Counting Collections

“…Children need lots of experience with counting to learn which number comes next, how this number sequence is related to the objects in front of them, and how to keep track of which ones have been counted and which still need to be counted (Fuson 1988).”

It makes sense, doesn’t it?

But, funny thing is, we don’t spend nearly the amount of time we need to just letting kids count.  Or, at least I didn’t.

Then I found Counting Collections.  I read it and realize that I hadn’t been doing things exactly right.  I thought about the first few weeks of school – mountains of spirals, rubs of glue sticks, pencils galore – all things begging to be counted.  Luckily, my students have a teacher that takes a LONG TIME to get organized!

So, we started counting.


 
I learned so much about the students by just watching them count.  I listened and watched. And we kept finding things and reasons to count.  I could look at out game tiles and ponder aloud, “I wonder how many tiles are red?”  Or, asking for help for my messy toddler, “I wish I knew how many army men are still in this bag!”

The funny thing was, it never got boring.  Counting was exciting.  Counting is engaging.  We will never run out of things that needed to be counted.

  
But we started finding that in order to keep track of things, we needed to start writing it all down so we could share our collections with other mathematicians in our class.  And so the hunt for efficient counting AND recording strategies was on!

   
 We started finding more and more efficient ways to keep track of our collections.  We started having long conversations about the way our fellow mathematicians were recording large numbers of objects.  Two of our favorites we made big and talked, in length, about why THEY thought these ways were great ways to show how the counted and how many their were.

   
  
Some students can get through 2 collections, counted and recorded.  Some are still exploring with different ways to organize.  

But I’m still watching, and listening, and learning so much about the students in my classroom. 

And finally!  I see the reason why semi-irratic disorganization in a room full of 21 first graders is a GREAT thing… Because it’ll provide us endless opportunities to continue Counting Collections.

Math Talk – thinking subtraction

Subtraction can be tricky.

 

Taking things away from six year olds is never a very popular idea.

 

But Quick Images, those are super fun!

 

So, I wanted to plan a Number Talk that would get us thinking about subtraction – but I wanted to change it up just a little bit from the 10’s frame and Rekenrek.  I wanted to use the most “handy” tool that I had access too – a tool that we all ALWAYS have access too…

 

My hands.

 

I am a huge fan of the Origo “Hands-on” approach where you spend time at the beginning teaching kids the special way of counting with their fingers- starting with the pinky, across both hands, ending at the opposite pinky, palms facing out.  When you are facing someone who is using the method to count, you can group fingers, count on from 5, count up to make a 5 or a 10 – lots of wonderful thinking to be had.

 

So, I just started with one that they could use an addition strategy previously taught to quickly identify the number; I put up a full hand of 5 and my thumb, making six.  After surveying the room, the general thought was that I showed the number 6.  When I asked for how they knew it was six, here are some of the responses that I got…

 

“I counted by 1’s – 1, 2, 3, 4, 5, 6”

“I saw 5 on one hand and I counted on one more – 5, 6”

“There were 5 and 1 more – 5+1 equals 6”

 

From there, I moved on to my second flash of fingers; starting with the pinky, 4 fingers up, thumb down and zero on the second hand – showing 4.  Again,  the group was pretty certain there were only 4, and here is why they thought that…

 

“I counted by 1’s – 1, 2, 3, 4 – and that was all”

“I saw 2 and 2 more, and I know that 2 plus 2 is 4”

And, what I was looking for…

“If you had one more up, it would be 5.  But it was 4.”

 

Inside, I was smiling everywhere, but outside, still, calm face.

 

“Can you tell me more about that?”

 

“Um…yeah.  You have 5 fingers, but 1 is down.  So, there are 4.”

 

So I recorded 5-1=4.  And I asked someone else, someone who I knew was following that line of thinking, and I asked them to repeat what that student had just said.  

