Planning Primary Fluency Progressions

Friday, February 24, 2017 / 1 comment
Current status... I'm planning a fluency progressions training for elementary and, damn! There is so much going on in TK and kindergarten (In California we have Transitional Kindergarten - similar to a Pre-K) and it absolutely lays the foundation for fluency! Years ago, when I first took a look at Fosnot's landscapes for learning (addition & subtraction), I thought to myself, "Why can't we just have bullets, left to right, top down?"

I also thought she must be an artist, turns out, she paints.  Who knew?!
Fosnot's landscape is making more sense to me now.  Everything is a big web.  So. Many. Connections.  There is a progression, for sure, but learning can go in different directions.  Looking at it also reminds me of problems we all have when we say that our kids have holes, but we aren't sure what they are.  I find this to be a great tool to use to identify those holes.  (I especially like the app to use as a documentation tool and digital portfolio.)
I'm learning that I'm going to have to spend a significant chunk of my measly hour and half that I have with teachers on these big ideas that really describe what number sense is made of before we can even get to a progression of mental math strategies that support fluency.  I'm hoping that first and maybe even second grade teachers can look to TK and kinder and see those big ideas as a possible intervention when their kids don't show up knowing all that we expect them to.

 I really wish I could spend an entire day with TK and kindergarten teachers!  I remember reading Van de Walle and over and over again he would say how incredibly important the learning is that takes place in kindergarten.  Kindergarten teachers do not teach the basics.  To say that I think is a discredit.  Without these understandings, the rest of us are screwed.

Hopefully all of my math friends are continuing to invite primary teachers to the "math party" not only to teach THEM more math, but to learn FROM them as well.
Now back to work...

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What do you do after notice & wonder?

Monday, January 30, 2017 / Leave a Comment

So, my blog site is more than a little dusty.  My kids began playing sports this year.  I had no idea how my family's lives would change.  I never would have dreamt we would have sports 6  days a week!

I have had so much fun with my first graders over the past few weeks!  Our mathematical goal over the past few weeks was to come to an understanding about the relationship between addition and subtraction.  I remember years ago just giving my kids the publisher's curriculum worksheets that the blank equations where kids just had to plug and chug and telling them what to do and why it made sense.  My poor little kiddos of course copied what I did.  Some were able to do other problems alone "successfully" and others, not so much...
The last few years, I have worked to become much better.  I created tasks for students to work within contexts, to notice that there's something going on with the numbers in the equations, and that it keeps happening over and over again.  We eventually came to a discussion about whether or not we think it would work every time, to use the same three numbers in all the equations.

This year, I began the same way.  Working within a context, allowing students to notice and wonder.  I recorded equations from student representations on chart paper and left them up in the room so each day we can refer back to them.  Leaving the work up, gives me the opportunity to say, "Hey wait, that's weird, we just noticed that yesterday... and the day before, and the day before, and last week..."
Last week we were at a point where we had collected a lot of evidence and I think to do that again would be pointless.
We began our lesson today by focusing on all the posters we had made about the equations we noticed.  I asked students to again, talk about what we noticed.  I told them, that I thought it was time to move from noticing and wondering to proving.  I gave students a few problems within contexts.  (Put together/take apart change unknown worked quite well)  Students focused on coming up with as many equations as they could. (Weeks have gone by where students created their own representations and created equations.  Now we are ready for the grade level math.)  They partner talked with neighbors to see if they were missing any.  Then, we came to consensus over all of the equations.  We did this about three or four times.  Then, we tried it with naked numbers (no context).  Again, our results were as predicted.
My recordings of what the students came up with.

One student finally said, "Okay, we get it..."  Me:"What do you get?"  Student: "This is always going to work.  The numbers are connected."  Me: "Find out what your partner thinks about what he said."  A few students shared that some of the numbers are parts and some are whole.  Me: "So what you're saying is, there is a relationship between these numbers?" Class: "Yes!"  Me: "Let's assume you're right...  How does understanding that relationship help you?  Find out what your partner thinks."  Students pretty much said that it makes it easier.  Some students weren't sure.  So I wrote an equation that is above their grade level standard and out of their comfort zone purposefully.

