Better Questions: Math Rocks Meets Open Middle

This year I have been leading a cohort of elementary math educators in my district. We met for two full days in July – you can read about that here and here – and throughout this school year we’ve met every other Thursday after school.

In December, our meeting focused on the work of Robert Kaplinsky, specifically his IGNITE talk about productive struggle and his website openmiddle.com.

At the start of the session, everyone reflected on what “productive struggle” means to them. This is important because as certain phrases become popular in education, they quickly become jargon. I wanted to ensure everyone had a chance to think about how they interpret the phrase and share that with the group. Then we watched Robert’s IGNITE talk.

The image that stood out most to me from his talk was the one of the mom riding the bike for her child. It seems so silly, and yet there are many instances as teachers where we can find ourselves doing the thinking for our students instead of letting them try either on their own or with our support.

At the end of the video, Robert puts out a call to action for teachers to create opportunities for students to productively struggle. And why not start by having the Math Rocks participants do some productive struggling of their own? Regina and I posted 10 problems around the room. We let everyone loose to do some math for 15 minutes. They dove right in!

All 10 problems came from openmiddle.com. If you aren’t familiar with the open middle problem type, here’s a brief summary: (You can learn more here.)

• they have a “closed beginning” meaning they all start with the same initial problem
• they have a “closed end” meaning that they all end with the same answer
• they have an “open middle” meaning there are multiple ways to approach and ultimately solve the problem

After debriefing as a group and sharing information about open middle problems, we came back around to the idea of productive struggle with this video from Michael Pershan. The whole thing is interesting, but for the purposes of our discussion, we watched the first 30 seconds of the video, and then we watched from 1:45 to 5:45.

By this point, we had made our case and it was time for the participants to take a stab at designing their own open middle problems. They had a choice of writing one from scratch or taking an existing problem from our curriculum and redesigning it as an open middle problem. A nice surprise is that our adopted textbook, Stepping Stones, already uses open middle problems in many lessons and activities! They don’t name them as such, but that’s essentially what they are.

We shared out the open middle problems they wrote. Afterward we gathered them together in this document if you’d like to see our first attempts. We closed the session with their homework assignment – giving their students an open middle problem and reflecting on it in a blog post. If you’re interested in learning more about open middle problems – especially learning from teachers trying them out for the first time! – check out our open middle blog post collection.

The consensus from the group seems to be that they can initially throw kids off if they’re not used to being asked questions like this, especially for those kids who want to neatly and easily come to the correct answer, but the questions provide opportunities for the type of thinking and struggling we want our students to engage in and we need to be using them more often.

My Favorite: Holidays at Target

Here we are in Week 2 of the ExploreMTBoS 2016 Blogging Initiative! This week’s challenge is to blog about one of my favorite things. During this school year, one of my favorite things has been visiting Target during the holidays. The holiday-themed merchandise is rich with mathematical possibilities! I already wrote three posts about a treasure trove of images from Halloween:

• Post 1
• Post 2
• Post 3

Valentine’s Day is around the corner, and I snapped some photos this evening to share with you. I’m going to cover a range of mathematical skills – mostly centered around estimation –  from Kinder through about Grade 6 to show you just how versatile this stuff is!

These first two images are good for estimating quantity. You can estimate the quantities individually. Don’t forget to ask students to estimate an answer that is TOO HIGH and one that is TOO LOW in addition to their actual estimate. Coming up with a reasonable range takes a lot of practice! You could also show students both images at the same time and ask, “Which package has more?”

I forgot to snap a picture of the answers, but I can tell you there are 15 bouncy balls and 24 eraser rings.

Here’s another one. How many Kisses are in the box?

I was kind of surprised that the answer wasn’t an even number like 10 or 12. This just seems oddly specific.

Students tend to estimate better when the quantities are smaller. Here’s a larger quantity package to up the challenge a bit. How many gumballs are in the bag?

I was kind of surprised to find out the answer myself.

This next one is tricky! How many truffles are in the box? Go ahead and make an estimate.

Now that you’ve made your estimate, I’d like to show you how deceptive product packaging can be. Would you like to revise your estimate?

And now for the reveal. How does your estimate compare to the actual amount?

