Some people love Common Core. Some people hate Common Core. When one digs deeper, I often find that the Common Core people haven’t done a good enough job of differentiating between what is Common Core (standards), what is curriculum, and what is good implementation of either the standards and/or the curriculum.
I personally like the Common Core standards. I have concerns about how they were created and who profited from them. I have concerns about how less-capable students will perform with the standards. I think most of the curriculum I’ve seen for Common Core is the same curriculum that I saw before Common Core (which was shallow then and remains shallow), but now has a Common Core seal on the front of the book. I think the language arts standards exclude an awful lot of reading response theory, which is as valid a purpose for reading (in my opinion) as is reading for information.
Regardless of what I think about Common Core, though, they are the set of standards that currently rule public education in this country. And as an educator, it is important for me to stay abreast of what’s happening. So, it was with great interest that I listened to this NPR report on how teachers were preparing to teach Common Core this year.
One of the resources discussed in this report was EngageNY‘s publicly-available units that have been specifically aligned to develop thought in mathematics and language arts.
As I’ve previously mentioned, I’ve somewhat given up on language arts instruction with L (the exception to this is spelling, which I’ll highlight in another post soon!). She reads so widely and comprehends what she reads, she responds to what she reads (not often in prolonged writing, but that seems to be a fine-motor limitation rather than a thought-based one), and she uses information for both personal and academic purposes.
I am, however, always looking for “good” math materials. I find a lot of what I come across overly shallow, relying on “tricks” or rote memorization. I want L to be able to think mathematically – to abstractly play with numbers, understanding that they are representations and that they can be manipulated in interesting and helpful ways.
It was with this eye that I began reading the EngageNY materials. I read my way through the kindergarten modules and didn’t find anything that we hadn’t already worked on. Part of the way through the first grade materials, however, I happened upon a concept that I knew she was on the verge of – and it used one of the tools that has been widely mocked by opponents of Common Core. Perfect for us to work with!
We started with first grade, module 2, topic A (Solve word problems with three addends, two of which make ten). She’s been working with word problems with two addends, beginning with making ten, extending through making less than ten, and is now pretty fluent with larger numbers, too. I wanted her to begin to think about how numbers work together, rather than picking one number and counting on from that number.
An example of a word problem from this lesson is: “Maria gets some new toys for her birthday. She gets 4 dolls, 7 balls, and 3 games. How many toys did she receive?”
We pulled out our whiteboard and I asked L to draw 4 dolls, 7 balls, and 3 games. Here’s what she produced:
I then asked her to look at the numbers at the top of the whiteboard and think about which two worked together to make a ten. She noticed that 7 and 3 made a ten, so I showed her how to circle them and write the 10 below them. I asked her to use that 10 and the 4 that was left to figure out how many toys Maria received. She quickly figured out that the answer was 14. Fantastic!
We worked a few more problems and L pretty quickly abandoned drawing the pictures. I attempted to get her to make dots, but she didn’t warm to that either. She really just wanted to find the pairs that made 10 and then move on from there. Ok! What can Mommy do about it when L is ready to skip all the scaffolding steps that Mommy had prepared? Go with it, I guess. That’s a life lesson for me. I will continue working on that =)
In any case, I then wanted to formally introduce the language of “number bond” to L. I started with a simple set of number bonds:
I asked her what two numbers could work together to make 4. She noted that 4 and 0; 2 and 2; and 1 and 3 could make 4. I showed her how to use number bonds to represent those relationships. I then created a “blank” set of number bonds to 10 with space for all 6 sets of addends. She talked her way through them while I recorded her work:
We then moved onto a later set of problems from the next lesson from EngageNY. In this one, kids are challenged to find the number bond pair that makes 10, circle it, and add on. L completed these four very quickly. She asked me to cover my eyes and then circled the number pair and wrote the 10 above them, then asked me to look. She was thrilled that she could finish quickly. I was surprised that the final one (where the number pair is separated by the third addend) posed no challenge to her. Speed-wise, it was no different than the other problems. You’ll also note that by this final problem, she felt confident in writing the answer herself. Representing her thoughts in writing continues to be an area for improving her confidence.
I commented to her, “It feels important to you to be able to do math quickly and accurately, huh?” She nodded. Good to know! Hands-on models will work for her only to build conceptual understanding. She’s more interested in demonstrating fluency than showing it visually. I love that if I look underneath what she says and does, I can learn more about how she prefers to learn, what motivates her, and in turn, how to be a better teacher for her. I love that my job gives me the flexibility to do this with her! I am a lucky mommy.