Latest / Math Therapy / Fluency & Flexibility aren't the math F-bombs you think they are w/ Christina Tondevold

Transcript

Fluency & Flexibility aren't the math F-bombs you think they are w/ Christina Tondevold · Math Therapy

• 0:03
  Christina Tondevold: at five years old We aren't expecting kids to come to baseball, being able to hit the ball into the outfield, We aren't expecting every kid to win, every kid to be perfect.
• 0:14
  Christina Tondevold: We are laying a foundation of we're all here, we're learning.
• 0:17
  Christina Tondevold: Unfortunately for some kids, they end up getting coaches who are all about winning, and all about getting it right, and then guess what happens?
• 0:25
  Christina Tondevold: They don't love the sport anymore, and they stop doing it.
• 0:28
  Christina Tondevold: And that's exactly what we're doing in mathematics, it becomes only about the winning, only about being perfect.
• 0:36
  Christina Tondevold: Flexibility is the piece that gets everybody feeling like they can do this, that they have a part.
• 0:42
  Christina Tondevold: And yet we have to balance it a little with, accuracy and efficiency do matter, but if we put too much focus on that, that becomes an issue, and then kids are performing out of fear,
• 0:56
  Vanessa Vakharia: Hello, and welcome to another amazing episode of Math Therapy, the podcast that unpacks math trauma and helps you build a better relationship with math.
• 1:04
  Vanessa Vakharia: I'm your host, Vanessa Vakharia, and I'm here today to get you pumped up about going back to school.
• 1:11
  Vanessa Vakharia: And yeah, I know, what a buzzkill when it's still summer and, like, 10,000 degrees out, but it's coming, so why not get fired up about it?
• 1:19
  Vanessa Vakharia: A new school year brings so many possibilities, one of which is the chance to redefine our terms in the classroom so they empower us, and today's word is one of the most vulgar F words in all of math: fluency.
• 1:31
  Vanessa Vakharia: We keep hearing that we can't, like, teach students to be fluent in mathematics while also honoring their progress and thinking, but today's guest, Christina Tondevold, joins me to tell you that that is total BS, and yes, you can have both.
• 1:43
  Vanessa Vakharia: Christina is a self-proclaimed recovering traditionalist who initially taught mathematics by expecting students to parrot back to her what she taught them.
• 1:51
  Vanessa Vakharia: But she now works with teachers in developing students' mathematical understandings in a far more balanced way, developing conceptual understanding while working on procedural fluency.
• 2:01
  Vanessa Vakharia: She does this through her site buildmathminds.com, where you can get PD literally at your fingertips.
• 2:07
  Vanessa Vakharia: She's a powerhouse.
• 2:08
  Vanessa Vakharia: She is, like, the person I think about when someone says fluency, and that's why I decided she was the person I had to talk to about reclaiming this F-bomb.
• 2:17
  Vanessa Vakharia: If you think that timing things in math will ruin a kid's life, and if you've ever been like,"Well, yes, I want my students to feel good about math and their thinking and themselves, but I also need them to be fluent in math, and it feels impossible to do both," or if you've previously thought, just like me, that fluency equals speed at the expense of all else, this episode is for you.
• 2:38
  Vanessa Vakharia: And if you're like,"Sorry, I don't even know what fluency means, period, why it's important, or why I should give a fuck," well, this episode is definitely for you.
• 2:45
  Vanessa Vakharia: All right, enough from me.
• 2:47
  Vanessa Vakharia: Here's my convo with the amazing Christina Tondevold.
• 2:52
  Vanessa Vakharia: Christina, welcome to the podcast
• 2:55
  Christina Tondevold: Thank you for having me.
• 2:56
  Christina Tondevold: I am excited to be able to chat with you.
• 2:59
  Vanessa Vakharia: I love how your, the first thing on your website says that you are a recovering traditionalist, and I kinda wanna just start there.
• 3:06
  Vanessa Vakharia: I wanna know a bit more about that.
• 3:08
  Vanessa Vakharia: What does that mean?
• 3:09
  Christina Tondevold: When I started sharing things online, I decided to call my blog that, The Recovering Traditionalist, because it really is a journey, and I feel like I'm never fully done.
• 3:21
  Christina Tondevold: You know?
• 3:21
  Christina Tondevold: Like I'm, i'm not just a thinker now.
• 3:24
  Christina Tondevold: It is really hard to get out of our traditional ways of teaching mathematics because if, assume that, you know, people my age, uh, I'm nearing mid-life, that we all kind of grew up with very traditional style of teaching of here's the procedure, learn it, memorize it, follow the steps, and you'll get to the correct answer, and that was how everything was graded in math, was did you follow the steps?
• 3:51
  Christina Tondevold: Did you get the right answer?
• 3:54
  Christina Tondevold: That was the way that I taught, was still very traditional.
• 3:57
  Christina Tondevold: I stood up there and gave students the notes and taught them the procedure, and then expected them to practice it as a whole group.
• 4:06
  Christina Tondevold: And then when they got to the independent practice time, it was like hands were going up, and I did not have another way to help them.
• 4:14
  Christina Tondevold: I just would repeat the rules and steps,'cause that's all I knew.
• 4:19
  Vanessa Vakharia: I wanna make sure I'm tracking here that when you say traditionalist, you are referring to, um, a, a historic way of teaching math that relies on procedure.
• 4:32
  Vanessa Vakharia: Is that correct?
• 4:33
  Vanessa Vakharia: Like, we're relying more on procedure, we're on...
• 4:35
  Vanessa Vakharia: Okay,
• 4:36
  Christina Tondevold: Yeah, and, and for years though, I think it's, you know, as everything in education, the pendulum swings.
• 4:41
  Christina Tondevold: And so the pendulum swinging away from the traditional style of teaching into more letting kids think and play around with mathematics, um, w- kind of went a little too far to where it was, let's just let kids play and discover.
• 5:00
  Christina Tondevold: And but we have to remember it's guided instruction still.
• 5:05
  Christina Tondevold: It's not just letting them play.
• 5:07
  Christina Tondevold: It is letting them play and explore, but we still have to use that information to then pull them, push them along their trajectory of learning.
• 5:16
  Christina Tondevold: It's not just let them play and flounder, right?
• 5:19
  Christina Tondevold: We need to learn how they're thinking and then use that to guide our instruction to move them through mathematical understandings.
• 5:30
  Vanessa Vakharia: Yeah, it does feel like the guided piece is what, when we hear about this in the media, gets missed.
• 5:35
  Vanessa Vakharia: And I, I, I'm actually curious, like, did we ever actually just, like, let kids play and flounder, or was there just, like, an idea that we...
• 5:42
  Vanessa Vakharia: Like, were we ever like,"Oh, we're actually not teaching anything"?
• 5:45
  Vanessa Vakharia: Like, just, I don't know.
• 5:46
  Vanessa Vakharia: Like, I know that there are some schools or, like, communities where that happens, but I feel like that was never, like, the instruction to teachers was never like,"Let them just, like, vibe," and, like, the end, right?
• 6:00
  Vanessa Vakharia: Like, it was like,"Let's figure out, like, how they're learning, what draws their interest, like, toward what their tendencies are," and then exactly like you said,"Let's use that to guide how we're gonna teach a certain concept.
• 6:10
  Vanessa Vakharia: Like, let's prov-" Right?
• 6:12
  Christina Tondevold: I could say even from, like, personal experience, but also stories, like my own children's experience
• 6:19
  Vanessa Vakharia: Yep
• 6:20
  Christina Tondevold: Um, I have four kids ranging from 18 right now to 12.
• 6:25
  Christina Tondevold: and there have been times where, I mean, they've had a whole range of types of teachers, especially around mathematics.
• 6:34
  Christina Tondevold: but there have been a few have taken things that they've learned and, like, wanting kids, you know, what we talk about of letting kids solve the problems, uh, not telling them how to solve it, kind of to an extreme
• 6:52
  Vanessa Vakharia: Okay
• 6:53
  Christina Tondevold: "Here's the problem," and they, and then, like, if they are floundering and they aren't even sure where to start or anything, th- then the teacher's like,"Well, figure it out.
• 7:02
  Christina Tondevold: What can you
• 7:03
  Vanessa Vakharia: Okay
• 7:04
  Christina Tondevold: you know, a little, like, not just play and discover, but even as we're open, giving kids an open task, and
• 7:11
  Vanessa Vakharia: open
• 7:12
  Christina Tondevold: yeah, too open, and we just, like, let them flounder a little too much sometimes.
• 7:17
  Vanessa Vakharia: I would love to actually talk about this because I think that this is one of the biggest issues that I'm hearing right now from educators, is like they know that the move isn't to, like, be so prescriptive, right?
