SPEAKER: It’s an honor to introduce you to Dr. Cathy Seeley. Dr. Seeley is a senior fellow at the Dana Center, where she works on state and national policy in improvement efforts in mathematics
education. And she’s currently leading the development of a fourth year math course to follow algebra 2 titled Advanced Mathematical Decision-making. Dr. Seeley’s experience includes teaching math
at the middle and high school levels, a mathematics supervisor for K-12, director of mathematics for the Texas Education Agency, and she also served as president of NCTM, or the National Council of
Teachers of Mathematics, where she served on the writing team for the curriculum and evaluation standards for school mathematics. For those of you who attended the NCTM conference last year, they gave
out her book, Faster Isn’t Smarter, and it’s really -- I’m a big fan of that book because it’s a lot of her shorter postings from whenever she was president of NCTM, so they’re very
thoughtful and short reads that are very easy for someone like me to digest. So please welcome me -- or please join me in welcoming Dr. Cathy Seeley. CATHY SEELEY: Thank you. Thank you, Cecil. And
good morning to everybody. It’s bright and early, isn’t it? Especially on Central time, by the way. So that’s a whole other thing. This is not an easy place to get to, but I hope it was
convenient for you. So I’m glad to be here with you. I’m from Austin, Texas. I work at the Dana Center, which is the University of Texas. We do K-12 math and science things. And I -- this morning,
what I think we’re going to be doing is thinking a little bit about -- starting to think about recognizing students’ potential in mathematics in general, but probably a little bit beyond
mathematics as well. And secondly then, I want to think about ways in which -- how we teach mathematics can nurture and develop that potential. I want to look at the ways we teach and how in fact
those -- the things we do in classrooms have something to do with nurturing students’ potential. And then finally, I want to share with you some thoughts about democracy in math class. I recently --
at the most recent NCTM meeting, I had the honor of doing the Iris Carl Equity Address. And in the process of doing that presentation, I thought a lot about -- democracy kept coming back to me, so
that’s what I want to end with today. And we’ll have a couple of times for you to talk to each other as well. And, in fact, I always have to put that up there because I forget otherwise. I think
the conference has a way for me to post the slides. I chose not to post them ahead of time. That was actually intentional because of the kind of talk this is, but I will post them afterwards. Or you
can email me directly. My email was on this title slide, but I’ll also give it back twice at the end of the presentation as well if you want to just email for a PDF of that. All right, so in terms
of recognizing potential, there’s a graphic on there that is just not up there. That’s kind of interesting. Okay. I want you to start by thinking about a question for you to reflect on for just a
bit. When you think about all the high expectations we have for students, although the good things we think that students can and should be able to do, many of you deal with many students who don’t
reach their potential or who don’t seem to reach the high goals that the policymakers have set, or don’t seem to reach the goals that you have set for students. So I want you to think for just a
second about what some of the reasons are that students don’t reach the goals that we set for them in mathematics. And as you reflect on that, why don’t you jot down a couple of things in front of
you and then we’re going to have you talk with a couple of people nearby. But first, just go ahead and either on your iPads, which I notice are all over the place, or on a piece of paper, just jot
down some thoughts about what are some of the factors that keep kids from reaching their full potential. And as you capture those thoughts, if you -- some of you may need to move a little bit, but
I’d like you to find at least one other person, preferably a couple of other people, to share your thinking with about why it is some students may not reach their full potential. And then we’ll
have a couple up to share. SPEAKER: [inaudible] email from the person [inaudible] asking if there’s any way to end just a couple of minutes early just so that people can get through the lines.
