Info Gap Cards: The Hidden Gem

May 2016 seems so long ago. I actually had to look it up on a calendar because I really thought it was more than 1.41666years ago. That was when I officially started this journey with Illustrative Mathematics. Our kickoff meeting was in Chicago. I was pumped to learn about this new adventure I was embarking on (and honestly quite scared too). One of the things I distinctly remember taking away from that meeting was this idea of an Info Gap. I hadn’t learned much about math language routines just yet but this Info Gap thing sounded really cool.

As I dove into this new project and flailed around learning about writing curriculum and style guides and all the correct language I had to use, I was still wrestling with this idea of an Info Gap. Lucky my colleague Dave Peterson started us off with one. After reading his example I understood it a bit better. This is what I know….

An Info Gap card routine is an activity involving two students. One student gets a problem card and one student gets a data card. Each student has enough info to get curious about the question but not enough info to answer the question individually. The problem card mostly contains a problem for students to answer.

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The data card mostly contains information needed to answer the question.

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[Info Gap student materials] [Info Gap teacher materials (requires free registration)]

One of the purposes of an Info Gap is for students to use mathematical language to communicate with each other in order to answer one (or more than one) question. For example, a student with a problem card knows what items are being purchased from a sports store but the student with the data card has the prices for the items being purchased. Now….you’re right…students COULD just sit there and hand cards to each other to get info but an important part here is the ROUTINE! The routine looks something like this:

Data: “What specific information do you need?”

Problem: “Can you tell me (a piece of information they need)?”
Data: “Why do you need that info?”
Problem: “I need that info because…..”

This interaction might happen more than once until the student with the problem card determines they don’t need any more information and can answer the question. They would solve the problem and proceed to explain their reasoning to their partner. The student with the data card would listen to their partner and ask clarifying questions if needed. After the routine is complete they switch roles and get a different set of cards (we always wrote at least 2 different sets) and go through the same routine. Overall you get the idea but if you want more info, read about them here.

Most people know instructional routines are MY JAM! So it might seem obvious why I like this whole Info Gap thing. However to take this a bit further…..

In June 2017, I was sent to PHX to get trained as an Illustrative Mathematics facilitator for our professional development. On day 2, we get to participate in an Info Gap as though we were students. I was pumped about this for a few reasons:

  1. I get to be a student of math again. One of my favorite things! (even though it is middle school content, ALWAYS LEARNING!)
  2. One of the Info Gaps used in the PD was one that I WROTE!
  3. I really wanted to see how this whole interaction went down in an Info Gap.

My partner and I did the routine. Now of course it was shaky it was our first time but again ROUTINES build over time so I wasn’t worried about it. The biggest thing that got me sooooo excited about Info Gaps was the thinking and discussion that was happening in my head and between me and my partner!! I had to think a lot about the problem, what info I need to solve it. Form a plan of attack, if you will, then decide what info I needed. Then I had to communicate that to my partner clearly enough so that they could rifle through the info on their card and share it with me. As all this was happening I was being forced to really think through my plan of attack because my partner keeps asking me why I NEED the info!!! Then I got my answer and had to convince my partner of my plan of attack. Then we switched cards and roles and I really was trying to figure out my partner’s plan as she was asking me for info.

Now taking a step back to think about all the things I was doing here….

The amount of metacognition happening as I engaged in the routine had me really analyzing my plan I formulated. It helped me get through sticky things in the problem and make mistakes (by just asking for needless info sometimes) and I also reevaluated my plan again when I had to explain it to my partner.

The second layer to this was that math language I was using throughout the routine. What to specifically ask for, how was it given on the card. Is this really info I need? What info do I need after that? I had so many questions for myself!

Then this got me thinking beyond the math classroom. What skills is this building that a human might use to be successful in the workplace. And THAT my friends was where my mind was BLOWN! I couldn’t name them all!

  • Determining a plan of action
  • Communicating to someone what you need and why
  • Re-evaluating an original plan as you start to implement it to make sure what you anticipated happening is still going to happen
  • Explaining to someone why your plan works or why your plan might be better than a different plan

This training left me with this hype about Info Gaps that I can’t begin to describe to other educators. I have referenced these routines time and time again since our curriculum has been released. I don’t know if this is true or not but sometimes I feel like they are our hidden gem.