The first few images dealt with disorganized quantities. Once we move into organization, the thinking can extend into multiplicative reasoning. The great thing is that it doesn’t have to! Students can find the total by counting by 1s, skip counting, and/or using multiplication.

There are several questions you can ask about these pictures. They’re of the same box. I just gave different perspective. I’d probably show the almost-front view first to see what kids think before showing the top-down view.

• How many boxes of chocolate were in the case when it was full?
• How many boxes of chocolate are left?
• How many boxes of chocolate are gone?

Here’s another package that could prove a bit tricky for some students. How many heart stickers are in this package?

Students might notice that the package says 2 sheets. If they don’t, you might show them the package from a different perspective.

And finally, you can reveal the total.

This next package can be shown one of two ways depending on how much challenge you want to provide the students. Even with some of the hearts covered, students can still reason about the total quantity.

This next one could simply be used to ask how many squares of chocolate are in the box, but what I’d really like to know is how many ounces/grams of chocolate are in the box.

After some estimating, you could show your students this and let them flex their decimal computation skills to find the total.

However, the reveal is likely to raise some eyebrows.

And finally, you can do some more decimal calculations with this final product. How much would it cost to buy all of the boxes shown?

And if you bought all 6 boxes, how many ounces of chocolate would you be getting?

Ten minutes in the holiday aisle and my iPhone are all it took to gather this wealth of math questions can now be shared with students. Even better, I didn’t have to purchase any of these products! Even better than that, I can go back for every major holiday to capture new images that will feel timely and relevant!

By the way, feel free to use any and all of these images with your own students. They’re fairly low quality so I don’t recommend printing them, but they should look just fine projected or shown on a screen.

Happy Valentine’s Day!

A Day in the Life of a Curriculum Coordinator: Tuesday

Here are links to all of the posts I wrote this week:

• Monday
• Tuesday
• Wednesday
• Thursday – Out sick
• Friday

Tuesday

So in stark contrast to yesterday, today was quite the whirlwind! I started the morning at our office where I checked email, drank a cup of coffee, and chatted with Regina about our fraction PD sessions tomorrow.

Before I knew it, it was time to head out to the principals meeting to present about the upcoming STAAR math test. The principals meeting was being hosted at Dell this month instead of at our Admin office. When I arrived, a panel of Dell excecs was imparting leadership wisdom and answering the principals’ questions.

After the panel discussion ended, our elementary science coordinator spoke about the successes of implementing the Writing in Science program in our district over the past 4 years. It was really impressive to see photos and videos of the program in action, and it reaffirmed that the next chance I get, I need to attend one of her trainings to learn more about it! We have a couple of instructional coaches who are already looking at how to adapt and extend the components of Writing in Science to math, and they’re planning to share this during a summer PD session in July. I can’t wait!

After that inspiring presentation, I had my turn at the podium. The session went well and I got some good questions from the principals. One of them was if I’ll be repeating this session for the teachers. It got me thinking that I could probably do it as a webinar that teachers can attend live, but those who can’t attend could watch a recording of it after the fact. Now I just need to figure out the logistics and schedule a date!

On my way back to the office, I decided to stop for lunch at a local restaurant. It’s close enough to the office that I was able to call Regina to invite her to join me, and she convinced our elementary social studies coordinator to come along. That was my calm moment for the day. I enjoyed getting to eat and talk without worrying where I was off to next.

After lunch, I headed back to the office to answer emails before heading out to a meeting at one of our elementary campuses. While I was back in the office, I realized that we have more interest in our upcoming Developing Number Concepts session than I can accommodate in one day. Rather than turn people away, I’ve decided to add a second session a week later. This way we’ll be able to host almost 100 teachers, up from the original 60. I’m really excited that so many people want to attend this training!

Unfortunately I didn’t have enough time to email principals about the new session before I hopped back in the car and headed over to one of our elementary campuses. Since October, principals have been meeting in groups once a month to take various Heinemann online courses together. The elementary curriculum coordinators were each invited to join one of the groups.

