Developing & nurturing data literacy using slow reveal graphs to empower K-5 students

All right, welcome. Thank you so much for being here. Um, I'm just going to very briefly introduce our keynote speaker, um, Jenna Lee. She is, uh, math educator working in, uh, K8 space and the person who has invented slow reveal graphs, which she's going to talk about today. It's very exciting. So, um, yeah, let's welcome and I'll turn it over to Sounds good. All right. So, today we're going to be talking about developing and nurturing data literacy and the strategy that we'll be focused on to use it is slow real graphs, but I think that this is broader and that it opens up to lots of different things that you could use within the classroom. So, with that, I will say I was like, "Oh, of course I'll go gravitate towards that side because that's where all of you are, and I forgot that I need to be able to click slides." So, I'll probably be over here. Do you want me to click slides? No, it's all good. So, do you have any idea how many articles there are about how data is the future and how we need students to develop all these data skills so that they can be a part of our future? There are so so so many of these. I did want to share one quick things from the first the last one here which was the role that data will play in our future. They all kind of seem very like science fictiony and like sometimes that's like provoking for students or like teachers will be drawn to that sometimes not so much. But the opening line of this one was data is not the new oil. Data is the new air. What I liked about this was that oil for me conjures up all these feelings of like consumerism. It's literally fueling the climate crisis. It's destructive in that way. Whereas air felt very like immersive and refreshing and like this is something we need lots of clean air like we can really get into this and it will be important for our future. But before we continue, I did want to share that I've left off a little bit of the quote, which is it continued with we breathe, we generate, we consume data through every step that we take and every interaction we participate in, which very quickly goes from this like, oh, we're breathing in all of this data and we're developing these beautiful consumers of data to more like this. a lot of surveillance capitalism and that we need to be careful with how we're interacting with data, how we're producing data, and also how we become critical consumers of data. So, as we're thinking about what future we envision for today's students, is this movie like people have still seen like Minority Report from a long time ago? It's very insidious. So, the first one here, so what future do we envision for students? Are we thinking about data as air of like this is something that is productive we can build or we can develop these really interesting ideas about the world and we can make more productive decisions or in this dystopian world over here um they're using data to predict who will commit crimes and then um convicting them before they actually commit them. So are we using data basically for good or for evil? How are we developing good citizens? And the questions we're going to be exploring today What does it mean to be data literate and how do we support students in developing this data literacy? So I assume that many of you are here today because you were like oh it is the keynote and we probably should go to that. Um but you still had a choice. I know there's other sessions at this time. You still made a choice to come here. So I wanted to say that you're at the right place if you believe that data literacy is a critical part of global citizenship and that as teachers we are cultivating that within our classroom. We're developing not just thinkers but future citizens. You want to engage students in sensemaking and mathematical discourse. We're talking a lot about student talk in the classroom. Not just students completing worksheets although that can also be helpful. and you love to celebrate your students brilliant ideas. They already have such great thinking and even with that great thinking, we want to nudge them forward to develop things further. So going to quickly look at this graph. I'll do a little bit of talking aloud, but first I want you to just take 10 seconds to yourself. Think about what do you notice about this graph? What are you wondering? What is this? So, we're going to have opportunities later to discuss a lot of what like what you're noticing and wondering. I'll do a quick note or quick think aloud here of what I was thinking as I noticed this. First of all, I noticed that I'm not fully certain immediately what the axes mean. We have these numbers here along the x- axis, numbers here along the y axis, and I don't really know what they are. I do notice that there's color coding. Always drawn to color coding. Love that. Um, and I see that there's one red dot. It's labeled USA, which made me think these are probably countries. It's hard to see other ones. N probably Norway. DEU, I think probably Germany for Deutseland. Tur is probably Turkey. So I noticed that and then as I'm thinking about it, okay, so like the US is way over here. It seems like these quadrants are important and that I notice that there is some labels there. So I see health spending is up here, life expectancy has an arrow going down, which to me then I interpret that as okay, so the healthcare spending is up, the life expectancy is down. So, they're spending a lot of money, but that isn't translating into greater outcomes for life expectancy. Start to notice over here. Okay, all the green ones. Oh, those say lower spending, higher life expectancy. And I noticed that those are things like Spain, Espa there, Korea. I was kind of thinking it was maybe going to be some of the ones that have like more staterun care like Canada or Great Britain. Those are actually kind of over here. I'm a little surprised by that. And it honestly as I was like looking at all of this and trying to make sense of all of these numbers like is this standardized in some way like does this account for currency differences does this which seems to represent one is that just like the average life expectancy across the world and then this would be like 2% higher 1% less not really certain and there was so much that I had to do to do that it was a very heavy lift and it took a lot of processing and thinking That's because I have some practice with data literacy, but if you threw this in front of a lot of students, it can look overwhelming, especially in the things that are missing. So, with that, oops. Um, as I was thinking about how we support students, I think it's