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Info Gap Cards: The Hidden Gem

Only a few months behind schedule….

After attending Twitter Math Camp (TMC) most people normally write a blog post about their experiences, sessions they attended or whatever they end up writing. I am not good at doing things routinely. So for the past three years I have written nothing. However this year something has been following me ever since #TMC17 in Atlanta, GA. And I finally made the time to get it down on paper. (Literally, because if you didn’t know I write every blog post or email on paper before typing it up. I know I am ridiculous!)

During #TMC17 there was a whole “thing”. I don’t care to give this “thing” energy because honestly it was a waste of time and effort to give it any of my attention [feel free to judge me here, I give no shits]. However, this “thing” did plant a seed in my brain about challenging ourselves…..See for some, TMC is this event where people who have mostly socialized online (via Twitter) are all together, in real life, socializing at a math conference. The online social interactions are normally around ideas/concepts that the individuals both agree on (for the most part). At TMC, you get to meet this person and continue (or start new) conversations around like ideas. I mean it makes sense right? People find commonalities and use those comfortable things to keep their connection.

However, I left TMC this year thinking how to push myself to see things differently. I asked myself:

  • How do I get better at something that is unfamiliar to me?
  • How do I learn about something on the “other side of the fence”?
  • Maybe there is something on the “other side” that would push my current thinking?

This is the learner in me!

Quick side note: I took this strengths finders test a few weeks ago (for work) and guess what my #1 strength was??!! YUP, you guessed it…..LEARNER! OK, now back to the main event!

Visually I see myself as this curious human [highly questionable here] poking around at stuff that is unfamiliar to me. Wanting to put myself in uncomfortable, unfamiliar and weak positions in order to deliberately fail and get challenged by something. After TMC this year, I asked myself why do I do this? Why do I continue to challenge myself? And the answer was right there….

In  order to push our current boundaries we need to know our weaknesses, what makes us uncomfortable, what makes us vulnerable. Then we need to knowingly (and willingly) put ourselves in situations where we are having to face these challenges. That way we are actively seeking new and better strategies to deal with things that are hard for us.

When I think about what I am saying it really sounds insane! Put yourself in situations that you are bad at (on purpose!) in order to get better at them!!???

But isn’t this what learning is all about?????

As teachers, we need a constant reminder of how challenging learning actually is. For the most part, teachers already “know” what they are currently teaching. So how do we remind ourselves of the struggle that our students endure every day. every period. in every content area?

More times than not we forget about this aspect. The true torture of learning. It’s messy, it’s ugly, and often times we feel lost and confused for most of it. But in the end we realize that through that foggy haze of learning we did actually learn stuff. We obtained a new tool for our toolbelt, heck maybe even more than one!

So I guess what I am saying here is, what are you doing to push yourself? What new person are you chatting with that you don’t share commonalities with? What new thing are you engaging in to push back on your current thinking? How are you making yourself uncomfortable in order to learn a new thing?

Pushing yourself doesn’t mean taking on a huge new project or doing extravagant huge things. It might be that you are going to listen to that “other side” or allow yourself to taste a new food (for more than one time) or maybe just smile more often. The main thing is that you are putting yourself in uncomfortable, unknown or vulnerable situations to challenge yourself. To learn and be a role model for your students, who every day face their own challenges in every period in every content area.

Come to think of it. Maybe they are our real role models!

Only a few months behind schedule….

What is this you speak of…..curriculum.

Allow me a few mins to dust the cobs webs off and get rid rid of all these bugs that have accumulated on this blog from years of not posting.

 

 

Don’t call it a comeback….

I’ve been here these past years……

I just haven’t had much time to sit down and write about the ideas floating around in my head. I’ve been busy learning about this new journey I so luckily got to be a part of.

I am a part of the amazing team that wrote the Illustrative Mathematics middle school curriculum for Open Up Resources. I am not going to lie (cuz when do I ever not say the thing??) but there is no way I would’ve guessed that after 11 years working for the Hawaii Dept of Education, I would be writing curriculum.

