Common Core Math

Point #5: Math teaching needs to change
One of the main goals with the development of Common Core was to solve the issue of curriculum that is "a mile wide and an inch deep." For years, teachers and researchers have known that teaching a different math skill every day was not working. Kids never had the time to fully understand concepts because they were moving so quickly from thing to thing. We were compensating for that by reteaching the same things in grade after grade, and it wasn't working. Common Core has tried to cut down on that. There is still a definite progression from grade to grade, and students are often introduced to a concept in one grade, then expected to master it in the next. However, the concepts have been grouped by grade. For example, we used to teach mean, median and mode in 5th grade and 6th grade (and maybe 4th grade as well). Now, they don't even touch it in 5th grade, but we spend a lot of time on it and measures of variability. However, we don't even touch perimeter anymore. We expect them to have that mastered by sixth grade.

Now, this is one of the few claims of Common Core that teachers will dispute with you. We were promised a narrower, more focused core, and when we looked at it for the first time, we thought, "There's still SO MUCH THERE! This isn't narrower!" I felt that way too all the way up until this evening. As I started thinking about it, I realized that it IS narrower. Instead of teaching 5 things, we only teach one: we just have to teach it from 5 angles. So, we need to teach distributive property. However, kids need to know how to do it backwards, forwards, from story problems backwards and forwards, in normal numbers and in algebraic equations. Well, that's actually a good thing: by the time you've hit distributive property from all those angles, the kids have it down cold. Unlike our previous core, Common Core actually outlines this. So, before, we should have been teaching distributive property in all those ways, but we couldn't because we had too much to teach. Now, we are being told to teach it in all those ways, which feels overwhelming and makes the standards seem just as big as before, but they're really not. The other issue we're having is that we're still trying to fill gaps made by the transition. As those gaps disappear, I think we will be more convinced of the narrowness.

Also, the scope and sequence of the math standards IS based on research of how kids learn. It is designed so kids have all the background knowledge they need before learning a new skill.

Common Core Approach to Teaching Math
Ok, now the answer you've been dying for (I'm sure): is Common Core focused on algorithms or story problems? It is balanced between both, just as is should be.

For example, in the fifth grade math core, it says, "Fluently multiply multi-digit whole numbers using the standard algorithm." In this case, fluently means reasonably quickly. To do that, the kids need to have their times tables memorized, and they need to know how to use the standard algorithm.

However, there is also a lot of emphasis on helping kids conceptually understand multiplication by making models, using different strategies, and connecting it to real life problems. For example, "Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division" and "Solve word problems involving addition and subtraction of fractions referring to the same whole."

This is probably one of the most controversial parts of Common Core, but it's important. How many of you, as children, forgot the zero when multiplying a 2-digit number? Everyone forgets it occasionally, but some kids do it. Every. Single. Time. Why do they forget it? Because they don't understand why they're putting it there. It has no meaning. This memory of "Put a zero there" has no connections to other neurons, so the brain drops it. However, when a kid understands that they are putting the zero there because they are actually multiplying by a ten, then they are far more likely to remember it.

One of my teammates said it perfectly today. A number by itself is meaningless. It has no meaning until you put it into a real context. I've seen a picture floating around of a dad who was irate because his daughter wasn't allowed to just had to add 4 + 7: she had to model it. (I tried to find this again so I could double check my facts, but had no luck. If I didn't get it exactly right, my apologies.) His daughter already knew the fact: why should she have to show this other way. I can understand the dad's perspective, but really: what is the point of being able to add 4 + 7 unless 4 and 7 are real things?

Understanding multiplication from multiple perspectives prepares kids to actually be able to apply multiplication in real life. I don't know about you, but when I face real life math problems, the fabric, bottles of oil, or dollar bills don't whisper to me, "First you need to times this then divide that." If you understand that multiplication is groups, arrays, and sometimes cutting wholes into smaller parts, you will know when you need to multiply in real life.

Is it sometimes hard to do math in this way? Yes! Why are we shying away from that? It's good for kids to learn that they can do hard things. It helps them develop self confidence and resilience for the future. Is it sometimes hard for the parents too? Yes! Again, our generation didn't understand math very well, so it's going to be hard for us too. Does that mean we should teach our children the same crummy way we were taught, so that we feel comfortable? That doesn't sound like a very good plan to me.

Research supports this balanced approach, and the vast majority of teachers will back that perspective up if you ask them. Yes, kids have to know their times tables and algorithms. If they don't, they can't do the complex problems expected of them in upper grades in any sort of reasonable time frame (and watching them count on their fingers in sixth grade makes my eyes twitch). However, if they don't understand why they're doing the steps of algorithm, they make dozens of insane, incomprehensible mistakes. Balanced math is the way to go.