wonderful to give them this and to like have them talk it out, but I think there's other strategies that we can also use to scaffold it and to make it so that students can go through similar processes even if they're not quite as trained in it. This is all part of the statistical problem solving process. This is from gay which is the guidelines for assessment instruction of statistical education also endorsed by NCTM and ASA which is the American statistical association. So the guidelines say that it's really important to go through the entire data process. So you formulate that statistical question. You consider and collect the data. You analyze the data. You interpret the results. You can see the arrow cycling back. Maybe as you analyze the data, you need to go back and change your question a little. Maybe as you're interpreting the results that makes you think about how you collected the data. And it's important to go through these whole processes. And I know that since I'm in classroom still, this is not a fast process. This is not a like we got 20 minutes, we're going to just blow through that whole thing. So, we have to also incorporate other ways to build in opportunities for students to interact with these skills. We'll be talking mostly about these two. Analyzing the data and interpreting the results as we're thinking about data literacy, thinking about the long talk aloud I did. I had some graph skills started to get some data analysis and then we're also going to start to think about critical literacy. Graph skills are the reading and understanding of the features. So that's the like figuring out what those numbers mean. Can you interpret what a point means? Data analysis is analyzing, interpreting, and evaluating that information. Thinking about what does it mean? The US seems to spend a lot of money for not great results. That is a big takeaway that would be in that data analysis category. And then we have critical literacy. considering the context for the data, what's missing, multiple viewpoints and bias. Something that I noticed about that initial graph is that there was a lot of European countries and a couple Asian countries listed. I didn't see a lot of African countries listed or I didn't see color coding for different types of healthare systems. And I wonder how that would change our viewpoint. So what we're going to explore and what will be more interactive is what does it mean to be data literate? Thinking about those three things. So again it was thinking about graph skills, data analysis, critical literacy and then how do we support students in developing data literacy. So one way and again this is just one way. There's lots of ways to do this in the classroom is to use something called slow reveal graphs. Have any of you used these before? You can just do like a me too. Not us. I'm actually really excited that you haven't because it means that we'll get to do something new together. Um so gap is an instructional routine. Instructional routines um things like have you done number talks in the classroom before or like a which one doesn't belong? So, it has that predictable structure that you can rely on, but it has a novel new context. And the benefit of this is that kids know exactly how to interact with this. They know what it's going to feel like. Um, and then the math swaps out or the context changes so that they can focus really intensely on the math and the context. So, we are going to try one out because I think that is the best way for you to learn the structure and also the most fun. So in a slow reveal graph, everything is stripped down. At first things have been removed. There's a lot more to this graph than what you are currently seeing. But I want you to just take a look at the strip down one. Think about what you notice. Think about what you wonder. I would like you to turn and talk with someone near you. Think about or share with them what you noticed, what you wonder about this one. I know these are all elementary people. What did you notice or wonder? I'm wondering what each box represents and what the different what the line in the pink is like. Why? I know. Kind of weird, right? So, like you're allowed to make mistakes. That was, you know, the making mistakes. So this kind of ties in with it because make mistakes when you're you can redo your thinking which is I think the slow that's a huge thing. Will you share that later? Maybe not right now but very soon cuz it's a huge thing. Just point at me and tell me. Yes. What's your name? Lisa. Lisa. Nice to meet you. So I'm going to have you have some people share with the microphone. Fantastic. All right. I'm going to have you back up here in three, two, one. Apologies if I cut off any conversation. Hate doing it, but it happens. Um, it was really nice to hear some of the things you're noticing and wondering. Joyy's going to go around. Who would What' you say? Someone Jenny is going to go around. Thank you, Jenny. Yeah. Um, who would be willing to share something that you noticed or that you wondered about this particular representation? Go ahead. Um, I know it's pretty small talk. We need it for Zoom and accessibility. Um I noticed that there is a shift in um color from the bottom to the top to a pink background from a white. So you're talking about the background here. So you know it's like a white background and then this upper part is pink. Very nice. Anyone want to build off of that or share something else that you noticed or wondered back here? Thanks. how this is working. Uh I notice that going from left to right and then uh down to up there's like a direct relationship between it going across. So like as you move from left to right the things are going up. Yeah. So you can see like it's increasing. I think when I've done this with kids often say like oh it looks like staircases cuz like staircases are often things that will continuously go up or down. So we have that. I heard someone had actually noticed the color too. So like the background changes color, but we also have the bars seem to change color. Anything else that you wanted to share before I reveal some more information? All right. So with that, there is more to learn. Here's a little bit. Do you see what information just popped up? What information did we just learn? Someone can raise a hand and I'll just repeat it in the microphone so that people at home can hear. What information did we just get? What is that? So, I hear you saying sound. I don't see anything that says sound. What makes you think it's sound? What did we actually just learn? Like what's the what popped up? I know you guys are already jumping to like the data analysis part. We do have we have