And not just any curriculum!

Curriculum with a cause!

However, this post is not about the curriculum itself. This post is about my view of curriculum in general and how it has evolved over the past few years and especially now after my experience behind the scenes of the writing game.

Let’s take a trip back in time….to the first few years of my teaching career. I was HORRIBLE!! I mean who isn’t their first year??? I wasn’t sure if I was going to make it as a teacher. But then I grew, got a smidge better. Had a class or 2 that changed my life yaddah yaddah!

During that time, I never had a textbook, curriculum or any real resources until I was first introduced to the Interactive Mathematics Program (IMP). It was nothing like I’d ever seen. After 4 years of making stuff up and having my students do activities in a way that I thought made sense, I get exposed to this curriculum that has a very open feel to it. Long story short, for the journey my school was on this curriculum didn’t serve it’s purpose. However, the exposure to a resource that I could use as a teacher and not have to focus on creating stuff that meets standards, engages students, you know all that jazz, was kind of rad! I didn’t have to create content from scratch AND put time into mapping out my teacher moves. Instead I could really focus on students’ learning, meeting their needs better and the teacher moves that are a crucial component to learning in the classroom.

Fast forward to a few years after the intro to IMP and I am back to creating content: lessons, homework, all that stuff!

Note: I am not complaining here, just pointing out that I had this extra burden on my shoulders.

During this time, I had various resources I used, random texts, blog posts, etc. But never did I find any text or curriculum that I felt met the teaching philosophy I had in my head and emanated throughout my classroom. Pretty much every text I encountered looked like a replica of what I experienced as a student and that is DEF insufficient.

At this time, I didn’t get the whole curriculum thing. I was like curriculum schmiculum, my students are FINE, they are learning and every thing is fine! You could say I didn’t really believe in this so called “curriculum thing”.

Fast forward to a few months ago….I had been working on this curriculum project for almost a year, learning lots of things about math and teaching. But I could say that I was still on the fence about this whole curriculum thing. The best way to put it would be…yeah so here is great curriculum that I wrote but ask me if I’d 100% use it…?????? (shhhhhh don’t tell K8!)

However, as I was helping my coworker pick student work for a professional development, I had to go back to read through a lesson to understand what student strategies we were looking for in this student work. As I am reading through this lesson

BOOOOOOOOOM!

IT FINALLY HITS ME! HOLEY MOLEY!!!!

When you have quality curriculum like this you can spend way more time focusing on the moves you make with students to support their learning!!! soooooo wait….WHAAATT!!????

My brain had to pause for a second…..

What I came to realize at this moment was that good curriculum, curriculum that does a lot of the heavy lifting in math content, coherence and some teacher moves (5 practices) allows the teacher to re prioritize the work they need to do in order to support quality learning.

I was astounded by this and realized at this point that for years I had this mentality that I had to do all the work (mostly cuz nothing was good enough) however when there is good curriculum involved the work I put in gets more focused on important things like: what questions should I ask to get Xavier to make connections to today’s lesson (or previous/future lessons), how can I reach all these students in their classroom, how do I teach all these different learners at the same time!

I realized at this moment that a big piece to this puzzle is good materials that allows teachers to practice their craft and allows them to build a classroom environment that engages students in thinking, looking for patterns, making sense of the math around them and have them really engage in math itself. Not materials that tells students what to do and have them go through the motions 100 times after they “learned” it.

My next natural reaction was….Ok I am ready to go back to the classroom now! Which you might know I have been waiting for a few years to do. No such luck on this yet.

However, I feel as though I am looking at teaching through a whole new lens. A lens that focuses on the craft and art of teaching. No not the book. But instead a lens where the complexity of this profession is opened up and looked at to see what areas we can better support teachers with. Where can we help lighten the load so that teachers can shift their focus to these moves that determine quality learning for ALL students. Where teachers can fine tune that craft of teaching. Focus more on pedagogy and can leave the task of curriculum writing to those that have the time to sit with content for days, weeks, and months on end thinking about ways to teach a concept and interweave it into all the other learning throughout the year. I’ve learned through this past year and a half that writing curriculum is a full-time job. Teaching the future of the world is also a full-time job. And both of these are equally important to change the way humans view math in the world around us.