• 7:29
  Vanessa Vakharia: They're like,"Okay, I get that I'm not supposed to give the kid a problem and then, like, a step-by-step formula on how to solve it.
• 7:33
  Vanessa Vakharia: I understand that.
• 7:34
  Vanessa Vakharia: But at the same token, I know I'm not supposed to just be like,'Okay, well figure it out.
• 7:39
  Vanessa Vakharia: Like, see ya.
• 7:40
  Vanessa Vakharia: I'm gonna go eat a peanut butter sandwich.'" Like, do you know what I mean?
• 7:42
  Vanessa Vakharia: Like, that's not the move.
• 7:43
  Vanessa Vakharia: So it's like, but I also do feel like teachers are constantly being, like, wrist-slapped for doing too little or too much.
• 7:51
  Vanessa Vakharia: This feels like a Goldilocks situation, actually, right?
• 7:54
  Vanessa Vakharia: Like, it's like
• 7:55
  Christina Tondevold: Yes
• 7:56
  Vanessa Vakharia: too cold.
• 7:56
  Vanessa Vakharia: What was it?
• 7:57
  Vanessa Vakharia: It was too hot or too cold, the porridge, I think, right?
• 7:59
  Vanessa Vakharia: And then there was, like, the middle.
• 8:01
  Vanessa Vakharia: What are some tips you can give on, like, what you might ask yourself in terms of what the right balance might be?
• 8:08
  Vanessa Vakharia: Like, what is that, that not too hot, not too cold bowl of porridge?
• 8:13
  Vanessa Vakharia: Like, what should they do?
• 8:14
  Christina Tondevold: In general what I try to keep in mind Is I don't want to start by telling.
• 8:22
  Christina Tondevold: Actually, okay, so w- in our talk that we had a couple days ago, we mentioned our friend Raj, right?
• 8:28
  Vanessa Vakharia: Oh my God, Raj, what a vibe.
• 8:30
  Christina Tondevold: Raj is so fun.
• 8:31
  Christina Tondevold: So in I got to chat with Raj for a thing that we have upcoming that Vanessa's a part of, and one of the things he mentioned to me that still is- is on my brain is that we can always go back to direct instruction.
• 8:46
  Christina Tondevold: But our default has been, let me first tell you how to solve it, and then you work on parroting back and mimicking what I've just told you.
• 8:57
  Christina Tondevold: So instead, like, to just get started and, give kids a problem.
• 9:03
  Christina Tondevold: Just give them a problem, and see what they think.
• 9:07
  Christina Tondevold: And you should always have in mind, though, where you're wanting to go with them.
• 9:13
  Christina Tondevold: Like, what is the ultimate goal?
• 9:16
  Christina Tondevold: And, a lot of times we think our goals are the standards of students will be able to blah blah blah.
• 9:23
  Christina Tondevold: It's not about what they're able to do.
• 9:25
  Christina Tondevold: It's about what they understand.
• 9:27
  Christina Tondevold: And so we need to keep in mind is it that I want them to understand about this?
• 9:34
  Vanessa Vakharia: I love this'cause, like, uh, what I'm hearing, and this makes so much sense, it's like d- direct instruction or just telling, okay, let's just call it just telling'cause I hate all the jargon.
• 9:43
  Vanessa Vakharia: Just telling someone is in your back pocket that you can use any time, right?
• 9:47
  Vanessa Vakharia: But asking somebody, like asking somebody to notice for the first time can only happen in the beginning.
• 9:56
  Vanessa Vakharia: You can't tell them and then ask them to notice for the first time, right?
• 10:00
  Vanessa Vakharia: Whereas, like, the telling could happen at any time, so it kinda makes sense to front-load your instruction with the stuff that can only happen at the beginning as like an experiment, right?
• 10:09
  Vanessa Vakharia: Like, to be like,"Oh," like,"what would you do if you saw this with no information?"'Cause once they have the information, they can't like imagine they had no information and like, right?
• 10:18
  Vanessa Vakharia: Like you can't like you--
• 10:19
  Christina Tondevold: something
• 10:20
  Vanessa Vakharia: to unsee
• 10:21
  Christina Tondevold: pretend
• 10:21
  Vanessa Vakharia: and you can only be...
• 10:22
  Christina Tondevold: Yeah
• 10:23
  Vanessa Vakharia: Exactly.
• 10:24
  Vanessa Vakharia: So I kind of love that of being like, fine, like especially for the teacher who's like,"Oh my God," but like,"What if I have to..." It's like, great, you can tell them.
• 10:31
  Vanessa Vakharia: I almost wonder if like a nice little therapeutic way to like acclimatize yourself to the thinking model or, or getting farther and farther away from telling is to even set a timer and be like,"I'm not gonna tell them anything for two minutes." And then the next day be like,"I'm gonna set my timer for three minutes," like I'm not allowed to tell anything for th- you know what I mean?
• 10:52
  Vanessa Vakharia: Like you can build your tolerance from uncertainty this way.
• 10:56
  Christina Tondevold: Here's one thing I would recommend.
• 10:57
  Christina Tondevold: If your lesson is on doubles plus one, right?
• 11:02
  Christina Tondevold: And they aren't getting it in the first 10 minutes, uh, might be some deeper issues at, in play.
• 11:09
  Christina Tondevold: Because mathematics is really a web of understanding, and we try to teach it in isolation.
• 11:17
  Christina Tondevold: Like, here's your doubles, here's your doubles plus one, here's your make tens.
• 11:20
  Christina Tondevold: Or with multiplication, I don't know how you learned them, but I learned them times ones, then times twos, then times threes.
• 11:26
  Christina Tondevold: Like, total isolation.
• 11:28
  Vanessa Vakharia: Yep
• 11:29
  Christina Tondevold: and now we know, like, okay, well, if you know your tens, those are connected to your fives.
• 11:34
  Christina Tondevold: And twos are c- can help you with your fours and your eights.
• 11:36
  Christina Tondevold: Like,
• 11:37
  Vanessa Vakharia: We never did that, did we?
• 11:39
  Christina Tondevold: No.
• 11:39
  Christina Tondevold: No, never.
• 11:42
  Christina Tondevold: Never.
• 11:43
  Christina Tondevold: And, and so I could, I could envision, like, you know, I, I don't want people to take away that, oh, okay, today we're learning our times twos multiplication facts.
• 11:54
  Christina Tondevold: Um, and if they don't have it by the end, I'm just going to give them a bunch of flashcards to practice it.
• 12:00
  Christina Tondevold: Like, there, there are really big things in mathematics that just take time.
• 12:06
  Christina Tondevold: They take time to build.
• 12:08
  Christina Tondevold: And one of the things that really bugs me in our standards, actually, is we do a really great job with addition and subtraction facts because it starts in kinder, then they, every state is technically different.
• 12:22
  Christina Tondevold: In, in Canada, yours might look a little different as well.
• 12:25
  Christina Tondevold: But typically in the United States, um, it's second grade that it talks about being fluent with addition and subtraction within 20, which is your, your quote, unquote facts.
• 12:37
  Christina Tondevold: So they have kindergarten, they have first, they have second grade that they are building an understanding of what addition and subtraction are.
• 12:45
  Christina Tondevold: And then by the end of second grade, they're supposed to have become fluent with it.
• 12:50
  Christina Tondevold: Well, then, here in the United States, then third grade comes along, and all of a sudden they're supposed to master multiplication and division facts all in one grade level.
• 13:00
  Christina Tondevold: Like, that's, I mean, that is an unrealistic thing.
• 13:03
  Christina Tondevold: Um, and so I'm just saying, like, sometimes our standards are great in giving us time to build these things for kids, and sometimes it's just thrown at us and then we're like,"I've gotta get kids fluent with these all in one year?" And so we get the pressure of, oh, I just gotta tell you, I've just gotta tell you.
• 13:24
  Christina Tondevold: But there's a lot underneath that we can build that will help them be able to see a lot of connections, and the more connections we can make, the easier it is to recall info.
• 13:35
  Vanessa Vakharia: I'm gonna be honest here.
• 13:37
  Vanessa Vakharia: I'm listening to this, and I'm stressed.
• 13:39
  Vanessa Vakharia: Like, I'm listening to it, and I'm like,"Oh my God," there are so many variables here.
• 13:44
  Vanessa Vakharia: Again, no pun intended.
• 13:46
  Vanessa Vakharia: But there's so much going on, right?
• 13:47
  Vanessa Vakharia: Like, you're kinda like, you're kinda like, l- like, there's a lot of messages.
• 13:51
  Vanessa Vakharia: And this is interesting.
• 13:52
  Vanessa Vakharia: I remember talking to another educator earlier this week, and she was like,"You know, sometimes teachers just want, like, what are the questions I should ask?
