A wild idea for the beginning of the year

Last week I went to the Responsive Classroom training. This week I'm at the local Audubon site learning about integrating field work and inquiry into the science standards.

The overlap and connections are exciting.

I'm not going down that rabbit hole right now, however.

It has gotten me thinking about the beginning of school, and that's what I'm here to publicly process. (Because don't all writers need an authentic audience?! Remind me of that come Writers Workshop time.)

For grad credit, we need to create a unit where we are integrating inquiry and field work into one of our science units. We have time during the class to work on it, with the expectation that we will teach the unit in the fall and come back together in November to reflect together.

This all sounds great-the only problem being that we don't actually know which units and standards we are teaching in 4th grade this year in my district. I get that we still have 3 more weeks before school starts, but that's not good enough for me. I'm a slow processor and I like and need the summer to process and plan and just think about what I'm going to do.

And oh yeah, I have this unit I need to create. Today.

So I've been thinking about my Responsive Classroom training and how to structure the first six weeks of school to create a place of belonging, significance and fun for and with students. I read Tracy Zager's post on the Stenhouse website about how to start the school year with math tasks and cultivate a classroom culture of mathematics. And of course this class about inquiry in science: open ended questions, field work, being vulnerable with students to not know all the answers.

And I got to thinking: don't we want to foster a love of learning for all students across content areas? Don't we want them to be good thinkers, questioners, perseverers, etc. across content areas? Aren't the qualities of a good scientist the same as the qualities of a good mathematician and a good social scientist? Don't we need to create a classroom community of inquiry and curiosity? And don't we need to create a classroom community where students feel like they belong, have significance and have fun (a la Responsive Classroom)? So that they can be good mathematicians, scientists, etc. etc. etc.

So why is everything so separate? Why can't I spend the first six weeks (or maybe a little less) creating classroom community and learning the habits and skills of being good learners. Across content areas. Making connections.

So this is what I'm thinking:
(My thinking is in it's very beginning stages)
a week (ish) of focusing on math task(s)
a week (ish) of focusing on science experiments/questions
a week (ish) of focusing on social studies big questions

All the while doing Interactive Modeling on the routines and procedures students need within the classroom context. Reading books and writing reflections. Charting our thinking on what it means to be a great learner based on what mathematicians, scientists and social scientist do. Learning about each other.

Clearly I need to continue to think through this. I don't want to bite off more than I can chew with 4th graders. I need to remember that I don't know my students-they are not the ones I left at the end of last year. I'm considered the "progressive" teacher in my school so these ideas would be very new for students. This would require a lot of planning to make sure that we are still mastering the routines and procedures we need.

I'm running off to my class, and I'm only going back to proofread this for typos-because I hate typos-but not for clarity. My thoughts are messy and I'd love your help and feedback to refine them.

Interactive Modeling a la Responsive Classroom and Problem Solving

I spent last week at a Responsive Classroom training. And it was amazing. If you don't know anything about them, go check them out right now. Really, check them out! They believe in a high quality education for everyone everyday. They give teachers concise, positive, effective strategies to do that.

One of those strategies is called Interactive Modeling. It's not mind blowing. It's basically just the teacher modeling certain things you want students to do correctly. And that there is only one way to do it. It could be things like throwing something away (walk to the trash can, put your hand over the can before you place the trash in there, and walk back) or how to talk to your turn and talk partner (turn your body so you are sitting in front of your partner, be an active listener, and turn back when you are done). This type of modeling is different from other ways since after you model what to do, you ask for feedback from students about what they saw you do. Students have ownership over the procedures so it's not so teacher directed.

At one point while talking about Interactive Modeling, we got into small groups to brainstorms ways that we can use it in an academic setting, rather than just about classroom procedures. Remember, the purpose of this strategy is when there is only one way to do something. Immediately another teacher in my group came up with problem solving in math.

We can teach kids through Interactive Modeling (remember: only one way to do something) how to solve a word problem, suggests one of my group mates.

Yeah, step one, circle the key words, chimes in another.

And this is when I just don't know what to do. Should I speak up and say "wait, there is more than one way to solve word problems!"? It wasn't the point of the activity. We were talking about Interactive Modeling, not problem solving, not math. So I just kept quiet.

Was that the wrong thing to do? Would that have been a perfect opportunity to let others know that key words don't work? That there are other strategies? Get on my soap box about math instruction? Show them about Numberless Word Problems and Notice/Wonder?

Is there a right way to have this type of conversation in this type of context?