My group is made up of about 6 principals, and we’re taking Steve Leinwand’s Making Math Far More Accessible to Our Students. It’s been a lot of fun! The material is great, and the discussion it prompts among us is so valuable. Today’s session was about the importance of using multiple representations and supporting students’ language development in mathematics. We had a great discussion at one point about strip diagrams, and I was clapping on the inside when one of the principals referenced the notice and wonder strategy as a way to make sense of them.

It was during this meeting that I realized I’m getting sick. Boo!

I have a full day of PD planned for tomorrow. I can’t be sick! Well, I can. If necessary, Regina can lead the sessions on her own. I just don’t want to do that to her. I’m crossing my fingers that I’ll feel better after a good night’s sleep, but I still went over the 4th grade presentation with her when I got back to the office just in case!

At 3:30, an instructional coach followed shortly by a team of 2nd grade teachers showed up to our K-2 open planning session. The 2nd grade team are our regulars. They come each time and plan the assessment for their upcoming unit. It’s awesome! Today I worked with them to create assessment items for a geometry unit. We also had a 1st grade teacher show up. She worked with the instructional coach to plan activities for an upcoming addition unit. So, not a huge turnout, but incredibly productive for those who were there!

At 5 o’clock, I helped Regina load up her car with the materials we need to take with us to the PD session tomorrow, and then I headed home. At this point it’s becoming clearer and clearer I’m under the weather, but I’m still holding out hope I’ll feel better in the morning.

 

A Day in the Life of a Curriculum Coordinator: Monday

I’m always a sucker for a good blogging initiative. As luck would have it, my online PLC, #MTBoS is kicking off just such an initiative this week! If you’re interested in joining or if you just want to find out what the MathTwitterBlogosphere is all about, head on over to the ExploreMTBoS site.

We were given two options for blog post topics this week. The first is to write a post about one good thing. The other is to write about a day in the life. The assumption is that you’re a teacher and you’ll write about a day in the life of a teacher. However, I’m not a teacher currently. I’m the elementary math curriculum coordinator for my district. I don’t imagine many people know what I actually do – Dan Meyer had lunch with my secondary counterparts last week and was surprised to hear our jobs weren’t terminated once the scope and sequence was in place – so I thought this is a timely opportunity to share a sliver of what my job entails.

We’ll start with Monday. If all goes well, I’ll write a short post each day. If all does not go well, then you might just get Monday. At least I can guarantee one day in the life!

[UPDATE] – I did manage to write a post each day:

• Monday
• Tuesday
• Wednesday
• Thursday – Out sick
• Friday

Monday

In many ways today was not a typical day which is why I’m hoping to write a few posts this week. On the other hand, I’m not sure there is such a thing as a typical day in my job, so today’s post might be just as representative as any other day I could have chosen to write about.

The first hour of my day I spent reviewing, editing, and finalizing a presentation I’m giving to all of our elementary principals tomorrow. I have about 50 minutes to do an overview session about the state math test (STAAR) and give some tips and advice for how teachers and students should spend time between now and then.

SPOIILER ALERT! I’m going to tell them their teachers should stay the course. The year is only half over and there are still a lot of concepts to introduce. If anything, now is a great time to revisit how things are going and work together with grade level teams to ensure they are providing the best lessons and experiences they can during the upcoming units. Teachers can and should review concepts along the way, but massive test prep is not called for at this time.

While putting together the presentation, I got to try out Snap & Read, some new software our Special Education Department purchased, though it’s going to be available as a general instructional tool for all students. It’s a Chrome extension that allows users to highlight text and have it read out loud. I didn’t get to do a whole lot with it, but it was nice to discover how quick and easy it is to use. Students should be able to pick it up immediately!

The rest of the day I prepared for a PD session I’m leading on Wednesday. This year I received funding from our superintendent – a huge thanks to Dr. Flores! – to purchase multiple copies of the books Beyond Pizzas and Pies and Beyond Invert and Multiply for our intermediate elementary teachers. In addition, I also received funding to provide a full day of PD to one grade 3 teacher from every campus and one grade 4 teacher from every campus.

There’s a lot of information in the books, so my partner Regina and I opted to do two half-day sessions for each grade level. Back in December we facilitated part 1 for each grade and this Wednesday we’re facilitating part 2. We didn’t have enough money to bring grade 5 into the fold so we’re offering them a 2-hour session on an early release day in February.

