Pam  00:01

Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able! And I'm Pam Harris... Oh, my goodness. Why did I just say "and"? "And I'm..."

Kim  00:10

I was too busy trying to decide if you're going to say Pam or Pam Harris.

Pam  00:14

I'm Pam Harris. And a former mimicker turned mather. And your Kim Montague.

Kim  00:25

A reasoner who now knows how to share her thinking with others. At Math is Figure-Out-Able, we are on a mission to improve teaching. (unclear).

Pam  00:34

We know that algorithms are amazing historic achievements, but they are not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.

Kim  00:47

In this podcast, we hope you teach mathing, building relationships with your students, and grappling with mathematical (unclear).

Pam  00:55

What is so funny? And we're glad that...

Kim  00:58

I got stumbled on "mathematical".

Pam  01:01

We invite you to join us to make math more figure-out-able. Alright, that intro was maybe the worst we've ever done. But...

Kim  01:07

I would doubt that. 

Pam  01:10

Here we go. Kim, what are we talking about today? 

Kim  01:11

Hi.

Pam  01:12

Hey.

Kim  01:12

We got some good stuff for today. We are going to get to share about Slow Reveal Graphs. And like, they're just fantastic. And we're going to talk about them a little bit. But I do want to say that we had Jenna Laib, who is the curator of the website, and just a brilliant person. We had her on our last challenge. And she was delightful, and knowledgeable, super fun. And like the people who were joining us just were super excited about her. So, she hosts a website called Slow Reveal Graphs. Which is just amazing. And we get to share about it today. 

Pam  01:15

she did an amazing job! Such great facilitation. She facilitated a Slow Reveal Graph routine with us. Worked the crowd so well on Zoom. Did an amazing job. We experienced a Slow Reveal Graph with her. And boy, that was really different than just reading about them. So, I was really glad that she was able to join our challenge. Ya'll, if you have not joined a Math is Figure-Out-Able challenge yet, get on it. Like, it's totally free. We have a blast. We have special guests. And Jenna did an amazing job. And that Slow Reveal Graph was really, really cool. So, listeners, today, we thought that we would kind of run through a Slow Reveal Graph example. I know it's kind of weird. We talked about whether this was going to work or not. So, please let us know if you're like, "That didn't work." We're going to try our best to describe what you would see, so you kind of get a feel for what it means to do a Slow Reveal Graph routine. Yeah? Yeah,

Kim  02:46

Yeah. And we're going to share the link to the one we're talking about in the show notes. So, you know, if you want to look at it as you're listening, that would be (unclear).

Pam  02:57

And maybe I'll say... So, we'll share that link. But the website slowrevealgraphs.com has a ton of amazing (unclear).

Kim  03:06

Oh, yeah.

Pam  03:07

They're all ready for you in a Google slide deck. So, Kim and I are actually looking at the Google slide deck that Jenna Laib used in the challenge. But there's a whole slew of other ones. And you can actually sort them. Ya'll, give Jenna Laib just a huge round of applause. And thank you. Oh, and before I forget, I'll also mention you can find them, all of them, all of her collection. And she's a curator, so she's created a bunch of them. She's also had several people donate the ones that they've made. We really appreciate everybody who has also put their examples of Slow Reveal Graphs on there. You can also find some of those examples at SEMBL that we talked about in a podcast episode not too long ago. So, SEMBL, sembl.app, where they have assembled lots of good tasks. You can also find some of the Slow Reveal Graphs. Okay. So, are you ready to dive in and see if we can do this (unclear)...

Kim  04:03

Yeah.

Pam  04:04

...visual thing over (unclear).

Kim  04:05

Sorry, Jenna if we...

Pam  04:09

We won't do as good a job as Jenna did for several reasons. A, we're not Jenna. And B, we're doing it audio, which is... She's probably like dying right now. She's like, "Oh my gosh (unclear)."

Kim  04:17

"Why would you do that?" 

