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.

Delicious lentils!

I have been feeling like I am eating too much meat lately.  It is very easy to have a meal that is tasty that is high in protein and fat-- things I want to make sure I and my daughter are eating enough of.  But I have realized that I don't like the way I feel when I eat too much meat.  It is hard to explain what I mean.  In any case, I have been looking into what i can do to have more vegetarian meals that are tasty and chock-full-of protein and healthy fats.  Lentils are my preferred protein source at the moment.    

I made a really delicious lentil dish last night.  Well, it was a dish that took about 4 days to make but that was only because I can't make enough time these days to make an entire meal all in one shot.  I can do some prep on this day, some prep on another day, etc.  

It is very easy: sauteed roasted red peppers (this was roasted a while ago) with tomatoes and minced garlic.  Separately sautee chopped onions.  Toss all into a crockpot with lots of lentils, water, and two tablespoons of miso soup paste.  

YUM!  

The miso was added because we couldn't find broth.  But now I think miso is a better accompaniment here because it adds the umami I want in my bean stews.  It worked really well with the garlic and tomatoes.  

I can't include a picture because the look isn't as appealing as the taste.  I think cooking lentils in the crockpot always makes it look like a brown mess.  I can't figure out a different "look"-- and as a Chinese descendent, look matters almost as much as taste and texture in my foods.  I am going to have to figure this one out before I can serve it to others (beyond J and j).  

    

Awe

This is a pretty cool video about how going into space affects astronauts: http://www.upworthy.com/some-strange-things-are-happening-to-astronauts-returning-to-earth?g=2&c=ufb2

It is pretty profound to hear these astronauts, from early in the space exploration age to fairly contemporary astronauts, talk about how awesome (and in the traditional sense of that word) it is to be able to look at the planet.  I particularly like the commentary from the astronauts more than the comments from the philosopher, but that is mostly because I know I am somewhat prejudiced.    


The thing that struck me is that, even in our "advanced" age, astronauts can still be blow away by something.  In the current day, we see images of the Earth and other planets from space on a fairly regular basis.  And yet, the astronauts STILL are struck in a very deep way by what they see when they go out into space.  One of the astronauts described it with the terms awe and awesome, and pointed out that she had a deeper understanding of those words now.  

So I can imagine that one day space travel will be common place, like flying on a plane is fairly common place.  Then looking onto the planet and the stars and the sun will be lovely and fascinating but may not be as awe-inspiring as it currently is.  This initially made me a little sad.  

But, it is a nice thing that human beings are limited in what we can know/do/etc.   No matter how much we "advance" and learn, there is still always going to be something we have no clue about.  So there is aways the possibility for awe.

Career Potential

World, I would like you to consider offering alternate career options for my daughter.  While being a "Pretty Princess" is certainly a possibility, have you also thought about other options like "Industrious Dictator" or "All Powerful Generalissimo" or "Imperial Monarch"?  I think she is developing qualities that might, with the right kind of training, just fit the bill for those other job positions.  For example, she is getting quite good at yelling out orders (e.g., "NO MOMMY!") and falling into fits of full-body rages.  Just a thought.

Old Themes Revisited

Last night, I had a tense dream/borderline nightmare I hadn’t had in a long while.  The basic theme is that I am teaching and the class is slowly unraveling.  I am unable to manage the class and no one is paying attention to the thing I want them to do.  Instead, students just want to socialize.  Usually, this is part of a series of dreams I have right before I start teaching a new semester/course/year/etc.  (Yes, I think I am a little nervous about my next job)

In last night’s version, I was to train new science teachers.  The cohort I was to work with were 50 (yes, FIFTY!) new teachers who looked so young, they seemed like they had only just hit puberty.  They also acted like it.  I remarked to my boss in my dream, “How old are these folks?  They look really young.  Are they really allowed to teach?” And “I don’t know how I am to get collaborations and deep conversations going with that many folks.”

