Counting Collections

One of the (very few) benefits of not exactly knowing what I am going to teach Monday morning (ahem, don't judge) is that when a blog post about exactly the content we are working on comes my way, I have no qualms about using it.  

Ok, really, stop judging me.  I brought home my Investigations book, ready to dig in to whatever lesson my team said we were going to do.  It was about even and odd numbers and making groups of 2s, 5s and 10s.  We were working on it last week, too.  So I had some idea of what we were going to do.  I also knew that Kristin's (@mathminds) 2nd grade teachers were working on the same thing, because yes, I shamelessly stalk her on Twitter.  So when I saw a blog post that she was planning some 2nd grade content, I knew I was in for a treat.

The lesson she was planning was about counting collections of objects which I find students just love to do.  (I'll admit, I also love to organize and count the coins in my piggy bank!). You can find her prep for the lesson here https://mathmindsblog.wordpress.com/2015/12/06/planning-k-5-literally/ and her reflection after the lesson here https://mathmindsblog.wordpress.com/2015/12/08/2nd-grade-even-and-odd/.  In all honesty I haven't read her reflection post yet since I wanted to get my ideas down first.

So, Monday morning I get my collections of items and find pairs for my students based on ability.  I don't often do this, but today wanted my students to work with a math peer rather than just someone with whom they feel comfortable.  I didn't give too much direction to my students, just that they needed to tell how many of the item they have.  I did tell them that they were going to be required to share their ideas on Seesaw so the expectation was that they could take a picture of something.

I set them to work.  One of my favorite parts of a super engaging lesson is that immediately students find a private corner of the room and the noise level is at a relative minimum.  Students are engaged with what they are doing and therefore not distracted by whatever else typically distracts them.  There is something special about Monday morning and just taking a moment to realize that students love math.  I even have students writing poems about math! But I digress.

Walking around the room, I saw a variety of different strategies.  This partnership decided to organize by color.  When they finished, they had a fairly nice looking array, but when I asked how many tiles they had, they didn't know.  They eventually decided to do the second picture below.  Still organized by color, but at least now in groups of 10.  

Another partnership chose to organize by color also, but immediately knew that they were going to put them into groups of 10. This partnership was of two students who rarely feel confident in math.  I wanted them to productively struggle together.  Well, from what I could see, they were just productive, without the struggle! This was great for this particular team because they needed some confidence.  Here they are organizing and getting ready to group by 10s.  Even the fact that they had their sticks organized into arrays, but not yet by 10s, as you can see in this photo, is total progress.

I also of course had students who decided to group by 5s or 10s immediately, and some even organized the groups into arrays. 

The group with the pennies knew to put them into groups of 10, but then realized that they had so many groups that it was going to be hard to count all of them and not lose track of which ones were already counted.  They ended up using Seesaw to help.  Talk about perseverance! 

As an extension for many students, I asked them to count their items in a different way.  Everyone had a less efficient way and told me so, meaning the first way they did it was most efficient.  Gets me thinking-did I actually ask them an extension? 

After everyone finished, we made a list of the different ways that students decided to organize and count.  The students who organized first by color realized that it was not the most efficient way, and we agreed that groups of 10 was usually the most efficient grouping.

I then gave them a totally different bag of items and asked them to make 2 equal teams.  Was it possible?  When I asked the question, I got an immediate "huh" from many of them, and reminded them of SMP 1-make sense of the question and persevere in solving it.  Off they went and again I had a variety of strategies.  My favorite is that my partnership of low confidence math students immediately knew what to do.  One student called me over (for help, I incorrectly assumed!) to show me that they were finished.  I saw 2 groups of 16 pencils.  Based on their explanation from Seesaw, it sounds like they counted by 10s and put 10 into each group, then by 1s, and put 6 in each group.  For these two students, this is a total success to be celebrated! (They even took a video of their work to explain it!)

For other students, this work was not as intuitive.  I had several groups who still didn't understand what I was asking them to do.  Relating it to soccer, they knew their two groups were not the same, and therefore the teams were not equal. Some groups had trouble figuring out how to make them equal once they figured out what the problem was asking. 

