The power of the Common Core Math Standards: a story of one kid’s math fun

 Lil j and I were playing with numbers to make a subway ride more fun.

(Above ground subway ride, M and Lil j.  M and Lil j have been doing a few simple sums and started to do a couple of subtractions)

M: What is 10 minus 5?

Lil j: Huh?

M: Oh, um, what is 10 take away 5?

Lil j: Oh, 5. 

M: Cool.

Lil j: What is 100 take away 5?

M: I don’t know.  What do you think? 

Lil j: I don’t know.

M: (pause) How could we figure it out?

Lil j: Um (pause) Oh, wait, I know.  It is nine tens and a 5.

M: (pauses to think) oh yeah!  That is really, really cool!

And later that night, we relay this story to Big J and Lil j represents her final answer as “Nine tens and a half of 10.”

Ok, so first off, I am super proud of my kid.  She is 5 yrs old and doing this!  Ok, now that is out of the way, the point of this post isn’t really about showing off how cool my kid is nor to say that this is a spectacular example of parenting.  She isn’t particularly talented and gifted (a piece of evidence for this is that she didn’t score particularly high on the G&T exam and I know a kid who is supremely talented in math and my kiddo is not at all like that).  She is more or less your average kid.      

The point of this post is to talk about the Common Core Mathematics Standards.  In NYS, where we live, the NYS Math curriculum is built around the Common Core Math Standards.  Here it says that for Pre-K kids, it says that teachers should be aiming towards helping kids develop the following math ideas during the whole pre-K year (I’ll just highlight the ones I think most relevant to this story):

Operations and Algebraic Thinking

·       Understand addition as adding to, and understand subtraction as taking from.

·       Understand simple patterns.

So, I see Lil j knowing that there is this pattern that 100 is made up of a bunch of tens—in fact ten of those 10s to be exact.  AND that “taking away 5” means to remove 5 from one of those tens.  And that when you remove 5 from one of those 10s, you only have 5 left (or in her second effort, this is half of 10).  Yeah, I’m pretty blown away by all that math that she is doing all by herself and NOT BECAUSE I TOLD HER WHAT TO DO!  This is the kind of math I see adults do all the time with money; a math historian said, this is what is called “Money Math.” 

Awesome, she is developing great skills that will help her deal with her financial life!!!  As an aside, as a daughter of a small business owner, this makes my heart and my Chinese immigrant parents’ hearts sing.  Yeah, she is 5 (ok, the proud parent is saying this but really I think we can help most 5 yr olds to do this kind of thinking). 

Next bit, she is showing to me she is able to do some of the math practices (types of “habits” that math people and people good at math do):

·       Make sense of problems and persevere in solving them.

Example: Lil j didn’t know the answer at first.  I let that slide because I knew that if she couldn’t figure it out now, that is ok.  As her mom, I had the luxury of time to work with her on this.  And right now, my goal was to have fun with her, to let her feel ok with not knowing the answer, and to have her know that this is something we can figure out but sometimes figuring things out might take time.

·       Reason abstractly and quantitatively.

Example: I don’t know about the reasoning abstractly yet.  But I can see that she is able to reason quantitatively.  She can get to the same correct answer for 100 – 5 using two different ways.  Ok, so what is cool is that it is not a way I had originally thought to do so I was delightfully surprised.  What I also don’t know is if she can explain to me why she thinks those are the right answers and if she thinks those answers are the same.  So that is the next step for me to follow-up on to see how she develops with this.  Why is this kind of explaining important for thinking about how to “reason abstractly and quantitatively”?  I think, for me at least, it is mostly because it can help me see how she is thinking.  It may not necessarily help her get better at doing arithmetic just by being able to help me she how she is thinking (though it might because it can help her walk herself through her own thinking).  It will be important to be able to hold her thinking out for other people to see so they can critique her thinking—something she will need to get comfortable with later in life if she is ever to work with other people or wants her own ideas to get better.  The hive mind is so much better than the single mind. 

·       Look for and make use of structure.

Ok, so this is where I think I can see some evidence to show me that she is doing this: She is using the structure of “10 take away 5 is 5” AND she is using the structure of “10, 20, 30, 40….100” are a group of numbers that are just clusters of 10s.  So 100 is a group that has 10 of those tens.  Again, as I said above about money math—she is so ready to be taking on the Benjamins (and the Lincolns and the Hamiltons!).  I’m sure this kind of math thinking is also going to be helpful for other things in life too, but really, for most of us, this is about as basic as it can get in terms of utility of math.    

 

·       Look for and express regularity in repeated reasoning.    

I think I see her doing this too.  For me, the evidence of this is the same as the above bullet point. 

So why did I just make you read through all of this?  I want to thank the Common Core Math Standards (and all the smart people who helped to write it) for helping my kid learn how to do all of that cool math!  Here is how I think it worked out in this situation:

1)      I am a STEM teacher educator and have learned a lot about the Common Core Math Standards.  I now have a tool that helped me see and understand what math growth could look like—one that really helps kids develop strong, powerful tools that will help them in life.  At home, I am learning how to supplement her math learning.

2)      The Common Core Math Standards is what NYS is using to guide its curriculum expectations—meaning this is what they use to guide what they think teachers should focus on in NYS schools.  All of those things are simply guides and how they are used really depends on the district, the schools, and the teachers.  My kid has had the wonderful opportunity of being in a class of a special teacher who created a classroom environment that helped her develop this way of thinking.  She spent at least 8 hours a day, 5 days a week with this wonderful person.  That is a heck of a lot of time to be learning how to be a human being with one person.     

Basically, the Common Core Math Standards created a situation where my kid is surrounded by adults who learned how to value, see, and create learning experiences where she could do this kind of awesome math thinking.  I think the theme I might be trying to promote here is that the Common Core Standards are really helpful IF we can get parents and teachers to align together with them.  And then when that happens, really really cool things can grow. 

     

Ok, the next step would be to figure out how to actually get parents and teachers to work together on this to make the magic happen.  I’m sure there are lots of smart folks out there who can chime in on this.