I know this will happen again. I just hope to be better prepared next time.

End of Year Math Survey

As the year comes to a close, there are a thousand things I should be doing. Paperwork type stuff. But my brain is otherwise occupied. Today I gave my students a math survey. Inspired by this blog post. And all I want to do is dig in.

As I dusted off my blog here, I noticed that I hadn't written anything since the very beginning of the school year. So I guess it's fitting that I'm here to reflect at the end of the year. Or rather look at student reflections from the year. Or some combination of both, I'm going to guess.

I gave my students 6 questions to answer via Google Forms. I wanted it to be as anonymous as possible. I wanted my students to speak freely and I didn't want to be concerned about who was saying what. The questions are all open response types, because I only have 20 students and I wanted to hear what they wanted to say.

Question #1: What makes you a great mathematician?
I purposefully did not ask if they think they are a good mathematician or not. I know I have a handful of kids that would have answered no (they've said it to my face) and that would have shut down the rest of their thinking. Did this skew the data? Maybe. But I got some amazing answers.

Some I expected:
thinking
using tools
using strategies

And some that really wowed me:
I work even when it's hard
using different ways to show my thinking
to know what the problem is saying to me
the class [mates]
I work hard to try to find the right answer

Nobody said anything about working fast or getting the right answers all the time. It was all about the process.

Question #2: What do you want to do to be a better mathematician?
Better strategies, better tools and understanding the problems were themes. Most kids still want to work more on division. But again it wasn't about working faster. Or getting answers right. It really is about sense making.

Question #3:What has helped you be a great mathematician this year?
This is where I got some real gems.

ms Talia,ms houstin and my self and me making mastaks

doing math with a partner so that we both can share strategy's and do the work together

I am really not sure, but if I must answer this, it would just be time. I just need time to figure it out.

Kids are so smart! They know it's important to make mistakes, work with a partner and just needing time!

the teacher. but the reason why is because we usually do fun activities like the math games the estimating stuff and looking at pictures. That kind of stuff. Except more of it.

I try to be as focus as i can be and so i can stopt chating weth my friend

my flexabilaty with numbers and my great stradagies my teacher tought me

learning strategies.having two teachers to help on math

other new strategy's that other people or Ms. Talia tech me this whole year and that is how I got to be a much more better mathematician.

Notice the shout outs to #estimation180 and #noticewonder there? And what about learning from their classmates?! And strategies, strategies, strategies!

Question #4: What has Ms. Talia done to help you be a better mathematician this year?
My favorite answer:

One or two decent strategies. (maybe three)

Ha! Gotta love the sense of humor!

Question #5: What could Ms. Talia do differently next year?
I got some interesting feedback:

make more posters.

it would be better if you would't talk as much as you do now.

Ok, message received, less talk and more posters. (But goodness, how polite that feedback is!)

And maybe my favorite comment of the day:

still never give up on people

Question #6: Is there anything else you want to share with Ms. Talia about math this year?

i think you should still do those math problems on the board and we or someone that agrees with you they can defend your answer. Oh and when you let us debate about our answers.

I really like the way that you do with the notice and wonder problems and the number talks and the ones from Mr.Flecher

math was fun this year with the games and figuering out the problems.

Ms. Talia has though me to never give-up on a problem that you don't understand always cut the problem in little parts so you could understand it better. to never give up always try. 

That it was the best and funnest math I have ever had at school here!

She is the best teacher for math and every thing else! She is so much fun!

Some more shout outs to #noticewonder, Number Talks and Graham. They value defending their answers and debating about answers. Figuring out challenging problems. Persevering. Having fun in math!

And one friend who thinks that when all her friends know the answer and she doesn't, she feels like they know more than her.

some times al my frinds now the anser and i dont id i fill like tay now mor then me

Takeaways:
First I must be skeptical.
Did they just answer what they thought I wanted to hear?
Did I set them up to mostly give positive feedback?
Did they think someone else  was going to read this (even though I told them it was for me?)

Are mathematical mindsets really changing?

I've worked really hard on the areas students are commenting on, so I guess that means the work is paying off. There are still a thousand things that I want to do better, but if students think they need tools, strategies, partners, and time to be great mathematicians, then I'm going to call it a success.

Now if I really want to dig in further, I'm going to have to give them a survey about the other content areas in which I don't work nearly as hard.

New year, new country, new school, new grade level, new language.