things along the x- axis. I will say these are categories. You saw with other ones we'll have like quantitative data along the x-axis. These ones are categories listed for the bars. Bar graphs are often representing categorical data but not always. So, and you had said sound and that was interesting because we have raindrops, conversation, city traffic, vacuum cleaner, TV, stereo and headsets and rock concert. Do we feel like those are all sounds? Anything else that these could be because it doesn't actually label anything. If these are in fact sounds, do the bars match your expectation of what you might see for the data representation? Yes. Why does it match? Let me get the microphone back to you. Sorry. Gonna keep you busy for a couple minutes here. Go ahead. Over here. What's your name? Adrienne. Adrienne, go ahead. The categories represent the model um because you would see things getting progressively louder in that list of um categories. So, conversation would be a louder thing than raindrop. Traffic would be louder than conversation. Um etc. Oh, it's interesting the way you describe that because I feel like often I'll get kids being like rock concerts are really loud, raindrops are really soft. But you were comparing individual bars too. So you were saying that conversation is louder than raindrops and city traffic is louder than conversations and that we can actually tell a relationship between many different bars, not just the extremes, which seems important. I'm going to reveal some more information. So you were right about sounds. So what new information did we just learn? Can you see it? Go ahead. Um, it's measuring. So, he said it's measuring dec. And in fact, it is. So, we just learned that the smallest bar popped up and it says 40 dB. Are people familiar with measuring things in decibb? Decb are the way that we'll measure sound. It's a very abstract con or concept. Um, and like honestly pretty hard for kids to get, but that here we have at least a representation. So like if this is 40 dB, does this change your thinking about any of the other bars? Are you able to predict any of the other values? Turn and talk with someone near you. How can you use that new information to predict other values? What do you think? I'm going to assume each one is 10. I know the K35 example. It is. How did you know them? 40s got 10 + 10 + 10 + 10. That's No. And like kids will come at it different ways. Some kids will say the division and some kids will be like oh well like it's like kind of a guess and check with a big is it tens? Tens feels right. They have like a gut feeling. Yeah. Like something playing sound too loud. That's what at talking about. Interesting. All right, I'm going to have you stop and get back up here in three, back up here in two, back up here in one. Back up here in zero. So, I will say as I was listening in, you guys are very data literate. People are already starting to jump into like analysis and critical thinking, which I think is awesome. I will say most kids at this point are still kind of like fixated on the 40 dB, but we can talk about whatever it is that is going on in your head. So, first we have the 40 dB for this particular bar for raindrops. Does that help you predict values for other bars? Yes. How does it help you predict the values? Would you want to share? There's four boxes and 40 dB. So you have to assume that each box is then 10. So there's four boxes representing 40 dB. Thanks. I'm just going to try to repeat it for now, but like we'll have you over here. So four boxes, 40 dB, that would then 40 divided into four equal parts, 10 each. So if each of these is 10, we can then understand or we can predict what we think conversation will be worth. What do you guys think conversation will be worth? Everyone can just do it together. 60. All right. So conversation 60 city traffic is vacuum cleaners are TV stereo headsets interesting you guys are so good al together doing it corally and then it changed a little bit and I know that people already had this question about like it switches to pink what's going on there people have some ideas before we get to the ideas about the switching to the I think let's see if we can even just get the value here. So the next one I think reveals some of the values. That one is in fact 100. Does 100 make sense? Yes. Why does 100 make sense there? 10 boxes. 10 boxes. What about this one? 105. So I heard people say 105. Do a me too if you agree. Raise your hand if you disagree and are brave enough to share why you disagree. We feel good about the 105. Why is it 105? So, I'm hearing people are saying like that's half a box. It is really hard to know. Um I will say like there's a picture later on where you see kids like rushing with like um rulers. I've seen kids rush with rulers at many different graphs because they really have to know like they want they'll come up to the board and be like, "Is it in fact?" It looks pretty close to a half. So, I will say in the next reveal, I think you can see it. It's 105. And then the last one was 140. You might also notice, although I don't think I heard this coming up with anyone that I heard talking, this bar is not labeled. So, we have something that's not there. But people were also starting to think about what that pink means. I actually thought that would come up around now. So you will see actually the next reveal is a little box. What does this box say? And there's like a question mark in there, too. But what new information did we just learn? Go ahead. We learned that the um the pink boxes represent where where the decibel is damaging to hearing. Is that something I think I had heard like in both groups over there in the back? Yeah. So they were starting to think about like all right so this pink switches is that where it's dangerous and in fact that is where it's dangerous although I have hidden and the information about what that level is. Can you figure out what that level is? We'll reveal that part. I know I've been over there a lot. What about you guys? Can you figure out what that level is? Oh, so you're like thinking about like what is the 140? I was actually even thinking about like what is the like decel level but we'll come back to the airplane thing because that airplanes are very loud. Still think it's my daughter but you know at 140. How old is she? She's 14 but very capable. Pretty pretty. Um my kids can also like they have powerful lungs. It's a source of pride and a source of pain. Um, so decibb and above can damage hearing. What is that line? What is that level? Did you figure it out? Go ahead, Adrian. 