Normally I have a lot of different tasks to jump between each day, but somehow I only managed to schedule PD prep today, and I sure needed the time! Regina is handling the grade 3 session which left me with the grade 4 session. I had to figure out what I was going to cover from the 3 chapters I chose for this session, make slides, plan out activities – specifically modifications I wanted to make to the activities shared in the book – and get copies made of all the materials teachers will use.

All in all I’m happy with how the session has shaped up, and I look forward to working with the teachers on Wednesday. Now I just have to hope we can get through everything I planned! That’s one area I’m still learning with regard to PD planning. I feel pretty good about the amount of content in my sessions, but I find that I always tend to put just one too many things in every session. Or two or three, but usually it feels like it’s just a bit too much.

I also did some odds and ends throughout the day whenever I needed a short break from PD planning:

• I shared a reminder about this week’s open planning sessions on our grade-level Google communities. Once a month, Regina and I host two open planning sessions after school – one for K-2 teachers and one for 3-5 teachers. All teachers from the district are invited to come and collaborate together on upcoming math units. Regina and I are there to help answer questions and take part in the process. This year is the first time we’ve offered this. The sessions aren’t attended by a ton of folks, but the teachers who do come let us know how valuable they think the time is. I actually just got an email this afternoon from an AP who shared some feedback a teacher gave her during a pre-observation conference: “Going to open planning was the best decision we’ve ever made. It helps us understand the TEKS and pace our unit.” Hooray! I think this also counts as my one good thing. 🙂
• I emailed a vendor to get a quote for some books I’m going to purchase for our K-2 teachers. For each campus we’re purchasing multiple copies of books 1-3 in the Developing Number Concepts series by Kathy Richardson. (Another thanks to our superintendent, Dr. Flores!) Regina and I will be leading a full day PD session on those for K-2 teachers in February.
• Speaking of, I emailed back and forth with a couple principals who are hoping to get a few more teachers signed up for the February PD session I just mentioned. Win!
• And finally, I watched an Ignite talk that one of our instructional coaches shared with me. Gradual release of responsibility has come up somewhat frequently recently and we’re still trying to wrap our heads around what it should/could mean in math. My fear is similar to what’s shown in the video, that it becomes all about what the teacher is thinking and getting students to merely reflect/parrot that.

There you have it. A day in the life of an elementary math curriculum coordinator. This was a fairly calm day, and I am so appreciative of that. Tomorrow is looking to be a bit more hectic. Hopefully I’ll have a chance to blog about that when it’s over.

Go Big or Go Home: Math Rocks Day 1

My brain is full! I just finished two amazing days of PD with about 30 educators in my district. I promised I’d blog about it, and I need to because I just have so much going on in my head right now. Like I said, my brain is full!

This school year, I’m leading an advanced course with elementary teachers in my district. I didn’t really have any guidance beyond that, so it was left to me and my co-worker Regina to set some goals and make a plan. All we started with was a name: Math Rocks. And that’s only because our district already offers an advanced course called Reading Rocks.

Back in May, Regina and I put together an application and asked teachers to apply for this course that has never existed before. Amazingly enough, about 36 people took the time to apply. We read through their applications and selected 24 educators to be in our inaugural class. What I like about it is that we have a wide variety of folks – general education teachers K-5, a few instructional coaches, a TAG teacher, and a few interventionists. And within that group we have dual language teachers and inclusion teachers. They are so diverse; I’m excited about the varied perspectives they’ll bring to our work.

We kicked off the course yesterday and today. We’ll continue our work online for the next month before school starts. Once the school year begins, we’ll meet every other Thursday after school throughout the fall semester. We’ll continue into the spring semester with a final meeting in early February. It’s going to be awesome!

But let’s get back to the first two days. This is the most we’ll ever be together in one place: 12 intense hours across two days.

We opened the first day with a little estimation from Andrew Stadel’s Estimation 180. We of course did the task that started it all: How tall is Mr. Stadel?

After everyone made their estimates, we had them take a walk. Every time we asked a new question they had to find a new partner and introduce themselves. We went through the usual Estimation 180 questions:

• What is an estimate that is too LOW?
• What is an estimate that is too HIGH?
• What is your estimate?