After spending several years teaching in Latin America, I'm back in the United States. In an interesting turn of events, I'm at a two way immersion school so I teach in both English and Spanish, my first time teaching in Spanish even though I taught in Latin America. I'm teaching fourth grade, a grade I haven't taught since my math teaching revolution. So it's essentially like teaching it from scratch again. And I'm also working with the most diverse group of students ever: linguistically, culturally, economically, special educationally (is that a thing?), behaviorally, etc. 

In so many ways, I feel like a first year teacher again.

Except I can say with gratitude and confidence that I am not. I have a whole tool box of strategies, resources and people. 

So when I was given the Eureka Math teacher book and told by the district to "keep up", I knew exactly what to do. 

I have spent the last month since school started looking at my ridiculously long and boring Eureka lessons and figuring out what is the goal of the lesson, going to the standards (can't emphasize this enough!) and figuring out how to make it more meaningful and engaging for my math anxious students.

We started week 1 with number talks using dot images. We worked on the (modified for 4th grade) shepherd problem from Robert Kaplinsky. We have used Which One Doesn't Belong images.  We have used numerous estimation images, mostly from Ryan Dent's K-2 collection, and put our estimates on a clothesline number line. We have noticed and wondered. And we've done this all in English and Spanish!

Mostly we have spent our first month setting the expectation that everyone can do math. That its ok to make mistakes. That math can (and should!) be fun. I even received feedback from my math coach who joined us one day that I had several students engaged and actively participating who last year never said a peep during math. For me, I'm going to count month 1 as a success. 

Note: Month 1 did not include a paper and pencil assessment. That was thoughtful and purposeful. The tone for math has been set.

This year is going to be a challenge in so many ways, but I'm embracing all the pieces of it. 

Mathematical Goals and Geometry and WODB

(Full disclosure: I was totally inspired for this lesson by Tracy Zager [as I often am] and her recent blog post Straight but Wiggled in which she uses this same image.)



Today was one of those math conversations that just got us all pumped up!

To talk about today's lesson, I have to start at yesterday.  Or even several weeks ago, with a conversation with Jamie Duncan about planning with mathematical goals in mind.  She tweeted to me this image yesterday.  

I had this immediate feeling of frustration and disappointment in that day's geometry lesson.  Although students really enjoyed using the different tools available, I felt like we were missing depth to our work.  They made three sided shapes.  Called them a triangle.  Missing depth for sure.  We were missing the mathematical goal.  I knew I wanted and needed to do something different for the next day.  

Missing depth!

Today we started with this Which One Doesn't Belong image:



Usually when I do WODB I ask students to pick an image, go to the matching corner of the room and talk with the other classmates who are there about why it doesn't belong.  Kids liked that, but it didn't allow for any discussion: they are in the same corner for the same reasons, mostly!  Today I decided to keep everyone on the carpet together, and boy am I glad I did!

After displaying this on the SmartBoard, out of the corner of my eye, I saw my most nervous mathematician raise his hand quickly and then put it right down again.  I can imagine his brain thinking "I have some ideas but hellllllll no am I going to share them!".  I've been trying all year to boost his confidence in math in a really authentic way.  He has some big holes in his math understandings, but I want him to feel confident in the things he does know.  Because he knows a lot.  So I went over to whisper and ask his ideas.  I told him I was going to call on him and I did it immediately.  

He shared this idea: "[the top right] doesn't belong because it's black".  But he wanted to go on! "[The bottom right] doesn't belong because it has 5".  Another student chimes in "five what?" and he confidently answers "5 sides".  This is a low floor task and he could enter and stay inside.  He was hooked!

The conversation quickly went to looking at the top left corner.  One student said "[the top left] doesn't belong because the others are fat and this one is thin".  Immediately another student said "I want to add to his ideas".  He added "because of the short lines".  I pushed him to explain how his idea actually relates to his classmates' idea.  This led to another student saying that the lines are different sizes on that top left shape.  

This was the first time anyone had mentioned anything about the size of the sides rather than the amount of them.  This led to some classmates disagreeing and saying that the lines on the pentagon were also different sizes.  This led to more disagreement and we figured out how to find out if they were the same size or not.  We took out the ruler on the SmartBoard, but couldn't manipulate it to measure those top diagonal lines.  So another student mentioned that we could trace each line with the SmartBoard marker and then move it on top of the other lines.  Wow.  Minds were blown.  The sides of the pentagon are in fact the same size!

Energy level was high! Kids are pumped!

But the conversation goes on!

