A few weeks ago I was lucky enough to hear Brian Bushart (@bstockus) and Regina Payne (@reginarocks) talk about Numberless Word Problems at NCTM in San Antonio. Brian and Regina left me with lots of ideas to think about, and one I’ve started working on already is numberless graphs. By the way, Brian blogged about this idea and I found that post to be a really helpful starting place when trying to figure out how to do this.
I happened to have a planning meeting with 4th grade teachers coming up right after NCTM in which we were planning a unit on data, so I thought I’d try this routine out with them. (By the way, I called it Notice and Wonder Graphs because it seems to be about more than being “numberless” to me.) This was the first image I showed teachers. I asked them:
What do you notice? What do you wonder?
Here’s what they said:
Notice:
“I think there are two groups being compared.”
“It looks like the difference between the dark and light green are shrinking over time.”
“The third pair of bars looks different that the first two.”
Wonder:
“What do the numbers on the bars represent?”
“Do the dark green and light green go together?”
“Are the same two things being compared each time with each pair of bars?”
Then I revealed a little more information with this image.
I asked “What do you notice and wonder now?” “How does the new information change your thinking?”
Teachers wondered:
“Are three different things/categories being compared? Or is the same thing being compared over three different times?”
“Are the numbers percents? Why don’t the three pairs of bars add up to the same number? Why don’t they add to 100?”
“Is this graph based on a survey question?”
Next I revealed the title of the graph.
Again, I asked “What do you notice and wonder? How does the new information change your thinking?” (What a beautiful routine for practicing revising your thinking, right?) and “Considering the title of the graph, what do you think the x-axis labels might be?”
The teachers thought the title was referring to the third pair of bars, considering 53% is close to half. However we all agreed that “More than half” could apply to the 84% or the 82% as well.
Finally, it was time for the big reveal!
“What surprises you? What are you still wondering? What questions might you ask about this graph?” I asked.
Teachers still wondered why the first two sets of bars adds to 96% but the third adds to 94%. We decided that some people were so disgusted by the idea of pineapple on pizza they refused to even answer the question.
I love this routine for many of the reasons that I love Brian’s numberless word problems–it slows the thinking down and focuses on sense-making rather than answer-getting.
But I also love it because it brings out the storytelling aspect of data. So often in school (especially elementary school!) we analyze fake data. Or, perhaps worse, we create the same “What is your favorite ice cream flavor?” graph year after year after year for no apparent purpose.
I’ve decided to make it a goal to think more about data as storytelling, data as a way to investigate the world, and data as a tool for action. In my next two posts (YES, people! I’m firing the ole blog back up again!) I’m going to delve into the idea that we can use data to discuss social justice ideas and critical literacy at the elementary level. I’m just dipping my toe into this waters, but I’m really excited about it!
Have you tried this routine with students or teachers? I’d love to hear more about your experiences.
Math Exchanges 
Not to mention getting to have conversations like this – with teachers or students – is so much fun! I do like Notice and Wonder Graphs. It’s a more versatile title. The reason we even tried it out is because we noticed that our students consistently missed critical information in graphs so Regina and I wondered if we could apply what we learned from the Numberless Word Problem routine to graphs. If numbers appear in the first image, as they do in yours, then it doesn’t make much sense to call this a “numberless” problem.
The graph you chose is fun, too. I love the idea that data tells a story, and graphs like this do such a good job in such a small amount of space. This reminds me I owe you another blog post about a different graph that I think you’ll like. My to-do list of blog posts is getting longer than I’d like. I need to set aside some time to sit down and write.
This is exciting work that you’re doing, and I look forward to hearing about your further adventures trying it out with teachers and students!
It always focuses our attention too, doesn’t it, the gradual reveal. That’s a thing about storytelling too, I guess;
This particular one says something else to me, about the independence of variables. If you were just number-crunching, you might think you could just arrive at the percentage who like pineapple on pizza by doing something with the liking pizza and liking pineapple figures. We all, quite viscerally, know that’s not true though. The tastes ‘interfere’. This is another advantage of real data – that it says other things apart from the main focus, that are also worth experiencing.
It strikes me we could do with a directory or bank of these, maybe with the gradual reveal slides included too. I’ve looked at real data with students, but not in this numberless way. I like the idea a lot!
I agree about having a bank of these, Simon! I’m going to try to create this for/with the teachers I work with and will definitely share!
I’m a fourth grade teacher who loves notice and wonder and numberless word problems. I can’t wait to incorporate this awesome data work in our upcoming unit. I know that my students are going to notice so much more and be far more engaged. Thanks for sharing this!
Thanks, Marie! I’d love to hear about what graphs you use and what yours students notice and wonder!
Wow! Thanks for writing this! So exciting to hear a great title, Notice and Wonder Graphs. I agree with Brian and love it. That is the key to a problem that Brian and I are trying to solve – helping students slow down and think about the story being told – to notice and wonder as the story unfolds. The end objective of continually going through this routine with a variety of graphs is that students begin to see the story in the data they collect as a “normal” happening for their thought processes as they analyze the data and clarify understandings. I can’t wait to hear what happens next.
This is yet another time I’m excited about the direction math instruction/learning is moving. The focus on asking students to think and question rather than memorize is a challenge for me, but one worth facing. I’m really looking forward to your future posts!