We also added some questions of our own:

• Where’s the math?
• Which grade levels could do this activity?
• Which process standards did you use?

This was a great way to get everyone up and moving at 8:30 in the morning, but it also started something they weren’t going to be aware of immediately. One thing I did very intentionally throughout the two days was embed FREE resources from my online PLC, the Math Twitter Blogosphere (MTBoS). Unbeknownst to everyone, one of my primary goals for the course is to connect them with this inspiring community. And what better way to entice them than by taking these two days to show off some of the rich resources this community creates and shares freely?

After our getting-to-know-you activity, we moved into a community circle. Regina set the tone by talking about why our district is excited about and invested in this course. Then everyone went around to introduce themselves to the group and talk a bit about why they chose to apply for the course. Their reasons varied, but there were some overriding themes. For many of us in the group, math is not a subject we loved as a kid. In fact, several folks went so far as to say they hated it growing up. On the bright side, these same folks want their students to have better experiences with math than they did. Everyone agreed that math is a rich subject, and they want their students to experience and appreciate that richness.

Their stories during the community circle provided a nice segue into our next activity. We asked the participants to reflect on their own experiences learning math. They had to choose three images that came to mind that symbolize what math was like to them as a student and sketch them on a blank sheet of paper. When everyone was finished, we did a gallery walk.

There were a few recurring themes here as well. Many pictures showed formulas with variables. People said that they remembered being told to use these formulas because they would “work” but they never understood what they meant or why they were using them. Many pictures also showed numerous worksheets, indicating that math was more about quantity of problems than quality of reasoning or understanding. For those that said they disliked math as a child, we talked about when that started happening, and the group was split over it being Algebra or Geometry.

By the way, I’m sharing a lot of the negative experiences, mostly because I felt like I was hearing those most, but I do have to say that there were some voices of folks who did like math as a kid or they grew to like it as they got into higher grades. So negative stories were definitely not universal, which was encouraging.

After debriefing these experiences, we watched Tracy Zager’s talk from Shadow Con 2015. This was basically a small teacher-led mini-conference in the “shadow” of NCTM Boston (hence the name). All of the talks given at Shadow Con are available on the website, along with a facilitator’s guide if you’re interested in utilizing any of the videos in your own PD. Two of the videos really struck a chord with me and ended up becoming the inspiration for our two course goals.

Tracy’s video is called Breaking the Cycle. Here’s a short synopsis. I could write a whole blog post about this video and my thoughts on it, but really you should take 15 minutes and watch it for yourself. It’s powerful stuff.

The majority of elementary school teachers had negative experiences as math students, and many continue to dislike or avoid mathematics as adults. We’ll look at how we can better understand and support our colleagues, so they can reframe their personal relationships with math and teach better than they were taught.

We watched the video, debriefed, and then I shared our first goal for Math Rocks: Relationships.

We want our participants to focus on building relationships this year with:

• their teammates,
• their administrators,
• me and Regina,
• with their students, and
• with other educators.

We also want them to build their relationship and their students’ relationships with mathematics.

To help them start working on this goal, we took Tracy’s call to action from the end of the video. Each participant chose a word from a word cloud that shows how mathematician’s describe math. Over the course of the next month, as they attend PD and prepare for the start of the school year, their mission is to plan for math instruction with that word as an inspiration and guide. We’ll revisit how this went when we meet back in September.

And then it was time for lunch. Whew! We crammed a lot in that morning.

After lunch we did a little math courtesy of Mary Bourrassa’s Which One Doesn’t Belong? If you’re unfamiliar with this site, students are presented an image of four things. They have to answer one question, “Which one doesn’t belong?” The fun part is that you can justify a reason why each one doesn’t belong. Here’s the one we did as a group:

Everyone had to pick one picture that doesn’t belong and go stand in a corner with other people who chose the same picture. Once they were grouped, they discussed with one another to see if their justifications were the same, and then we shared out as a group. Here are some of their reasonings:

• The quarters don’t belong because they equal a whole dollar. The value of each of the other three pictures equals part of a dollar (4 cents, 5 cents, 40 cents).
• The quarters don’t belong because the word you say for their value (one dollar, one hundred cents) doesn’t start with “f” like in the other three pictures (four, five, and forty cents).
• The pennies don’t belong because they are not the same color as the other coins.
• The pennies don’t belong because they are the only coin where the heads face right instead of left.
• The nickel doesn’t belong because there is only one.
• The dimes don’t belong because they are the only one where the tails side is showing.
• The dimes don’t belong because the value of a dime has a 0 in the ones place. All the other coins have some number of ones in the ones place (5 ones in 25, 1 one in 1, 5 ones in 5).