We end up talking about the bottom left shape.  By this time we have lost all form of organization and control.  Some students are sharing out their thinking while others are desperately waving their hands in front of me to be called on!! {Side note: this is a challenging moment for me.  I want students to be able to just free flow with their ideas, but some students are just not into that.  And if we're all free flowing, we can't listen to each other's thinking! And we typically agree to raise our hands to talk.  I just love when a conversation is flowing! I don't want to stop it to call on kids-but I know it's not fair for those kids who are following our agreements!}

We talk next about how the bottom left shape is a diamond.  Rhombus?  Is it a square? What if I turn it a bit? Is it a square now?  What does that do to the other shapes? Does this change their names?

I finally had to end the conversation.  I heard "It's not fair!" and "Awww!".  I love that.  I want to end the conversation right at that sweet spot.  Not once they are bored and disengaged anyway!

This was our final image from our conversation:

Doesn't quite capture the depth nor emotion of the conversation!

Their task for today was to create shapes (triangle, quadrilateral, pentagon and hexagon) with pattern blocks and tangrams.  They had to use at least two shapes to create another.  I was hoping for some creativity!

I discovered that the grand majority of my students (all of them I might venture to say) think that it's only a shape if the angles are convex [my word, not theirs].  I got a lot of shapes like this:

I talked to one student who was just pulling her hair out trying to make a hexagon.  I caught her with the hexagon she currently has here in this photo:

I asked why she couldn't use that one.  She didn't think it was a hexagon!

I talked with another student who had created a shape similar to this:

She called it a hexagon.  See why?  She only counted the four "corners" (as they were taught in first grade) and the two tips of the triangles.  When I asked how many sides it has, she said 10.  

Great conversations.  Great understandings and great misconceptions.

Takeaways: 

-Plan my math lessons with the mathematical goal in mind.  We won't have as many shallow lessons. 

-Use activities like this as pre-assessments and information gathering.  I glean so much more than when using a paper and pencil assessment.  (Need a better way to keep track of what I learn about individual students, for now I just have information about my class in general.) 

-Keep reading other people's blogs.  I always get amazing ideas from them. 

-Keep using and promoting low floor, high ceiling tasks.  They let everyone enjoy the math!

-I need to show the same enthusiasm for read aloud as I do for our math talks.  Those are really falling flat.  Any tips?!

Boy does it feel good to get these ideas out of my very busy brain. 

3 Act Reflections

I just watched Kristin Gray's Ignite about Creating a Culture of Learning and it inspired me to do a little of my own reflecting.  Don't get me wrong-I'm always reflecting.  Stewing, perhaps, would be a better word.  But yeah, let's call if reflecting.  Sometimes I feel the need to do it more productively than just going over and over it in my mind.   So here goes.

Last week we did one of Graham Fletcher's 3 Act Tasks called Downsizing Tomatoes (a task to which I have a special bond via a ketchup bottle).  Basically Graham pours "ketchup" out of a larger bottle into smaller bottles.  The question is, how many bottles can he fill?  We are knee deep in subtraction and we needed to shake something up a little.  Somehow we had found ourselves in a rut and I needed to dig us out! 

We hadn't done a 3 act in a while and I knew the problem was going to be hard.  I planned to give us a couple of days to work on it, but that was probably the extent of the planning that I did.  Routines are pretty solid in my class: we know how to notice and wonder, we know how to estimate, and we know where to find tools.  I knew it'd be challenging, but I was totally confident that we could do it.

Well, results were mixed, as expected.

Firstly, students were really bent out of shape that the liquid inside the bottle was not actually ketchup.  They noticed it was honey, maple syrup or apple juice.  They just couldn't believe that it was water and food coloring.  We decided to call it fake ketchup. They could deal with that. 

I also had a lot of students who noticed that there were 10 small bottles and that really got in the way when they were trying to figure out how many little bottles were filled.  It comes down to many students not knowing what question they were solving.  

This student, for example, really persevered and found out how much ketchup Mr. Fletcher would need to fill up all of the 10 bottles.  Great strategy, nice use of base 10 blocks...not the question we were answering! (We have the information to solve this problem, but considering I wanted us to have the potential for subtraction, this was not the question we were going to use.)

Then we have this students' work.  She was making groups of 64 on the 100s chart.  She seemed to have made sense of the problem and certainly persevered in solving it.  But she has some scribbled out numbers that apparently don't count, and only made it to 300, instead of 397. (Upon revision of her work, she realized her mistake.)