• 13:58
  Vanessa Vakharia: What are the rules I should follow?" And it's like, y- this is where your teacher's intuition comes in, right?
• 14:03
  Vanessa Vakharia: Like, as educators, we are healers.
• 14:05
  Vanessa Vakharia: We have an intuition.
• 14:07
  Vanessa Vakharia: We have experience.
• 14:08
  Vanessa Vakharia: We know that certain students need this.
• 14:10
  Vanessa Vakharia: We can feel the energy of a class when things are being understood and not.
• 14:13
  Vanessa Vakharia: And I feel like we have to, like, pause and be like,"Listen, we're saying a lot of things here, and none of these are prescriptive." You kinda just have to feel it out and trust that you're doing the right thing.
• 14:24
  Vanessa Vakharia: That being said, it's kind of hard to hear, you know, that in grade three we have this basically, like, impossible standard, and it's gonna be really, really hard, but also, you gotta just, like, know what they need to understand about the standard, and it's not about the standard.
• 14:38
  Vanessa Vakharia: It's about them.
• 14:38
  Vanessa Vakharia: Right?
• 14:38
  Vanessa Vakharia: Like, it's like, oh, my God.
• 14:39
  Vanessa Vakharia: And now-- And, like, I, I get that almost in a way this is supposed to chill people out, to be like,"Don't worry so much about the standard.
• 14:46
  Vanessa Vakharia: Just, like, make sure they're understanding some stuff that's gonna be important." But what if...
• 14:51
  Vanessa Vakharia: Can we take a step back and, like, forget the content, forget the actual things, and, like, what is something that a teacher, especially a beginning teacher who's hearing all this, what's something that might give them a bit of hope and relief to-- if they're l- kind of like,"Yeah, man, like, this feels hard.
• 15:07
  Vanessa Vakharia: It feels like some kids aren't gonna be, like, getting all this content.
• 15:09
  Vanessa Vakharia: It feels like I've gotta do too much." Like, what is your, like, go-to, like, just remember this, this, this thing.
• 15:16
  Vanessa Vakharia: Like, j- what-- Like, do you have something?
• 15:19
  Christina Tondevold: Yep.
• 15:20
  Vanessa Vakharia: Oh, okay, great.
• 15:21
  Christina Tondevold: Is not a set of isolated things.
• 15:25
  Christina Tondevold: It's all connected.
• 15:26
  Christina Tondevold: And so it does seem overwhelming when you, like, you open up even your standards and you're like,"Oh my gosh, I have to get all of this in this grade?" Especially when w- I have students maybe coming with some gaps or two back.
• 15:44
  Christina Tondevold: and when I saw mathematics is so connected, opened up a whole world for me.
• 15:52
  Christina Tondevold: Like, I was middle school, so I w- at one point I was doing sixth, seventh, eighth grade.
• 15:58
  Christina Tondevold: Um, in the, in the sixth grade textbook, there's a chapter on decimals, there's a chapter on fractions, there's a chapter on percents Those are all the same thing.
• 16:12
  Vanessa Vakharia: Yeah.
• 16:13
  Christina Tondevold: Tho-
• 16:13
  Vanessa Vakharia: I love it
• 16:14
  Christina Tondevold: the same types of numbers, yet we teach them in isolation without connecting them together.
• 16:20
  Christina Tondevold: Fractions are, you know, like a part of a whole.
• 16:24
  Christina Tondevold: I mean, that's a simplified version of it, right?
• 16:27
  Christina Tondevold: It's
• 16:27
  Vanessa Vakharia: I loved it.
• 16:27
  Vanessa Vakharia: It was cute.
• 16:29
  Vanessa Vakharia: Yeah
• 16:30
  Christina Tondevold: decimals are just special fractions because they have denominators that are a power of 10.
• 16:35
  Christina Tondevold: They're a 10th, 1000th, right?
• 16:39
  Christina Tondevold: And then percents are even specialer because they are out of 100.
• 16:44
  Christina Tondevold: So it's a fraction, but always, you know, percents are basi- based out of what it is out of 100 of something.
• 16:51
  Christina Tondevold: And yet those are not connected together.
• 16:54
  Christina Tondevold: I didn't learn them as connected together, and I didn't teach them as connected together, and then I had this group of kids in front of me, uh, when we get done with it, and they don't see those connections.
• 17:05
  Christina Tondevold: Like, once I realized how connected mathematics was, it made me really start to look at the textbook, the standards, and say,"Okay, hold on.
• 17:16
  Christina Tondevold: So these are all listed individually, but what actually connects together?" And there is great, a great document out there, um, by Achieve the Core, and it talks about the...
• 17:28
  Christina Tondevold: I mean, they're not the power standards.
• 17:30
  Christina Tondevold: That's not the phrase that they use.
• 17:32
  Christina Tondevold: I think they call them content emphases.
• 17:35
  Christina Tondevold: but it's like what's the major work at each grade level?
• 17:39
  Christina Tondevold: And then they also talk about what ones are connected, they support that major work.
• 17:44
  Christina Tondevold: And then it also shows which ones are just additional.
• 17:47
  Christina Tondevold: Like ex- for example, kindergarten, basically everything is connected to the s- the work.
• 17:55
  Christina Tondevold: The major work in kindergarten is getting kids to count, understand how numbers work, you know, like the, the, the number system of how things work, and a little bit of addition and subtraction.
• 18:07
  Christina Tondevold: Well, everything you're doing, if you're working on geometry stuff, of recognizing shapes, and then you ask a kid,"So how many circles do you have?" You're really also working on counting.
• 18:20
  Christina Tondevold: Like, it's all
• 18:21
  Vanessa Vakharia: It's all co- Well, I also feel like it's like this is, like, a message of hope to be like anytime you're working on anything, you're working on something else, too.
• 18:30
  Vanessa Vakharia: Like, you're getting more bang for your buck than you think.
• 18:33
  Vanessa Vakharia: So it's like I really like that example of being like fractions, percentages, and decimals.
• 18:37
  Vanessa Vakharia: You're looking at it being like,"I've got three chapters to teach," right?
• 18:40
  Vanessa Vakharia: When really it's like what if we look at it as, like, you have one chapter with some tentacles.
• 18:46
  Vanessa Vakharia: You know what I m- oh, I hated that I said that.
• 18:47
  Vanessa Vakharia: I'm sorry.
• 18:48
  Vanessa Vakharia: That grossed me out.
• 18:49
  Vanessa Vakharia: But do you know what I mean?
• 18:49
  Vanessa Vakharia: Like, you have, like, one chapter with, like, w- like, if you teach fractions, you've now taught, you've taught a third of percentages.
• 18:59
  Vanessa Vakharia: You know, if you teach fractions and decimals, you've taught two-thirds of percentages.
• 19:02
  Vanessa Vakharia: Once you close it off by being, like, percentages, now you've taught the entire thing.
• 19:06
  Vanessa Vakharia: Oh my God, I just turned the chapters into a fraction.
• 19:08
  Vanessa Vakharia: Did you see what I did there?
• 19:10
  Vanessa Vakharia: I think that worked, right?
• 19:11
  Vanessa Vakharia: Like, right, right, right?
• 19:14
  Vanessa Vakharia: I think, as we know, time is, like, one of the biggest struggles for teachers, and it's always like,"I'm running out of time, I'm running out of time." So if you can feel like you're doing more, like, th- whatever work you're doing now is investing in all the future chapters.
• 19:26
  Vanessa Vakharia: Like, if they're understanding fractions, they've already understood a third of percentages.
• 19:30
  Vanessa Vakharia: You're getting there.
• 19:31
  Vanessa Vakharia: Like, you're filling that.
• 19:32
  Vanessa Vakharia: I do really like the way of looking at- I Can I switch gears for a sec?
• 19:37
  Christina Tondevold: absolutely
• 19:38
  Vanessa Vakharia: Okay, you've said a word several times, and it is what I think of when I think of you.
• 19:43
  Vanessa Vakharia: And it's a word I feel we throw around a lot in math ed and don't define, and that word is fluency.
• 19:49
  Vanessa Vakharia: You've said fluency, kids being fluent, and I think when people hear fluency, what they think of is speed, and I know that we're missing the mark on that, and I feel like you're, like, one of the fluency experts in my world, and I would love to hear from you what fluency means.
• 20:07
  Christina Tondevold: So I will say everything I learned is from other people.
• 20:11
  Christina Tondevold: Again, I, once I start seeing connections, I, I learn something over here from somebody and something here, and I bring it together to make it make sense for me.
• 20:20
  Vanessa Vakharia: Yeah
• 20:20
  Christina Tondevold: so I, I really love Susan Jo Russell's definition of fluency.
• 20:25
  Christina Tondevold: She had a article back in 2000 called Computational Fluency.
