Can't wait to start math instruction? Me too!

As a part of my job as elementary math specialist this year, I am teaching a demonstration classroom full of third graders.  I am so excited about what I am going to learn this year!  Yes, I that's right, I said it... I am teaching a demonstration classroom and I AM GOING TO LEARN!  I have spent 4 years studying theory and preaching to teachers about implementing Cognitively Guided Instruction, the Common Core State Standards for Mathematical Practice, and the Purposeful Pedagogy and Discourse Instructional Model.  Now it's time to practice what I'm preaching.  I plan to demonstrate how to make it all work in a school district that uses standards based reporting.  But first, I have to figure it out.

Today was the second day of school.  I have been granted a 90 minute block for math instruction.  Today my plan was to focus on procedures... How do we treat our manipulatives?  How do we use them as tools?  How can we organize them for easy use?  That was my plan.  What transpired, though, was a different story.  I did math... on the second day of school.  Am I crazy?

Here's how it started.  First, I posed a problem to the students: We need to figure out how to move our book boxes off our table and onto the shelves at the same time as taking our math toolkits off the shelves and putting them on our table.  We want to make sure and do this without putting anything on the floor and without having all 24 students up at once.  Innocent enough right? It was.  The kiddos came up with a few possible solutions right away, and we voted on which team's procedure would be the most efficient.  Done 25 minutes down. 

Now that we had the math tools on the tables, I told the kids a story.  "This morning I got here really early... at 6:45a.m.!  I worked and worked and worked to organize your math tools, but I ran out of time.  At 7:15, you all were here and ready to come into the classroom.  So I had to hurry to finish what I was doing."  At this point, I couldn't help it, I let the first math question sneak into our day, "How long did I work on the math tools before you got here?"  Really though, I was working on procedures, the students learned how to give a thumbs up when they had the answer instead of raising their hand.  :)  Carlton was the first to share his strategy, "6:45 is just a quarter from 7:00 and a quarter is 15 minutes.  Then from 7:00 to 7:15 is another 15 minutes, and 15 plus 15 is 30 minutes."  Now the kiddos got to learn the "me too" signal. 

 



So, you see, I really was focused on procedures.  :)  After we had our short elapsed time discussion, I explained to the students that because I had run out of time, I needed their help to open up our fraction squares and circles and remove the stickers so they could be used more easily. 

The kids enjoyed this activity and I did too. They got to "play" with the tools, and I got to facilitate a discussion about how we treat our tools.

After we finished breaking apart the fraction manipulatives, we had to squeeze in a brain break from www.gonoodle.com!  This was definitely a highlight of the day.  But even as I introduced brain breaks, we had to vote on our classroom champ, and I created a tally chart.  Which turned into a quick number talk.  How many more votes did Flappy Tuckler get than McPufferson? See I really just can't help myself. 

After a quick "Happy" dance and a calming stretch we moved on to the real problem of the day.  I had passed out place value blocks, but after I had counted out all the hundreds of unit cubes, I didn't have enough time or energy to count out the tens rods and make sure each team had the same amount so I just grabbed a pile and put some in each tray.  Now, in my classroom there are four table teams, and two math toolkits per table.  I could smell a number talk/collection counting activity coming and like a preditor hunting it's prey, I pounced on the opportunity to dig into some student thinking. 

 

The kids were in complete agreement that things must be fair, and therefore we must count the tens rods, and determine how many, if any, needed to be redistributed so that each table team would have the same amount.  So it began, they counted and I observed. They added and I listened.  Then we "fishbowled" and the class counted together as Marissa moved the rods on her desk.  Then again, the class counted as Henry moved the rods on his desk.  This is what I observed. 

 

Henry's blocks

Marissa's blocks



As the class counted, Marissa moved the blocks and grouped them into tens. Two groups of ten and 6 more. 

Henry, on the other hand, grouped off the first set of ten, and then grouped all the rest together. 

What does it mean?  I don't know.  Is it significant?  I think maybe.  Am I overanalyzing?  Likely.  

Oh well, moving on.  After counting the number of tens rods in each tray I recorded that information on the board, and what do do you think I did next? A number talk of course! 

A little bit of mental math, some strategy sharing, and some answer defending and in no time at all we had totals per team... 51, 50, 48 and 62 tens rods. 

I love strategy sharing.  I am always amazed at how they think about numbers.   

So that was it.  I ran out of time.  I wanted to keep going, but the kiddos were obviously over it.  It's the second day of school and I got in as much as I could without going overboard.  Crazy? Maybe.  But do you blame me?  I hope not.  

*Children's names have been changed.



Common Core or Common Sense?



As I was trolling my facebook page one evening this week, I happened upon a post by one of the second grade teachers that I work with in my district.  She was expressing her frustrations with all the negativity surrounding the Common Core and gave a fabulous example of something that happened in her classroom which she attributes to the Common Core.  I just had to share:

I have read so much negativity about common core lately that it makes me want to invite all the Negative Nancy's to my classroom to see it in action. In my opinion, and it's only my opinion, common core would have gotten a better following if they had named it Common Sense standards...because that's what it really is. Common sense! The following is an example of Common Sense in my classroom.  

