Ep 118: Time and Elapsed Time

Pam Harris  00:00

Hey fellow mathematicians. Welcome to the podcast where math is Figure-Out-Able. I'm Pam. 

Kim Montague  00:07

And I'm Kim. 

Pam Harris  00:08

And you found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But it's about making sense of problems, noticing patterns and reasoning using mathematical relationships. We can mentor mathematicians as we co-create meaning together. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be. So Kim, workshops start today. Oh, it's so much fun. We love our online workshops, where we can take a deep dive into content. It's so cool to interact with people in the comments and message boards. Y'all, if you happen to miss registration, this time around, we open registration three times a year, September, January and in May. So sort of those three kind of teacher ish times of the year that makes sense for PD. So arrange your funding for January for our next time that workshops open if that is your goal. All right, let's get to today. 

Kim Montague  01:12

Okay, so in today's episode, we're going to chat a little bit about something that we hear teachers and parents talk about quite a bit. And that's the fact that kids these days, I'm kind of air quoting, kids these days, don't have a clue about how to tell time, much less read an analog clock. So today, we thought we would talk a little bit about ways to help your students and personal kids make more sense of time, and have more experience with telling time. So we have three broad suggestions today.

Pam Harris  01:42

So let's talk about three ways to really help get time better with our current generation, in maybe ways that you hadn't thought about. Yeah, so all right, here we go. Number one: let's help kids and students, so our personal kids and students get a better feel, develop intuition for benchmark units of time.

Kim Montague  02:07

Okay, so what do we mean by benchmark units of time? Well, you and I probably-

Pam Harris  02:11

Hey, Kim. Hang on just a second. I mean, just a minute. I mean, give me, give me-

Kim Montague  02:15

(laughs) I was like, Wait, I'll give you a minute. But actually not a minute, right? 

Pam Harris  02:21

No, don't give me a minute. That'd be terrible on a podcast. Silence for a whole minute? Or did I mean a minute? Do I mean a second?

Kim Montague  02:29

So we do that, don't we? We use incredibly fuzzy language. When we say just a second, just a minute. 

Pam Harris  02:35

Will get to that an hour?  

Kim Montague  02:37

Yes, yeah. So we are going to recommend that as often as possible, you use precise language. So if you mean, 'in a minute', like it should actually mean about a minute. Like nothing is just a second, right? So we got to tone down that language, and really start considering how long things take. And the more that we consider how long things take and how long actions that our kids are doing take, they'll get a better feel for how long those things take. So listen, when I tell my kids, when they come up to me and say, "Hey, Mom, when are we going to whatever?" I'll look at the clock. And I'll say things like, "About 10 to 12 minutes." So I'll give them a range, right? And I'm going to give as accurate as I possibly can. So number one, I'm considering how long things take. But also I'm giving them a framework for doing the same thing. And instead of just saying just a second, or - just a second, doesn't usually mean leave me alone? I mean, sometimes as mom that's what it means.

Pam Harris  03:41

A window into the Kim household.

Kim Montague  03:45

So I'm just saying like, I just think it's really important that we give as accurate as we can. Or you could say I'm not sure I think it's probably going to be about this long based on this.

Pam Harris  03:55

So like be transparent about what you're thinking about. Yeah, even if it's, "Hey, right now, don't ask me that question. Walk away." You know, like, I've actually heard you say that. And I do think we can, rather than just a minute, hang on in our, you know, five minutes from now? 10 minutes, 15 minute, whatever your pat answer is that you sort of give kids when it's, when you mean, I don't know, don't ask me Don't bug me. 

Kim Montague  04:19

Yeah.

