Inverted Workshop Resources

Good morning, friends!  This week has been so bizarre-o and crazy.  I don't know how it happened, but somehow I've been acting like I'm in college again; staying up until 12:30 or 1:00am and then sleeping late.  It is not my most favorite schedule, but I'm having a very hard time breaking the cycle.

You're probably thinking by now that the only thing I know anything about is math.  That's only part true.  ;)  Before I wrap up this series on the inverted workshop model in case you were interested in learning more about it.  I'll recommend 3 books to you that I've found helpful while implementing this in my own classroom.                                                    
This book is excellent!  What I really like about this book is that it's divided by topic, so if you're looking for a good question to ask about measurement, for example, you can go to the measurement section and then within that section they'll have grade-level band questions AND they even tell you what to look for in student responses.  That was extremely helpful to me when I was first getting started and I wasn't totally sure what to be looking for.  This book is also really user friendly.  It's incredibly simple to just turn to the page you need, type the question up, and use it with your kids.
                                              
This book is much more dense, and I really like it, but I have to be honest--I use this book more in kind of a consultative way.  It's hardly ever the book I turn to first because there's just more information in it and sometimes all you want is an idea for your next math workshop.  =)  But when I do take the time to read an entire chapter at a time I also find this book really useful and generally come away with at least one new idea that I'm ready to try out.
                                                  
This book is super interesting; I actually got it at a math workshop that I attended this summer, so I haven't read the entire thing yet, but it's a really easy read and I find it really interesting.  This book actually focuses more on the Standards for Mathematical Practice (SMP) that come at the beginning of the Common Core and how to implement the SMP in your own classroom.  Even thought it's not directly about the inverted workshop there's a clear connection between the two.  Focusing on the SMP at the beginning of the year can help you implement a strong community of learners that will really embrace the inverted workshop.

That's it for me today, friends.  I am really starting to feel very nervous about back to school!  Here in DC teachers go back on August 19th and kids start on August 26th.  I feel like August 26th is going to be upon me in about 2 seconds I have SO MUCH to do before then, so I'm going to get to it.  Enjoy your day!  I'll be back tomorrow or Friday with some more ideas to share.  =)

Teaching at the End

Hello again, friends!  I almost said good morning, but the clock on my trusty laptop says it's 12:12pm, so I can guess that's not the appropriate greeting anymore.  I'm hoping to get accomplish lots of pesky goals today so I don't feel bad about going to the pool this afternoon.  I mean, it's 80 degrees and 40% humidity right now.  That NEVER happens in the DC summer.  And while I am very happy about the beautiful break in the otherwise oppressive summer it definitely makes it hard to do anything indoors. So let's get right down to it.

The biggest change, for me, with this inverted math model was teaching at the end.  When you do your launch at the beginning of the lesson you're just priming their brains for the job they have that day.  You're not really smacking them with any knowledge until the debrief at the end.  And what's even harder is when they collectively don't really get the idea on day #1 and you have to do the whole thing again the next day, or the day after that.

So as I mentioned earlier, at the beginning of your math block you'll have a 5-7 minute launch (potentially longer if you're teaching older kids) where you're basically reading the task, making sure everyone understands what their job is for that day, and potentially brainstorming some strategies.  You are NOT modeling an example, a similar problem, or showing them how to get started.  That's what they're figuring out with their partner.  Then they're spending all this time working and you debrief at the end.  During the time students are working you're circulating the room, observing and conferring.  I generally won't talk to my kids for the first 3 minutes or so of work time because it gives me a chance to see what they're really thinking and it gives them time to get started, and it breaks most of them out of the habit of using me as a crutch to get started.  Ideally, as you're circulating you're going to find a kid or 2 or 3 who are solving this problem in either a) the way you envisioned, b) a really cool way that you weren't thinking about but does work, or c) a rudimentary way that still works.  When you find a kid on target you want to ask them (or tell them) to share at the end.

Everyone runs their sharing differently, but during math mine basically works like this.  I would bring all the kids back to the carpet, and I will have the work of the kids who will share.  I'll generally praise the class for their hard work, because, really, this is hard work for kids who are only 6 or 7 years old.  Then I tell them that I want to show them what Mathematician X did that day.  I'll put that student's work up on the document camera and then I kind of take a step back and let that kid tell everyone else what he did.  I'll ask a few questions, but basically it's the kid's show at the point.  They get probably 1-2 minutes.  Then, I'm either going to bring up another kid who solved the problem correctly, but differently OR I'm going to jump in to wrap up.  My wrap up is really when I'm hammering that teaching home.  It's a mind-blowing light bulb time for them sometimes and it's so exciting to see their little math brains growing.  Basically, my wrap up is going to be a summary where I'm going to recap the work we saw and I'm going to leave them with a teaching point for future math work, sort of like the Lucy Calkins' writers workshop idea; something like "Today and everyday mathematicians, when you see a two digit number you'll know that that number is made up of tens and ones".  And then we're going to move on to something else in our day.