One group knew they had 71 items (I'm not sure how they figured it out), but then were trying to separate their items into two groups.  When I pushed their thinking into even and odd numbers, they were able to realize that it was an odd number, and just like with the number 5, they would not be able to decompose the number into even groups.  (Sounds like a great opportunity for A/S/N!). 

I had another student who approximated 2 equal groups, then counted each and moved some of his items from one group to the other to make them even.  Turns out he had an odd number.

I also had a group (the same one with the colorful array above) who had no idea where to start, according to my TA.  I did not have a chance to work with these two, but my amazing TA alerted me to the need to check in further with them.

All this great thinking and problem solving is happening, but of course it's time for recess.  I ring the chime to clean up and hear an immediate "awwww" because they want to keep working.  That truly is music to my ears at 8:30 Monday morning!

I may not have had my lesson planned days in advance like my coworkers, but I walked quickly back to my classroom to get started after our Monday morning assembly while I saw some slowly moving feet from others.  My enthusiasm is certainly contagious to my students.

Content Standards addressed:

CCSS.MATH.CONTENT.2.OA.C.3
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

CCSS.MATH.CONTENT.2.NBT.A.1
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. 

CCSS.MATH.CONTENT.2.NBT.A.2
Count within 1000; skip-count by 5s, 10s, and 100s.

*****I'm seeing ways to extend this lesson to even more content standards!

And just as importantly, the SMPs utilized:

Standard 1: Make Sense of Problems and Persevere in Solving Them

Standard 3: Construct Viable Arguments and Critique the Reasoning of Others

Standard 5: Use Appropriate Tools Strategically
Standard 6: Attend to Precision
Standard 7: Look for and Make Use of Structure

Takeaways:

-I am long winded.  Boy can I write! Cheers to anyone still reading!

-So important to engage with other teachers at your grade level.

-Seesaw is amazing to document student work.

-I do a lot of reflecting after lessons, I want students to do that, too.  Seesaw or their math journals are a good medium for this.  I wish I had more math time! 

-I need to be better at looking at all this wonderful data (yeah it's data, even though it's not a paper/pencil test) and deciding next steps.

-Kristin has amazing ideas.

-I need to plan more in advance to anticipate student answers and misconceptions.

-Most students have mastered efficient ways to count.  Next time I work on this with students who only looked at color, I would probably give them a set of items with only one color to see what happens.

-Giving students a context for a new task I am giving them is helpful (2 teams like in soccer)

-Not a new idea, but low entry, high ceiling tasks are the best! Naturally differentiate without having to plan different lessons for different students and keep track of it all!

-I just realized the standard only requires students to determine odd or even of up to 20 items.  All students were working with bigger numbers.  Did I push their thinking or did I go out of my lane?! Maybe it's a standard we are ready to move on from?

Im open to any and all feedback, I'm certainly here trying to grow and learn.

And I'm doing this on my iPad, so the formatting may not be nice and fancy.

Student Made Anchor Charts

For the first time ever in my teaching career, students made their own anchor chart.

It felt like a big deal.  My students felt like it was a big deal.  I could tell because of the feeling of anticipation over who was going to be chosen to write and what color marker each student was going to choose.  (We don't use markers often, and especially not Ms. Talia's special smelly markers!)

We've been working hard on Number Talks with addition strategies for the last several weeks and it's time for us to head in a different direction with Number Talks.  But I wanted some closure to what we've been working on.  And during conferences last week, many parents mentioned that they wanted to know more specifically what strategies we are working on.  And of course Graham planted the idea of  student created anchor charts in my brain.  So it all came together today.

As students walked in the door, I gave them an entrance slip.  Solve the problem 27 + 8.  Solve it in one or two of the most efficient ways that you know how.  As students talked to their Turn and Talk partner about their strategy, I quickly went through the entrance slips to see which students were ready to showcase their strategy to the whole class (and now the whole world, thanks to Twitter!).

I found 4 learners to help share their strategy: the one for whom learning in general is hard, the one who has been unmotivated to learn lately, the one who is just this year beginning to learn English, and the one who floors me everyday with her math thinking.  