That’s totally at your discretion. CATHY SEELEY: Okay. Okay, I will try to do that. Yeah, I think I’ve adjusted the slides. It’s always -- I always think I have plenty of time about halfway
through, and then -- thank you, Cecil. I will try to do that. We’ll take a few more seconds for you to make sure everybody’s gotten to share. And if you want to bring that to a close. Some good
conversations going on, I can tell. All right, what’s one thing that you -- we do have a microphone here so we make sure that everybody can hear. What’s one thing that you came up with that might
keep kids from reaching their goals? AUDIENCE MEMBER: Just attitude, the attitude that I can’t do this, this is too hard. CATHY SEELEY: Okay, an attitude and especially thinking that this is too
hard for me. AUDIENCE MEMBER: I thought the teacher or, you know, poor instruction. CATHY SEELEY: Poor instruction. Okay, right in front there. AUDIENCE MEMBER: Lack of that automaticity of the basic
facts. I’m thinking very elementary, but they haven’t learned those. They -- CATHY SEELEY: Okay, so no foundation there in terms of number. Okay, what else you got? AUDIENCE MEMBER: Well, with
some students there are basic lacks like, for instance, a child that I have who cannot like recognize the difference between four and six on dice. So that really -- number sense really doesn’t have
at all. CATHY SEELEY: Number understanding, okay. And there was one over here, Cecil. AUDIENCE MEMBER: Lack of relevance in their lives, so they don’t feel that they need the [inaudible]. I think a
lot of them rely too heavily on, well, I’ve got calculators out there will my cell phone and all that. And I think, you k now, we still need -- CATHY SEELEY: Lack of relevance, okay. What else?
AUDIENCE MEMBER: Absenteeism. CATHY SEELEY: Absenteeism. Okay. And right back there. AUDIENCE MEMBER: I’m a high school teacher. Sometimes it can be motivational factors because they attach
something to math. You know, that statement they attach. I can’t do it, I can’t do it because they -- you know, they’ve had problems all along. CATHY SEELEY: So it’s sort of built up
motivation. That covered a bunch of different facets there, motivation and attitude and a lack of confidence. Okay, what else? AUDIENCE MEMBER: Not only automaticity, but I think they have to have a
conceptual understanding of what it is that’s taking place because with that understanding, then they can make things work. CATHY SEELEY: That’s great. I think you all don’t need the rest of the
slides, but okay. What else you got? Right next to you, Cecil. AUDIENCE MEMBER: I’ll just add reading comprehension issues, where you can’t get to the vocabulary and the understanding of what
needs to happen. CATHY SEELEY: Yeah, more and more. A friend of mine says you went into math thinking that there wasn’t going to be any words in it. All of a sudden, now you’re grading essays,
right? Okay, anything else you want to throw in the mix here? AUDIENCE MEMBER: Parental support and their expectations. CATHY SEELEY: Parental support and expectations. Okay. Excellent, good
conversation. In fact, when we think about some of the factors to consider, you’ll recognize this list because you’ve mentioned pretty much all of these. You talk about factors related to students
in terms of their motivation and what they bring to it. You’ve mentioned factor -- well, you may or may not have mentioned factors related to intelligence, but actually what students brings to it in
terms of facility, we’re going to talk a lot more about that one in a minute. You talked about instructional factors, the kinds of activities that students -- that we give students to do, or the
nature of the mathematics we ask them to do. And a big, big, big one that we’re going to talk about this morning, whether or not students actually have an opportunity to struggle and wrestle with
mathematical ideas and think about things that are hard. We’re going to talk a lot about that. And expectations that they will succeed. And we heard expectations. Whose expectations might influence
what a student does? Their own, their parents’, their teachers’, their peers’, all of those. And I believe that one of the big factors to consider is also sort of the nature of the mathematics
classroom, whether or not it’s taking place in an environment where students feel like it’s safe to try to offer up an idea because it’s acceptable in this classroom that we learn from different
strategies, different ideas, whether they lead to solutions or not. And a group of what I call insidious factors that we’ll just mention briefly here shortly. So when we think about all these
different factors, you may not see the immediate connection, but I hope you will here shortly. I want you -- how many of you know who Joshua Bell is? Okay, two people in the room know who Joshua Bell
is. Joshua Bell, this lovely young man, this gorgeous young man who is sort of a rock star in classical music, he’s one of the world’s greatest violinists, classical violinists. And he’s won all