However, we all know that sometimes our first graders aren't exactly hitting the nail right on the head, and if that's the case then I'll just lead the share at the end.  I'll grab a blank sheet and model (quickly) how I would have done this problem, and model how I would think through the problem out loud.  Then, I'll finish with the same teaching point.  Again, the share, just like the launch is under 10 minutes.  5-7 is your best bet, because they were just working for so long.

It's so great when all these pieces come together and you have this full inverted workshop running in your classroom.  I really feel like students have a much deeper understanding of their math learning.

Evaluating Inverted Workshop Math Products

Greetings, and happy Sunday, friends!  I don't know about you, but I'm really starting to feel the back to school pressure.  Which is why I was so happy when the weatherman predicted a gross Sunday, because it's much easier to convince the hubs that I need to spend a (summer) weekend working on school stuff when the weather is yucky.  And it doesn't hurt that we both shirked all adult-like responsibilities and went to the pool all. day. long yesterday.  It was glorious!  And then we acted like we were both 22 again and went out way too late last night with friends.  Whoopsie!  But all in all it's been a very fun weekend; I even made eggs benedict this morning (first time ever)!  You can start calling me Martha Stewart whenever you're ready.  ;)

Today, I want to talk about evaluating student work/products in an inverted math model, especially since it's much less cut and dry than a typical word problem.  Of course there are still answers that are right and wrong, but there's a lot of information you can learn from your students' work, even if their answer is ultimately incorrect.

Initially, I was using a simple check/check plus/check minus system to evaluate my littles' work during this time, but I really felt like it wasn't really meaningful for them or for me.  And if evaluation isn't driving future/forward progress then what's the point?  So I spent some time brainstorming and trying to think about what I really wanted out of my kids' work, and how I could communicate it to them in a kid friendly way.  I've always liked the idea of rubrics, but conversely also frequently had a hard time using them in a meaningful way in my classroom.  And then I was paging through this unit that I bought from Deana Jump and DeeDee Wills and they had a writing rubric inside that was based on smiley faces, which I thought was really brilliant, and it was sort of like the clouds parted and I had this flash of teacher brilliance:  I could use a similar evaluation system for the math work that I was doing with my kids.  But one thing that was really important to me is that my kids bought into the rubric, also.  So I brainstormed the things that I really wanted to make sure were included in the rubric, and then I sat my kids down on the carpet the next day for math and I told them that we needed to think about what the very best first grade mathematician work looks like, and what it looks like when you're not doing your very best work and this is what we came up with.

After we made this chart, we had an epic dance party because we spent so much time on the carpet making it, then I laminated it and it hung up in our classroom the rest of the year.  The next thing I did that I really think helped my kids have a clear understanding of the work at each level is that we evaluated some anonymous work together as a class.  We went over what different mathematicians produced and I asked them what symbol they would have put on it, and then I showed them what symbol I actually gave it.  We did this for about 2 or 3 days so that they really understood how to get smiley face exclamation point (which, by the end of the year, was one long word in our classroom--smileyfaceexclamationpoint).  I really feel like this rubric helped my students be clearer about the way I was evaluating their work, and it gave us all a common language to use around discussing our mathematical work.  It was great to see kids using the chart with their partners to think about what they needed to add to make their work even better.

For those of you wondering how I tracked the data across units, I'm here for you.  =)  I really tracked this data in 2 ways.  I would create a chart in word of the problems we were doing each week, and all my kids names and then I would just put the symbol they earned in their box.  This allowed me to look across the week and see if there was a student who really understood and should maybe be pushed harder, or if there was a student, or group of students who really didn't seem like they were understanding our content that week.  The other way I tracked it was numerically, in a grade book so that I could use these symbols to factor into my students' math grades at the end of the quarter.  I just used a 4/3/2/1 system, with the 4 being equivalent to the smiley face exclamation point, and the 1 being equivalent to the straight face.  I didn't use 3/2/1/0 because I feel like zeros can really wreck an average.  But you are, of course, the boss of you.

Honestly, I had planned to talk about evaluation and leading a share/debrief in the same post, but I feel like this is already a super long post, so we'll save leading the debrief for tomorrow.  And last but not least I am working hard at making my debut on Teachers Pay Teachers, and I'll be sharing the documents that I use in my own classroom to make this model work--planning guides, tasks that I've already written, blank rubrics for you to fill in, and maybe a quick how-to guide, if you think that would be helpful.  I hope to have all of those documents ready to go by this Wednesday.  If there's anything else you'd like to know let me know!  I aim to please.  =)

Enjoy the rest of your Sunday!
Rachel

More Math!

Friends!  Before I tell you more about this rad type of math that I'm working on I have to tell you what I did today.  (pause for dramatic effect)  I went running outside today for the first time today since the end of the school year.  It's been super nice out for 2 days in a row; normally DC is about 95% humidity in the summertime because the Founding Fathers decided to drain a swamp to build the nation's capital.  I felt like it was a sign that I should head outside for a run. When I opened my Nike+ app it totally shamed me.  It said "it's been 8 jillion days since your last run".  So embarrassing.  But then I did a 5K, and I didn't die so I'm going to go ahead and label that a success.