• 20:29
  Christina Tondevold: It was published by NCTM, National Council of Teachers of Mathematics.
• 20:33
  Christina Tondevold: And she talked about three things that make up fluency, one is efficiency.
• 20:39
  Christina Tondevold: We do need to be fast.
• 20:41
  Christina Tondevold: I mean, that is part of And I feel like fast has kind of gotten a bad rap
• 20:46
  Vanessa Vakharia: Yeah, agree
• 20:47
  Christina Tondevold: of all the trauma that comes with it, that the way that we have used speed and timed activities in the past has been harmful.
• 20:58
  Christina Tondevold: But the, the need to be efficient and fast still is a part of our world.
• 21:05
  Christina Tondevold: We do want to be able to get things done quickly.
• 21:08
  Christina Tondevold: Um, and, and this isn't just for mathematics.
• 21:10
  Christina Tondevold: This, this version of fluency, uh, for those that are listening, think of anything you feel like you are fluent at or trying to become fluent at.
• 21:19
  Vanessa Vakharia: Like a language obviously we'd think of
• 21:20
  Christina Tondevold: A language.
• 21:22
  Christina Tondevold: Yeah, yeah.
• 21:23
  Christina Tondevold: If you're fluent at driving your city that you live in, right?
• 21:27
  Christina Tondevold: You are efficient.
• 21:28
  Christina Tondevold: You know the fastest way to get somewhere.
• 21:30
  Vanessa Vakharia: we've used speed and timed in a way that was harmful, can you say a bit more?
• 21:35
  Vanessa Vakharia: Like, how have we used it?
• 21:36
  Christina Tondevold: The classic of the timed tests of you have to get this many in a minute, and then you, uh, switch papers and somebody grades you.
• 21:46
  Christina Tondevold: You know, and so everybody's seeing it.
• 21:48
  Christina Tondevold: And then, um, if you don't get 80 problems in a minute, I'm totally exaggerating, but 80 problems in a minute, you have to stay in at recess, and you don't get your name up on the wall with a star that you have achieved, uh, this thing or whatever it was.
• 22:06
  Christina Tondevold: I mean, f- there for a while, the multiplication sundae, I don't know who started that, uh, but it was, like, everywhere that you would get a scoop for every, you know, you learned your
• 22:18
  Vanessa Vakharia: Like actual ice cream?
• 22:20
  Christina Tondevold: Like, they would make a sundae.
• 22:22
  Christina Tondevold: And then when you got your sundae complete, you could have, like, you got to join in on the ice cream sundae.
• 22:30
  Christina Tondevold: Like, I
• 22:30
  Vanessa Vakharia: Wait,
• 22:30
  Christina Tondevold: was
• 22:31
  Vanessa Vakharia: what?
• 22:31
  Christina Tondevold: years ago.
• 22:32
  Vanessa Vakharia: didn't have this.
• 22:33
  Vanessa Vakharia: I would like an ice cream sundae.
• 22:35
  Vanessa Vakharia: Okay
• 22:36
  Christina Tondevold: right?
• 22:36
  Christina Tondevold: But everybody who, who was good at it loved that.
• 22:40
  Christina Tondevold: But those kids who struggled and never achieved that 80 in a minute or whatever it might have been, uh, never got their scoop on the wall, never got to participate in the, the sundae party that everybody else got to.
• 22:55
  Christina Tondevold: So the timed activities, those timed tests, the mad minutes, all of that was used as punitive.
• 23:02
  Christina Tondevold: It was as a punishment, not as some- And we thought it would motivate kids.
• 23:08
  Christina Tondevold: We thought if they got to see their name with a star up there, that would motivate them.
• 23:13
  Vanessa Vakharia: and that's the thing, it's like, I mean, this is a whole other conversation of how do we define motivation, because like, okay, I guess it did motivate some kids, but like out of fear, right?
• 23:25
  Vanessa Vakharia: Like, it's like, yeah, like that's like not really motivation exact- Like it is motivation, but it's like
• 23:30
  Christina Tondevold: true.
• 23:31
  Vanessa Vakharia: of motivation that we like want Let's just like for argument's sake say we are gonna time you to do like 20 questions in a minute, or 10 questions in a minute, whatever.
• 23:40
  Vanessa Vakharia: There's gonna be no sundae, there's gonna be no star, there's gonna be no nothing, but you're still gonna be timed.
• 23:45
  Vanessa Vakharia: Would that be okay?
• 23:46
  Vanessa Vakharia: Is it the way we treated the entire thing as...
• 23:50
  Vanessa Vakharia: Yeah?
• 23:51
  Vanessa Vakharia: Okay.
• 23:51
  Christina Tondevold: Yeah, yeah.
• 23:52
  Christina Tondevold: So actually, the research around- so there's, uh, a What Works Clearinghouse and the Institute for Educational Sciences, IES.
• 24:03
  Christina Tondevold: Um, two groups look at all the research that's out there because we can say,"Oh, well, research says this, research says that." That might be one study, right?
• 24:14
  Christina Tondevold: What Works Clearinghouse and the IES puts together these practice guides.
• 24:18
  Christina Tondevold: And, um, back in 2009, they did the first one that I ever saw, maybe there was one before it, but the first one I ever saw for what works with students who are struggling with mathematics.
• 24:30
  Christina Tondevold: And then in 2021, they just released, an updated one.
• 24:33
  Christina Tondevold: I said just released.
• 24:34
  Christina Tondevold: That was, like, five years ago.
• 24:36
  Christina Tondevold: Uh,
• 24:36
  Vanessa Vakharia: it
• 24:37
  Christina Tondevold: very many people know about it.
• 24:38
  Christina Tondevold: We,
• 24:39
  Vanessa Vakharia: Yeah
• 24:40
  Christina Tondevold: So this document has six recommendations that have strong research evidence to back them up for what works.
• 24:49
  Christina Tondevold: One of them is timed activities.
• 24:52
  Christina Tondevold: So
• 24:53
  Vanessa Vakharia: what works for fluency
• 24:55
  Christina Tondevold: f- for, no, just mathematics in general.
• 24:58
  Vanessa Vakharia: Oh, okay
• 24:59
  Christina Tondevold: So it's, um, what works for students who are struggling with mathematics.
• 25:03
  Christina Tondevold: It's actually a guide for t- for intervention, what intervention should look like around mathematics.
• 25:10
  Christina Tondevold: So there's things like, um, vocabulary, like getting clear on vocabulary helps kids, being precise in your language, using word problems, using lots of representations in mathematics, so models.
• 25:22
  Christina Tondevold: Um, everybody seems to be, to love the first five recommendations, and then the sixth recommendation is to use timed activities.
• 25:31
  Christina Tondevold: And people are kind of a little like, hmm, I don't konw about this."
• 25:37
  Vanessa Vakharia: I'm so into this because this is juicy,'cause it's kind of like I'm just, I don't know, I'm processing this with you right now, but it's like you're right.
• 25:45
  Vanessa Vakharia: We have our backs up with speed.
• 25:47
  Vanessa Vakharia: As soon as someone says speed, I'm like Like as soon as a kid is like,"I'm not fast," I'm like,"Oh my God." Like, that's not the thing.
• 25:53
  Vanessa Vakharia: But you're kind of right.
• 25:54
  Vanessa Vakharia: Like, there's nothing inherently wrong with wanting to be efficient with something, let's say, but there's so much baggage that has come with it that I now think we're almost doing an over-correct.
• 26:08
  Vanessa Vakharia: Like, the pendulum is swinging where we're like, oh my God, like, no, like, speed doesn't matter at all.
• 26:13
  Vanessa Vakharia: But, like, doesn't make s- what if it took an hour for someone to add two plus two?
• 26:17
  Vanessa Vakharia: Like, we would- like, that, that's too long.
• 26:20
  Vanessa Vakharia: That's not good
• 26:21
  Christina Tondevold: Yeah.
• 26:22
  Christina Tondevold: So we, again, it's a thing of balance, right?
• 26:24
  Christina Tondevold: Like, we shouldn't be only focusing on efficiency.
• 26:27
  Christina Tondevold: That is only, I'm gonna use a fraction again, one third,
• 26:32
  Vanessa Vakharia: Okay, tell us the other things.
• 26:35
  Vanessa Vakharia: Yeah.
• 26:36
  Vanessa Vakharia: Okay, I love it, I love it.
• 26:37
  Vanessa Vakharia: Wow, we are doing the whole unit.
• 26:39
  Vanessa Vakharia: Yeah, 30.3.333.
• 26:41
  Vanessa Vakharia: Oh my God, we're, we just did it.
• 26:42
  Vanessa Vakharia: We just converted them all.
• 26:43
  Vanessa Vakharia: We just taught, we just taught three chapters of math in one second.
