How Many Ways Can YOU Multiply?
Have you ever looking at your child’s math homework and wished for the “good old days” when math was simple?
I know I’m not alone in feeling more and more confused about the math homework my children bringing home each day. In our time, learning math meant filling out worksheet after worksheet filled with addition, subtraction and multiplication problems. The teacher taught you how to do it, you did it. You didn’t know why you did it… but who cares? You learned how to do math, right?
Or did you?
Ask a typical adult what multiplication is and they may have trouble explaining it. On the other hand, when I asked my daughter about multiplication, a concept she was already starting to learn in the 1st grade, she simply explained, “It’s just repeated addition.”
Oh… yeah… that about covers it.
One Question Quiz Math Quiz
So, now with that context in mind, I’ll am going to give you a quiz. (Don’t worry, it’s only one question):
You might figured out, that the correct answer is “c”.
If you answered “a” or “d” though, you are far from alone.
My guess is that most parents are highly capable of calculating the results to double-digit multiplication problems. That said, it is more than likely they were only taught one method to do this. Today, students are expected to do multiplication in multiple ways.
This shift in instruction is being brought about by the new Common Core State Standards in Mathematics (CCSS-M). These standards set expectations for students beyond mere calculation in that they expect In some cases, the differences between the instruction that parents and teachers received and the way students are currently being taught are creating more than a little confusion, anxiety and outright frustration for some folks.
“Why mess with a good thing?” many parents wonder while trying to figure out math homework they have never seen before. “It worked for me. What was wrong with the way I learned it?”
Common Core, why is it different?
The simple reason is that the way we learned math was only a part of the equation (pun intended.) In order to be “good at math”, you need to know more than just how to calculate algorithms (equations or problem-solving operations), you need to actually understand math to solve real-world math problems.
Here’s a great video by Samuel Otten who does a great job of explaining this idea.
What good does a tool do you if you don’t know how and when to use it?
I have seen this many times in my work as a former high school improvement coach. Algebra teachers and Physics teachers constantly lamented, they could teach students how to do algebraic equations, but year after year they struggled to get students to understand why and when to use various formulas.
I saw it myself. Give students an equation and they can calculate the answer. Ask them how they got their answer? They doesn’t know. Ask them how to solve a problem that requires them to choose an equation to solve it… they’re stumped.
In my parents generation there were no calculators or computers to do complex mathematical equations. It was important for our education system to make sure students knew how to solve math problems quickly and accurately, so instruction focused a LOT on rote memorization of math facts (e.g. “1+1 = 2”) and algorithms (e.g. “a(b + c) = ab + ac”). Our children will graduate into a world where computers will know how to execute math algorithms we did not even think possible in our day. As these shifts have occurred, it has become more and more important to go beyond memorizing the multiplication table.. to really understand understand how math works.
So what does it LOOK like?
Here’s a great example of elementary students actively working with math concepts using manipulatives to understand fractions.
— Michelle Schmitz EdD (@mschmitz_1) January 28, 2015
At the high school level it means students modeling algebraic or physics concepts using real-world problems, and being able to explain (like real mathematicians!) how they got their answers.
It’s OK to Feel Weird About Change
With all this change going on, it makes sense that we adults would feel uncomfortable about the shifts we see in math instruction. We all want to help our kids feel successful and share what we know about the world. Unfortunately, when our children come home asking for help with math homework we don’t even recognize, it can be more than a little unnerving.
What’s worse, we can often feel like we are letting them down at their time of need. I can tell you personally, it SUCKS looking your 4th grader in the eyes when she is struggling with double-digit multiplication and asks, “Mom, what’s partial product multiplication again?” and all you can say back is “Partial what?”
So How Do We Help?
What we learned in school wasn’t wrong, per se, it was only a piece of the Pi (OK, I’m sorry, I just couldn’t help myself! … But I know my math teacher friends are smiling.) The best way for us parents to help our kids to to model what it means to be a learner and learn math with our kids!
So how do we do that? YouTube of course 🙂
Below I’ve gathered a variety of examples of YouTube videos I’ve used to learn and reinforce math learning for my girls. This is just a sampling of the content that’s out there. It may not be the best. But it has definitely helped me get a handle on some of the cool new content my girls are learning in school (Thanks again Ms. Mackey! You ROCK!)
I’ve listed a few of the most commonly taught methods (based on my very limited understanding of math… I’m an English teacher by trade.) That said, I think it’s a good start.
Traditional Multiplication (Standard Algorithm)
I’m starting with this method because it’s the one most adults learned in school. In my experience, students DO NOT start learning this algorithm using arrays and the area model. This is a great video by Classroom Caboodle covering this multiplication method.
Multiplication Using Arrays
An array is a graphic way of representing a multiplication problem. This is usually the first way that students learn to approach multiplication.
Multiplication Using Partial Products
This allows students to take multiplication products apart to understand how the math works. It relies on a solid understanding of place value.
I like this one because it looks cool. The Lattice Form of multiplication has actually been around for a long time and takes its name from the fact that in order to do it, you fill in a grid which resembles a lattice which you might grow plants on.