But I have to defer to the fact that research says that neither conceptual nor procedural fluency is better than the other. That they both are a dynamic duo that serve to make a student flexible with numbers and able to tackle abstract concepts with more than just speed and accuracy. They help as student be flexible in their approach to numbers and concepts/skills.
Let's say I wanted to decompose five-fourths to express why it's equal to one whole and a fourth.
Knowing all of the different ways to decompose the number 5 (1+4, 2+3, 4+1, 5+0, 0+5 and 3+2) all serve to help me understand that I can decompose five-fourths using the facts (1+4 and 4+1) into four-fourths and one-fourth. That coupled with the understanding that four-fourths is related to one whole, conceptually helps be better prove why 5/4 = 1 and 1/4. I don't have to worry about dividing 4 into 5 and finding the remainder. Although that abstract understanding will follow; this way I have built a better foundation of understanding behind why I even divided to find that mixed number rather than a rote "because my teacher said to do it this way".
So I stick to my argument that conceptual focus BEFORE procedural focus, builds a better equipped WHOLE student.
Think about this. What happens when I need to subtract 300 - 234 and I don't know how to subtract across zeros? Yes, I could learn how to regroup in 1st and 2nd grade, but what is regrouping anyways? It's simply decomposing a number different ways. So 300 can really be two hundreds, and one hundred ones (or ten tens) which might look like this 299. NOW, I can easily take away 34 ones from one hundred ones or three tens from 9 tens and so on! This is all about decomposition...which builds from a conceptual understanding of numbers!
So, for my 1st and 2nd grade teachers who serve our babies on the front lines of fact fluency.
Here's a video series for you, that encompasses teacher and student stations for your classroom. All around facts (addition/subtraction) from a conceptual standpoint! Before a baby ever gets on a computer to play a fact game, this helps build their foundation of numbers so their fluency truly is procedural in that they can manipulate numbers rather than "rotely" spew out facts with speed!
*********************ADDITION STATIONS*************************
FILL A FRAME (Station 1)
DECOMPOSE THEN MAKE 10 (Station 2)
DOUBLE AND NEAR DOUBLES (Station 3)
*******************SUBTRACTION FACTS*********************
DOWN THROUGH 10 (Station 4)
TAKE FROM 10 (Station 5)
Have Fun!
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