• 26:47
  Christina Tondevold: There we go.
• 26:48
  Vanessa Vakharia: Oh my God.
• 26:49
  Vanessa Vakharia: Okay
• 26:49
  Christina Tondevold: efficiency is one piece.
• 26:51
  Christina Tondevold: Let me get all three of them out so then we can
• 26:52
  Vanessa Vakharia: Okay.
• 26:53
  Christina Tondevold: it,
• 26:53
  Vanessa Vakharia: Yes, yes, yes
• 26:54
  Christina Tondevold: all together.
• 26:55
  Christina Tondevold: So efficiency is the speed part.
• 26:57
  Christina Tondevold: And then accuracy.
• 26:59
  Christina Tondevold: Correct answers do matter.
• 27:00
  Christina Tondevold: And again, the pendulum swung away from
• 27:04
  Vanessa Vakharia: ChatGPT, yes.
• 27:05
  Vanessa Vakharia: Oh my God
• 27:06
  Christina Tondevold: You know, it's been like, oh, it doesn't matter if they get it
• 27:09
  Vanessa Vakharia: Hmm.
• 27:09
  Christina Tondevold: or wrong.
• 27:10
  Vanessa Vakharia: Oh my God
• 27:11
  Christina Tondevold: thinking.
• 27:12
  Christina Tondevold: I'm sorry.
• 27:12
  Christina Tondevold: Correct answers do still matter in
• 27:15
  Vanessa Vakharia: It matters
• 27:16
  Christina Tondevold: They need right answers.
• 27:18
  Christina Tondevold: Accuracy is important.
• 27:21
  Christina Tondevold: yeah, it is important to look at their thinking, but they also need to be told when it's wrong, like,
• 27:29
  Vanessa Vakharia: Oh my God.
• 27:29
  Vanessa Vakharia: Yep
• 27:30
  Christina Tondevold: That matters.
• 27:32
  Christina Tondevold: And then the third one is flexibility.
• 27:35
  Vanessa Vakharia: What's that?
• 27:36
  Christina Tondevold: that's been my focus is because for the longest...
• 27:39
  Christina Tondevold: I mean, I've been doing this a long time.
• 27:44
  Christina Tondevold: I started teaching, I graduated college in 2000.
• 27:47
  Christina Tondevold: So I have been in the education space for a long time, and focusing on building number sense and, and flexibility for more than 15 years of that time.
• 28:03
  Christina Tondevold: and so I have pushed heavily on getting teachers to focus on flexibility.
• 28:07
  Vanessa Vakharia: What is it?
• 28:08
  Vanessa Vakharia: What is that?
• 28:10
  Christina Tondevold: about, uh, that in a
• 28:10
  Vanessa Vakharia: Doing math when on, in a handstand while doing the splits
• 28:14
  Christina Tondevold: yeah, yeah.
• 28:15
  Christina Tondevold: Let's see how, how good your downward dog is or whatever, you know.
• 28:19
  Christina Tondevold: Um, but the hard part is that that put the focus away from the first two of accuracy and efficiency.
• 28:26
  Christina Tondevold: So I'm gonna talk about flexibility, but do not take away that that is the only thing we need to build.
• 28:33
  Vanessa Vakharia: We're just defining it
• 28:35
  Christina Tondevold: And I've, I've had to, like, say that now because I've put so much emphasis on flexibility and people have, have gone all the way to the
• 28:43
  Vanessa Vakharia: Okay
• 28:43
  Christina Tondevold: the other side.
• 28:44
  Christina Tondevold: So flexibility is just having alternate routes.
• 28:49
  Christina Tondevold: So let's go back to, you know, if you're, if you feel like you're fluent driver in your city, what happens if there's an accident and
• 28:56
  Vanessa Vakharia: Oh, God.
• 28:58
  Vanessa Vakharia: Oof.
• 28:58
  Christina Tondevold: Do
• 28:58
  Vanessa Vakharia: I'm stuck.
• 28:59
  Christina Tondevold: to get there without
• 29:00
  Vanessa Vakharia: No, absolutely not.
• 29:03
  Christina Tondevold: You're not
• 29:04
  Vanessa Vakharia: I am not.
• 29:05
  Christina Tondevold: your...
• 29:05
  Christina Tondevold: right?
• 29:06
  Vanessa Vakharia: I'm not
• 29:07
  Christina Tondevold: That's, and that's essentially what our kids are.
• 29:10
  Christina Tondevold: So they might have one way to do it, and that's also been an, an issue is, like, once all these different strategies came around, it's like, well, if kids have one way to do it, that's fine.
• 29:19
  Christina Tondevold: They don't need to know other ways.
• 29:22
  Christina Tondevold: what if that one way doesn't work on that problem?
• 29:25
  Vanessa Vakharia: okay?
• 29:25
  Vanessa Vakharia: I'm gonna do a little recap for the listeners, and for myself, quite frankly.
• 29:28
  Vanessa Vakharia: Okay, there are three aspects to fluency.
• 29:31
  Vanessa Vakharia: We have efficiency, which has to do with speed.
• 29:34
  Vanessa Vakharia: We have accuracy, which has to do with getting the right answer.
• 29:37
  Vanessa Vakharia: And we have flexibility, which has to do with being able to, to do things in different ways depending on the circumstances.
• 29:43
  Vanessa Vakharia: Context dependent.
• 29:45
  Vanessa Vakharia: Having to...
• 29:45
  Vanessa Vakharia: Okay, so now...
• 29:47
  Christina Tondevold: love that.
• 29:47
  Christina Tondevold: Yeah.
• 29:48
  Vanessa Vakharia: Okay.
• 29:48
  Vanessa Vakharia: Oh my God, thanks.
• 29:49
  Vanessa Vakharia: Okay, so now I'm like, oh my God, you are so right that we have g- we have completely over-corrected.
• 29:57
  Vanessa Vakharia: It's almost like, because flexibility wasn't a thing when, you know, like 20 years ago, we didn't care about it.
• 30:03
  Vanessa Vakharia: We only cared about efficiency and accuracy.
• 30:06
  Vanessa Vakharia: Now we're like,"Oh my God, flexibility," like,"We left you out." Now we're gonna, like, focus on flex- it also feels like, to me, flexibility is like the feel-good one of the gang.
• 30:16
  Vanessa Vakharia: It's like, and you know what I mean?
• 30:18
  Vanessa Vakharia: It's like, oh, you'll feel good.
• 30:19
  Vanessa Vakharia: Don't worry about getting it right.
• 30:20
  Vanessa Vakharia: Don't worry about being fast.
• 30:22
  Christina Tondevold: Yeah, it's like everybody wins kind of
• 30:25
  Vanessa Vakharia: Everybody wa- so it's giving participation ribbon.
• 30:28
  Vanessa Vakharia: Oh my God.
• 30:29
  Vanessa Vakharia: what?
• 30:30
  Christina Tondevold: I mean, we need that.
• 30:31
  Christina Tondevold: We need everybody to feel like they have a starting point, like they have a way to contribute, like they have a way to participate in mathematics.
• 30:40
  Christina Tondevold: That's, we do want that.
• 30:41
  Christina Tondevold: I'm not saying it's a bad thing,
• 30:43
  Vanessa Vakharia: I'm having a real epiphany.
• 30:44
  Vanessa Vakharia: I'm like,"Oh my God." I do think, I do think...
• 30:49
  Vanessa Vakharia: You know all the haters on the internet that are like,"Oh my God, they're treating kids like snowflakes"?
• 30:54
  Vanessa Vakharia: I don't know if I'm using that right, but do you know what I mean?
• 30:56
  Vanessa Vakharia: Like, participation ribbon, da, da, da, da, da, da.
• 30:58
  Vanessa Vakharia: It's like they're not actually entirely wrong, okay?
• 31:01
  Vanessa Vakharia: So, like, let me just say that, right?
• 31:02
  Vanessa Vakharia: It's like I get where they're coming with this.
• 31:05
  Vanessa Vakharia: Like, for sure, if we really were like,"Don't worry, take two hours to add two plus two together.
• 31:11
  Vanessa Vakharia: Don't worry if two plus two equals five or six or seven, but, like, as long as you're doing something, you get an A+," that would be a problem.
• 31:18
  Vanessa Vakharia: I agree, that is a problem.
• 31:20
  Vanessa Vakharia: But I think what's actually happening, and tell me if I'm wrong here, I feel like flexibility is not only useful, but it is the inroad for the math-anxious student into doing what is needed to get to an efficient, accurate place.
• 31:35
  Vanessa Vakharia: The flexibility is the thing we can be like,"Look, do it whatever way.
• 31:40
  Vanessa Vakharia: We can reward you because everyone has their own way of doing things." Now you feel more confident, and because you're feeling more confident, you're not gonna freak out when you get something wrong or you're too slow.
