Doing Math with #ElemMathChat

Last night we kicked off the fourth year of #ElemMathChat. Yay! It’s so exciting to spend an hour each week talking with and learning from so many passionate educators.

One thing I’ve often heard from participants is that they like that we regularly do math together during our chats. I didn’t want to disappoint in our first chat of the year, so I dropped in a few tasks. I thought I’d collect them together in a blog post in case anyone missed the chat or wants all the pictures gathered together in one place. So let’s get started!

How Many?

This task actually appeared before the chat. I’ll admit that I sometimes try to cram a bit too much into our hour together – I want to do it all! – so I opted to move one of the questions out of the chat and instead turn it into something fun for folks to play around with during the day leading up to the chat.

I saw two common answers to this question throughout the day:

1. I assume you mean triangles. I see 4.
2. How many what?

I owe Christopher Danielson thanks for turning me on to this deceptively simple question as well as for engaging with some of the folks yesterday who were tackling the question as it relates to this image.

I highly recommend checking out Christopher’s blog post where he talks more about this question and shares some images you just might want to use in your classroom. He only asks that you let him now what kids do with those images and ideas. You can share with Christopher on Twitter @Trianglemancsd.

Let’s Estimate!

For our first task during #ElemMathChat, I asked everyone to estimate the number of hats in this sculpture:

Source

When I first saw this sculpture at the Fort Worth Convention Center at this year’s CAMT Conference, I was instantly curious how many hats were used to make it. It took some digging, but I finally came up with all the information I needed.

I asked participants to share their too LOW, too HIGH, and just right estimates. What I’m really looking for is the range they’re comfortable with. How risky are they willing to be with their estimates?

• This is a low-risk estimate: “My too low estimate is 10. My too high estimate is 5,000. My just right estimate is 500.”
• This is a riskier estimate: “My too low estimate is 400 and my too high estimate is 500. I’m pretty sure the number is somewhere in the 400s.”

Notice the difference? One person isn’t as comfortable limiting the range of their estimates while the other person has narrowed it down to “somewhere in the 400s.” I don’t really care about the just right estimate so much because I value helping students come up with estimates that make sense and are generally close rather than valuing whether or not they guessed the exact number. Helping students get better at estimating and be willing to make riskier estimates takes time and practice, but it’s valuable work.

Here’s the final reveal with some additional information about the sculpture, in case you want to do this activity with your students:

Numberless Graph

As much as I love numberless word problems, I’ve been fascinated with numberless graphs this past year. I knew I wanted to include one in our chat! When I shared this first image, I asked my go-to questions, “What do you notice? What do you wonder?”

The engagement was high and it was so much fun to see what people noticed and wondered as they looked at the graph.

We moved on to another question before coming back for the second reveal. Again, I asked, “What do you notice? What do you wonder?”

Adding the scale and currency amounts just increased the wonderings about what this graph could be about.

Finally, after building anticipation and making everyone wait through another chat question, I finally revealed the full graph and asked, “What questions could you ask about this graph?”

Source: SensorTower “Japanese Players Lead Pokémon GO Spending Three Times the U.S. Average Per Download”

 

 

 

The noticing and wondering didn’t stop! It was great!

In case you’re wondering, Pokémon GO is a game you can download on mobile devices. The game is free, but there are things you can buy within the game. So what this graph is showing is the average amount people spent buying things inside of the game. In Japan, for example, looking at all the people in the country who have downloaded the game, each of those people has spent $26 on average. In the US, on the other hand, the people who have downloaded the game have each spent $7.70 on average. The interesting thing about this is that the data is a bit misleading if you don’t know more details:

Source: SensorTower “Japanese Players Lead Pokémon GO Spending Three Times the U.S. Average Per Download”

This leads to a great discussion to have with kids, “If US players aren’t spending nearly as much in the game as players in Japan, then how come the total amount earned from purchases in the US is over $100 million more than in Japan?”

A Lens Looking Forward

This isn’t doing math together, but I did want to share the final question of the night.

My lens for a long time has been play, but I think I’m due for a new one. Not sure what it’s going to be yet. What about you? What word would you choose to use as a lens for the work (and fun!) ahead this school year?

 

 

 

Sink your teeth into data. Don’t just nibble.

Looking for math all around started as a challenge I made for myself and I’m realizing it’s becoming a full-fledged theme for my year. When I had to think of a topic to moderate this week’s #ElemMathChat, I started by asking myself, “What’s a topic we haven’t talked about since the chat started in August 2014?” After some brainstorming, I eventually came up with analyzing data. What a great topic for my theme! I don’t think I could throw a rock without hitting some data in the world around me.

In fact, as I was fleshing out the topic for the chat, I was regularly checking some real-world data online. After a long dry spell, we finally got some rain in Austin. And by “some rain” I mean a deluge. On a couple days last month it just kept pouring and pouring. Throughout each day it rained, I found myself checking our neighborhood weather station on Weather Underground to see how much rain had fallen. By the time October was over, we had received 10.3 inches of rain in my neighborhood! That simple piece of data became the catalyst for tonight’s #ElemMathChat.

