= 2^2 √ 2
= 4 √ 2
Or how much easier it would be to simplify this:
Instead of agonizing over this, first being puzzled, then realizing that they have to “figure out” their powers of 2, students would instantly recall the relevant fact:
log2 (32) = 5, since 2^5 = 32
And there are other situations in Algebra 1 and 2, Trig, PreCalculus and Calculus, which would be easier if students simply memorized the basic powers of 2.
If you’re thinking that the students would object, saying they “are not able” to memorize these facts – or that it will take huge amounts of time — I have news. They will. But you as the teacher can respond that it is actually quick and easy to memorize these facts. Most students can do this in less than a day; some in as short as 10 minutes.
As a tutor I require my late Algebra 1 and all Algebra 2 students to memorize these facts. And they all get it done in 24 hours.
Here are a few mnemonic tips, serving as the proverbial “spoonful of medicine” …
2^4 = 16 [Remember the reverse — 4^2 is also equal 16. This math “coincidence” helps students remember this one.]
2^5 = 32 [5 = 3 + 2]
2^6 = 64 [6 is the first digit of 64; next digit 2 less]
2^7 = 128 [Ignore both 2’s, and you get: 7 = 1 8. Think of this as backwards reading: 8 – 1 = 7. A bit complicated but it works for me, and I’ve seen it work for students, too.]
2^8 = 256 [8 = 2 + 6]
2^10 = 1024 [1024 starts with 10, then just add 2 x 12]
If your students don’t like these mnemonic devices, suggest that they develop their own. But most importantly, take the mission seriously. Give your students graded quizzes on these facts till they have them down cold. Or play “Fact Baseball” with them, choosing teams and having them compete at beating the other team.
A few years later, when you see them after high school, they’ll tell you that they’re the only one in their Calc 2 class who knows these powers without a calculator. And if you look closely, you’ll see a little “thank you” half-hidden in their expression.