kinds of awards. He’s an amazing person. And he’s young and charismatic and just very, very appealing sort of and talented young man. Well, not too long ago, the Washington Post, a reporter on the
Washington Post contacted Joshua Bell and asked if he would take place -- take part in a social experiment. And he agreed to do it, and so what he did was he put on street clothes and a baseball cap
and he went to one of the metro subway stations in Washington D.C. early one morning during rush hour. And he opened his violin case and he started playing. And there’s a short video I want to show
you. It’s about a two-minute video that sort of summarizes the experiment, some reporter talking about it, an online reporter talking about it. As you watch the video, I want you to think about the
lessons that this particular scene or experiment might tell us as educators. And I’ve done this now with a couple of different groups and I’m always fascinated by the insights that people have
into what this -- the message that this particular video has. I was fascinated by it, so I encourage you to think about it as you listen to the video. And it’s a little bit hard to see sometimes,
but I think you’ll get it. [VIDEO BEGINS] REPORTER: Joshua Bell, the international violin sensation who recently held an impromptu concert in a D.C. subway station. You know the web was in
attendance. The performance, which occurred during the middle of the morning rush hour, was orchestrated by the Washington Post as an experiment that begged the question in a banal setting at an
inconvenient time, would beauty transcend? [MUSIC PLAYS] REPORTER: This from the Post itself. In the three quarters of an hour that Joshua Bell played, only seven people stopped what they were doing,
at least for a minute. And 27 gave money for a total of $32 in change. That leaves 1,070 people who hurried by oblivious to the performance of what the Post calls one of the finest classical musicians
in the world playing some of the most elegant music ever written on one of the most valuable violins ever made. [VIDEO ENDS] CATHY SEELEY: Okay, I find that a fascinating story. And by the way, the
woman at the end there, you may have heard her. She said, I saw you at the Library of Congress last night, where, by the way, she had paid over $100 for her seat to do so. And then she said, this is
one of the only -- D.C. is one of the only places that this could happen. So what I want you to do is I want you to think about this little experiment from whatever perspective struck you as you were
looking at it. And just think in general with whoever -- a couple sitting around you about what lessons this might offer us as educators. And then I want you to think about disguises that our students
may wear in terms of not helping us see their talents that they may have, and ask a question just for you to think a little bit about the potential of students and where the Joshuas may be hiding. So
why don’t you turn to a couple of people nearby and have a conversation about Joshua’s experiment. We’ll take about one more minute. Okay, if you want to bring that conversation to a close.
Before we share, I wanted to find out a little bit. How many of you are classroom teachers? How many of you are school-level administrators? Central office folks? Other? What are all the others?
There’s a lot of -- AUDIENCE MEMBER: University. CATHY SEELEY: University. Okay, all right. And others, others probably, right? All right, great. How many of you see yourself as primarily elementary
or including elementary? You can raise your hand more than once. Middle school? High school? What a diverse group of people. Okay. All right, so as you thought about Joshua’s experiment, what came
to you in terms of a message for education? Right back, our high school guy right here. AUDIENCE MEMBER: I just thought of three things. Stopping, listening, and thinking. CATHY SEELEY: Stopping,
listening, and thinking. On the part of who? AUDIENCE MEMBER: On the part of the students because, you know, sometimes I’m trying to -- I’m so concerned with the standards that I have a tendency
sometimes to rush in my classes when I feel I’m not where I should be. And instead of maybe, you know, me slowing down, getting the students to slow down, get them to listen a little bit more
carefully, maybe approaching them differently and come up with different ways, and have them thinking about what I’m saying. Sometimes I get caught up in that rush and, you know, the standards and
everything that’s required to be done. And I’m just looking at those people blowing by him, and maybe you do have a minute to stop to think about what’s -- you know, what’s happening and to,
yeah, stop, listen, and think about what’s happening. CATHY SEELEY: Okay. So how many of you feel like you’re rushed to cover content? Most teachers that I talk to these days feel that they’re
not supposed -- don’t have the luxury, really, of taking the time to do the depth of development that they think their students and that they know in their hearts that their students would need.
