Knowing from memory means not having to think about it.
Two of the best standards from the Common Core State Standards are on our home page:
By end of Grade 2, know from memory all sums of two one-digit numbers and
By the end of Grade 3, know from memory all products of two one-digit numbers.
These standards name the most important elementary math skills of all, because they are the foundation of all further work in mathematics. But what does it mean to say students know math facts “from memory?” It means that students don’t have to stop to figure it out. Say for example a student is adding nine plus seven. A student can figure that out by thinking that because 9 is one more than 8 and 7 is one less than 8, the answer to 9+7 would be the same as 8+8, which is 16. This is a smart strategy for figuring out the answer, but knowing it from memory means the student simply remembers the answer is 16.
So if second grade students know from memory the sums of all single digit numbers, they can answer any of those problems without hesitation, without having to stop and think about them. That takes practice, to build up the neural connections, so that students remember the answers instantly without some intervening thought process. That’s what Rocket Math is specifically designed to do. Practicing figuring out the answer to facts is NOT the same thing as recalling them from memory. So any practice procedure that allows students a long time to answer facts, allows hesitations, will not be very helpful in achieving that status of “knowing from memory.”
The peer practice procedures in Rocket Math require the “checker” to follow a “correction procedure” whenever there is a hesitation. If the student has to stop even for a second to “think about it” they need more practice on that fact to commit it fully to memory. The “correction procedure” provides that extra needed practice. Having students complete worksheets on their own will NEVER eliminate that “stopping to figure it out.” That is why the oral peer practice in Rocket Math is essential. And that is why Rocket Math really will help students come to “know from memory” all sums of two one-digit numbers.
This topic of “know from memory” is something I have been digging into as a special educator. I wonder what your thoughts are about whether certain accommodations from these “know from memory” standards would actually be modifying the curriculum?
For example, if we used “extra time to respond” and the student had to use their fingers or some other method to count, would they then not be doing the standard?
This relates to where I’m at in middle school math, but I think that it’s reflected in the continuum of the common core maths.
Thanks.
Actually, your example is very clear that it is not “knowing from memory.” You are describing “deriving from a strategy” or what I call, “figuring it out.” When you know it from memory, when you recall the answer, then you stop having to “figure it out.” These are two very different things. I used to ask workshop participants to imagine sitting next to me in a bar and asking me for my name. If I said, “Wait a second, I have it here on my driver’s license,” they would likely move away from me while wondering what kind of traumatic brain injury I had sustained! They would very likely say, “OMG, that man doesn’t know his own name.” The purpose of the verbal rehearsal that is a daily part of Rocket Math is to cement these facts in memory. Then when a student says to themselves, “8 times 7 is,” the answer pops into their mind with no effort. It takes quite a bit of practice to achieve that. However, the ability to instantly recall the answers to basic math facts makes doing mathematical computation a relative breeze. It make seeing relationships among numbers very obvious. It makes reducing fractions and finding common denominators easy. That’s why the Common Core thinks “knowing from memory” is so worthwhile. It’s why I began promoting Rocket Math in the first place.