85. Why 85? Because that's the point that it switches from purple to pink. And you might even be able to build off of like the 80 to be like, all right, so it's 80 and then it looks like a half more, half of a block. That half a block is five. So it's going to be 85. Quickly reveal that it is in fact 85. And then we have this last one. So John was thinking airplane. What do other people think? Airplane. Other things. Give you like 10 seconds to turn and talk with people around you. See what ideas you can come up with. Yeah. Hand dryer. Oh, they're miserably loud. My six-year-old is like very sensory sensitive and like now we know all the loud noises. All right, let's see what we can generate. Eyes up here in three, two, one, zero. So, I will say that one thing that felt a little bit less authentic to me is not just that you guys aren't seven-year-olds, but that you had like all this deep thinking very quickly that seven-year-olds do get to, but it takes them a little bit longer. Usually, when I'm facilitating these in a classroom, I'm writing all over the board. I'm recording their ideas. I did not want to write on this beautiful um projector sheet and unfortunately like it would be a little bit too large for the board, so didn't go with that. Um, but I did want to say that I think annotation is super important. We want to honor kids ideas, build from them, represent them. So, one idea was that this could be airplanes. Did we have other ideas? Lisa, what was your idea? Oh, I said, you know, they said the different football games in the football stadiums or if they did a concert in them, but there was they actually caused earthquakes. So, that happened at a Taylor Swift concert, didn't it? Yeah. Yeah, she figured it was lion blog. Yeah, I did figure it lion. It was a little too soon for that one. Right. And we have rock concert here, but like maybe there's more extreme rock concerts that are like even louder than like typical ones. Any other ideas we can get up here? Motorcycle. What' you say? Train. Fire truck. Fire truck. And lots of big urban noises. Go ahead. So, we talked about um you know comparing it to the Barbie next to it. So, it's going to be louder than the guitar. Yeah. But it's not as loud as an airplane, maybe. Um so, maybe I thought of like power tools where workers need to ear to wear ear muffs. Um maybe a electric saw or something like that. So it's it's going to be like compared to the the bar next to it. So it's a bit louder than the guitar, but not as loud as an airplane. Yeah. And in fact, do you ever see a construction workers will have like ear protection on and then I'll be walking by like I know they're there for longer, but should I also have ear protection? Go ahead. One of the folks online suggested school fire alarm. Ooh, those are so loud. School fire alarms. Lightning bolt. Lightning bolt. Feeling pretty good. I would say with the planes, the first thing that came to mind, I have no idea if this happens everywhere, but I'm from Boston and every year we have these super loud sonic jets fly over on the 4th of July. It's a tradition. It's a tradition I hate. They're super loud and they make everything like pop and you can like feel windows shaking and they do it in a celebratory way, but like it's very loud. So, here is what it is though. You guys here with a great list, but guess what? The real answer is not on your list. So, people seemed very willing to continue to add to the list. Lisa, I think now would be a time for you to like share something that you were noticing early on. Jenny, can we have the microphone? Thanks. A few years ago, I was at the same conference and the keynote speaker was about rough draft math and how you can go through and change your thinking even though you already gave an answer. So, this would be a great time, you know, all of us went, "Oh, when we did fireworks." So you can go through and you can change what you're thinking, especially when you use or when you get more information. So I'm writing up here for like people that want to check it out. Manny Jansen wrote a great book called Rough Draft Math. These are like we've talked about some of these ideas too together of like it's okay to revise your thinking here and in fact it is expected that you will revise your thinking and there is no shame in throwing something out and then be like oh I was wrong. Like do you feel bad for saying football stadium? No. No one should feel bad for that because you had this amount of information and then we're revising it. Even when people say things that aren't true given the current information, I find students are more forgiving in this routine because they're just expected to do it all the time. Like we're constantly like, "Let's change it. Let's change it. Oh, this new information changes everything." And then we're building these ideas. So if we're going to recap what just happened, we started with the totally stripped down graph. Then I added some category labels. Not all of the category labels, but most of them. You guys very quickly were like, "Oh, it's about sound. You jump straight to the inference level." Then we added some quantitative numerical information. In other graphs, you'll see in other grades it'll probably be along the y- axis, but these one were more directly labeled. We revealed the meaning of the colors, which people had noticed at the very beginning. In that very first stage, people were like, "Oh, the background changes. Oh, the bars sometimes change." So, that was something that was probably lingering in your head. So, that when we got towards this reveal, people were already thinking about it. It was multiple independent groups I heard already thinking about when we were talking about what is this one that had that half bar. People couldn't stop themselves from also thinking about what that pink meant because it had already come up. And then we integrated everything for the final reveal. And I will actually show you how kids did at the end too to like continue it and continue sense making about the data. So the questions that kind of propelled this and made it a routine were that it always launch with what do you notice? What do you wonder very open-ended totally okay to get things wrong in that moment and you have to be willing to revise your thinking. Then with each additional slide added, what new information did we just learn? Which I know felt a little silly to some people at first of like, yeah, that thing just popped up. Why do I have to say it? But it's important for us to all be on the same page and understand what is the new thing that's changing our thinking. It's the telling of the story. And so I think it's important to make that part really explicit so that we can talk about how that will then revise what we're thinking. So