CCSS 2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 

From the beginning of the year, my class sat on the floor in a rectangular array. They had no idea that was what it is called. I say "class, class please go sit four on the floor." The students move to the floor and sit four students across and five students back....20 students. We did this all year with no problems. Recently, we got another student. This happened right about the time we started learning about arrays. The students started complaining that it just didn't work out to sit four on the floor anymore. They always had an odd man out. So, I told them to see if they could come up with a way to fix our problem. And they turned to each other and communicated, they discussed, they planned, and they reported their ideas all while I sat there and watched and listened in amazement. They used the "smart part" of their brains and came up with two solutions 3+3+3+3+3+3+3=21 or 7x3 and 7+7+7=21 or 3x7. They also discussed which array would fit best on our carpet space. See Common Core really is Common Sense!

I just wish my teachers would have taught Common Core... I mean Common Sense standards, I might have enjoyed school a whole lot more.

The Common Core State Standards do not mandate HOW this teacher must teach in her classroom.  They do not require that her students use specific strategies to solve problems (until the expectation of the standard algorithms which come in the intermediate grades).  They do, however, expect that she develops innovative thinkers and problem solvers who don't have to rely on a given procedure to find the solution to a problem.  Kudos Amy Barnett for embracing the Common Core and preparing your students for tomorrow!

A Letter to Frustrated Parents of Common Core Math Students

Dear frustrated parents of Common Core math students,

Think back to your math education, did you learn the steps required to add numbers? To subtract numbers? Did you learn another set of steps for how to add and subtract fractions?  How about a procedure for how to add and subtract negative numbers?  Were each one of those procedures different and specific to the "type" of number you were adding or subtracting?  What about as you got older?  More procedures?  Were you successful?  If so, you likely had a great capacity for memorization.  The ability to memorize multiple steps and multiple procedures and know when to apply each of those procedures.  What happened when you forgot just one step?  The procedure failed to produce the correct answer.  Were you ever frustrated because you couldn't figure out why it didn't work? No? How about your classmates? Any of them ever confused? Don't know? Try this, survey one hundred adults.  Ask them, were you good at math in school? Did you love math? Did it make sense?  I guarantee the majority will have a negative response. Our generation is full of math haters.  Think about it, you would never hear someone say, I'm just not a literacy person, reading was always hard for me.  On the contrary, I'm just not a math person, it never made sense... that's common place, socially acceptable.  I was never taught to make sense of numbers, I was taught one way to solve every problem, every problem had ONE way, memorize these steps and you will be able to solve this problem.  Sorry if you can't remember the steps.  This is how we do it.  I was robbed.  I was not taught to persevere and try to make sense of the problem... who cares what it means, here's how you do it, just do this.  

Hold on, why am I crossing out this number and changing that one? 

Because you don't have enough to take away.  Just do it!  

But wait, I have 453 and I'm just trying to take away 17 I think there is more than enough to take away.  

No you can't take 7 away from 3... Just cross out the 5. Just do it!

But wouldn't 3 take away 7 be negative...

NO! You can't take a bigger number from a smaller number, sit down, JUST DO IT MY WAY!

Hold on, why do I have to have common denominators? 

Because you can't add apples and oranges! Just do it!  

But... but... If I add 2 apples to 3 oranges I get 5 fruit... 

Stop being sarcastic! Sit down, find common denominators... JUST DO IT!  

I was wondering... why do I have to flip the fraction upside down if I'm dividing? 

It's not your place to reason why, just invert and multiply!  JUST DO IT!

Don't get me wrong, like some of you, I had a high capacity for memorization.  I just did it, I memorized and memorized and very rarely made mistakes.  I graduated in the top 3% of my almost 400 member class and I went on to high levels of math in college and was quite successful.  Now, I'm a math specialist.  It's what I do.  I have spent four years studying and researching math instructional methodologies. Nothing but math every day for 4 years. Do you know what I've discovered?  I didn't have any conceptual understanding of math. That made me angry. I have learned more about numbers and how they work in the last four years than I learned  in my 19 years in public and post-secondary education.  I have also learned how to help young students make sense of numbers, using their own innate understandings, their own built in mathematical ability.  I have learned how to start with what they know, and what they understand and refine that into efficient strategies.  In addition, I have also learned that it takes time.  I must first allow them to be creative with numbers before I push my own ideas of how they "must" solve a problem.  If I have patience and let them make sense of it, they will adopt the most efficient method, and they will become successful in math, not only knowing how to do it the way we learned it, but why that way works and when it's the best strategy. 

The "new" methods you're seeing are not being taught.  They are methods that students naturally invent.  Just the way that mathematicians invented them before our formal mathematics system existed.  Believe it or not, simplicity and efficiency are at the forefront of our classroom discussions EVERY day. We are guiding students through their own sense making methods not only to understand numbers and operations but to find the most efficient methods for each problem.  

I understand your frustration.  I was frustrated at first too. Remember, this is not the way I learned it either.  Please be patient. Please reach out to your school's math leaders to help you understand. Please don't rob your child of the opportunity to make sense of math.  We are trying to develop math lovers, problem solvers, and creative thinkers.  How can that be wrong? 

Sincerely, 

Lover of math and children