232 - 17 = 215 (Kids looked relieved after I wrote the answer.)
Then I wrote
232 - 215 = _____  The kids yelled, "17!" in just a couple seconds.
Me: "How were you able to figure that out so quickly?"  The kids described that the first one helped them.
Then I wrote
17 + ____ = 232  Again, students responded 215 with ease.
Then I wrote
215 + ____ = 232 Even more students responded 17 right away.
Me: "Let me ask again a little differently... How can you use what you know about this (pointing to the first equation), as a strategy to help you solve these? Find out what your parter thinks."
Students talked with their partners.  I had them switch and they talked to a different partner.  Sadly, we were already late to recess at this point so I had to let them go.  I would have loved to collect a reflective math journal right at the end of the lesson.  I think that is where we should pick up tomorrow.
What I like about what I did with my kids this year, is that we really sat in the pocket of proving our conjecture before just saying that we accept that this will always work.  We worked collaboratively to prove that this is true, and that we discussed and worked through how we can use this knowledge as a strategy to help us.  I don't think my kids last year really got the "So what?" part of the understanding.

As always, I want to keep working on my questioning, so if you have any tips, please share!

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My Favorite Thing About Math

Sunday, May 29, 2016 / 4 comments
So my "math boss" is leaving. He is moving from California all the way to Idaho!  I won't tell you what a mess I've been the last two weeks since I found out, but I did want to share with you, all of the awesome things my kids had to say about their "favorite thing about math."
I took all of their writing and put it together to make a class book as a thank you to Ryan.

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First Grade Fraction Talks... What?

Wednesday, May 25, 2016 / 20 comments

Since the idea of fraction talks first came through my twitter feed, I was intrigued.  My first thought, was, "Oh, that's so cool for the big kids." My next thought was, "Hmm...  Some of the best learning my first graders have done has happened when I've stolen ideas from upper grades.  I wonder what ideas I can steal here that would benefit my student's mathematical understanding?" My colleague, Allegra once said that teachers are like swimmers, and there are three groups of swimmers.  The first group dives in and explores and pilots new ideas.  The second group watches the first group to make sure they do well and make it to the other side. The third group won't stick a toe in. They say, "No way! Not gonna do it!"  I am totally a swimmer from the first group, so I dove in... and here is what happened.

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First Grade Math Fight... Fractions, Proportional Reasoning, and Algebra, Oh my!

Monday, April 18, 2016 / 18 comments
Okay, so I knew this "Math Fight" was coming. (Thank you, John Stevens)  The standard I was going after was 1.G.3

Although, this is the performance standard (a very simple standard at first glance) that students need to be able to do, my mathematical goal was different. Further down (like about 3 pages later) in the CA math framework, I find this beauty of a mathematical goal: (Mathematical goal meaning - What is it about math you want students to understand?)

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Good vs. Evil: Pedagogy in the Classroom

Sunday, March 27, 2016 / 14 comments
My school district has been piloting math materials for the past two years. Now that the second year is coming to a close, tensions are rising between teachers.  Differences in pedagogy are bubbling to the surface. Amongst other things, it is very apparent that inquiry-based instruction is on one side and direct instruction is on the other.  It's a battle of good versus evil, the Dark Side versus The Rebel Alliance, or is it?

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Discovering Relationships Through Context and Inquiry

Tuesday, March 1, 2016 / 5 comments
This year, the idea that there is a relationship between addition and subtraction was discovered in a Number Talk, a Number String to be more precise.

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Number Talks Wanderings and Dispositions

Sunday, February 14, 2016 / 16 comments
I have come to a place in Number Talks where I feel like some of my students are wandering in circles. We do Number Talks almost every day.  We have spent a great deal of time with dots, double ten frames, triple ten frames, equations, and lately number strings.  Through Number Talks my kids have discovered the identity property, commutative property, associative property and have worked on all of the following mental math strategies:

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Notice Wonder Meets Numberless Word Problem

Saturday, November 21, 2015 / 13 comments
First, let me tell you how much I love Twitter for the #MTBoS.  This connection has allowed me to collaborate with the great, Kristin Gray, all the way in Delaware from California!  That in itself is pretty awesome!

Kristin Gray (A.K.A. @mathminds) recently tweeted that she was going to begin working on planning a first grade lesson and posted a blog a few days ago about 1st Grade Story Problems.

After all of the discussion about the lesson that she was going to do (and a little peer pressure) I decided to scrap my lesson on time for the day and give the lesson a shot.  It was the last day of school before Thanksgiving break anyway. ;)  (I told my student teacher that this was a "Do as I say, not as I do" situation.)

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Thursday, November 12, 2015 / 12 comments

Common core standards have brought with it many new expectations for teachers and students.  Most of the new expectations aren't due to the content standards themselves, but the standards of mathematical practice.

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