Pam  04:18

So, you''ll have to tell us Jenna what you actually think of whether this was worth it or not. Hopefully, it will just drive a ton of people to these examples because, ya'll, this is such a good task to do with your kids. Alright, so the idea is that you give, you show a graph, some kind of data representation, but you have stripped off a ton of it.

Kim  04:41

Yep.

Pam  04:42

(unclear).

Kim  04:42

Almost everything, yeah.

Pam  04:43

Yeah. So, the first image I'm going to let you, Kim, describe what you see.

Kim  04:48

Okay.

Pam  04:48

Very first image. What do you see?

Kim  04:49

Alright, so there are some bar graphs. And they're actually like little tiny rectangles stacked on top of each other. 

Pam  04:59

Okay.

Kim  04:59

And as you go from left to right. So, there's 1, 2, 3...7.

Pam  05:05

Bars.

Kim  05:06

Bars. And as you go left to right, they increase. And about halfway up there is a pink bars, so... Ugh, not doing a great job. There's a rectangle, and the bars are within the rectangle. So, there's no titles. There's no numbers. There's no any information other than these bars. And about... They're mostly purple. But then at some point, the background shifts to pink. And all the bars that are taller and they rise into the pink section, that portion of the bar turns pink. So, the first ones all purple, all purple, all... Bleh, I can't say it. But the last three columns, the last three bars have purple at the bottom. But then the top of them are pink. (unclear) changes at a particular point.

Pam  05:53

Yeah. And I'll add one slight detail. You said that as they increase left to right, they get bigger left to right. If you look at the background, the bottom half of the vertical space is white, the background. And the top half of the vertical space is pink, the background. So, as you get into that, like you said, (unclear), but I just kind of describe. Iit's like half of its white, half it's pink. And the bars that sort of flow into that pink half, they turn this dark pink.

Kim  05:53

Yeah, so something's popping about this pink. Yeah, something. Your eyes are drawn to the pink. Like, why are they pink? 

Both Pam and Kim  06:32

Yeah.

Pam  06:33

And so, the question that Jenna gives...it's wonderful, helpful...says what do you notice? What do you wonder? And what do you think this graph might be about?  And I think a lot of our participants notice things like it's increasing, that it's getting bigger, that there were in a smallest bar there were four chunks. And then you can see those chunks. So, that same size chunk repeats itself. So, like the first bar is 4 chunks, and the next bar is 6 chunks, and the next bar is 7 chunks, the next bar is 8 chunks, and then you get where it starts getting into the pink and only half of one of those little chunks is in the pink. Which is kind of cool. Do you remember anything else that people said?

Kim  06:43

Yeah. I think somebody said something about the pink would be like above average. Like, as if this shift from white to pink was like that was kind of the average. Yeah.

Pam  07:24

Yeah, cool. Alright, so then you reveal some things. And when we hit the next graph, what you can now see is everything we saw before, but we now have some little icons below 6 of the bars and some words below the icons. So, the first icon has some water droplets. And underneath it, it says "raindrops". And the second one has a little... What do you call that (unclear)?

Kim  07:48

Talk. Speech. 

Pam  07:48

Speech bubble, talk bubble. And underneath that it says "conversation", and then it says... The next one says "city traffic" with a car. The next one says "vacuum cleaner" with a vacuum cleaner. The next one says "TV, Stereo, and headsets" with like a monitor kind of picture. And then the next one says "rock concert" with a guitar picture. So, as we go left to right, raindrops, conversation, city traffic, vacuum cleaner, TV, Stereo, Headset, rock concert definitely getting louder. And I think a lot of people at this point said it had something to do with loudness. And some might even said decibels. And then somebody noticed that the last column was not that she didn't... She didn't give us the last column. They were like, "Tell us the last column!" And that wasn't revealed. Purposeful choice not to reveal what went under the last column. Which is way more into the pink zone, right? 

Kim  08:39

Right. 

Pam  08:39

So, in fact the rock concert is in the pink zone, and the TV, Stereo, Headset is into the pink zone. So, then... Oh, go ahead. 

Kim  08:47

Oh, I just realized that the icons, those two icons, are pink while the other ones are blue. I hadn't noticed that before.