I didn't plan this.  I didn't plan those particular four students.  But those four friends showed that they were ready to have their learning be permanent and shared with others.  

Before I called each student up one by one, I asked the other students what they should be doing while waiting for a friend to share their strategy.  "Watch and try to understand their thinking" was their response, as if  --DUH-that's what we do--.  

And that's just what they did.  They watched students carefully pick their favorite color, carefully write their equations and their thinking, and tried to make sense of what they saw.  They used our hand signal to show they agree or used the same strategy, they shouted out the name of the strategy each student used, and I think they were inspired to be the next ones to make their own anchor chart.  

They will never forget making their own anchor chart.   The first of many to come.

And now I share it with you.  Enjoy!

Planning: Then and Now

In my previous teaching life (you know, like 4 years ago), planning was neat and controlled.  I had a compact list of math standards I had to hit and they were broken down into units.  The Saturday before the next unit was going to start, I brought home my standards and my calendar and starting matching.  Each day was a different standard.  Maybe two days for one standard.  That was the only planning I did.  As long as I knew what standard I needed to hit, I was ready to teach.  

I didn't plan what problems I was going to give students, never-mind actually doing the problems myself.  I didn't plan how I was going to make the math meaningful or relevant.  I didn't plan how I was going to engage learners.  I didn't plan for interventions or extensions.  As long as I knew what standard I needed to hit, I was ready to teach.  It was survival mode, after all. 

It was also satisfying and neat.  I could assure everyone (myself, really) that I was doing what I needed to do.  I was crossing standards off and crossing days off.  With a set routine, students knew the expectations.  I was in total control.  And it sure looked like that when you walked in.  Imagine it--my students sitting neatly in my meeting area.  I was at the front by the small whiteboard with a problem on the board.  Students had their math notebook open, writing down notes and steps.  Student desks were arranged facing the large whiteboard where I wrote down practice problems.  All students following along.  It was total control.

In my current teaching life, I plan week by week with my three other team mates.  We look at what standards we want to hit and what activities we are going to use each day.  Then, I take it a step further.  I look at my week as a whole, rather than day by day.  I think first about what Number Talks I want to do to help students along to the standards that we said we were going to teach.  Then, I think about how I can arrange the activities we said we were going to do in a flexible way rather than by day.  But then, I also think about what other activities we can do so that we are doing more math than just the one standard that's on the list.  We don't have time to cover each standard in isolation.  

So, my math time has become flexible.  There are no assigned desks, no chime to indicate switching to a new station.  Students work on the activity of their choice, wherever works best for that particular activity on that particular day.  Students work on the required tasks and the optional tasks within the time that we have.  We use timers and students are creating a sense of time and becoming more responsible with it.  I pull students to work with me for the time necessary, not just until I ring the chime again.

I don't have to worry about students finishing their "have to" work because I trust them.  And they don't want to lose that trust.  I think they also trust me that I am giving them work to do that is going to help them be better mathematicians. They know that's the goal.  So they do it with an open mind.  They persevere to solve problems.  They use the right tools in the right way.  They explain their thinking and try to make sense of the thinking of others.  They model with mathematics.  They look for and make use of structure.

They are mathematicians!

I'm a little nervous for parent/teacher/student conferences this week because I don't have a math test to show with a percentage grade like they are used to seeing.  But I do have excited mathematicians and flexible thinkers.  I do have math journals and a digital portfolio.  I think it will be enough.

Late Night Reflection

I think back to my second year as a homeroom teacher.  A mere 4 years ago.  I was a different person.

I was seeking out some sort of routine or structure for my math time.  It was the first part of my day and I remember thinking that as long as I could get my kids through to snack, we were going to be able to survive the day.  It was survival mode.

I was living in a small, rural, touristy town on the top of a mountain in the Cloud Forest of Costa Rica.  The school was a tiny, non-profit, sustainable school with very limited resources.  Most students are on scholarship and 95% are English Language Learners.  My classroom was literally surrounded by rain forest.  I would frequently have to stop my lessons to check out the birds or monkeys hanging from the trees outside our windows.  We had a view of the Pacific Ocean from 5,000 feet up.  It felt like you could just jump right off the mountain into the ocean.  I had never ever seen the sun set into the ocean from above.  It was amazing.

