Clearing Up a Common Core Strategy

I spend some of my evenings wasting time on Reddit instead of finishing The Picture of Dorian Gray, which is a brilliant book but is taking me forever to finish. If you’ve heard of Reddit, you may think “cat gifs” or “nerds,” but I assure you, there’s much more to it. In fact, I recently found this picture with an interesting conversation about “new math” and “Common Core” attached to it.

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I’ve asked Chris, one of our math writers, to help me figure out what’s going on with this question and to sort out the responses to it.

Chris:

From a SOLARO perspective, this question is poorly written. At SOLARO, we teach students with short, accessible lessons, easy-to-follow step-by-step examples, and carefully crafted assessments designed to test the students’ knowledge without distracting them. In this example, the student is replying correctly based on what the question appears to be asking. Better worded questions might ask the following:

Add 8 + 5 by grouping into tens first.

or

Use the strategy of making 10 to add the numbers 8 and 5.

One comment on this picture reads as follows:

Unfortunately this is the way they are teaching math now. My daughter is bringing home stuff like this. Instead of the kids just learning 8 + 5 = 13 they are teaching them to take away from the lower number to round the higher number to 10 then add the remainder. It drives me crazy. I had taught my daughter addition, subtraction, and multiplication prior to entering second grade and now they are forcing her to do it this way. I understand the concept. They are breaking things up into 10s to make them easier to add but it seems like a lot of extra work for something that isn’t that difficult to begin with. (jasonahoule)

Comments like this one stem from two things: First, terminology—the parents don’t understand the language being used, even though they may understand the concepts (the question is actually valid if students know what “making 10” means). Common Core State Standards break down the terminology of making 10, decomposition, and using the relationship between addition and subtraction by citing examples. Secondly, some parents don’t actually understand the concepts: they know how to do the math, but not necessarily why it works. Common Core is about the why, about understanding the math. If parents don’t understand the why, they may dismiss it as dumb or stupid. This is a common response to new ideas.

Another fascinating aspect of this issue involves the level of difficulty. The question 8 + 5 = 13 is quite basic; but, we should always start with easy questions. A subsequent comment points out that the strategy in the picture is more commonly used with larger numbers:

The goal in that picture wasn’t to somehow jam 8 and 5 together and make 10, it was to show that an easier way to do math is to simplify numbers to make addition and subtraction easier. For instance 57 + 98. You could either add the 8 and the 7 together, write down the 5 carry the 1, etc like we were taught as children or you could round 98 to 100 by adding 2, then take that 2 from the 57, leaving you 55 and quickly come up with 155. (mw9676)

Many parents don’t understand the point of adding 8 + 5 by making 10, which I (kind of) get, especially coming from a generation of learning mathematics based on memorization. But, there are a couple of things to remember. First, when kids are learning a strategy for the first time, they don’t know how to do it yet! I know it seems strange, but people forget this. The concepts that you learn in math one year are often a struggle; but, two years later, it’s like you’ve been working with this knowledge forever. Imagine being in Grade 1 or 2 and adding numbers that require regrouping for the first time. You wouldn’t have a clue! That’s what teachers are for. Teachers are specifically educated to take concepts that seem like second nature and translate them for those who have never encountered these concepts before. So, yes, regrouping numbers to solve 8 + 5 = 13 might feel a little pointless, but you have to start somewhere.

As an example, the method of multiplying two-digit numbers I taught in middle school was simple, but I didn’t use long multiplication.

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Typically, if students reached me in Grade 8 or 9 without the ability to multiply a two-digit number by a two-digit number, changing the method was a good idea. I would start by teaching them something simple, like 34 × 7, before moving on to something more challenging, like 34 × 72. Almost all students had a solid method (long multiplication) to solve 34 × 7. But, they couldn’t understand how to use that same strategy with 34 × 72. So, I taught them to use a diagonal grid method to solve 34 × 7 first and encouraged them to trust me. Then, once they understood how the diagonal grid method works, I taught them 34 × 72. Together, we had to take a step back so we could take a step forward.

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Once students could multiply 34 × 72, they could multiply numbers of any size. This, to me, was like taking about five giant steps forward.

Here’s something else to keep in mind: these concepts are not new! We’ve been teaching “making 10” in schools for ages, not just because Common Core came along. Using different strategies for adding numbers is actually in the wording of several former state curriculums. This is a common mental math strategy. None of these strategies are new; we’ve been using them in the classroom for years. I studied them in university a decade ago.

When thinking about comparing strategies, I liken it to emotional intelligence. Is it better for your children, as they grow into adults, to do something because they are told to, or because they understand why it needs to be done? If we want to raise a society of critical thinkers, then we need to encourage critical thinking at a young age. Generally, this is what Common Core (or at least Common Core math) is about. It’s about critical-thinking skills. It’s about considering why things work, not just knowing that they work. The assessment focuses on these same principles, which is the reason we aren’t seeing as many simple knowledge questions. Instead, we are seeing questions that require kids to think about what needs to be done and why it works.

Tweet us at @mysolaro if you have any questions about Common Core or math strategies!