Okay, what else came to you? Right here. AUDIENCE MEMBER: I guess for me, I thought that they went right to the assumption that people who were boarding the trains weren’t paying attention and they
weren’t getting anything. And I kind of put myself in one of those positions and I thought, you know, I probably would have noticed that, recognized that, and had some appreciation, but because I
had a destination, I had somewhere to get to, that, you know, I didn’t stop, but I still took note. And I think about that as it relates to teaching and learning. And I think, you know, when the
student is ready, the teacher appears. That, you know, we still may be learning lots of lessons that we don’t know how we’re going to apply until later on. CATHY SEELEY: Okay, so sometimes it may
be that there’s another -- like a student has another goal in mind, or the teacher has another goal in mind, and so they’re -- that’s not appropriate at the moment, but there -- it’s in the
back of their mind and it may come back later. Okay. What else? Right here. AUDIENCE MEMBER: Familiarity and relevance. If it’s not familiar to you and it doesn’t have some relevance to you, you
probably don’t pay attention. CATHY SEELEY: Maybe you’re not a classical music fan or you have something else on your mind, so whether or not it’s immediately relevant to what’s going on in
your life makes a difference. AUDIENCE MEMBER: And that’s true with math as well. It doesn’t feel familiar to a lot of kids because of what they’re bringing to the class. And it doesn’t feel
relevant to their daily lives. And so they kind of tune it out. CATHY SEELEY: Okay. All right, what else you got? I saw some other hands. Right here. AUDIENCE MEMBER: You know, I noticed when they
were rushing and everything, he did something to try to get their attention. He was faster. And when they slowed down, it affected him to. So that’s what kids do in the classroom as well. CATHY
SEELEY: All right. Right back here. AUDIENCE MEMBER: I just thought of the word agenda. Whose agenda is operating? You know, the people who are commuting, they have their agenda. The Washington Post
has their agenda. That’s what happens in the classroom. You have your agenda. The students have their agenda. You have to make sure that there’s some overlap. CATHY SEELEY: Okay, and so sometimes
the students have something in their minds and what interests them and where they’d like to go, and you have something in your mind and what interests you and what you think you need to do. And
those things may not always fit together very well. All right, what else? Right here. AUDIENCE MEMBER: I would just say from experience because I lived in the Washington D.C. area, you have stuff like
that going on all the time. So sometimes it’s the familiarity and it’s like, oh gosh, another one. And you just keep going. It doesn’t matter how good the music is. CATHY SEELEY: Exactly. And so
you’ve seen it a lot and maybe you don’t notice that this -- wow, this is, you know, one of the most amazing things -- musical pieces that’s ever been played, but maybe that’s not relevant
because you’ve seen so many all the time you don’t notice it. Okay, what else? Right here. AUDIENCE MEMBER: The context in which this man is playing. I mean, here’s someone who is, you know, a
wonderful artist. And he’s playing in this place you wouldn’t expect him to be playing. And so it’s -- if you were in a math class, you might not expect to find something that’s really
wonderful and beautiful. And maybe you could. CATHY SEELEY: That’s a perfect segue to the second question up there. Sometimes we don’t notice the talents and the beauty of our students because
they’re wearing many kinds of disguises. In this case, Joshua Bell’s disguise was just being an everyday person instead of in his tuxedo in the Library of Congress, where you paid a lot of money
to see him. What are some of the -- we’re not through yet, Cecil. What are some of the disguises that our students might bring to disguise their mathematical potential? AUDIENCE MEMBER: I think, you
know, they don’t want to appear smart in front of their peers. They don’t want to be outstanding, you know, to their peers. CATHY SEELEY: Okay, so it may be peer sort of -- a peer issue. They
don’t want to look smart because that’s not cool. What else? What other kinds of disguises? AUDIENCE MEMBER: Well, my child with a numeracy problem was a superstar when it came to fractions. I was
totally floored and I realized if he’d been in a regular classroom, he would still be working on addition and subtraction, which he doesn’t have, instead of moving on with a fourth grade class and
doing fractions. And I never would have discovered that if I hadn’t figured out a way to keep him in there even though he didn’t have the computation. CATHY SEELEY: So sometimes the disguise is
something in math that we don’t know. And we generalize from it. We see that, oh, this kid can’t do his times tables, or this kid really doesn’t understand multiplication, or basic place value