Needless to say, the classroom management issue here was trying to get these FIFTY young folks to focus on the hard task of understanding what it means to teach science, when, really, all they wanted to do was to socialize.  In dreams like this, my approach is to just soldier on with the task I had planned and hope that they will come around to doing it.  I usually wake up before it is done but never at a point where things have turned around or is going well.  Hardly anyone ever comes around in these dreams.  I am thinking that in real life this is probably not the best approach- the students and the teacher living in non-intersecting worlds in the same classroom.  Maybe in cases like this, I might want to have a conversation with the students about the problems I am seeing (and possibly problems they see) and how we as a community of folks can come together to figure out how to get out of these problems.  I wonder if I will be aware enough in the next time I have this dream to do this.  It would be nice to figure out how to "fix" this dream.      

Now I am waiting for the other dream I often have when I am about to teach- the one that involves the never-ending wad of gum.  I cannot even begin to think of how I would get out of that one.    

Update: lots of happenings

In the last few weeks, lots of things have occurred that bare commenting.  One of the things I am continually surprised by is the amount a human being (namely me and my husband) can handle at any one point in time.

J was organizing a conference with three other colleagues in his field (field of Visual Practitioners: http://ifvpcommunity.ning.com/).  They were not fortunate to have an organizing structure/organization that helped them deal with the logistics, as I had when I helped organize a conference last year.  So not only did they have to plan out the content of the conference, they also had to deal with how to manage people signing up for workshops, negotiating with the hotels for space, finding workshop space in places outside of the hotel, etc, etc, etc.  After seeing J help deal with all those things, include trying to find and coordinate keynote speakers, I really appreciated the American Association of Physics Teachers for helping us last year with all the logistics stuff so all we had to do was deal with the content and keynote speakers.

Ok, so while J was doing that, I was in the last CRAZY bits of finishing our curriculum, putting together the teacher materials for the curriculum, and planning the week-long professional development workshop that was to take place THE NEXT WEEK IN MICHIGAN (just outside of Detroit).  So this is a Mon-Friday, 8 AM-4 PM workshop for high school teachers who are interested in using our curriculum.

And while that was happening, we were also trying to pack up our apartment so we could move to our new apartment.

So this is how the last two weeks played out: 1) J's conference goes from Tuesday to Friday.  A friend also crashes at our place for the conference, which at this point is slowly filling up with cardboard boxes and dismantled furniture.  I am also the main child care person at this point in time.  2) We celebrate little J's birthday on Saturday with dimsum and a break in our packing.  3) Sunday, we finish packing as the movers come to move our stuff out to our new apartment. 4) Sunday late afternoon, my boss comes to pick me up from our new place to drive me to Michigan.  5) My PD workshop starts Monday at 8 AM (we get to the place at 7 AM to quickly set up).  6) while I am in Michigan, J finishes our move, cleans the old apartment and starts the process of resettling in our new place.  J is also the main child care person at this point in time.  One night, he is at the old place until 1:35 AM cleaning.  Little J, thankfully, slept through it on the floor on top of a quilt.

When I got back on Friday night, J and I spent Saturday and Sunday unpacking and cleaning our new place.  We decided to take a break on Monday with a brunch and a nap while little J was at daycare.

I am surprised that 1) J and I are still standing, still going and 2) we have had less fighting and tearing into each other than I had expected.  It is pretty remarkable what a human being can take on.  I think it helps that we (J and I) have been pretty good at communicating and appreciating what the other person is doing...and also forgiving each other for mistake and mishaps.  I think we are getting better at doing this (life?) as partners. 

To be honest, these last couple of years have showed me just how much one can take on and still keep going.  Also that if you have to do it with someone, it really helps if you can figure out how to do it together rather than at odds with each other.  Actually, correction, it is much nicer to go through it with someone you have a very good working relationship with if you can.

Major fail.

When one wakes up to a dream where one has killed one's child, that is starting the day off with a MAJOR fail. It is a terrible terrible way to wake up. Thank goodness we co-sleep. I was able to check in on her (lots through the night) to make sure she was still ok.

Sigh. Lately I've been feeling like a failure, both as a mom, a productive worker, as...well as just about everything (though can say I have most of my basic biological functions down...well except for sleep).

Sigh.

Ok, enough griping. Hoping to get through this week reasonably. Just one more day then the weekend.