• 31:48
  Vanessa Vakharia: You're gonna keep at it because you have some con...
• 31:49
  Vanessa Vakharia: Like, am I onto something?
• 31:50
  Vanessa Vakharia: You know what I'm saying?
• 31:52
  Christina Tondevold: Absolutely.
• 31:53
  Christina Tondevold: And, and as, as an, um, a sports mom, you
• 31:57
  Vanessa Vakharia: Okay
• 31:58
  Christina Tondevold: I can see the analogy too with the participation trophies and the, and the entry points in, right?
• 32:03
  Christina Tondevold: Like, if, if at five years old we're expecting kids to come to baseball, being able to hit the ball into the outfield, and know which- where to throw it, and know which way to go.
• 32:15
  Christina Tondevold: Because, uh, if you've ever seen, like, play T-ball, they hit the ball and then they'll run to, like, third base, not first ba- Like, you know, they're learning
• 32:23
  Vanessa Vakharia: Oh, cute.
• 32:24
  Vanessa Vakharia: Right
• 32:25
  Christina Tondevold: not They don't have the accuracy and, uh, all the, that stuff down.
• 32:30
  Christina Tondevold: And, and so we do that build that and, and allow for all kids to have an entry point, right?
• 32:37
  Christina Tondevold: We aren't expecting every kid to win, every kid to be perfect.
• 32:42
  Christina Tondevold: We are laying a foundation of we're all here, we're learning, right?
• 32:46
  Christina Tondevold: And then unfortunately sometimes, uh, for some kids, they end up getting coaches who are all about winning, and all about getting it right, and will yell, and all of that kind of stuff.
• 32:57
  Christina Tondevold: And then guess what happens?
• 32:58
  Christina Tondevold: They don't love the sport anymore, and they stop doing it.
• 33:01
  Christina Tondevold: And that's exactly what we're doing in mathematics, is that we might be having these entry points, you know.
• 33:07
  Christina Tondevold: Like, again, we've, we've gone to the wayside where we're just letting everybody come in and have this entry point piece, but we also need to balance that with, hey, they Uh, like, we do need to get to the efficiency and accuracy part, but even then it's still flexibility.
• 33:24
  Christina Tondevold: The flexibility still matters.
• 33:26
  Christina Tondevold: It's not like flexibility goes away.
• 33:28
  Christina Tondevold: that's unfortunately sometimes we see in sports, is it becomes only about the winning, only about being perfect.
• 33:35
  Christina Tondevold: And then kids are playing out of fear because they're, uh, s- scared their coach is gonna yell at them or bench them because they did something wrong, right?
• 33:43
  Christina Tondevold: Like, there, there's different styles of coaching, for sure.
• 33:46
  Christina Tondevold: I've done Uh, this is part of a keynote that I do.
• 33:49
  Christina Tondevold: Um, so it's something I love talking about.
• 33:51
  Christina Tondevold: But the same is true for us as educators, that we- that flexibility is the piece that gets everybody feeling like they can do this, that they have a part.
• 34:03
  Christina Tondevold: And yet we have to balance it a little with, you know, accuracy and efficiency do matter, but if we put too much focus on that, that becomes an issue, and then kids are performing out of fear, and they're motivated only because those external things that they're afraid of.
• 34:21
  Vanessa Vakharia: I wanna bring this all home for us here, which is gonna be a bit hard, and that kind of is a baseball metaphor that I'm sort of using, I think.
• 34:29
  Christina Tondevold: Yeah,
• 34:30
  Vanessa Vakharia: right?
• 34:31
  Vanessa Vakharia: Uh, is that where it comes from?
• 34:32
  Vanessa Vakharia: Is it like ra- is it-- Oh, my God, Christina, wow, we are basically sports commentators.
• 34:36
  Vanessa Vakharia: Okay, this is gonna be hard to track'cause I have about 30 thoughts in my mind, but here are some of them.
• 34:43
  Vanessa Vakharia: The first is, I think we have to recognize, for anyone listening, I don't think anyone who thinks this listens to my podcast, but if you are listening and you're like,"I hate this flexibility stuff.
• 34:53
  Vanessa Vakharia: It's all about speed and accuracy," I'm so glad you're listening.
• 34:56
  Vanessa Vakharia: Actually, thank you for taking a chance on the podcast.
• 34:58
  Vanessa Vakharia: Thank you for being here, and here's what I wanna say.
• 35:01
  Vanessa Vakharia: If you're like,"Well, exactly, like, we are losing those things at the expense of flexibility," here is, here is my thought on that.
• 35:07
  Vanessa Vakharia: I actually think we have to recognize that historically math has been such an anxiety-inducing subject that so few students are willing to walk in the door.
• 35:16
  Vanessa Vakharia: And because of that, it behooves us, I don't know what behooves means, but it feels like it fits in the sentence.
• 35:23
  Christina Tondevold: Yes
• 35:23
  Vanessa Vakharia: It behooves us to actually put an emphasis on flexible thinking as a starting point because it allows the most flexibility in terms of who can walk in the door.
• 35:33
  Vanessa Vakharia: Because, you know, there are not many ways to think incorrectly.
• 35:37
  Vanessa Vakharia: If you're thinking, if you're doing something in any way, you are doing something, and that is what flexibility is all about, right?
• 35:42
  Vanessa Vakharia: So, like, it kind of makes sense for us to be really emphasizing that so we can get all the people in the door.
• 35:47
  Vanessa Vakharia: Once they're in the door, we are, we are dedicated as educators to helping them solve the problem and get the correct answer and to do so efficiently.
• 35:56
  Vanessa Vakharia: But, like, let us, let us emphasize flexibility for a bit, because the lack of flexibility is what has led to so much math anxiety, hence so few people walking in the door.
• 36:06
  Vanessa Vakharia: What do we think so far?
• 36:07
  Christina Tondevold: Mm-hmm.
• 36:07
  Christina Tondevold: Absolutely.
• 36:08
  Vanessa Vakharia: Okay, so great.
• 36:10
  Vanessa Vakharia: So that's nice.
• 36:11
  Vanessa Vakharia: But now you're making me think too, we've now really centered on the concept of fluency, right?
• 36:16
  Vanessa Vakharia: But it kinda, I know that fluency isn't the only goal in math, right?
• 36:21
  Christina Tondevold: well, so that could
• 36:23
  Vanessa Vakharia: It feels like,
• 36:24
  Christina Tondevold: right?
• 36:25
  Christina Tondevold: I
• 36:25
  Vanessa Vakharia: it feels pretty good.
• 36:26
  Vanessa Vakharia: It feels like it covers a lot of bases.
• 36:28
  Vanessa Vakharia: Oh my God!
• 36:30
  Christina Tondevold: We're just gonna keep at it.
• 36:32
  Vanessa Vakharia: Okay
• 36:33
  Christina Tondevold: um, I've had to really rethink my own understanding of the purpose of mathematics,
• 36:39
  Vanessa Vakharia: Okay
• 36:41
  Christina Tondevold: My traditional view of mathematics was I use mathematics and solve problems, like, I'm just doing math.
• 36:52
  Christina Tondevold: However, to me, and, and I got this from, we in the United States call it Singapore math, Ban Har says,"It's just math, but we do it in Singapore." And their focus is
• 37:07
  Vanessa Vakharia: Hmm.
• 37:08
  Christina Tondevold: We want kids to be problem-solvers, and we do that with mathematics.
• 37:14
  Christina Tondevold: Um, and so fluency, uh, like even in the United States, though, even with this flexibility piece, we still do have this push of get them fluent, fluent, fluent, fluent.
• 37:24
  Christina Tondevold: When, is mathematics, like, being fluent in mathematics, like, the end-all be-all?
• 37:31
  Christina Tondevold: Or is it that we want kids to be capable thinkers and problem-solvers, and we
• 37:39
  Vanessa Vakharia: it sounds...
• 37:40
  Christina Tondevold: through mathematics
• 37:41
  Vanessa Vakharia: But hold on, fluency sounds, the tenets of fluency, efficiency, accuracy, and flexibility, is that not what it takes to solve a problem?
• 37:52
  Christina Tondevold: It is, but it's, it's, it's flipping how we're looking at it.
• 37:55
  Christina Tondevold: Like, the end-all be-all...
• 37:56
  Christina Tondevold: 'Cause okay, so, um, let me see if I can reframe this too.
• 38:00
  Christina Tondevold: Like, I always thought, like, even on, when I first started becoming more of a recovering traditionalist, I still thought my job is to teach the mathematical skills, to help them understand the mathematical skills, like the operations,
• 38:15
  Vanessa Vakharia: Yes
• 38:16
  Christina Tondevold: that they can solve problems, right?
