Surviving a 2/3 combo: Take 1

Tuesday, September 5, 2017 / 4 comments
I feel incredibly guilty admitting this, but this summer I found myself dreading going back to work. I didn't feel the spark that excited me to try new things with my kiddos.  Last year was incredible.  I got to team teach with my best friend on campus who happened to have my son in her class.  It was the greatest gift to get to watch him develop over the course of the year.  As school was approaching, this guilt really began to weigh on me.  I wouldn't want my child to be in a class where the teacher wasn't totally excited to be there! Then, a good friend at my site got an opportunity to be an assistant principal which opened up a spot in a 2/3 combo.  It wasn't really even a question in my mind, I just knew I needed a change and applied for the position. So fast forward to now... I actually have to teach this!
So I come to you today to ask for your expertise.  Language arts, social studies, science... I can make those work in a combo. The math however... that's a different story.  We haven't done much of the math together.  There may be times when we can, and I feel like after I live in these standards for the year, I will be much better at finding and creating tasks that we could do together.
The hardest part for me is that third grade is off and running early with multiplication and division so they can meet those fluency expectations and second grade needs to lay the foundation for that understanding first.

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The Mother of Fluency

Thursday, March 30, 2017 / 5 comments

Teachers all over are beginning to freak out about now.  Winter is coming.  Testing is coming (Note to self: must stop watching Game of Thrones).  I've heard it across the district, kids don't know their facts. They are in fourth and fifth grade and are still using their fingers.  Obviously, the answer to this major speed bump (cough cough) is practice in the shape of a timed test.  What is it about the timed test that will help our students become more fluent?  What does fluent even mean?  Oh yeah, the California math framework spells it out for us.
What jumps out at you?  There's a lot that jumps out at me.  "culminations of progressions of learning, often spanning several grades... conceptual understanding, thoughtful practice, support, reasonably fast and accurate, does not slow down or derail the problem solver... Procedural fluency requires skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.  Developing fluency in each grade may involve a mixture of knowing some answers, knowing some answers from patterns, and knowing some answers through the use of strategies."
So if the standards are telling us that in order to be fluent, kids need to be flexible, accurate, efficient, and appropriate, what the heck does that even mean for our instruction? Not to mention, how does running copies from help us achieve that goal?  How do we teach kids to be fluent?  What are the best practices???  A great question from my good friend Katie: If we don't use timed tests, how do we monitor our students' fluency?  Which lead me to my next question... What are we really monitoring with timed tests anyway?  How is using assessments such as these helping us toward our goal of knowing some answers, using patterns, and using strategies?
In my own humble opinion here, I think what is happening is that teachers don't want to let go of one thing until we have another to hold onto.  A question I have for myself is, how do we help teachers develop enough confidence in better instructional practices that they would be willing to let go of not the old, but really in this case, the harmful?  I have some thoughts... but I am more interested in yours.
So where do we go?  What do we do?  One of the best answers I know of is Number Talks.  We as teachers, cannot afford to say that we don't have time for Number Talks, I don't care what grade you teach.  In my head, I figure you either pay for it in the beginning or the end.  Isn't it usually cheaper in the beginning?
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Planning Primary Fluency Progressions

Friday, February 24, 2017 / 5 comments
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 / 2 comments

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 / 5 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 / 21 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 / 20 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 / 10 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 / 17 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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