What is this you speak of…..curriculum.

#TMC2015 Better LATE than NEVER!

So I’ve been hesitant about writing this one.  Not because I didn’t have an awesome time or because the time wasn’t well spent but because this time around I put myself in positions to really push myself personally in order to push myself professionally.  I’m not all that open about who I am in my personal life and this year’s conference put me in a place where I had to start doing that.

To start it all off I got to pick up my favorite and amazing colleague Mitzi Hasegawa at LAX.  While we were there we also picked up two more hitchhikers, Teresa and Megan. Chatty filled drive to the hotel to drop off our cargo and then get settled in at our adobe for the week (Mahalo Judy!).

It started Wed night with game night! What fun that was! I loved the environment of being able to mingle and just walk around, make new friends and also tackle hug old friends.  Thank you to all who helped support this night of casual fun!

Morning Session


Comings and Goings: Building a Shared Understanding of Math Education from K-Calculus (Tina Cardone, Jennifer Bell, Brian Bushart, Michael Pershan)

Go to meet and work with lots of new stars that I chat with often on Twitter. Had great convos around K-Calc progressions.  How and where to make connections and building ways to use models that span K-Calc content/courses.  For example: equivalence, distributive property (models for this), proportional reasoning, and much more.  Conversations were rich, thought provoking, and challenging.

Quick side note:

I’ve reflected on and thought a lot about the structure of the morning session.  One of the greatest things about this special session is we get to work as a group for 3 solid days on a big idea and actually produce some kind of product.  This doesn’t happen at any other conference I’ve attended and I very much love the focus this allows us teachers to have on improving our craft of teaching.  Mahalo again TMC team for this special morning session!

Thursday Keynote


Growing our own practice: How mathematics teachers can use social media to support on going improvement (Lani Horn)

I don’t need to say much about her because her work, book and research pretty much speak for her awesomeness! LANI HORN!!!! How amazing is she!!!!! Biggest take away for me from this talk was the discussion around classroom ecology.  The huge dynamics of classrooms and how these dynamics affect our teaching and students learning.  No joke I am still processing this information.

Thursday Afternoon Sessions


Accepting our Powerlessness in the Classroom (Megan Schmidt)

All I have to say is MAHALO to Megan for opening this up to me.  I needed this personally.  I cried my eyes out and totally pushed myself in so many ways at this conference starting with this session!  Not enough thanks to you Megan!

Half Hour of Cool (Sadie Estrella, that’s me!)

I was VERY nervous about this 30 min session I came up with on a whim by an idea John Golden gave to me on the day of the TMC submission deadline.  I had no presentation, no handouts, NOTHING! I had 7 measly index cards with norms, some guiding questions and a closure statement.

As more and more people filed in to be in my session the more nervous I was!!!!!  I mean people…..IT’S 30 MINS OF TALKING!!! YOU DON’T WANT TO COME HERE BELIEVE ME!

Everyone proved me wrong!  So many great stories were shared.  Memories of students and the weird stuff they do that drives us crazy but we also can’t live without. Those quirky awkward moments that stick in our brains forever.  These experiences only allowed to us because we take that crazy, psychotic decision to get paid less for more work, to be a 2nd parent, to have our lives consumed by these part human, part teenager alien students that we absolutely adore and could not see our lives without.

Therein lies the one of a kind experience that this profession has to offer and we got to honor that for 30 mins and take the much needed time to celebrate ourselves and our profession.  Mahalo to everyone who attended.  I am humbled by your commitment and passion!

Friday Keynote


Math from the Heart, Not the Textbook (Christopher Danielson)

Christopher Danielson is one of my favorite humans of all time! Such a thoughtful person.  This session reminded me that I need to go back in the classroom. He asked us all to find what we love and do more of it.  I cried a bunch during this session because his message is so down to earth and simple.  Be passionate about something and do more of it in your classroom with your students.  I asked myself this questions during this entire session and I can’t deny it that the thing I love to do the most is……

TEACH STUDENTS!!