• 38:20
  Vanessa Vakharia: it
• 38:20
  Christina Tondevold: can solve problems.
• 38:22
  Christina Tondevold: When I heard Dr.
• 38:23
  Christina Tondevold: Bonhar talk, he said,"Our goal is to help kids be problem-solvers, and the byproduct of that is they learn some math skills along the way." And so it's the rever- Like, just
• 38:39
  Vanessa Vakharia: Oh,
• 38:40
  Christina Tondevold: is our
• 38:41
  Vanessa Vakharia: yep, yep, yep, yep, yep
• 38:42
  Christina Tondevold: wa- I was still focusing on help my kids learn the math skills, help my kids learn the math skills, and if they become great problem-solvers, that's a great byproduct.
• 38:52
  Christina Tondevold: But instead
• 38:53
  Vanessa Vakharia: hear you.
• 38:53
  Christina Tondevold: let's put
• 38:54
  Vanessa Vakharia: I hear you
• 38:54
  Christina Tondevold: And so even if we're like,"Okay, fluency will hit all of that stuff," it's still we're putting the focus on fluency, fluency, fluency, and then if they become thinkers, eh, a great byproduct of that.
• 39:08
  Vanessa Vakharia: Oh, wait,'cause it kind of seems like fluency, if we think about the w- you remember, you were, like, fluent in driving, fluent in cooking.
• 39:15
  Vanessa Vakharia: It almost feels like fluency is dependent on the thing you're fluent in.
• 39:18
  Vanessa Vakharia: You can't just be, like, fluent in life.
• 39:20
  Vanessa Vakharia: Whereas you can be a problem-solver in every domain, fluency is domain-specific, and right now we're talking about fluency in the domain of mathematics.
• 39:28
  Vanessa Vakharia: Oh my God.
• 39:29
  Vanessa Vakharia: Oh my God.
• 39:31
  Vanessa Vakharia: Okay.
• 39:32
  Vanessa Vakharia: And I think, we're gonna wrap here, but it's okay that we don't have a conclusion.
• 39:36
  Vanessa Vakharia: I actually think it is for the educator listening or whoever listening to be like,"Huh, what is my approach going to be?" Right?
• 39:44
  Vanessa Vakharia: Like, what is it?
• 39:44
  Vanessa Vakharia: Like, is it, is it going to be fluency first, problem-solving second, or is it gonna be pro- Like, and again, I actually don't know that there is a generic answer.
• 39:56
  Vanessa Vakharia: I think it can depend on your situation, on the student.
• 40:00
  Vanessa Vakharia: Maybe a student's really interested in some mathematical concept, and through that they develop fluency, and through that they learn how to solve problems.
• 40:07
  Vanessa Vakharia: Maybe a student's...
• 40:08
  Vanessa Vakharia: Right?
• 40:08
  Vanessa Vakharia: Like, do, do you think, do you think there's a right answer to this?
• 40:11
  Christina Tondevold: well, I would encourage, I guess, um, maybe it's the recovering traditionalist in me that we start opening our mind to maybe it is more about the problem-solving si- piece of it, and that when we have that as the center goal, it makes all the other things seem easier it all connects back to that one thing.
• 40:39
  Christina Tondevold: like fluency with math facts still connects to that because we do...
• 40:43
  Christina Tondevold: If, like, if we're out solving the, like, some problem comes to mind when we're out there, we do need to be quick that so that we can figure something out in the moment, right?
• 40:53
  Christina Tondevold: Like, I, know.
• 40:55
  Christina Tondevold: I- it's a good conversation to keep going and a, a, a good one to really think and grapple with.
• 41:01
  Vanessa Vakharia: Yeah, think about it
• 41:02
  Christina Tondevold: the center focus of this,
• 41:04
  Vanessa Vakharia: we're ta- w- you know, a lot of people listening are, teach math.
• 41:07
  Vanessa Vakharia: And I'm like,
• 41:08
  Christina Tondevold: Mm-hmm.
• 41:09
  Vanessa Vakharia: Have math as a gateway.
• 41:11
  Vanessa Vakharia: Like, I, I mean, I love math, but I don't particularly, I'm not like,"Math is the most important thing." I'm like, math is just the most beautiful gateway to so many things.
• 41:19
  Vanessa Vakharia: And one of the gateways that it opens up is the ability to problem solve, right?
• 41:23
  Vanessa Vakharia: Y- yes, you're learning content and you're learning skills, and you're becoming fluent in this and that, but at the end of the day, the, the broader skills you're learning is how to solve a problem, right?
• 41:32
  Vanessa Vakharia: So I guess I'm kind of thinking, like, because at your disposal, what you have is math content that you have to teach.
• 41:41
  Christina Tondevold: Mm-hmm.
• 41:41
  Christina Tondevold: Mm-hmm.
• 41:43
  Vanessa Vakharia: that's kinda what you, you're supposed to be doing anyways.
• 41:47
  Vanessa Vakharia: I don't know, I'm stuck at that end of that sentence.
• 41:50
  Vanessa Vakharia: But I'm kind of like, so if you, if through teaching a child to be fluent in math facts, that was your way to teach them to be a problem solver, that almost seems like starting with the trees instead of the forest.
• 42:07
  Christina Tondevold: Yeah, it's an interesting conversation of just, um, trying to grapple with, you know, all these things that come at us.
• 42:15
  Christina Tondevold: You know, there's, oh, well, oh, now we should be doing which one doesn't belong, and now we should be doing
• 42:20
  Vanessa Vakharia: Cat
• 42:21
  Christina Tondevold: word prob- Like, there's so many different, like, things that we can be doing in the math classroom, and now, like, high-quality instructional materials and, and all of those pieces that get thrown at educators.
• 42:34
  Christina Tondevold: And so whether you have been teaching for 30 years or you've been teaching for three years, you've probably already noticed this pendulum swing and bandwagon.
• 42:47
  Christina Tondevold: You're getting on the bandwagon of this new next thing, and then guess what?
• 42:51
  Christina Tondevold: We're gonna hop off that here in six months, a year, maybe two years from now.
• 42:56
  Christina Tondevold: And so it's not about the things that come along.
• 43:01
  Christina Tondevold: we really do need to think about the bigger picture what our goal is when we are helping students learn mathematics.
• 43:10
  Christina Tondevold: Um, and I think that's something we all need to grapple with a little.
• 43:14
  Vanessa Vakharia: Well, this is perfect,'cause I was gonna say, can you leave th- us with something?
• 43:18
  Vanessa Vakharia: It is summer.
• 43:19
  Vanessa Vakharia: I want you to leave us with a, like, what's something we can do right now so that when we get into the classroom, you know, when school starts again, we feel more centered?
• 43:28
  Vanessa Vakharia: And I think that's the thing, is to think about what you feel your purpose is up there in front of the classroom.
• 43:35
  Vanessa Vakharia: What is the point of what you're doing?
• 43:36
  Vanessa Vakharia: What's the point, and then let your answer to that question guide how you teach.
• 43:41
  Christina Tondevold: Let your own answer to that, and then what you're hearing from your students where they are in their learning guide the instruction moving forward.
• 43:51
  Vanessa Vakharia: Ugh.
• 43:52
  Vanessa Vakharia: Okay, this was so fun.
• 43:54
  Vanessa Vakharia: I have two questions to ask you that I ask every podcast guest, and you have 30 seconds to answer both of them.
• 43:59
  Vanessa Vakharia: But I do have to tell you,
• 44:01
  Christina Tondevold: Speed.
• 44:02
  Vanessa Vakharia: this is...
• 44:02
  Christina Tondevold: I
• 44:03
  Vanessa Vakharia: Right?
• 44:03
  Vanessa Vakharia: You gotta be fluent.
• 44:04
  Vanessa Vakharia: You gotta be fluent.
• 44:06
  Vanessa Vakharia: Okay.
• 44:06
  Vanessa Vakharia: Someone's listening to this podcast, they're like,"I love everything Christina said.
• 44:10
  Vanessa Vakharia: Honestly, that's so interesting," and like,"Yeah, for sure, maybe I have some math trauma," like maybe that's not why I'm good at math, but honestly the truth is I'm just not a math person.
• 44:18
  Vanessa Vakharia: How do you respond?
• 44:19
  Christina Tondevold: Mm.
• 44:21
  Christina Tondevold: you have a wrong version of math because your version is probably like mine.
• 44:29
  Christina Tondevold: I th- I had the opposite.
• 44:31
  Christina Tondevold: I thought I was good at math until I had to go teach it, I learned that I was good at arithmetic, mathematics.
• 44:40
  Christina Tondevold: And so you may see yourself as not good, but you've been not good at the arithmetic part of mathematics, of getting correct answers, and there's so much more to math beyond just correct answers.