I think this routine actually in most iterations will touch on all three components of data literacy. We'll have graphing skills. You guys were really really good at identifying quickly that that 40 decel bar that had like the four little boxes. Um that that's going to represent 10 each. You had some good data skills. Then data analysis people were really quick to dive into. you were analyzing, interpreting, what does it mean that it's a little bit more like what does it mean when it gets above the pink level? And then there's critical literacy when we're thinking about the bias, what information is included, what information isn't included. Um, I will say I actually have I think the data John for the like a sonic jet or something and it goes higher than the fireworks. So there's information that is here, there's information that isn't here. And to dive a little deeper, I want to show you what some kids said. So these are from three different classrooms. This is a second grade classroom this last December. And so we were thinking about how can we assess their graphing skills and did this help them think about things. This particular graph I love for first and second grade because it builds off that tens and you have that half bar that kids always get really like invested in. Um so you have like the tens and the ones. It's really nice with first, second grade standards, but we also wanted to see could students interpret new data. So, I actually added on another category of the blue whale, put it up there. Can students now independently figure out what that is given that it also has one of those little partial bars at the top? And do students know how to add data? So, we gave them a choice. Um, they could do rustling leaves, a whisper, jet engine at takeoff, or a volcano. And they could then add it on to see like, do they understand enough of the graphing skills part of this graph to be able to draw their own. So, that first part was interpreting the new blue whale one. Um, and you can see I did not match the font. You can see that's all just added on. Um, and you can see these two different student work samples. and give you a couple seconds to just think about what you notice with them. What's the same? What's different? So, what do you notice? What's the same about these? What's different? They look very, very similar at first glance. The one on the left you did the work for you count 10 20 30 goes up from there. Yeah. So this kid is stip counting. Continue on the right. They have to do the they have to count by get up there. They have to do do the math. So and this is all like the students writing it. So I think this is like showing how they had solved it. I'm just going to repeat back what you had said for the microphone. Um so this one shows 10 20 30 40. You can see the skip counting going up. and that this one just labels it 10 10 10 and then that student would then have to figure out how to wrestle with like all of these tens and fives. Um, in both cases they are building up to that 185. But this kid was skip counting and this kid does see like those iterations. I also wondered if like I had shown some of that on the board. I think I had written in like 10 10 10 at some point and so they thought that was like how they represent it. They both seem to understand how to deal with all of those tens because they got to the 185. Um, but they've labeled absolutely everything along that line. This kid did not label everything. You can see that this kid decided to start from a different place. Can you see where they're starting from? So, we have like that 140. They seem to be skip counting just like that previous student. 140, 150, 160. And then like the shorter is worth five. they had labeled that directly. Um, that was actually more exciting to the teacher because she was like, "Oh, they're not just skip cutting. They're able to like count on by the tens." And this was showing like a new form of thinking for that kid. She was super excited. Um, this kid was inaccurate, but that's [Laughter] okay. I like showing lots of different examples. It's not like we do this and like 100% of kids got it. close to 100% of kids did, but we did have a couple kids that seemed to have this partial thinking that the teacher and I discussed because we're like, well, we want to remember that the kid didn't fully get it. And also, what can we build off of that they know? So, something we noticed was that they had those little jumps. It's like, oh, they seem to be noticing that increase that it's constantly increasing, but I think they thought it was supposed to be a constant increase and it's not 40, 60. They skipped 50. They didn't seem to notice that part. 70 80. But look, they wrote skip and then it says 09. They meant 90 when we asked them. It's like, oh yeah, that's 90. Working on trying to get them to write it more conventionally. So 40 60 80. And then they could see this 60 70 80 90 100. And so they're seeing that increase. They're seeing that pattern. They wrote if 105 is one less than 110. So that would be like the 110 would be like that next one. But unfortunately, it's not 110. It's still less than 150. When we spoke with this student, because I honestly was not fully certain what this part meant, but when we asked him, he was like, "Oh, well that's the 150 cuz like this goes up and then he felt like this was that same jump." Like it kind of felt like it was a roughly the same size even though it's a five and not a 10. So if you start at 140, the next 10 is 150. You have a question? Is that 110 or is it 140? Is it for which one? Oh, less than 140. Oh, this is a 140. Yes. So, one is one less than 140. You are correct. I had misread it in the moment, too. So, like this is 140. That's the one less. It's still one less than 150. I guess he's like maybe thinking he described it as like plus 10 when we talked with him. So, like this was like a plus 10. and that would be a missing plus 10. And then that would be a plus 10. Now, that is not a plus 10 jump. You can see that that went way up. However, he's doing some great thinking that we could then build off another time. Um, and clearly he's got some other things that they're working on too, given that second grade still writing 09 for 90. Um, but it's really helpful to approach it from an asset orientation where the teacher could see like, oh, he's not just a blank slate. It's not just like we're looking at this student's work and like he didn't get it at all. He was building from something and he got something out of the conversation. Um, and then this one was Raa at the very end. She had decided to add on all of the categories and this was a previous iteration of the worksheet