But still, I was in survival mode.  I sought out my good friend and principal of our school, Kris, and told her I needed some help structuring math.  Because I thought structure and routine was what I needed.

We ended up with the following plan: Number of the Day routine (thanks to Pinterest, of course!), mini lesson (I do, We do, You do), go back to your desk to practice, some challenge problems with bigger numbers if you finished, and an exit slip before snack.  Well, I thought I had nailed it!

Kids knew what to expect, I knew what to plan for, standards were covered.  It was manageable.

Kris wanted to push me even further as the year went on and I developed Math Mix Up Day when we did something totally different than our routine.   Maybe we did it once a week.

Kris then wanted to push me to think about creating UbD units and that was the first time I thought to use the internet to actually help me create a more cohesive plan.  (Remember, this was rural Costa Rica and I still had a USB internet device that I paid for by the hour!)  It was my first sampling of really seeing what other teachers were doing.  I was hooked. 

I ended up leaving that school after that year and went to a big, international school in Panama, where I currently teach.  One of the main reasons I left was feeling like technology in education was moving at a faster speed than I could keep up with on top of the mountain.  I had to catch up.  My first year in a new country and at a new school was again survival mode.  We had Everyday Math and it felt like a minor miracle to just follow along what the teachers book said to do.  I felt relieved when many of my students already knew what we were talking about thanks to the spiral structure of the program.  The pressure was finally off to actually teach my students math.  (Never mind the fact that most teachers were not teaching it to fidelity and the general consensus was that we didn’t really like the program.  At least there was something.)

About three quarters of the way through my second year at this school, I got an email saying that a math coach from the U.S. was coming down to teach us how to be better math teachers.  Ugh!  From the U.S.?!  We are an international school.  How could someone from the U.S. teach us how to be better math teachers?  I was skeptical. 

But damn, my mind was blown the first moment Graham Fletcher starting talking.  I don’t even remember what he said.  Maybe it was a funny math video.  Maybe it was taking out some math tools and having us do some math.  But damn, my mind was blown.  Those little dendrites grew in a way that I didn’t even know was possible (I didn't even know what dendrites were!).  He taught me how to change my math class right now.  Changes I could put in place tomorrow.  Ways to talk to kids, ways to structure my time, places to find resources, multiple ways to solve problems, Twitter.  He introduced me to it all.  My mind was blown.

Since then, I’ve been on Twitter daily, encountering new ideas daily.  Something I can do with my mathematicians tomorrow.  (Case in point-Clothesline, Estimation Station and Meatball Surgery.) I share with my coworkers, I lead a weekly informal math gathering, I am excited about math daily.

Every once in a while, someone comes into your life and just blows it wide open.  Kris was spot on with what I needed at the time.  But I always knew something was missing about the way I was teaching math, I just didn’t know what it was.  Graham came to my school at exactly the right time and influenced me in exactly the right way.  I have become a better mathematician.  My students have become better mathematicians.  And to quote my 2^nd grader Paulina: “Ms. Talia, I think I get it, my head hurts and it was awesome!”

I still have math first thing in the morning and now it literally propels me through the day.  I haven’t taught a mini lesson in forever!  I do a Number Talk everyday and my students know it's okay to disagree respectfully. We are explicit about the Standards of Mathematical Practice that we are using to become better mathematicians.  We play math games and use tools and explore 3 Act Tasks.  My kids love math.  And I do, too. 

I think back to those 4^th grade students who struggled together with me through long division and decimals.  I wish I could go back and do that year again.  Let Fabian and Cristian and Ashanty know that I made a mistake, and let’s try to learn math together again.  I always keep those students in my heart and know that going forward I still have so many more mathematicians to influence.

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I’ve never blogged before-never thought I was the type to do it.  It requires you to be a bit vulnerable (will anybody actually read this and care?!) and a bit proud (I have something important enough to share with the world!).  Perhaps I am the only one who will read this and I may never write another post. But this, this reflection, I needed to get it out.