Pam  08:53

(unclear). I don't think I noticed that either.

Kim  08:55

And so, the questions for this particular slide in the deck are what new information did we just learn when we reveal the categories at the bottom? What do you think this graph might be about now? What might the bars measure? And what would the pink region mean? So, really nice questions to draw attention to different parts that people might be thinking about.

Pam  09:18

And I think what Jenna asked that somebody said something about decibels, and sound, and what would the pink region mean? Ooh, and maybe that's like where we're getting into sort of danger zone kind of things with sound. Yeah? Okay, so then the next one. In the next one, there's only one thing revealed, and it's above the first tiniest column. And above the first tiniest column, it says 40 decibels.

Kim  09:44

Actually, there's also a title that's added.

Pam  09:47

Ah, you're right! Ooh, I didn't even notice that. (unclear).

Kim  09:49

Yeah. I'm loving that we're doing this again because I'm noticing things that like as a learner in that moment, the first time I was guessing. And I was like, "I don't know," and I was trying to take it all in, but there was not enough, too much maybe to take in. So, now looking again, I'm like listening, like I'm thinking about the construction of it as a teacher. And so, that's been really cool. And it says "Sound too loud" question mark.

Pam  10:16

Yeah! 

Kim  10:16

And the first column, like you said, has 40 decibels.

Pam  10:19

So, now the questions say, "What new information did we just learn?" "What are decibels?" If raindrops are roughly 40 decibels, how many decibels do you think conversation is? TV? Etc." And this graph is very nice, because 40 decibels... I don't know if you remember. I know I don't expect you to. But in that first column, there are 4 chunks. So, 4 little rectangles make up the raindrops, 40 decibels. Oh, bam. Now, you can tell what a chunk is, right? Little division going on there. So, each chunk is 10 decibels. Go ahead. 

Kim  10:48

Yeah, I don't think I explained that part well that it was little rectangles stacked on top of each other. So, incidentally, she's asking about conversation and TV. But I know that in a classroom, kids are going to be checking out all the columns, right? They're going to be like, "Ooh." And I'm thinking like is one of them double the other one? Or, you know, how far away are some of the decibel amounts from vacuum cleaner to raindrops (unclear).

Pam  11:14

I started thinking about if I know that's 40 decibels, then what's the pink? 

Kim  11:18

Yeah.

Pam  11:18

Because it looks to me like that 40 is right below the pink, but it's not quite. If you get kind of... There's this half thing going on, but yeah. Yeah, kind of cool. So, around 80 decibels is where you're kind of in the danger zone. Alright, so the next one, Kim, I'll let us say. What shows up in the next one? 

Kim  11:32

so in the next one more amounts for different bars are revealed. So, we find out now that conversations are 60 decibels, and city traffic is 70 decibels, vacuum cleaners 80. So, you can maybe imagine now why they're going up kind of like a stair step. And then we see that TV, Stereo, and Headsets are 100 decibels. And there's a question mark for rock concert. Which is the sixth bar. Okay,

Pam  11:33

And I can totally see how just having had the 40 decibels, we actually could have answered the rock concert question before. So, this one might be kind of quick. They might be like, "Oh, you guys are so sharp. You already actually answered that one." But now, a thing to maybe note about the rock concert is there's a half. There's a bunch of bars, and then there's just a half a bar. So, they have to use some reasoning about half of a bar to get the number of decimals for a rock (unclear).

Kim  12:29

The question about this one is what new information did we learn? But I love this question because it's not what is the decibel amount for rock concert? It's how can we determine how many decimals a rock concert might be? So, it's way more open to just what number is it? It's like, where did you start? Like, how did you think about it? Addition? Subtraction? Like, what... Yeah. So many different ways kids can answer.

Pam  12:56

I appreciate that you noticed that her question wasn't just answer focused, that it was strategy focused. Nice.

Kim  13:01

Yeah. 