(preferably Math but I’ll take anything)

Mahalo Christopher for reminding me about what which I am extremely passionate about…..TEACHING!!!

Friday Afternoon Sessions


Supporting Small Group Instruction with Math Workstations (Sadie Estrella & Mitzi Hasegawa)

Mitzi and I were excited to share out ideas.  We think it went really well.  We haven’t kept up on what we said we would provide for our attendees yes but I am hoping to catch up with that soon!  Sorry everyone!

Planning and Assess-Respond-Instruct Cycle in Mathematics (Michelle Naidu)

This session was kind of amazing!  I loved how this session deliberately addressed the needs of students.  The big idea was using workstations to make sure students had the previous knowledge before new learning was introduced.  It was very intentionally planned to addressed previous knowledge needed in order to get to the new content that needed to be taught.

Plus Michelle had some of the best cat videos!

Friday Night BBQ


Very fun, social, great food, and hosted by amazing, loving people!  Mahalo Jed, Matt, John, all their families, Mathalicious and the many others involved to get this event planned and happening!

Saturday Keynote


Teacher Woman, because Teacher Man is Taken (Fawn Nguyen)

There are no words to describe Fawn’s session.  I didn’t get to finish watching this whole presentation because I had to drive to the airport to fly home but the half of it I was there for I laughed, cried and was reminded what a strong role model for students should look like. I mean the woman has come so far personally and the way in which she leads by example is the most humbling.  I only wish that someday I’ll be able to be that role model for my students.  Fawn you inspire me to be a better me every single second of my life.  Mahalo for all the inspiration.

My TMC journey this year was an emotional rollercoaster.  However, it was time for me to be challenged in a different way than I have been putting myself in.  I am ready to go forth and take my learning journey with me.  Mahalo everyone for the great experiences, conversations and memories.  See you next year TINNISOTA!

#TMC2015 Better LATE than NEVER!

Another Rad Resource

Well I’m back with another recommended resource book I just finished reading.

I know, I know, I’m a horrible blogger and TMC attendee because I didn’t do my required TMC aftermath post before this one but I assure you I will be getting that blog post done within the week.  Now on to the resource…………

Mathematical Practice #4 is all about modeling.  I have a confession though….no matter how many times I read the description of MP4, look at related tasks and/or chat with people about the amazingness of mathematical modeling I’m always unsure of how to fit it in the classroom.  I’m guilty as a teacher for being one who says

“Gosh, I know how important it is but where will I fit it?  I don’t have time!”

So when I saw Modeling with Mathematics by Nancy Butler Wolf and learned that it was for middle school (maybe some HS) I jumped on the opportunity to read this bad boy and start figuring out a solution to a problem in my classrooms (instead of playing the BLAME GAME of course).

The #1 thing this book has is great tasks you can use with your students.  There is the infamous Barbie Bungee task in there but there’s also a lot more tasks that can be used right from the book without modification (there is also room for modification too).

Something I really love is how the author points out what makes a task a modeling task and goes further to even compare the difference between word problems, problem solving and modeling problems.  This helped me to see clearly the definitions because to be really honest I’m not sure I really knew the difference with as much clarity as i do now.

Majority of the book is dedicated to the process of modeling.  There are chapters that refer to each “step” in the process ad those chapters go into detail what you as a teacher do to help facilitate the process with students.  There are short vignettes that give examples of conversations between student and teacher which totally helped me to make sense of how to facilitate this scary modeling process.

Process of Modeling

My favorite part of the entire book however was the section about Mathematical Autonomy.  I had to stop myself from highlighting the entire section!This part spoke to me because it was really about classroom culture, being student centered and allowing students to be leaders in their own learning journey.  This is one of the biggest struggles I see with teachers in classrooms (even in my own): How to build a truly student centered classroom environment where there is respect from all parties involved in the class.

Student Autonomy

This resource would be great in your classroom if you’re like me and was (past tense because I feel a bit more confident  now) intimidated by the idea of integrating modeling in your class.  She provides a framework to move through and lots of ideas of how to start having students engage in modeling.  It’s scary but the thing that the author says about modeling is it is the way to get the best bang for your buck!