Like Estimation 180, this activity was included intentionally because this is yet another FREE resource created by the MTBoS (pronounced “mit-boss”). It’s actually inspired by another FREE resource created by someone in the MTBoS, the Building Better Shapes Book by Christopher Danielson.

After talking about money, we prepared to watch Kristin Gray’s talk from Shadow Con. Hers is called Be Genuinely Curious, and you should take a few minutes to watch it for yourself:

When students enter our classroom, we ask them to be genuinely curious about the material they are learning each day: curious about numbers and their properties, about mathematical relationships, about why various patterns emerge, but do we, as teachers, bring that same curiosity to our classes? Through our own curiosities, we can gain a deeper understanding of our content and learn to follow the lead of our students in building productive, engaging and safe mathematical learning experiences. As teachers, if we are as genuinely curious about our work each day as we hope the students are about theirs, awesome things happen!

Again, we watched the video, debriefed, and then I shared our second goal for Math Rocks: Curiosity.

We want participants to use their time in this course to get curious about mathematics, about teaching, and about their students. We also want them to find ways to spark their students’ curiosity about mathematics.

When you’re curious about something, you need resources to help you resolve your curiosities. I didn’t want the folks in this course to feel like we were going to leave them hanging. That’s when I formally introduced the MTBoS.

I told them the story of how I joined the MTBoS back in August 2012. (On a side note, it’s hard to believe I’m approaching my third anniversary of being part of this amazing community of educators!) This is a community that prides itself on freely sharing and supporting one another. If the educators in Math Rocks really want to take their math teaching to the next level, getting connected to a network like the MTBoS is the way to go.

One of the amazing things the MTBoS has done to help new members join and get started is to create Explore MTBoS. Periodically, the group kicks off an initiative to help new members start blogs and Twitter accounts. Unfortunately, there isn’t an initiative starting up right when Math Rocks is starting, so I started one up myself. I created a blog where I tailored the existing missions from Explore MTBoS to guide our group as they become members of this online PLC. We did the first two missions to wrap up the first day of Math Rocks. Each person had to make a blog and create a Twitter account.

I’ll admit, I was super stoked about this, but I’ll be honest that I threw more than a few people way out of their comfort zone that afternoon. Despite that, they still made their accounts, wrote their first blog posts, and sent out their first tweets. I am so proud of them for taking these steps, and I am eager to see where it leads from here.

That wraps up Day 1, our first 6 hours together. I’ll share Day 2 in another post.

Exploring MTBoS: Mission #2

I like blogging. I have mixed feelings about Twitter.

With blogging, I am free to talk. I can say a lot or a little, though I mostly say a lot. With Twitter, I feel like I’m writing snippets of thought without much context. Some people love the challenge of limiting their messages to 140 characters. Some think that this forces us to get to the essence of our message and cut out all the bullshit.

It generally frustrates me because I feel like I’m not being understood or I’m just not speaking clearly. But like it or not, I still read my feed every day and tweet to various folks. I may not love everything about Twitter, but I find it valuable enough.

So what don’t I like? In addition to the character limit, there are a few other things that get under my skin. The first is the endless platitudes and affirmations. They drive me nuts. If they inspire your or make you feel better during a tough spot in your day, then I’m happy for you. They don’t do that for me. I wrote about this after my very first Twitter chat. I think part of the problem is that because of the character limit, we’re left with hollow messages filling up our feeds day in and day out. The solution is that I should probably weed my list of who I follow. I need to start removing folks who add noise, not content.

