Updated: Aug 17, 2020
My student was reeling from how useless her million-mile-high stack of flashcards seemed. They counted for points toward her grade, so she'd duly slogged through making them. When I asked if she knew how to use them: no. Did her teacher mention anything about using them: no. Is there a note in the syllabus for a YouTube/website/TikToc: no.
Her points added up, but her knowledge did not.
Flashcards build flexibility, through recognizing the pattern within the answers. In the addition and multiplication tables, each answer is larger than the last by a specific quantity. So, in the three addition or multiplication tables, each answer gets bigger by three units. As your student comes to know the patterns cold, they allow easier work within and between the tables.
If you're planning on flashcarding the addition, multiplication, subtraction or division tables with your student, here are a few things to keep in mind.
One, only use cards for equations your student has memorized! Flashcards are part of retrieval practice, or more stressfully, the testing effect. By either name, it's the process of pulling up information from your memory, which makes the recall sharper and longer-lasting.
Two, your student needs to make the cards from memory and only as they have the facts memorized. There is an enormous benefit to writing out information we're memorizing: hand-eye coordination is vital to our brains catching new information and attaching it to other memories. Again, the process makes the memory stickier.
Three, use the cards in order. When your student is just starting out, the stress of not recognizing a fact will literally shut your student's brain down. They won't be able to think or recognize the next fact, even if they know it.
Four, if your student bogs on a fact, don't automatically flip the answer over! Remind them to use the pattern (+1, -5, whatever table you're in) to jog their memory. Use manipulatives to work the equation. Re-write the card.
Five, once your student knows those three facts, use the cards less frequently, but don't drop them out of the deck.
Flashcards are a super-simple concept with some great applications for discrete pieces of information, like history dates/names and places, vocabulary words, noun declensions, formulas and math facts. They're not a silver bullet for math operations tables, though, and used improperly can be a stumbling block.
The pattern of the tables gives rise to math flexibility. And flexibility leads to fluency.