um when we had a choice for 120. I cannot remember what the 120 is off the top of my head. Um, but you can see that she had not only added them all in, she was like careful about the five bar. Um, but then when I talked with Raa about her work about like why did you decide to like stick that in the middle because it's kind of hard to put in the middle. She's like well it belongs in the middle because it's in between those two numbers. And she actually, you can see had lined that up. She had used the 140 to build down to the 120 and then up to the 155. So through the independent activity after the conversation, we were able to see what graphing skills they had from this and also see kids flexibly building up, building down, which was exciting because they were about to go into the big second grade addition subtraction work where it's like that is the meat of second grade and she wanted to see if how ready they were. So in a different classroom in a first grade last May same activity we spent about 30 minutes doing the slow reveal graph and then this was kids analyzing the feature. So you can see here's me writing all over. I had probably erased some of them. These kids I remember in that second grade class explicitly writing like 10 10 10 because we wanted to remind them of the first grade work of building off tens. You can see in this class I had written like four 6 7 8. We hadn't even gotten to the tens yet. This was just like the kids had counted the bars and so they wanted to have that listed. But you can see they went 46 78 and then they were like uh they weren't fully certain because it was like what do we do with this? It changes the color and it's half. That felt weird and different to them. And it was first grade so they had just done some of the fraction work around like what is a half? You can see I had labeled that there. They had also wondered why do three towers have pink but four do not. That I left on the board for a while to kind of like ruminate, let it stick in their brain because that would be a big thing later on. But as we were analyzing the features, you can see there still has the four six seven8 label, but now we have all the tens labeled like that. 10 10 10 10 10 10 and then we got all the tens and then it says half of a block and just talking about that what is that half of a block mean was really challenging for the first graders and we had let's see doesn't fully zoom in but you can see we had like there's that five there but they had wrestled with like is it half of a block what if it's four what if it's six does it have to be exactly half is the half going to be like always there. Here's that half of a 10 block. Um, and so as they're analyzing the features, they were also they had realized then the high volume related back to this question. So they were fixated on like what do these numbers mean now that it's pink? But really what's happening is that these are all the things that are high volume that will damage your hearing. And because we had already talked about this, it was more likely to come up in their conversation. Lastly, to talk about some critical literacy. This is actually a different first grade class in June. Here's what theirs had looked like. You can see I write all over the board everywhere. Sometimes I'm good about erasing things we don't need anymore. Often I'm not trying to get better. But you can see like they had done the same thing of like, oh, I had labeled them four, six, seven. And then the kids had had me. I remember this boy Daniel was like, "Don't write four. Make it 40 now. Make that 60 now." And they could actually see the tens emerging. Um it was a little bit more awkward for this one, the 105 because like 11 and or 10 and a half doesn't work for them like that. Um and you can see he had actually written an equation there. Um they had talked about all of these different things. Oh, those are the ones that hurt your ears. And one student was like, "Well, what about the blue whale? Those are super loud." And I was like, "Oh, yeah." But I assumed it was going to be less than like fireworks. And he was like, "I don't know. They're very big." I was like, "Hold on." So I checked on my phone really quickly, Googled it. How many decibels is the sound of a blue whale? And it's 180 or 180 plus. That is immensely loud. And the kids were like, "Oh, but like we don't hear blue whales all of the time. All of the other sounds that had been chosen seem to be ones that we might encounter in daily life, particularly living close to a city. Um, but we don't encounter a lot of blue whales, so maybe that's why blue whale isn't there." But then the kids were like, "Well, what other really loud things are not on there? We must be missing a lot of things." They want to talk about that, but also we want to talk about who would find this graph valuable. So when I asked them that of like, okay, so this graph, I found it in like a Scholastic magazine. But why would someone create this? They clearly made choices about which sounds to include because they didn't include a blue whale. It's not what's the loudest sounds on Earth. They made choices to communicate something. So who would want this graph? Who would make decisions based on this graph? And they were like, well, scientists. scientists that study sound would really want this, which is a wonderful first grade answer. And of course, I'm thinking like, uh, scientists that study sound probably don't need to know this particular information. They might be a little further along, but I think that's a great start. They also have a unit in first grade about sound, so this was like perfect for them at this point in the year. Um, and then another kid was like, well, what about doctors? Like, why would doctors want this graph? like, well, doctors can then give you advice. If doctors know that certain things hurt your hearing, they can tell you to avoid those things. Like, oh, and then another kid was like, well, what about us? We find this graph helpful then because it helps us make safe decisions. I was like, oh, that is a wonderful idea that this graph might be really good for us to make decisions. One kid was like, oh, there's so many sounds in the world that hurt our hearing, like, let alone the blue whale. But like rock concerts, things that we encounter regularly can damage our hearing. And then one girl was just like, why do people go to fireworks if it hurts our hearing? Like they started to get really indignant and mad. And I feel like if we had just shown them the initial graph and asked them to like tell us how much like this bar is like the typical kinds of data questions we ask young kids, um they're not going to get