My other problem is attitude. This is another issue I wrote about previously, here and here. I can’t stand the attitude among some educators that all teachers should be in a Twitter PLN, and the implication that teachers who aren’t “connected” 24/7 are somehow terrible, uncaring teachers. Look, some people love teaching so much that they like to think and talk about it all the time. “Hi, my name is Brian, and I’m an eduholic.” It works for me, but I don’t begrudge those that want a life away from their classrooms. Heck, I even want time away sometimes, and I’m not going to feel guilty about that.

The thing is, neither of these issues really apply to #MTBoS. I’ve never felt like I’m having to read crap. Instead there are always lots of interesting discussions going on about teaching, students, and math. Just within the past 24 hours I talked about strategies for getting students to be better estimators, the reasons people leave teaching, and the need to be explicit in our meanings of terms like direct instruction. Those are extremely satisfying interactions, and it’s because of my connections through #MTBoS that I had them. If it weren’t for the folks I’ve connected with in #MTBoS, I probably would have ditched Twitter completely last winter. Thankfully that isn’t the case, and I appreciate this group more and more every day.

Exploring MTBoS: Mission #1

Starting this week I’m taking off on an 8-week adventure Exploring the MathTwitterBlogosphere (Explore MTBoS for short). I’ve been loosely connected to the MTBoS since last August when Dan Meyer encouraged educators to start blogging. Like many people, I went all in for a while, but then life got in the way, and I haven’t really maintained my blog so much lately. Thanks to the Explore MTBoS program, I will at least be blogging and making connections for the next eight weeks, and perhaps it will give me the motivation to keep it going after the eight weeks are up.

Mission #1

We had to choose from two prompts. I chose:

What is one thing that happens in your classroom that makes it distinctly yours? It can be something you do that is unique in your school…It can be something more amorphous…However you want to interpret the question! Whatever!

For whoever happens to read my blog for the next part of this mission, I’m actually out of the classroom currently. I was an elementary school teacher for 8 years, and for the past four years I’ve been a math curriculum developer. However, just because I’m out of the classroom doesn’t mean my memory has gone foggy or anything.

With regards to math education in particular, what made my classroom distinctly mine, even though I got the idea from a co-teacher, was Problem of the Day (or P.O.D. as my kids liked to call it). As the name implies, the students were presented a new problem at the beginning of every math class.

At the time, I had a specific goal for doing Problem of the Day. The high stakes test in Texas, the TAKS test (which is now the STAAR), had six objectives and the sixth objective was called “Mathematical Processes and Tools”. It was a doozy of an objective because it wasn’t really about any particular math concepts. Rather it was about asking students a variety of questions that required problem solving and reasoning. Supposedly having good teaching methods while teaching the core content was enough to prepare students for Objective 6, but after many years in the classroom I knew that my students could easily be thrown for a loop by those questions. So during Problem of the Day I often used Objective 6 questions from released TAKS tests.

(As an aside: Looking back, I’m not proud that I focused on doing this for test prep. I am not a fan of high stakes tests, but the reality at the time is that it was my responsibility to prepare my students and this is the method I chose to try. As it turns out, it worked out amazingly well, and I see now that I could use Problem of the Day, or a related structure, to actually enhance my general math teaching.)

So as I said, I presented a new problem every day. Our school used a problem solving structure called FQSR (Facts, Question, Solve, Reflect). My students would divide their paper into a grid and label each section F, Q, S, or R to represent their work in that section. The first thing they had to do after they read the problem was to write down whatever facts they felt would help them solve the problem. Then they had to write the question they were being asked. (This actually made for some great conversation and also gave me some wonderful insights into how students comprehended what they were reading.) Next, they had to solve the problem in whatever way made sense to them. Finally, they had to write a response (reflection) that explained why they did what they did and what their answer to the question was.

When they were done, they would bring it up to me to read over their work. I wouldn’t tell them if they were correct or incorrect. Rather, I would ask them questions or point out where I was confused while looking at their work. The student would go sit down and use my questioning to continue working on their solution. Sometimes they would start over, sometimes they would elaborate more in their reflection, whatever they felt they needed to do. If I got a line of students waiting to see me, it was their job to share their work with each other in line while I continued reviewing work. Sometimes students would come up and see me 3, 4, or even 5 times to continue getting feedback on their solution. All the while, I never verified whether their answer was correct.