But back to this inverted math.  I'm pretty into it.  What I want to tell you about today is how crafting a task to use with this model is different from a standard or typical word problem.  I think one of the easiest areas to see this difference is in addition and subtraction.  So, when you teach a unit on adding and subtracting you're generally spending part of the time teaching students how to solve word problems.  A normal word problem might sound something like this:  "Mattison has 4 cookies.  James has 3 cookies.  How many cookies are there altogether?"  But when you're using the inverted model, you're going to write a task that is either open-ended, or has multiple answers (sometimes both).  Going to the original example, a task for this model on the same content might read something like this:  "In all, Mattison and James have 7 cookies.  How many cookies could each kid have?"  What you really want is a task that has multiple points of entry, and that kids could really spend a significant amount of time working to solve.  In this example, you could encourage kids to think about how many different ways they could put 2 numbers together to get 7.  It's also likely, in this example, that you would be pushing students to notice how turning numbers around represents a different problem.  I find that the easiest way to get started crafting tasks is by working backwards--starting with something more traditional or typical, and then thinking about how I could make it more open-ended or how I could turn it into a problem with multiple solutions.  One more piece that's important in this model is that students are generally using a combination of words, numbers, and pictures to show their work/thinking.  There's also a heavy emphasis on using labels, but I'll get into that more when I talk about evaluation and sharing.  

Another important part of this math model is that students are usually working with a partner, and that they almost always have a variety of tools available to them.  Obviously that implies that at the beginning of the year you're teaching your students how to work with a partner and use tools, but that's likely to be something you're teaching at the beginning of the year, regardless of the type of math you plan to use in your classroom.  Since you're also usually giving students a materials choice when using this model, you also have to help them figure out what tools are best for different tasks.  But I generally feel like these are things that smart teachers are doing at the beginning of the year, anyway, so I'm not going to waste your time talking about all of that here.

I'll be back tomorrow or Sunday (it's supposed to rain on Sunday) to talk about evaluating tasks and how the structure is different when you're teaching at the end, instead of the beginning of the workshop.  Happy Friday!

Brand Spankin' New!

I remember the very first teacher blog I read.  It was this lovely gem, right here, that I still read faithfully.

I actually found about this whole idea of teacher blogging from my mom.  She had mentioned to someone at her fitness classes that I was about to start teaching first grade, and they gave the website to my mom to pass along to me.  If we're being honest, I was skeptical at first.  I had never taught anyone as young as first grade before.  I was up to my eyeballs in preparation, and you wanted me to find time to read someone's blog?!  Which explains why I did not read said blog until mid-way of my first year of teaching first grade.  What an epic mistake.  It unlocked an unveritable treasure trove of ideas, resources, and headache easers.  I'm pretty sure I spent the next few hours bouncing from Fabulous in First to the brilliant ladies teaching first grade that you can find here, here, and here.  I truly believe that the blogs I first started following (and others that I've added along the way) have made me a better, and more creative, teacher.

Fast forward to now, and I'm getting ready to teach first grade for the third year in a row.  If you had asked me when I graduated from grad school what grade I thought I would be teaching it totally wouldn't have been first, but I have to say that I love those little firsties.  They're so darn adorable!  Which is why I have spent so much of my summer preparing for the school year, and why I am starting this blog.  I think that teachers sharing ideas with other teachers makes everyone better.  And that's the goal here--to share ideas, and to become better teachers all the time.

One thing that I've spent a lot of time learning about throughout the past 2 years, and this summer is this flip-flopped model of math (that goes by a thousand different names--inverted workshop, discovery math, and constructivist math are some of the ones I hear most often) where kids are working on solving really complex tasks and the onus of constructing meaning out of the work is on them.  It really changes the role of the teacher, in my opinion.  This model, which I tend to call either reverse or inverted workshop (because the learning comes at the end, rather than the beginning) really challenges students and teachers, and works in extremely well with the Common Core standards.

The basic idea is that you have a short launch with the kids (about 5 minutes), make sure everyone understands the task, and then you send them off to work.  And they work for a really long time--like 15-25 minutes (with one brief mid-workshop stop in the middle-ish)!  If you had told me I would get my kids working for 25 minutes on a math task before I started this model I would have told you you were living in a fantasy land!  But I won't tell you that anymore because I've done it with my kids, and that really is how long they work. =)  Then, you bring them to the carpet at the end and you share/debrief with them and THIS is where you're really teaching them rules/patterns/properties, etc. about math.  I've been using this model in a variety of capacities for about 2 years now, and I still think it's totally wild.  I really like it, but I also definitely think it has some limitations.  The biggest one, for me, is that some kids really don't (ostensibly) seem to make their own meaning, despite repeated exposure to the same idea or concept.  The biggest advantage to me, conversely, is that everyone can start the task in a place that's appropriate to their current understanding/level of learning.  So my questions are this:  have you ever tried a model like this?  Do you use it daily?  Would you try something like this?