Pam  13:01

Nice. Alright, so next one. We have two more values are revealed. The rock concert value of 105 is revealed. And then the last column, we still don't know what it is. There's still not any word or icon below it. But we do know that 140 shows up, so it's 140 decibels. And the question is what new information did we just learn? And what do you think the pink region means now? Which I don't know, I think maybe I was already kind of clear on the pink region before. I wonder if the... Let's see. Are we still on slide five, Kim? Yeah. What do you think the pink region means now? Do you want to add anything to that one, Kim?

Kim  13:38

No, I think that's good. Cool.

Pam  13:40

And then for the sixth one, there's a little tiny... What? Key kind of thing. And it says "question mark decibels". So, like "blank decibels and above can damage hearing". And that's kind of like pink, pink, pink. But they've left the blank. So, they haven't filled in how many decibels and above can damage hearing, but they're highly suggesting that it's this kind of pink region. And the question is "What number do you think completes the sentence blank decibels and above can damage hearing?" So, now you can kind of use our understanding about where the pink line is sort of hitting. Yeah? 

Kim  13:46

Mmhm. Yeah.

Pam  14:17

Okay. And then the next one. What is revealed? (unclear).

Kim  14:21

Well, so the question for that one is "Did you figure it out?" And, "What other values can we figure out?"

Pam  14:26

Oh, nice, nice.

Kim  14:28

Yeah. There's so many good questions.

Pam  14:30

Cool. And so, then it reveals that 85 decibels and above can damage hearing. Cool. Then in the next one, it says, "What do you think might be the 140 decibels?" So, that far right one. Now, we're focusing over on the one... Like, what could that... And now, that we have all this other information, what's that far right one that's 140 decibels. When you go to the next slide, it has a question mark underneath that. And then the next slide says... Want to say, Kim.

Kim  14:58

Yeah. Fireworks.

Pam  15:00

Fireworks. So, there were lots of good. In the challenge, lots of people had super good wonderings. I think somebody said airplane. And she said actually airplane's higher than 140. Or at least often. She also said that it depends on which fireworks you're talking about. Some can be less. Some could be more. Then the question below it says, "Are you surprised? Why or why not? And how loud do you think other common activities are?" Bam!

Kim  15:25

Yeah. 

Pam  15:25

So nice.

Kim  15:27

Listen, I wish we could capture the chat. I mean, we actually could, but I mean just that the energy in the chat. And people were like trying really hard to like get their words out. And, you know, say all the things they wanted to say. The engagement of adults going through this Slow Reveal Graph. You know, because it was the slow reveal of it I think gave people time to think and predict. And then when Jenna revealed in that moment, instantly people were re-engaging, new predictions, taking what they learned, to then, you know, move forward with that. 

Pam  16:08

Super nice.

Kim  16:08

Yeah, it was really exciting to be a part of. Yeah. Yeah.

Pam  16:12

And then even more, teachers. Jenna is amazing. She then gives a link to a student worksheet task thing. And on that student worksheet task thing, it says, "Add one of the following columns to the graph. Draw the bars." And she gives them rustling leaves at 10 decibels. Whisper, 25 decibels. Jet engine at takeoff, 155 decibels. Volcano at 194. And then she gives the graph, the exact same graph we've been looking at, with two slots open, so that you can like add the ones that you think would go in those two slots, or you could stick in the one that you want to. And then very lastly, she sticks in a graph with the blue whale on the very far right and puts the bars above it, and says, "How many decibels do you think a blue whale song is? Show or explain how you know?"  Yeah, super nice.

Kim  16:16

I love that she does that. It feels kind of like what I was saying with some of the other apps that we were talking about where it doesn't have to end right when the last slide goes. Like, when you're playing Number Hive, it's not over when the game's over. There are still things that you can do to extend into the classroom. They've had this experience now (unclear) more with it.

Pam  17:27

We did that when we wrote Bridges in Mathematics, right? 

Kim  17:29

Yes. 