indignant. And I really like that almost every time I do a graph, some kid will get riled up about why this is unfair or wrong. Um, so we actually did talk about it like, well, what do you think? Should fireworks be banned? There's reasons, yes, why they should be banned, and there's reasons why maybe you wouldn't want to ban them. So maybe you want to ban them because it damages everyone's hearing, and that's terrible. And it also has noises that frighten people and frighten animals and can like induce trauma. It's actually like not very clean to have lots of fireworks, but also they're beautiful and also it's tradition and people love them and you get to spend time with your family. So, there's all these beautiful things about it, but also all these destructive things. So, should we ban fireworks? And the kids often felt as I like asked them yes, asked them no, and we tallied it up on the side. A lot of kids actually said yes, we should ban them because they had just seen the graph and they were like, I don't want to damage my hearing. So yes, ban them. But other kids were like, "Oh, but like I always like going and it's really fun to go to the esplanade and see the fireworks." Well, okay. So these are all just our personal opinions. What if we make it bigger? And this is the big critical literacy part. Who is helped by communities continue to hold firework displays and who's hurt? So it's not just about you personally. It's about making it even bigger because there are people that are going to be hurt by it. And I've heard lots of things in recent years about like how vets who have like seen combat are really hurt by these. But also like clearly people like them because we keep having firework displays. So how do you make these decisions? Data can help us make these decisions. That graph doesn't say whether or not to ban fireworks. It can't decide for us, but it can be one piece as we are deciding. And I think a surprising number of graphs that we use actually can be used in this critical literacy way if it's about like real stuff and not just like what's your favorite color? Although maybe you can come up with something for that. I also have this graph that I do with fourth graders um that my friend Brian Bushart turned into a slow reveal graph. It's like a one that's full of drama. It's on the website. I can show you in a minute. Um but like look at when people hurt themselves with fireworks. it seems like there is a distinct trend. Um, so going back to the critical literacy part because I think that's one of the hardest to teach kids and I know when I have them do data projects where they ask a question and they gather the data, um, they're often not very good at picking out their own bias. They're just not used to it. They haven't done it. So I love doing it in slower real graphs because you can start to build those skills. So this is one from seventh grade that we'll look at quickly. So they'd already seen this. They'd already been like, "All right, so all the green bars are always the biggest one in that section. The yellow's always the smallest. The black's always in the middle." They were able to estimate some of the percentages. They were feeling good. And then I revealed this. So black is all participants, orange is men, green is women. And in they were just like, "For women, it's more." And then a kid was like, "Well, what about non-binary people? So you can see up here we actually then talked about who is left out then of this sample. It seems like it's everyone but just as all participants not all people who was left out. Non-binary and other genders left out. Not included in the data. Kids not included in the data. We have no idea how they feel about whatever this is. And in fact if we we noticed that the women were the highest on every single one. What would adding other genders mean? So like maybe non-binary would be the highest bar every time. And how would that change this all participants which is in fact the mean of the two because maybe you're going to have a lot of women participating and not as many non-binary. Maybe there's actually way more men participating than there are women and we can't tell because this is percentages. Then we revealed further that these are the countries Canada, US, Germany, Russia and I will say that this is in fact the headline of this is Canada is most comfortable with female leaders and they were like well of those countries but there's countries missing right these aren't all the countries in the world and the kids actually noticed that these are mostly they were like European I wrote Western um these because they're not European at all. I think they just kind of were like, we know that this is related to white people. So, these are specific countries that are and then we're saying that Canada's the most comfortable with a female leader. Well, what countries are left out and what would it look like for those countries? And I actually was able to find another graph from a website called the Arab Barometer. So, these are countries in the Middle East and North Africa. And if you look at Lebanon, um actually they have pink as men and purple as women there. They don't have that extra bar for the all participants. Those numbers are way higher than Canada's. And in fact, most countries were higher than almost all of these countries. Certainly higher than Russia, higher than Germany, which was surprising to me. My husband's actually from Algeria, which like they're not. They actually women are way more employed there than men. Um but like they still got a lot of colonialism issues to work out even among the lowest ones. It was still higher than these. But I did notice also this is it's based on a survey of 22,000 people across 11 countries very comfortable with a female leader. And this says strongly agreeing or agreeing. There can be little nuances in how you collect the data that can dramatically shift it. And so we need to be careful as we're thinking about how we compare things. But I think that this ambiguity invites discourse like what Lisa was saying earlier, making the connection to the rough draft math that these are things that are a little bit like sticky, have these little nuances. You can dig into the details, but that actually makes kids talk more. They'll get into little arguments and they actually will get deep into the math concepts. I know the example is from like a primary grade, but they went pretty deep into thinking about those tens and like dealing with that five um and things that the teachers had necessarily thought to give them independently all the time. This picture I really like. First of all, this was actually me doing a slow reel graph in