 

“If you have 5 fingers, and 1 of your fingers is down, then you have 4 that are still up”

 

So I moved onto my last flash of fingers; 1 full hand up, then 4 fingers up on the second hand, pinky down, showing 9.  This time, they were unable to wait to be called on – “Nine!” was being shouted all over the place.  After checking to see if there was anyone with a different answer, I asked how they got to 9, and here is what I got…

 

“There was 5 on one hand, and I counted on the other fingers – 5, 6, 7, 8, 9.”

“5 and 4 more equals 9.” – so, before recording that, I asked for more information on the 4, and we got to go through again, 5 fingers on a hand, but 1 finger was down, so that left 4 up (YAY!)

 

The room quieted, and I asked, “Did anyone get 9 a different way?”

 

And then 1 brave hand went into the air, and he said, “Well, you have 10 fingers, and all of them were up, except that pinky, so it would be 10 minus 1 equals 9”

 

I saw this face sprinkled across the room…

 

20151115_122854

 

(But older of course!)

 

…and I heard lots of “Oh yeah!  I saw that too!”

 

It took 7 minutes.  And then I could transition to my lesson about data.

 

But I introduced subtraction, the subtraction symbol, and the idea that subtraction can be a whole something, like a hand, spilt into 2 parts, fingers that are up and fingers that are down.

 

Lots of work to still do!  But I’ll mark a win for Number Talks for today!

 

 

 

 

Wonder

I often watch my baby boy experience the world around him as if he was a TV show.  Everything is strange and fascinating and beautiful.

  

…I think he mostly thinks everything is edible.  

But to him, everything is interesting.  Toes, water spills, cheeks; he could study and feel and wonder forever.

This past week I was introduced to “I noticed/I wonder…” By Annie Fetter – and I was incredibly excited to try it.  Six year olds love to ask questions, they wonder about everything!  Harnessing that natural response could be a powerful tool for engaging my students in mathematical conversations.

So, I dove straight in.

I posted a picture.  A simple picture.  

  
Luckily, I had asked a co-teacher to help with the scripting, because they were ready to tell me everything they noticed.  Hands were raised all over the room.  I didn’t need to encourage participation, they were ALL IN.

  
When we moved to the wonders, the conversations became even more natural. A lot of them were wondering where the people were. Were they inside? So, after the wonders were all wondered aloud, we talked about the people.  

If each house had 1 person inside, how many people are there?  How do you know?

If the bottom houses all had 2 people inside except the last one, how many people are  there?  Can you tell me how you counted?

What if some of the house are empty?   Which ones?  

SO.  MUCH.  MATH.

10 minutes.  

I am sure I did not do justice to this awesome process to get kids thinking, but I know it’s something EVERYONE is excited to try again.  It simple, natural, engaging, and fun.  I definitely will be read everything I can on this one.

I wonder what it will look like next time…

So they ARE listening!

I am constantly asking my students for more – asking what they were thinking, asking how they got their answer, asking them to prove to me why their answer is correct.

Sometimes I think that I’m driving them crazy.  Sometimes I feel like a broken record on repeat day after day.

But today, I found out that they are listening to me.

We were gathered on the carpet, journals open, white boards on our laps, and there were pennies everywhere.  We were using story mats to tell stories – I asked a few, and students worked in partners and small groups to solve the story.  I watch and listened (and even snapped a few pictures!) of the work that was happening all around me on the floor.

image image image

Then I turned it over to them – I asked if someone would be willing to share their story with the rest of us.

And to my delight, I had hands shooting up everywhere!  Look at the risk takers!

But the real surprise came on the second story; a little girl began with, “I have 9 pennies in my bag.  My mom gave me 2 more.  How many do I have now?” Students worked through the problem, and again, hands waved wildly to share their results.  She looked around, found a friend, and he answered confidently, “11!”

Then it happened.  She, with a kind and enthusiastic voice, uttered four words that began fireworks in my mind…

“How do you know?”

And without missing a beat, he explained the process he went through to come to 11.

I was stunned.  They had heard me time and time again asking for reasoning, and then, they started challenging one another for proof.  It has become the norm – we are going to hold one another accountable for our thinking.