After it seemed like most of the class was ready to continue, we moved to the presentation phase where students got up and shared their solution with the class. They stood up at the front and shared their work using our document camera. I stood in the back to make it clear that I wasn’t running the show. I let students ask the presenter questions to clarify. I would also ask questions to clarify. Usually we made it through 2-3 students before having a discussion about whether we could all agree on an answer. By this point students were generally in agreement (for good or ill), and I would finally give the answer.

When first starting P.O.D., I knew my students were going to be weak at showing their work and even weaker at writing their reflections. For the first few weeks, I would choose one of the students and I would model the solution and reflection sections based on their work. They would tell me what they did and I would talk about how I would show/write that on my paper. I did this for much longer than a teacher would normally feel comfortable, but I can tell you that it paid off big time. My students’ responses got better and better because they had worked with me to model what it means to write about math thinking. They understood the value of telling what nouns actually go with the quantities they were computing with, for example.

You’d think this would be a boring activity because I forced a structure on them day in and day out, but my kids loved it. Maybe it’s because of the classroom culture I fostered, maybe I had weird kids, or maybe it’s because I wasn’t the voice of authority. Sure, I would give feedback as they worked, but so did other students. Sure, I asked questions during someone’s presentation, but I was always in the back of the room, not in a place of control. Also, I didn’t ask as many questions as my students did. I was “with” them, not “above” them.

While my students learned a lot from doing P.O.D., it was a valuable experience for me as well. I learned that word problems can be much trickier than you’d think. Here are two examples. (I’m making up the wording, but the essence of the problems is the same.)

1. Matt baked 24 cookies. He ate 5 and his sister ate 6. How many cookies did they eat?

I kid you not, every year I’ve presented a problem with similar wording, my students invariably subtract to find the answer. Generally they do 24 – 5 – 6 to get 13. I’m sure you can guess why: Because cookies were eaten, and that just means the amount is going to go down. It just has to.

I LOVE talking about this problem with students during P.O.D.. (This actually isn’t an objective 6 TAKS question. I just snuck it in every year because I knew it would trip them up and lead to great discussion.) Even after talking about the problem with students, and finally getting a few of them to recognize their error in comprehending the question, I still have students after a good 15-20 minute discussion still unclear why the answer is 11. And I’m okay that not all of them get it by the end. Doing P.O.D. is about the process of learning to comprehend, reason through, and solve problems. I can take a loss here and there for the greater victory of developing strong problem solvers over time.

2. Jamal is going to the movies. He buys popcorn for $2.65 and a soda for $3.25. What information is needed to determine how much change Jamal received?

This is another problem that I love because it shows me very clearly that students can read words and completely ignore them. It also shows me that they make a lot of assumptions. Finally, it makes it clear why there is a step in FQSR where you identify the question – because it’s not always what you think it’s going to be! I was floored at how many of my students had temporary blindness when they got to “What information is needed to determine…” Once they got to “…how much change Jamal received?”, all of a sudden their sight returned and they started doing some computations with numbers. If you’re like me, you’re probably wondering how it didn’t occur to them that they had absolutely no idea how much money Jamal handed the cashier, but that did not phase a class of 22 fourth graders one bit. They happily presented me their solutions to the problem. It wasn’t until the class discussion that finally the idea was raised that a student wasn’t actually sure how much money Jamal had. I said that’s an interesting point and decided we should reread the problem together to see if we missed something. As we read “What information is needed to determine…” I stopped and asked my students what those words meant. Finally it dawned on them what they were being asked to do. It was a wonderful a-ha moment for them.

If you’re with me until now, thanks for taking the time to read all of this. While blog posts are encouraged to be on the concise side, I have lots to say, and saying it gets me excited and reinvigorates me.

Sure, in the end I did P.O.D. for test prep, and sure it turned out to be super effective with regards to my students’ scores on the objective 6 questions that year, but it turned out to be about so much more than that. It was about empowering students and helping them become the mathematical thinkers I wanted them to be all along. It gave me practice serving more as a coach and resource rather than as the voice of authority in my classroom, and it taught me a lot about how my students reasoned about solving problems. Now, if only I could have been on a TEAM of teachers that did roughly the same thing I wouldn’t have to be sharing it now as something I’m proud of that made my class distinctly mine.