So go out and read it and then come back and let me know how you liked it and use it in your classroom!

Another Rad Resource

Student Learning Objective (cont.): 3-5 Resources

My Student Learning Objective or School/System Improvement Objective (SSIO) this year was to add on to the K-2 bank of resources I created last year.

Everything in that previous post still stands.  I am still worried about all those things however I still want to share these resources so that whoever might have a use for them does.

Feel free to leave comments about mistakes or updates that should be made to them.  I hope to continuously update these as I continue to use them while working with teachers.

My main use recently for them is for finding workstation activities focused around a certain cluster.  That way the work station game can be used over for a longer period of time and address multiple standards throughout the year.

Enjoy!

Geometry

Measurement and Data

Number and Operations – Base Ten

Number and Operations – Fractions

Operations and Algebraic Thinking

Student Learning Objective (cont.): 3-5 Resources

A Useful Reference for ALL!

I finished reading Christopher Danielson’s (@Trianglemancsd) Common Core Math for Parents for Dummies book just yesterday.  It took me a while to get through it, which I think was partly because it wasn’t the most intriguing read for me.  Now that doesn’t mean I think this book is horrible!  Instead I think the EXACT OPPOSITE!  This book is a GREAT resource for anyone with kids or teachers grades K-12.  Now, I am a certified 7-12 mathematics teacher but that doesn’t mean I know the ins and outs of all things math or even the Common Core State Standards-Math (CCSSM).  That is why I recommend this to all K-12 teachers (that teach mathematics) and especially parents!

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Yup there are A LOT of tabs on that book! 11 to be exact.

This post is a quick write up of how I would (or plan to) use this resource in my current position.  I wrote this post while enduring a bad day at the beach.  A bad day at the beach for us who live here in Hawaii looks like this:

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Hamoa Beach, Hana, Maui

As for parents, you should read this resource to help you get a better idea of the how and why of what your child is learning in their math classes from grades K-12 and how you can help support a positive journey through learning mathematics.

As a resource teacher when I’ve worked with grade 3-5 teachers I’ve had teachers ask to have “training” to learn where their teaching of math gets applied beyond their 3-5 grade band.  After reading this book, I can see using this resource to provide a 1 day training, maybe even an ongoing book PLC where grade level teachers (K-8, maybe 9-12 too) could brush up on their grade level content standards.  In addition, teachers would engage in a conversation about how to approach teaching their grade level standards knowing where a standard comes from and goes to, previous grade level and post grade level.  This discussion is rooted in the Coherence shift of the CCSSM.

Other conversations that could be fostered, would be around the Standards for Mathematical Practice, domains of the CCSSM and/or specific topics that span CCSSM: linear equations , functions, arrays, etc.  This structure would work well for a course that would help teachers engage in the understanding of their content standards and span across a few sessions.  This would help teachers expand their knowledge of math beyond their grade level and feel more comfortable teaching at their grade level knowing where their students’ learning is coming from and going to.

Conversations and learning can most definitely be had around strategies of teaching concepts or even math strategies used.  These two could also be combined together and you could add in a bit of strategies in order to foster student discourse around these math strategies.  For example, on page 84 in the book

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I jotted a note in relation to a model and how might a teacher use it to teach a related topic.

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Allowing teachers to make connections between concepts within their grade level (horizontally) and between grade levels (vertically) addresses the Coherence shift again here.

When I started writing this post I had 2 ideas I wanted to share, however as I am writing it up more and more ideas are popping into my brain making connections to the two main ideas I started with.  I hope to mull these over more and since I said this post would be quick, I’ll leave it as is.  I hope I can make any of these ideas come to life sooner rather than later.  In the meantime, feel free to leave comments, feedback or updates on how you’ve used this resource.  In addition, feel free to contact me to have a more in depth conversation of how to use this resource

Lastly, MAHALO Christopher Danielson for providing us with a great resource to help support positive math teaching to students.

A Useful Reference for ALL!