They were listening.  And it was a Monday.  I’m excited for what’s to come!

The way they learn

I love the Rekenrek.

I love the visual it provides.  I love the way it can be used by kids to make numbers, the sounds the little beads make clanking together – not to mention, clean up is crazy easy!

I was literally bouncing off the walls with excitement, just waiting to share it with the class.  When the day finally came, I think I may have even dressed up for the event, and then…

Crickets.  Literal silence.  I probably looked something like this…

  
With a dress on.

What a sad day!  Why didn’t they love it?  Why wasn’t there unbelievable math happening all over the room?  They loved my Rekenrek last year!

I once was lucky enough to listen to one of my favorite Author’s, Cathy Collins, speak.  She hilariously told a story about how sometimes lessons bomb and it is best to cut your losses and just walk away.  

But that wasn’t me.  I kept at it.

And things just got worse.  

So, that night, I miserably sat down to make a plan for the next day.  The kids didn’t get it, and I knew it wasn’t their fault.  I did all that I could to force my love of the Rekenrek and the learning I wanted, and because of that, I might as well have dismissed the class for the day at 2:00.  Then I started thinking, what days did my KIDS feel successful in math?  What tools did they connect with, what sparked the deepest conversations?

I tried the next day with the same concept, but with a tool the students had been interested and more engaged with – the 10’s frame paddles.  And, of course, we were able to get where I was hoping to get the day before.  The kids were excited, I was relieved, and I think everyone shared a sense of accomplishment about what we were able to do.

I see now, as the old saying goes, “If they aren’t learning the way I teach, maybe I need to start teaching the way they learn.”

And I’ve got time – I bet I get them loving the Rekenrek yet.

So school started…

I wish I would have gotten some photos before 7:15 on day 1!  Before the milk from breakfast was spilt, before the random batches of school supplies started rolling in, and before papers/scissors/markers/broken pencils littered nearly every surface in the room.

But then, all of a sudden, eager eyes (and little, grabby hands) were here!  And something amazing started happening…

We.  Started.  Learning.

Messy, unorganized, loud learning.

Now, maybe unorganized isn’t fair to say after the hours I put in making sure everything was ready.  I wanted math to happen, right away, and I wanted to show my students that math tools were accessible and ready for them.

So, that is the picture I am choosing to share.

My picture is my proof that even though the floor is covered in goldfish, scraps of paper, rocks from the playground, and possibly a few playing cards, before they came I THOUGHT, and THOUGHT HARD about what I wanted them to see.

I wanted them to see ways to make math happen.

And I’ll leave you with a story!

After teaching my first graders the “special” way that we were going to use our fingers to represent numbers, we sang The Ants Go Marching and used our fingers to act the lyrics out.  Six year olds LOVE singing, and acting, and challenges.  So, I gave the this challenge: in partners, use something to help you act out the song.

Most of the class drove straight to what the were the most familiar with – connecting cubes.  A few first graders went for tiles, a small number went for tens frame paddles, no one (heart breaking!) was familiar with the Rekenreks – and one student picked up a deck of cards.

I wandered the room, listening to the sweet singing and discussions that were happening – and I hung around the partner pair using the cards and tens frame.  Partner 1 was very confused, 1 card for 4 ants?  How?  That couldn’t be right!


So I stepped in and asked, “Can you tell me what you are thinking?”

Partner 2 paused, looked at cards, now concerned that they were in fact wrong, and said, “This card has 4 hearts.  That’s a number 4.”
I smiled, thanked the student for their explanation and confirmed that there were four hearts, and they were singing about four ants, so that thinking made sense to me.

Then it got messy – and so exciting!  Students were going for dice, dominoes, even clocks (which unfortunately, I didn’t get a chance to hear the thinking behind), yet still no one brave enough to try a Rekenreks (soon first graders, very soon!) – but my students were wanting to explore the math tools that they saw.  And they could because they were easily located and ready to be used.

Learning is messy.  Six year olds are very messy.

It’s my job to organize what they need to be successful.