I think a third grade classroom. Um just like look how excited that kid is. Just like come on me. Usually I can get every kid to share. Um, not always in secondary, like in eighth grade classes. Sometimes there's a couple kids that won't share, but I can get most kids to share in front of everyone. Um, and that's because they're doing all these things that are like the mathematical practices. They're disagreeing. They're making an argument. They're justifying their thinking. Here's that one of the kids rushing up. Um, so this was in a fourth grade class. They were studying. Um, this was actually the introduction to like enslavement in America. Um, and this was from their textbook. I had taken something from the fourth grade textbook and I had done it as a slower real graph. You can see my writing all over the place. Again, not always good about erasing what we don't need anymore. Um, and this was about the decline of the number of people in the Tyenos. Uh, Tyenos is an indigenous group in Puerto Rico. So, this is before and after European contact. You can see it's three million there. And the kids because we had done the slow reveal graph, they had noticed that it kind of looks like it plummets, but it doesn't actually go all the way. Um, and you can see this is actually after the reveal of what that number is, but they could tell like, all right, it doesn't go all the way. What is that? It like drops down and then it kind of stays consistent for a little while at this small number. You can see these kids had like rushed. It was a little annoying at first, but then you get used to it. um they rushed with rulers to try and measure it and it turned out that on the board we were using this had projected and it was 10 inches which was like I could not have planned it better. Um and that this was like about an inch and they were like oh it's one out of 10 pieces of like this and that's a million I think. So yeah from zero to 1 million and they were trying to figure out like what's onetenth of a million. Turns out it's about 60,000, which is like not exactly right, but like that's pretty close. And so we were all of a sudden thinking about like huge numbers, fractions. They were getting into great math. So for what future do we envision for today's students? We go back to this idea of like are we using data to like make positive decisions and help our community become better citizens or are we using it to like be a little bit more insidious? I think that collectively it's really important that we inspire students to make decisions that use all three of these components. We don't want to just jump to critical literacy where we're thinking about like do we ban the fireworks. We want to make certain that we are developing their math skills. We want to make certain that they are thinking about what this data means and then leveraging that to go into the good decision making for a citizen. And I know it looks really cheesy like the make the world a better place, but like I honestly believe that that when we do these repeatedly and I'll just throw in slow real graphs like oh it's a snow day and everything's gotten like thrown off and the next day the teacher needs like something. to like orient us back. You can do them at any point for like they could just be a single, they could be a warm-up, they could be a whole lesson, we could turn to a multi-day thing, but that through this practice we are improving different things in the world that these kids are getting used to questioning data. They're getting used to thinking about the mathematical nuances of data and through that we're creating better citizens. So, I have thrown up like I think there's like 250 300 at this point on the website. We only have like a couple minutes left. I will click quickly on it so you can see what it looks like. So, this is the website. Um, and I did make this alone. I will say that um I worked early on especially with collaborators like my friends um Brian Bushart, Dan Meyer, um Heidi Fessenden, Casio Wedkin helped a lot and from there we built it into this and then I'm the one that like updates it. I do get emails from like people in Sweden and Australia submitting things which is super exciting. Um and then I also make a lot too. So if you click down here you can like click on this one. This was the most recent edition about high traffic on Everest. If you click there, it comes with the graph. And then I usually put questions there so that you have an idea of some questions you could ask in the classroom. Again, you can also just be inspired and create your own, but it's like a landing point. Um, and then often like I'll throw on additional things about like why this is important. like it turns out there's a lot of trash on Everest and that's one like and it's also super dangerous. Um I'll often list like the visualization source where the graph came from where the data came from. Those are different things and people are making decisions all along the way. The people that make the visualization have chosen to figure out like different ways to truncate that data and make it more palatable. Different collections or different connections you can make some text or things you can read. So you can just sort by like most recent that's on the landing page. But then there's also you can search by elementary. These are all the ones that I've tagged for elementary. Or you can do by graph type like if you really want to look at scatter plots. Here's all the scatter plots. And that is a potential resource for you. Something I did not point out. Oh no, wait. There we go. Sorry. Starting it back. Um, if you see in the bottom corner here, this URL, I have put on there slides, resources, so like articles that have been written about slow reveal graphs, a little video of like me doing one with some friends. Um, but also a quick survey. I know we're like out of time. The survey is mostly for you. What it is is it says like what's one thing you want to take away? and then it will email it back to you so that you don't have to like try and remember it later given that it's all fresh in your mind right now. So if you go to that that will have the quick survey other things and I did want to say thank you as we like really closely hit noon. Sorry about that. I try to end early and I'm not always good at it. Um but this is me if you want to contact me. This is my personal email. I still love Twitter. I know it's dying but I like it. Um I like to blog. I blog about things way like not just graphs, lots of lots of different things for my practice because I work in a building that's K through eight and then slow reveal graphs. So, thank you so much for coming. [Applause]