Pam  17:30

We were writers for Bridges in Mathematics, Version 2. And one of the things that we carefully put in there was if we had had kids play games, we would often then put a picture of the game, or a move, or questions about. Well, if you're in the middle of the game here, what would be a good next move? Or if you're in the middle of game here, and so and so made this move, why would they have done that? Or what might be another next move? Or what's happening in the game right now if this is the picture of the cards? Like, there's lots of things that you can do to kind of ensure kids are playing. And that's a small reason. But a bigger reason is to like take the reasoning further and pull it out.

Kim  18:08

Some connectedess. Yeah. 

Pam  18:10

Expose kids to other kids strategies. Lots of nice things. 

Kim  18:13

So, Slow Reveal Graphs are engaging, and they're fun, and it creates conversation. But there's some other reasons, probably more important reasons, to do them.

Pam  18:22

Mmm, mmhm.

Kim  18:23

In general, as a society. For sure a society. But starting with our students, we need to be better at data, and reading data representations, and talking about trends, and how graphs can be distorted depending on what somebody draws your attention to, the information that they may or may not leave out. So, looking at a piece of data, and then asking yourself questions. Like, what's missing here? Do I know what this is about? They're all very important parts of looking at data, so that we can help be discerning thinkers and not just take a quick glance at a graph and think we know what's happening. 

Pam  19:04

Mmhm. And also becoming discerning thinkers in how did the person who created this graph decide to display the data to perhaps give...  How am I trying to say this? Shed light on the data in a particular way that might sway an opinion. And so, we can become discerning that way as well. The more we sort of pick apart graphs, I think Slowly Revealing Things, can help students realize oh, that was a decision that was made that then makes the data look this way where we could have actually made it look a different way had we displayed it differently. That's going to be super important. Yeah. 

Kim  19:40

Yeah, for sure. When it's like when you are thinking about magnitude of something, how wide you make the graph or how narrow you make the graph to make people say, "Wow, that's really big," or like, "That's not too big," can reveal a little bit about the perspective of the person that has created it. I also really love this routine because you can change the content. Again, we've mentioned this several times. One of the things we love about routines is that once they become routine, you can change out content. You can have lots of different grade bands. So, you can use slow reveal graphs in social studies, in science, in, you know, all different ages of math classes because you can increase the difficulty. And students will become aware of different kinds of graphs and more complex aspects of graphs. You know, you can start with a really young, two column graph in kindergarten. But by the time that kids are getting older, there's so much more depth to a graph, and they've had experienced kind of through the ages, you know, understanding different types of graphs and what information is shared.

Pam  20:46

(unclear) And sorry. This search is so good because you can increase that difficulty as you go and get more complex. And like you said, change context. Yeah (unclear).

Kim  20:56

Yeah. 

Pam  20:57

Yep. 

Kim  20:57

Okay. So, I think I already mentioned this several times, but K-12 teachers could and should be using Slow Reveal Graphs.

Pam  21:07

And one of the reasons you just said once a routine becomes routine. If you use Slow Reveal Graphs in your grade, then it becomes routine, and now the teacher after you can use Slow Reveal Graphs. The teacher before you, if they do it, you could just pick up that routine. That's one of the reasons why it's brilliant to use routines across the grade levels. 

Kim  21:25

If you are a Slow Reveal Graph user, what do you think is the best part? How does that help you? Do you have a favorite graph that you use? We would love for you to share that with us.

Pam  21:34

Yeah, love that. Hey, and just so you know. At the slowrevealgraphs.com website, there are examples. Many of them have videos that talk about the example. Oh, sorry. I'm saying that wrong. There are tons of example problems that you can just use, that have the PowerPoints that you can just download... Download. You don't download a... Download a Google doc... Google slide. Wow, I'm not doing well. Google slide. The questions are there for you. But also, Jenna has created a three minute video to describe Slow Reveal Graphs. She's written up about it, and then lots and lots of examples. So, check out slowrevealgraphs.com. You can also see some of them at SEMBL. It's another place where you can find those. We love routines that we can use in lots of different areas in lots of different ways. And these are so well done, we highly recommend. Cool. Alright, ya'll. Thank you for tuning in and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com And thank you for spreading the word that Math is Figure-Out-Able!