I’m good with that.

Let’s talk about SHAPES, Baby!

…literally.

I started my journey this week with the intention to find and read about some new mathematical strategies for my classroom.  Immediately the works “Talking to your Kids about Math” (forgive the absence of a hyperlink – I am still trying to figure this out!) popped off the page.

Ways to help parents talk to their kids about math?  PERFECT!

But in my browsing, possibly because all I have right now is a 2D list of names and I struggling to wrap my hands around what exactly I need to prepare for, my teacher hat slipped off and my momma apron tied snugly around my waist.  The blog had different age groups for mathematical conversations, and, as my biggest little boy will be turning two in just TEN DAYS, I was interested to see what was there for me.

The video focused on talking with daughters about math, but it still made me think, “What conversations do I hold with Miles about mathematical concepts?”

Turns out, this boy is IN LOVE with shapes!  He can find an outline of a circle nearly anywhere, it’s amazing.  He loves pointing out stars and squares, and while oral counting to 3 is still difficult, he sure can identify an octagon!

And then it made me think, I’m a parent and my confidence in speaking to my toddler about math is shaky, and I do this for a living!  What a wonderful resource for me and my fellow parents!

I promise when I have a classroom full of 6 years that the stories revolving around my boys will be fewer… Maybe!  But I feel doubled excited to research all kinds of digital resources, all dressed up with my teacher hat AND mommy apron!  Let’s get started!

Goal!

Goals, goals, goals…

Scary word that is used a lot in our profession.  It carries a heaviness that gives many educators a slightly metallic taste because it can sometimes be accompanied by judgement if certain prescribed benchmarks are not met.

I am going to choose to read that word as if my 2 year old just scored in his first soccer game – maybe he ran down the field, without stumbling, and swung back his leg with absolutely no intended direction, but that ball, backed by all of his energy, hit the net with a sweet, soft, finality.  He did it!  He worked so hard!  GOAL!

That’s what I am choosing to work for, and by viewing them this way, I am excited to get to work.

So, here are my math goals for this upcoming school year…

1. To make math purposefully fun!  I want to see my students approach difficult mathematical concepts with excitement – NO TEARS!  This will take intentional planning on my part, and thoughtful modeling at the beginning so my students understand that we are going to work together, make mistakes together, and develop understanding together as a team.

2. To better document student successes and struggles.  I could listen to a student talk through their thinking for hours, and while I might at that time see why they recorded it the way that they did, 2 days later their scribbles and labels normally look a bit hairy to me.  I need to make sure I’m taking notes, everyday, on what these kids are explaining to me, and keep them organized and together so I will continuously be building a better picture of each young mathematician in my classroom.

Not big, flashy, or by any means ground breaking goals – but the impact it could make inside my classroom is giant!

Not that simply typing those goals means that they will be met.  Just like my sweet boy in his soccer game, there are lots of pretty flowers, shiny rocks, and mud that could trip me up along the way – not to mention, the running skills of a 2 year old, while adorable and entertaining, are still incredibly unsteady.

I can foresee 1 major roadblock, taking multiple shapes and forms, getting directly in my way this year – I AM normally TIRED.  Countless meetings on campus, runny noses that make sleeping difficult for the 2 kids under the age of 2 living in my home, getting behind in any (and possibly all) other content areas… Sometimes you just walk out of the door at the end of the day, shoulders down, hair looking crazy, searching for chips, salsa and happy hour.

… Sometimes those days happen everyday.

But, that’s when I need to remember how Miles, my messy, loud, wild 2 year old boy, would react to making that first score – he’d smile, cheer (for himself of course, he’s just 2 after all!), and he’d run down the field ready for the next one.

We can do this!

… And let’s be honest, happy hour NEVER hurts!

Hello world!

“What was your favorite thing about First Grade?”

Child taps their chin for dramatic effect, then smiles and says…

“Recess!”

Join me on my quest to make math JUST AS EXCITING as touch football, tag, walking imaginary puppies and the monkey bars!