I started digging into rainfall data for October, then rainfall data for other months, and finally I expanded my data dive into other cities in and out of Texas. When I was done, I had a spreadsheet full of various tables of data that I wanted to share in my chat. To make this chat work, I realized I needed to be intentional about how I shared the data in order to tell a coherent story. I also wanted to create a variety of data displays that would match the various data displays students encounter across grades K-5. As an aside, I think #ElemMathChat sometimes leans a bit heavy on content for grades 3-5, so I was trying to be mindful to show some graphs that could be analyzed in a Kinder or 1st grade classroom.

It took several nights to research, create graphs, and pull it all together to make a story, and in the end I’m proud enough of the final result that I wanted to capture it on my blog.

Before starting my data story, I shared the following guiding questions that tied into my primary goals for the chat.

My Data Story

Our story begins with the piece of data that started it all. I asked the participants to tell me what they noticed and wondered about this statement.

What do you notice and wonder?

Many people wondered how this amount of rain compared to other cities. Funny you should ask.

What do you notice and wonder as you look at this pictograph?

One thing I noticed is that I accidentally left the key off the graph. Oops! Each picture is meant to represent 1 inch of rain. Despite my mistake, several people liked that the missing key invited students to wonder about what the pictures represent. That sounds like such a wonderful conversation to me that I opted to leave the key off when sharing the picture in this blog post.

I had a little fun with this graph because I had to decide which cities to include. I decided to focus on other state capitals, but the question became, which ones? When I noticed how many start with A, I decided that was more interesting than picking random capitals. It just so happens that all the other capitals on this pictograph are all on the East coast, so I wonder if it would have been better to choose capitals with greater geographic diversity. In the end this is just a fun way to get our story started so I’m okay with what I chose.

Next we moved from cities outside of Texas to cities inside of Texas, specifically along the I-35 corridor from San Antonio to Waco.

What do you notice and wonder as you look at the October rainfall totals for these cities?

Now that I shared two different graphs, what questions could you ask students about these graphs? What math skills can students bring to bear to interpret and further understand the data in these two graphs?

One thing that we often do with graphs found in textbooks and tests is ask one question about them and then move on. How unfortunate! There’s so much rich information to dig into here. One of my key points for tonight’s chat was reiterating something I read by Steve Leinwand about mining data. Ask a variety of questions about data displays. Sink your teeth into them; don’t just take a small nibble.

The one thing that stood out to me and many others in the chat was how little rain San Antonio received. The difference between San Antonio and New Braunfels is quite striking considering how close they are to each other.

Other people felt that Austin’s rain wasn’t fitting with a general trend in the data. I didn’t want to get into it in the chat, but I’ve noticed the rainfall in my neighborhood tends to be less than other parts of the city. Our weather station recorded 10.3 inches for October but others in Austin clocked in at closer to 13 inches of rain. I thought about using the larger number, but because the catalyst for this whole story was my weather station’s data, I opted to stick with that. By the way, I don’t think it’s an issue with our weather station’s rain gauge. Over the years there have been many instances of rainfall in other parts of the city while my neighborhood in north Austin remains bone dry.

Now that we’ve looked at rainfall in and out of Texas, it’s time to drop a bit of a bombshell. With this new information, what story is the data telling so far?

Here’s what I see as the story so far: Austin received 10.3 inches of rain in October, which was a lot compared to areas outside of Texas, but fairly common for our area in Texas. Not only was this a lot of rain, but it also fell in a very short amount of time, 6 days.

Next, I asked for help. Now that you know it rained only 6 days in October, which data display would you choose to represent October rainfall?

Option 1

Option 2

Most people preferred option 2 because it shows the full picture of October. That was surprising to hear. In my mind, because we just saw the picture graph showing that it only rained 6 days in October, I didn’t feel option 2 was needed. I already know it didn’t rain on very many days, so why waste the space with all those days showing 0 inches of rain? Option 1 puts the focus squarely on analyzing the rainfall on the days where it actually rained. In the end there’s no “right” answer, it all comes down to how you justify showing what you choose to show.

We’re nearing the end of our story. There are two more graphs remaining. What does this next graph add to our story? What is one question your students could answer based on this data?

I love looking for relationships so here are the questions I came up with:

• Where do you see the relationship “three times as much” represented in this graph?
• Where do you see the relationship “half as much” represented in this graph?

I especially like wondering what students will come up with because both questions have more than one correct answer.

And now for the last graph. How does this close out our data story?

Here’s a follow up question for you. What could be the sequel to the story I just told? How could you and your students explore and tell the sequel? What other data stories could your students explore and tell?

I closed the chat, and I’ll close this post, with two key points I want everyone to take away from this conversation.

