Strategies, Algorithms, and Multiplication, oh my!

After watching Graham Fletcher’s ShadowCon 2016 video about telling a math story and getting back to the standards as our basis for what math to teach in the first place, I was drawn to some of what we may see as the most basic skills to be taught in elementary. Multiplication, its just multiplication, right? You just memorize your facts and use them over and over, right? Nope and nope, actually there’s an amazing depth to learning multiplication. I found that students are starting to represent multiplication situations in 2nd grade, then they take those experiences into 3rd grade where it becomes an exploratory wonderland of arrays, skip counting, hopping on number lines, mental math, mathematical properties, and so many more as shown in TEKS 3(4)(E)! The standards then begin to include multiplying  two-digit by one-digit numbers using these strategies and/or algorithms they have made sense of while playing with multiplication as seen below.

3(4)(G) Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy.

The student is expected to use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.

When we start teaching kids about multiplication in this wonderland, they will be able to discover what strategies, or even algorithms when appropriate,  make sense to them and help them multiply “flexibly, accurately, and efficiently” (National Research Council, 2001, p. 121) which is an essential piece of procedural fluency. And these students can then take those strategies and algorithms with them into 4th, 5th, and middle grades where they will be able to make sense of math operations even when they include fractions and decimals. No matter what the math is, we must remember that the strategies and algorithms are not what we are teaching, they are what our students are discovering for themselves!