Then we have this friend, who again was solving the wrong problem by focusing on the 10 bottles.  But when he got his answer, he did not put it back into the context of the problem to see if it made sense!  164 bottles?! (And yes, we need to clarify a bit on this repeated addition and multiplication stuff!)



I also had some students who clearly made sense of the problem, but didn't quite know how to use the math to get to the right answer.  



Some students were being very very creative with their tools-good thinking, but I'm not sure our balance scales are accurate enough to solve the problem like this!

Ok, it's not all bad.  I also have this student who revised her work THREE TIMES before she got the right answer.  She was so thrilled to do it! Talk about perseverance!  (Although I'm still not sure what strategy she used for all that addition!)



So after the second day, I felt super frustrated.  I still had a significant group of students who were just not making sense of the problem and determining the right tool to use.  After some conferring with Jamie Duncan I decided that we needed to go back to the basics.  I had a group of students to whom I gave some specific feedback using seesaw (my miracle tool!) who I thought could realize and revise their mistakes on their own.  And another group that needed to see 397 ones blocks in a jar get spilled out, 64 at a time, into smaller jars, replicating exactly what Mr. Fletcher does in the video.  Students put the 64 ones blocks into the cups.  Some students started working with money and realized they needed to do some decomposing! Students counted and recounted.  Students engaged in mathematical discourse.  We even talked about precision when students said a half of a jar was filled, instead of just a little more.  All good stuff!


We finally were able to share Act 3, students felt good about their work (regardless of whether they had the right answer or not), and all of our brains hurt! 


I have some takeaways:
-this group of students needs to make sure that they think about what tools they want to use and how they are going to use them before they even start.  
-students should write down in their notebook what problem they are solving to avoid frustration later!
-some of my students are still very concrete learners.  I need to plan better for this.  
-I need to solve the problem myself.  I know this-unfortunately the time crunch gets in the way (excuses, excuses).

We are going to do act 4 tomorrow.  I found a jar of Chili Sauce in my fridge that I emptied out (I think it was getting moldy anyway!) and will fill with water and food coloring.  I will pour it into a smaller jar, just like Graham does.  I want to see what students will do this time.  Will they go for the same strategy? Will they use a classmates strategy? Will they request the bottle to do the pouring themselves?  Will they learn from their past mistakes?

I'm also debating with bringing a Franks Red Hot bottle also. It's much bigger.  A couple of my students who are more experienced with addition and subtraction might enjoy a tougher challenge.  Or, maybe I just change up the question to have an open middle: {still musing on this question}.

Connections.

It's been a while.

A long while.

As I'm sitting here reflecting on some of the encounters I've had with a couple of students (and one in particular) I think, with whom can I share these thoughts who will actually get it? Relate to it? Care about it?

But really I think it's just about me.  Processing it.

I have a student named "Eleanor".  And she just keeps blowing me away.

Several weeks ago, during a literacy lesson on non-fiction, we were talking about needing to read the text and really stop to think about what we are reading.  I hear her say "we have to make sense of it, like in math".  Like SMP 1: Make sense of problems and persevere in solving them.  That's not just a math skill, and she knew that.

Later in that same hour, she was reading about soil and plants (we are in the midst of a totally integrated unit on plants) and she came to ask me "do all plants need soil?".  I gave her my standard answer-What do you think? After some conversation back and forth, we ended up talking about where soil comes from and decomposition.  So I ask, do you know that word, decomposition? Yes, she exclaims, like in math! <<MIND BLOWN>> Tell me more, I request.  Like in math, when we decompose a number. Yeah... We take the number apart.  She immediate understands organic decomposition, too.

This student was able to make a connection between what we were learning about in math and connect it to something else that she was interested in.  Something she wanted to know more about.

And today when a guest speaker came to talk to us about recycling and where our trash goes and how to help our environment, she knew all about decomposition and soil and the connection to our natural world.  And when I bring in my vermicompost (worm compost) pile to share with my students next week, she will get to see how the food I have placed in there is literally decomposing, being broken apart, just like the numbers in math.

And when she is doing a pre-assessment about subtraction and starts decomposing numbers all over the place and totally confusing herself, she is brave enough to say to me, I'm totally confused and can't figure it out.

And when we skipped our daily number talk today, she called me out! She knows subtraction doesn't make sense to her and she knows number talks help her. She knows what she needs.  And she knows to ask for it.

These are the moments that stick.  With both of us.  These experiences solidify my belief in meaningful education, integrated and connected education, and interest guided education.

I can't wait to see what she comes up with tomorrow.