Pam Harris  04:19

We could be a little more specific, or be clear that we're not being specific. That would be a way. Hey, another way that I ran into when you and I were using the curriculum Investigations in Data Number and Space, was they would actually have teachers work really intentionally to help develop these benchmark units of time. Like, they would say, "Hey, students predict how many (and then pick a thing). How many circles do you think you can draw in a minute? How many stars can you draw in a minute? How many times can you blink your eyes in a minute? How many times can you snap in a minute?" I think one of them was even like there's a length on the floor. "How many times can you run that length in a minute?" So you actually have students, a minute like, how am I, and then kids are like, "Oh a minute so long. I can draw 100 stars in a minute." You're like, "Okay, like write that down, estimate your-" Or "Oh a minutes really short." You know, you almost get a feel for what their, the adults in their lives are saying, you know. "It's really short. So I can only draw like three." And you're like, "All right, write that down." And then actually time them (clicking sound). You know like hit the stopwatch and say, "Okay everybody draw the stars. Here we go, already? (clicking noies)" And let a whole minute go by and kids be like, "Oh my gosh, that was forever long." Until then you have them go run the length. "Okay, how many lengths?" "Oh, well, you know, I could draw a 59 star. So maybe I can run 59 lengths." And you know that probably not as many of those. So that whole idea of give them a unit of time, like a minute, but you could also say, "Alright, now we're going to do this for five minutes. Alright, you are going to work on your project. You are going to read silently for five minutes. (clicking sound)" And then actually, I mean, I have no idea what that sound is coming across on a podcast, but I'm like clicking.

Kim Montague  06:02

It's a stop watch, right. 

Pam Harris  06:03

Sound like a stopwatch? Yeah, you know, I'm like I, you can tell I'm an athlete. We do a lot of things with stopwatches. So you know, like, actually hit it. Don't estimate it yourself, teachers, like to actually hit, have a one that has an alarm that comes off at the end of it. So that you have that noise and like, "How many did you get?" And then compare. Compare to your estimate, and ask them to revise, "Okay, based on you thought you could draw 59 stars. You actually drew 48 or 20 or 199, like whatever you actually drew. Now revise your estimate, we're gonna do it again." And give them a chance to kind of feel that one minute, that five minutes. Even you could say, "Math time is 90 minutes." See, you can see me wishful thinking there. Or we're going to spend 45 minutes in history or like, whatever it is, like this much time we're going to do (clicking sound). And then go do the thing. Like let the 45 minute go on the timer, ignore it even, and then let it go off and go. "Hmm, how do we do? Like, did we keep our (pick your thing, whatever it is), the time that we were working on writing? Did we keep that to the 45 minutes? Well, actually, we need some more time. That's interesting. That was 45 minutes." You're noticing that that time went by. So those are some benchmark times that we can help students develop intuition for. 

Kim Montague  07:24

And I don't think that it's a one time thing, right, because we've heard littles. I think you've probably heard this too, "Is it a short minute or a long minute?" And that refers to how long things feel when you're enjoying the activity or not enjoying the activity, right? Like it can feel a little different. So they just need a lot of experience with those benchmarks to know, this is 10 minutes. This is five minutes. This is one minute.

Pam Harris  07:51

Yeah, nice. Nice. Alright, So Kim, what is another broad suggestion that we have to help students with time.

Kim Montague  07:58

So the second thing we want to mention is that we need to just do a better job of noticing what time it is just in our daily lives, and ask what time it is. So I know that seems like a super obvious suggestion. But I think adults are aware of time, we're constantly checking the time, we like to look at the time. But we don't necessarily give kids the experience of doing that. So we're suggesting that you say the time a lot. We talk about time. And so what are some times that you can talk about time even more in your work day, in your day with your kids? I might say to my kids like, "Oh, hey, it's six o'clock, we're gonna have dinner in 45 minutes," or, "Hey," in the classroom, "Hey, it's like noon. And we've got about 30 minutes to do this next thing that we're going to do."