• 44:54
  Christina Tondevold: It is about a problem solver, and so, and everybody's good at that.
• 45:01
  Vanessa Vakharia: It's so hard right now because I know I don't have time for what I'm about to say, but I'm gonna have to say it.
• 45:08
  Christina Tondevold: Okay
• 45:08
  Vanessa Vakharia: I really don't like...
• 45:10
  Vanessa Vakharia: This is not your fault, okay?
• 45:12
  Vanessa Vakharia: And I love your response, but I don't like that in the response you put yourself down.
• 45:17
  Vanessa Vakharia: And the reason I don't like that you put yourself down is, is I don't like this new trend in general, and I'm not saying you're, like, sorry, but I don't like this trend of us in, in order to include more people in math, we now have to exclude people who were included.
• 45:32
  Vanessa Vakharia: I don't like this'cause I feel like it's like arithmetic is a part of math, and you were good at arithmetic.
• 45:37
  Vanessa Vakharia: It's not like it wasn't real.
• 45:39
  Vanessa Vakharia: Sorry, Christina.
• 45:40
  Vanessa Vakharia: I shouldn't be yelling at you
• 45:42
  Christina Tondevold: No, that's a good point because I say it a lot, um, and you're making me reflect on that part of it that I, I was good at a certain part of mathematics.
• 45:53
  Vanessa Vakharia: great.
• 45:54
  Vanessa Vakharia: No one's good at every part of mathematics, even like prolific mathematicians.
• 45:59
  Vanessa Vakharia: It's not like they're...
• 46:00
  Vanessa Vakharia: There's like game theory experts that don't know shit about like calculus.
• 46:04
  Vanessa Vakharia: It doesn't mean that they're like,"I was never actually g- Sorry, this is like I shouldn't be taking this out on you, especially within the time confines that I gave you.
• 46:12
  Vanessa Vakharia: Okay.
• 46:12
  Christina Tondevold: We're all on this journey.
• 46:13
  Christina Tondevold: That's why I call myself a recovering traditionalist.
• 46:15
  Christina Tondevold: Like, there are times that somebody needs to hold a mirror to me and be like,"No, I don't...
• 46:21
  Christina Tondevold: You're n- you're not saying that correctly," or, or,"Rethink about how you think about that."
• 46:25
  Vanessa Vakharia: Um, the n- final question, I swear to God.
• 46:28
  Vanessa Vakharia: final question is, if you could pick one thing to change about the way math is taught in school, what would it be?
• 46:33
  Vanessa Vakharia: One thing
• 46:34
  Christina Tondevold: Hmm, balance.
• 46:36
  Vanessa Vakharia: Hmm.
• 46:37
  Vanessa Vakharia: I love that
• 46:37
  Christina Tondevold: of balance becau- and it goes with our theme of the pendulum.
• 46:40
  Christina Tondevold: I wish I could tie baseball into this somehow, uh, but I don't see that.
• 46:45
  Christina Tondevold: Uh, that we, we swing one way, we swing the other, and, and we realize that's not working, and so we'll swing all the way to the other way.
• 46:53
  Christina Tondevold: And we need some of both all the time.
• 46:58
  Christina Tondevold: We, we do need some timed activities.
• 47:00
  Christina Tondevold: We need kids to be able to play and discover and guide their instruction.
• 47:04
  Christina Tondevold: We need, um, sometimes we need a lot of practice.
• 47:08
  Christina Tondevold: You know, when textbooks have moved one way and it's like a lot of contextual problems and discovery, and then those textbooks are lacking in practice, and we do need t- time to practice things.
• 47:22
  Christina Tondevold: So we, if I could change anything, it would be to find a way to have some balance of both sides of these pendulums that we find in math education.
• 47:34
  Vanessa Vakharia: I love this.
• 47:35
  Vanessa Vakharia: And honestly, to really take us home, David has texted me, I think your landing metaphor may be what you were looking for.
• 47:42
  Vanessa Vakharia: Not sure if it really is it.
• 47:44
  Vanessa Vakharia: He said,"Gotta play both offense and defense to win a ball game
• 47:50
  Christina Tondevold: Yeah.
• 47:51
  Vanessa Vakharia: Honestly, this was such a treat.
• 47:53
  Vanessa Vakharia: I've had so many epiphanies.
• 47:54
  Vanessa Vakharia: It was so great talking to you.
• 47:56
  Vanessa Vakharia: I can't believe how many metaphors we wove into one another.
• 48:00
  Vanessa Vakharia: Like, I, I feel it was truly prolific.
• 48:03
  Vanessa Vakharia: Um, thank you so, so much for
• 48:06
  Christina Tondevold: for asking me, and it's fun to get to chat with you, and hope to get to meet you in person one of these days at a conference.
• 48:13
  Christina Tondevold: So
• 48:14
  Vanessa Vakharia: me too, and I'm really excited for the World Series when the Blue Jays hopefully make it again, because this time when I jump on the bandwagon, I know that I have a baseball girly to talk to about all the things.
• 48:24
  Christina Tondevold: terminology, I'm
• 48:26
  Vanessa Vakharia: I do.
• 48:27
  Christina Tondevold: Yeah.
• 48:28
  Vanessa Vakharia: See you on the field.
• 48:30
  Vanessa Vakharia: Is that what they say?
• 48:31
  Vanessa Vakharia: No?
• 48:32
  Christina Tondevold: Play ball.
• 48:36
  Vanessa Vakharia: Okay, I'm dying to hear what you guys think because honestly I feel like my entire relationship with fluency has changed, especially when I start thinking about using that word in contexts other than math, right?
• 48:46
  Vanessa Vakharia: Like, the word is not polarized when it comes to languages.
• 48:49
  Vanessa Vakharia: Why has it been so polarized in math?
• 48:52
  Vanessa Vakharia: And I'm really curious if Christina shared anything that changed your mind and might even change your practice this upcoming school year, or if she said anything that made you double down on what you already think and what you're already doing.
• 49:02
  Vanessa Vakharia: Either way, we wanna hear from you.
• 49:04
  Vanessa Vakharia: Text the podcast, hit the link in your show notes.
• 49:07
  Vanessa Vakharia: It literally says,"Text us," so text us.
• 49:09
  Vanessa Vakharia: Also, if you want more of me and Christina, I'll be speaking at her free virtual thinking summit August 10th, 11th, and 12th.
• 49:17
  Vanessa Vakharia: You should totally come.
• 49:18
  Vanessa Vakharia: It's completely free, and there are such awesome speakers like Pam Harris, Zak Champagne, Deborah Peart, Juliana Tapper, Mike Flynn.
• 49:26
  Vanessa Vakharia: I could go o- Brittany Hege.
• 49:28
  Vanessa Vakharia: Like, there are so many people that you know and love that are gonna be speaking at this thing, and it's totally free.
• 49:32
  Vanessa Vakharia: So head to the show notes.
• 49:34
  Vanessa Vakharia: The link is in there to register for free, so come.
• 49:37
  Vanessa Vakharia: As always, thank you guys for listening.
• 49:39
  Vanessa Vakharia: I would love for you to do all the things I always ask you to do, like share this episode with a friend, rate and review the podcast, that stuff makes such a big difference to a small little operation like ours that is growing thanks to you and the amazing work you're doing out there.
• 49:54
  Vanessa Vakharia: But also, I know we're busy.
• 49:55
  Vanessa Vakharia: I know you are booked and busy.
• 49:57
  Vanessa Vakharia: I know the last days of summer are approaching, and you have a million other things to do, so if you don't wanna do any of that stuff, that's cool.
• 50:05
  Vanessa Vakharia: Just have the best day ever, and I will catch you back here next week uh, David, I have a producer's note from about half an hour ago when we were trying to find that fairy tale.
• 50:19
  Vanessa Vakharia: He's now said,"You've run out of pitchers in your bullpen and putting position players on the mound at this point", I don't know what that means.
• 50:25
  Vanessa Vakharia: Okay, here are the two questions.
• 50:27
  Vanessa Vakharia: You have 30 seconds for each, okay?
• 50:29
  Christina Tondevold: Toss me a softball question here.
• 50:31
  Vanessa Vakharia: Oh my God.
• 50:32
  Vanessa Vakharia: All right.
• 50:33
  Christina Tondevold: that
• 50:33
  Vanessa Vakharia: I,
• 50:34
  Christina Tondevold: to hit out of the park?
• 50:35
  Vanessa Vakharia: I do know that, from when I watched the Blue Jays World Series.
• 50:39
  Vanessa Vakharia: A soft toss.
• 50:40
  Vanessa Vakharia: So here are two soft tosses that you have 30 seconds to answer.
• 50:42
  Vanessa Vakharia: Okay.