In November of 2015 something amazing happened in my 8th grade Algebra class. Something that many viral social media posts and "news" articles stated was impossible and utterly ridiculous. Something that countless friends, casual acquaintances, and even some fellow teachers told me would never happen.
So what happened? What was this wildly inconceivable event?
I saw students remember and apply a particular solving strategy from elementary school to more challenging secondary content. I know, many of you are shaking your head in disbelief. How is this possible? How could this have happened? Does this mean that Common Core is working?
Now before you get your anti-Common Core panties in a bunch, let me explain. After I witnessed my genius students in action, I drew this picture (see below) to show the 7th grade teacher in my building what happened in class that day. The solving strategy in this case is called the area model because, in short, it takes a multiplication problem and visually displays the two numbers being multiplied as the side lengths of a rectangle. Then, you can use the fact that length times width equals area to find the product. It comes in handy for problems like the one on the left, where multiplying 24 by 35 in your head is a little tricky. It's much easier to split the two factors into "friendly numbers" and then add the partial products together. For elementary students, this process is very visual and helps to build their conceptual understanding of multiplication and decomposition of numbers. Ultimately, we want students to be able to use the traditional model for multiplication since it is usually more efficient but this is a great stepping stone to get there. Okay, moving on...
The example on the right is what we were learning about in Algebra when the miracle occurred. Multiplying two binomials, everyone remembers how to do that right? FOIL of course! Multiply the first terms, multiply the outside terms, multiply the inside terms, and then multiply the last terms. Makes total sense right? Not always. It's a fun little acronym that someone made up so that their robot students could memorize the steps and regurgitate an answer. Unfortunately, it doesn't really click for all students at first. So I sent my 8th graders loose on this problem to see what they would come up with. And low and behold, two of the five groups immediately drew the area model and started working to find the partial products. WHAT? How is this possible? I didn't even show them how to do this! I asked them to explain what compelled them to do such a thing. Their reasoning? The example on the left. They confidently told me that it's the same idea. Breaking down a number (whether it be a whole number or binomial) to more manageable components and then multiplying. It was amazing. Vertical alignment at it's finest. The whole class agreed that this was a great way to see the multiplication in action and how the two binomials become the longer polynomial. Then, as if on cue, a students raises his hand and asks "Do I have to draw those stupid rectangles and boxes every time? That's going to take forever!" Cue FOIL and the more efficient method. Which now, makes sense.
So I shared the picture above on my personal Facebook page. And then this happened:
See that? 9, 710 shares. That's 9, 710 people (give or take a few internet trolls) who basically said "Amen" to the reason behind some of these outrageous solving strategies we are seeing in elementary schools today. Just because a model isn't the most efficient or what you would do as an adult, doesn't mean it's not teaching your child something valuable, even if that valuable piece of knowledge doesn't show up again for a few years. Have a little faith.
After the great response from my Facebook post, I decided to start this blog. As a place to share my adventures as a math teacher, academic English language teacher (because we ALL are), and a Common Core lover.
Also, the picture above really has nothing to do with Common Core, for all you Common Core haters. Common Core is a book of standards. It tells you what to teach at each grade level. This was just a great vertical alignment example, that many teachers had been doing for years. Common Core just helps ALL teachers be knowledgeable and take advantage of these types of standard connections at purposefully planned grade levels. Let the miracles happen!