Updated 26-Sep-2023
Fluency and automaticity
Building fluency in math and language is significantly (though not exclusively) building automaticity in recognizing and recalling math facts, and the sounds, spelling, and meaning of words, respectively. Foundationally, building automaticity must in fact be based on tasks which do so. This seems obvious but isn't so, as an incisive article reveals:
There is a very simple question we can ask to see if math fact practice is likely to help in the most direct way: Are kids practicing remembering? Or are they practicing something else? ... Strategies are useful, but practicing with strategies isn’t retrieval practice.
The point is that if learners are successful at doing math fact sprints, then fine, but if they aren't it doesn't help them automatize math facts, but forces them to fall back on strategies of deriving the solutions. Strategies are great, but they key is to build automaticity, at least at those points when automaticity needs to be built.
Flash cards for building automaticity
Flash cards are a simple tool for building automaticity, for two useful reasons:
The basic answer here is “flash cards", which has two big advantages. First, if you fail you can turn over the card and stick the fact back in your memory, then try again. You aren’t left to derive the fact (though you can). Second, you can repeat problems frequently to practice the problems that you didn’t answer correctly.
Repeated deriving does not produce memory of the result
While procedures and strategies are obviously important to learn, they do not (at least necessarily) lead to memorizing their results (aka math facts).
People do not necessarily remember the things they derive. Repeatedly deriving something in a way is practice avoiding retrieval from memory, which is (I admit!) a very mathematical thing to do.
Reading facts (aka vocabulary)
The same is true of reading facts, that is automatically known words, their pronunciation, and meaning (and conversely, their spelling). The ability to sound out letters, to blend letter sounds, and to articulate those blends as words, does not in fact (necessarily, or at least for some learners) lead to remembering those words.
Using flash cards for math facts and word facts
There are a variety of ways to use flashcards for math and word facts.