Updated: Oct 17, 2021
Desiree Harrison 0:00
What is fluency? What's computational estimation? When should we use algorithms? And is an algorithm the same as a strategy? Previous episodes have given us a shared background to begin to answer these questions, and today's guests help us further explore the answers.
We know that fluency is about more than just accuracy - it's about being able to make good choices, about being able to become a critical thinker, and this episode helps us reflect on how to move this theory into practice.
To think about the when, why, and how of fluency.
And to help us adopt strategies that we can then use to empower children to become decision makers.
Desiree Harrison 1:14
Today, on the podcast, we have the authors of, Figuring Out Fluency in Mathematics Teaching and Learning: Moving Beyond Basic Facts and Memorization, Grades K-8.
Welcome to the podcast!
Jennifer Bay-Williams 1:32
Hi! It's great to be on Kids Math Talk! This is Jennifer Bay-Williams and I'm a professor at the University of Louisville.
John SanGioVanni 1:38
And, hi! I'm John SanGiovanni. I'll echo that, it is great to be here today. I am a coordinator of mathematics in Howard County, Maryland. About halfway between Baltimore and Washington, D.C.
Desiree Harrison 1:51
Alright. Thank you both so much for being here today. And, so, this book is relatively new.
So, it's August (2021) right now when we're recording this.
I've had this book coil-bound and then you can see I have tabs everywhere because I didn't want the spine to wear out because I was flipping back and moving through it so much because, I just have to say, this is just so well done and I just feel like everybody needs to read this book - educators, parents, administrators - it's just so well done. And so accessible.
It's not jargony, but you give us the language that we need at the same time, which is a delicate balance, but you all pull it off.
So, there's so much that I want to ask you to get some insights and to give our listeners a little bit about what this book is all about.
And, so, I just want to talk about the beginning, because you start us off from the beginning really strong and you give the reader a real purpose for the book.
And, so, you have the title that gives us the purpose, and then the title of the first chapter - What Does Fluency Really Mean and Why Does It Matter?
And you all also talk about that the math education field hasn't always done the best job of defining fluency. And on the podcast, I talk a lot about how definitions are so important so that we have a shared background and understanding, and I completely agree that this definition is very fuzzy and we have to move away from everything just being about theory and to move toward relatable conversations.
So, when educators are talking with parents, and other community members, what are some talking points that we should use as we answer these questions of what is fluency and why does it matter?
Jennifer Bay-Williams 3:43
So, with the relatable information about fluency I think begins with connecting it to literacy and thinking about what it means to be fluent, just in your own language.
So, you know, I'm a fluent English speaker, and I am a not fluent Spanish speaker. So, in English, if you say something, Desiree, right now, I could probably think of four other ways I could communicate the very same thought or a very similar thought.
But in Spanish, I probably have one way, if I'm lucky. And, to me, this is what we do with the math fluency, is that we give students maybe one way, if they can remember it, instead of giving them a collection of ideas that allow them to choose how they want to do their math problem.
So I think that connecting to fluency as we see it out there in the everyday world and relating that to math is a good start.
John, what would you say.
John SanGioVanni 4:31
Yeah, I think those are really - that's a great point Jenny. I think when I work with parents and try to communicate with them, I try to boil it down to something they're really familiar with. And I think about - something I think we wrote about in the book - and that's an activity about driving home.
And talking with a parents about - do you drive home from work the same way. What are those directions for going home - turn, by turn, by turn, by turn.
And then, okay, if you have to go another way, how would you go home turn, by turn, by turn, by turn.
And then, if you had to go home another way, what would be the way that you would go home.
And why I use this is - well, which way do you typically go home? Why do you prefer it? When do you use alternatives? Why do you use alternatives?
And if you're comfortable with going home in a lot of different ways, and though you have a preferred strategy or approach to getting home, and one maybe your spouse thinks is wrong way - that's fine.
This notion that you're armed with different ways to get there and you choose the ones that are most appropriate for the situation, and that's what it means to be a fluent driver, for lack of a better word.
I share that example because, again, often parents are like, "Oh!"
Families can wrap their heads around that and transfer that to language, as Jenny explained, which is an awesome example, or to computational fluency like we talk about.
Jennifer Bay-Williams 5:42
Yeah. And I would just add one thing. I think, you know, these - what's familiar to families - the fluency with language and then metaphors and other things like driving are really important. But also I think, having just math examples - so I'll just use money because it's the most common kind that we encounter.
And if you think about, like, Desiree, you have $42 and you just spent $39, how much money do you have left.
And then you have another scenario, like you have $142 and you just spend $37, how much money do you have left.
Well, in those two scenarios, the first one, you know, you're going to think about differently. You're probably right off the bat said, "yeah I've got 3 bucks."
The second one you're like, "Wait a minute. Give me some think time, please don't ask me that right now." Because they're just different - it connects to John's metaphor of the driving - when are you going to use a particular method, when are you maybe going to go to a calculator, and when are you going to use a strategy. (6:36).
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