Pam Harris  08:48

And as you notice those times, you can also and maybe meant this, but you could also like, look at the clock. So you're like, "Hey, it's 12 o'clock. Hmm, that's what the clock looks like, when it's 12 o'clock," whether it's analog or digital, and maybe both would be a fine thing to do. I can even foresee that if it's an analog clock, or you could go, "Hmm, it's 12 o'clock. Why is it 12 o'clock? Oh, yeah, cuz this hand and that hand. Okay, so it's 12 o'clock, hey, what would it look digitally?" And you can just like, slap that down really quick move on. Like, it's like a short, I'm noticing the time. We're not only noticing what time it is. But we're noticing what that looks like on a clock, analog and digital move on. Now, besides us just noticing, we can also ask students, right? So in that same moment, where we're like, "Hey, I'm going to notice, hey, y'all, what time is it?" Ask students, "Look at the clock based on what you see right now. What time is it? Hey, what would that look like on a digital clock?" Slap that down. "Hey, what would that look like?" You know, vice versa, whichever one you're looking at, like notice what it would look like any other one. Bam, done. It's not. It's not, we're not talking about a lesson. We're talking about, like bring this into your life a lot.

Kim Montague  10:00

Hmm. It's the experiences, right? You're providing constant little tiny nuggets of experience for kids.

Pam Harris  10:07

Absolutely. You know that reminds me, one of the things that was interesting for me when I spent time in Europe was the number of people that would tell time on a 24 hour clock. We could argue 24 hour 12 hour clock. That's not what I'm getting at. What I'm getting at is it was interesting to me, that people who weren't necessarily all that, how shall we say fluent in math (unclear) kind of other conversations with them, were really fluent in a 24 hour clock, far more than I was. And I was like, "Oh, that's because you deal with it all the time. Like, that's your experience, your experience has gotten you to where you can think about all the time." And they would say the same thing to me. They're like, "You're always thinking about the relationship to 12. Weird." I'm like, "That's what I grew up with." And so because each of us had those experiences, that's what you're mentioning. So we want to give kids experiences. 

Kim Montague  10:57

This is so funny that you're mentioning because, and I think we've talked about 24 clocks, I feel like we have at some point on the podcast. But my husband does military time, or 24 hour clock for work. And his and his clock on his phone is a 24 hour clock. And so you know, when I'm thinking about 24 hours, you know, what I do is I like literally count. And so because I don't have the experience, it throws me back into a counting strategy. And then maybe if I really stop and think about it, then I'll like subtract 12. But I just don't see it all the time. I don't make sense of it that well.

Pam Harris  11:34

So that's interesting, because we work with a person who deals with 24 hour time, doesn't live on the American continent, and deals with 24 hour time. And the other day, I asked a question about one o'clock. And I think it had something to do with like, nine o'clock to one o'clock. And she counted. 

Kim Montague  11:51

Yeah. 

Pam Harris  11:51

And I was like, Oh. And she's like, "Don't judge me. I know, I was counting." I was like, "No, no, it's something you have less experience with." She's totally on a 24 hour clock. And so that's interesting that sometimes you'll count when it's not your experience. And same thing she'll count when it's not her experience. When we don't, it's, y'all, it's so much about experience. So secondly, give kids experience, talk about what time it is, have them tell you what time it is often. Often ask them that. Yep. Cool. All right.

Kim Montague  12:20

So you mentioned a schedule earlier, and talked a little bit about times in classes. And so the third recommendation that we have is, is just that. So I have seen a lot of really great classrooms where the schedule of the day is written on the board, or there might be like a chart or bulletin board where it says, you know, at this time, we're going to math and at this time, we have lunch, this time we have recess. And sometimes it's in digital form on a clock, or it's just written out. Sometimes there are analog clocks next to those so kids get a feel for what that's going to look like. But I was in a classroom once where a teacher had the visual. And she added the time to it.  The visual schedule. The visual schedule with the little analog clock next to it. But I thought was brilliant, because she added a little piece of paper on her desk for each student. And every once in a while she would say, "Stop. We just finished Math, stop. Let's look at the clock." And then they compared what time was it? What time were we supposed to be done? And kind of said, how do we do? Did we end on time? Do we end a little early? Do we end a little bit late? And I just thought it was a really nice, really meaningful things for kids to compare their daily schedule with, you know, the suggested schedule with what actually happened.