Kickoff! #ElemMathChat

Tonight we kicked off a new weekly Twitter chat, #ElemMathChat. Hooray! As the name implies, the chat is designed for elementary school folks to talk about math.

I’ve been so excited to get this chat started! For the past two years, I’ve been a member of the MathTwitterBlogoSphere whose membership is primarily composed of middle and high school teachers. There are a few of us elementary-minded folks. We have appreciated all of the interactions we’ve had with the MTBoS. However, after meeting up at this year’s Twitter Math Camp, we decided our mission this year is to grow the elementary-side of the MTBoS.

And so it begins.

Tonight’s chat was a huge success! We had a great turnout with educators from around the US and Canada. (Thanks for catching my mistake @ChrisHunter36!) Everyone seemed excited about having a forum to discuss elementary math specifically. One person even commented that she was happy to have a place where she could be taken seriously. She said she’s tired of being considered “cute” for teaching first grade.

Our topic for the first chat was balancing problem solving with teaching/covering math skills. If you want to catch up on the conversation, you can check out the Storify put together by @davidwees. While the overall conversation was energetic and interesting, I was left a tiny bit disappointed.

I think it’s because I was the one who suggested this topic. Balancing problem solving and covering math skills is something I have struggled with myself as a teacher, and now as a district curriculum specialist, I am hearing from numerous teachers who are struggling to find the same balance themselves. So going in, I had some clear ideas of what I wanted to talk about and get out of the discussion.

The first question was “How do you define problem solving in the elementary math class?” This generated some interesting discussion. Some key points that rose to the surface for me were that problem solving involves thinking critically, collaborating, and using math as a tool. I especially like the “math as a tool” metaphor because it gives meaning to why we’re learning it in the first place. I think it’s often an implied message, but one educators need to try to make more explicit. I also liked how people described problem solving as a time to make kids get out of their comfort zones and make their brains sweat. I love the image that conjures in my mind.

The interesting thing that came out of this first question is that everyone seems to have different ideas about what problem solving is. Some people talked about it in a way that sounded like solving word problems, whereas others referred to rich and engaging tasks that focus more on the process than the endpoint. This is one area where Twitter chats can frustrate me. The conversation is happening so fast with so many people talking simultaneously that it can be challenging to pull the threads together into a coherent whole.

Maybe that’s what I need to learn how to do as a moderator. Instead of following my script of questions, I could have stopped and made question 2 be “So I’ve heard problem solving described as ___, ___, ___, and ___. What is one definition we can all agree on?” The conversation over the rest of the hour felt weaker because we didn’t necessarily have an agreed-upon definition to base our discussion on.

Question 2 also had some problems: “How do you define math skills?” This is where I had a clear idea of what I meant, but the majority of the group was on a different wavelength. Since we had just talked about problem solving, everyone seemed to think that I meant the Standards for Mathematical Practice or general thinking skills that are needed to solve problems. What I really meant, and I did try to clarify, are the nuts and bolts skills that teachers need to teach their kids: adding and subtracting whole numbers within 1,000, multiplying fractions with whole numbers, interpreting dot plots, and measuring angles, to name a few.

Here’s an example to illustrate the tension I was thinking about when suggesting this week’s topic. Learning a skill like long division takes time and effort. It is a very structured thing to do, but until students understand it, they are prone to making many errors. Can I do a few problem solving activities and have my kids somehow come away from the experiences as masters of long division?

You may be thinking right now, “But kids don’t actually have to know long division in order to solve problems. They just need a strategy that makes sense to them.”

I agree with you. However, in Texas and in Common Core, the standards do explicitly state that students learn to divide using the standard algorithm. So like it or not, it’s a skill that students are expected to learn.

Here’s where the tension comes in. Long division is just one skill. There are numerous other skills students are also expected to master in any given grade. How do you ensure the nuts and bolts mastery while at the same time providing ample opportunity for the types of activities that require critical thinking, collaboration, and brain sweating?

And please don’t take any of this the wrong way; I don’t fault anyone in the chat for not providing me a satisfying answer. To be honest, I don’t think a one hour Twitter chat is going to be the place to find concrete answers to big questions like this. It doesn’t mean I don’t want answers (hence the tiny bit of disappointment I felt), but I have learned over the past two years what Twitter can and can’t do.

What it can do is bring together like-minded people to fuel conversations and build relationships. The more I connect with people on Twitter, the more I get to know them. I can start chatting with them outside of our weekly chats. Perhaps I ask for help with a problem I’m having, or perhaps we set up a Google Hangout to have an actual conversation about a particular issue (good-bye 140 character limit!), or maybe we even collaborate on a proposal for a national conference.

Valuable professional relationships can grow from short, weekly conversations. It’s why I’m still here two years later, and it’s why I’m excited to get this specific chat launched. I’m eager to meet like-minded elementary folks and start forging some new professional relationships.