Pam Harris  13:42

Yeah, nice. It's a really nice way to notice and compare and get kids looking at the way time looks good.

Kim Montague  13:50

And it didn't take long, right? It was just on their desk and they just jotted down, but they got practice reading the clock, recording times and then comparing a little bit.

Pam Harris  13:58

Yeah, absolutely. 

Kim Montague  13:59

Yeah. 

Pam Harris  13:59

And, I would suggest that if when they're comparing, that's building intuition for benchmarks, because they're like, "Oh, we actually took an hour to do that even though we were only supposed to take 50 minutes." That's what that, that's what an hour feels like, longer than 50 minutes. But yeah, all that nice. Nice so, so first help students develop intuition for benchmark units of time. Second, tell time a lot notice and wonder what time it is. Alright, so the last thing we want to talk about today is also notice aloud how long things are taking. So put your thoughts about elapsed time out there for kids and students to hear what are you thinking not just about what time it is, but elapsed time and maybe I kind of just said that when I was talking about the hour and 15 minutes but even more so. What time has elapsed? Put it out there. So in what ways can we do that, Kim?

Kim Montague  14:54

Oh, well, I'll tell you what I did this morning as we were getting ready for school. You know we leave for school at the same time every day, like that's the goal, we try to get out the door. And so often my kids want to know, hey, do I have time to blank before? Can I play with my Legos or whatever before? And I will say to them, it's 7:35. And you still need to brush your teeth, grab your backpack, put your lunch away, you know, whatever list of things. And so like, I want to give them a feel for how can you get all that done? How much time do you have? And so I will ask them-

Pam Harris  15:26

Because they know what time you're leaving, right? You're leaving-

Kim Montague  15:29

They know what time we're leaving, 7:45. And we will talk about what time it is right now. And then naturally, they start to ask themselves like, "Oh, gosh, how much time do I have?" And like, "Oh, these are the things I got to get done." And so I'm just hoping to create like little bit of planning in them as well. 

Pam Harris  15:46

And if you find your student, your child isn't asking themselves, "So it's 7:35. You know, we leave at 7:45." If they don't then say, "Okay, so 10 minutes." If they're not thinking about elapsed time, then you could say, "So how much time do you have?" 

Kim Montague  16:00

Yeah.

Pam Harris  16:00

Now, you might not choose that on the day where you're running late. Taking that extra minute to like, you know, like, that might be kick you over the late move, you know, maybe that day. But as much as you can helping students think about elapsed time. And I think you could go back to your schedule a little bit. Maybe as you're creating those schedules, you could actually have students do that with you. Y'all if we're supposed to, help me, Kim, what's a thing I'm going to do during the day? If on that visual schedule, we're going to start reading at 10 o'clock, you know, we have to be done at 10:50. How long do we spend time reading, or in reading, or learning reading or whatever you do with language arts? Asking kids those elapsed time questions, when they say to you, "When are we going to recess?" You could say, "Well, what time do we go to recess?" "We go to recess at 215?" "What time is it right now?" They're going to read the clock and then, "Well, so how long do you have?" :ike press that issue especially in those moments when kids care. They're caring about, they're asking you about it, press that issue. In those moments, they might be just a little bit more willing to dive in with you as you do that.

Kim Montague  17:10

Yep. Okay, so let's recap one more time. So if you want to give your students and personal kids the opportunity to be better with time, if that's the goal, right, which time is always good? Yeah, that's a big goal. We want to give a feel for time amounts and benchmarks. That's the first one. We want to notice what time it is and constantly be telling time. And we also want to talk loud about how long things are taking as we go about our day. And we talked about theirs

Pam Harris  17:39

Nice, y'all 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. Let's keep spreading the word that Math is Figure-Out-Able.