or something. And we generalize that that means that they don’t get anything, as opposed to looking past that or having ways to look past it because there’s no reason you should think that
there’s more beyond that. Okay, what other kinds of disguises? Right here’s one. AUDIENCE MEMBER: It could be their behavior. I mean, if they have something going on at home, you know, they’re
focused on what’s going on at home, and so their behavior’s kind of hiding that. CATHY SEELEY: Well, and squirrely misbehavior in classroom or acting out or belligerence or reticence, timidity,
all kinds of behavior things can mask a student’s potential, can’t they? What else? What other kinds of disguises? AUDIENCE MEMBER: Student demographics such as economically disadvantaged. Some of
those kids have the best work ethic. Some of my most capable math students came from that subgroup. CATHY SEELEY: So we have demographic issues, high poverty, students of color, children from urban
areas, students from that neighborhood, or over there, or that city, or that school that we may make assumptions about may not have some potential. I saw another hand up over here somewhere. AUDIENCE
MEMBER: I think that as some of our students really struggle because of the way that they’re hardwired, you know, you have a student who’s very artistic and very creative, and you put them in an
environment which expects them to be very analytical and logical, and that’s tough for them. And so they are very bright and they are very smart, but it’s a struggle. They have to come at it from
a different angle. And we don’t always have the time or the resources to allow them to do that. CATHY SEELEY: Absolutely. In fact, if I forget to say it later, to me one of the most significant
things about teaching mathematics, the more we learn about it, the more we learn about learning theory and about how people actually do become smarter and learn more mathematics is that if anybody has
talents in any direction, especially the arts, which are in many cases very visual or very tactile or creative in lots of ways, those talents ought to be avenues into mathematics. There are parts of
mathematics that resonate with all the different kinds of talents the students may have. And so finding those ways and figuring out how to incorporate techniques that appeal to students who come at it
from different ways is a challenge, but it’s hugely rewarding if you can come upon a way to do that and realize that math doesn’t just need to be taught in a certain way. Okay, and then just this
got a mic right here. Hold on. AUDIENCE MEMBER: Students that come from other cultures. You’ve got some ESL students in there, so, you know, that could be an issue. CATHY SEELEY: That can certainly
last question here. Do you think that all students have equal potential? Are all students at their potential Joshuas or mathematical Joshuas? I see a no. I see an equivocation. Yes, uh huh? Wait, we
be an issue. AUDIENCE MEMBER: I don’t think that all children have equal potential, but I do think that if you look at every child as having a gift and trying to figure out what that is. And, like
you say, my daughter was an artistic kid and really had a hard time with math, but she’s going to take calculus 2 this year as a senior in high school and wants to major in math, so I feel like that
was a win. I definitely think that there’s a way to find that gift and bring that out, like finding the fractions in the kid who can’t figure out the difference between four and six. So I think
you can do it. CATHY SEELEY: So maybe not equal potential, but maybe different kinds of potential. Anything else you want to add to that? AUDIENCE MEMBER: I guess I was thinking of -- they may have
equal potential, but they don’t have equal opportunity. And, you know, I guess we need to talk about how you’re defining potential. CATHY SEELEY: Well, we’re going to do a little bit of that.
Okay, so there’s opportunity as well as what students bring to it. And, in fact, there’s a whole experience that students have had before they ever get to you that has something to do with it as
well. So keep that in mind as we think for a minute about intelligence because for some time now, there’s actually been two basic camps of thinking about intelligence. One is called an entity vision
of intelligence, a notion of a fixed idea of intelligence that says basically you’re born with a certain amount of intelligence, certain nature of intelligence, and that’s what you’ve got and
you carry it through your life. Now if you believe that, if you accept the fixed model of intelligence, then if you have trouble in math, what is your logical assumption? I’m not one of those
people, right? Yeah, so I’m not going to get it. So why would you work hard at that point? You figure that, shoot, I’m not going to get that. She’s got it. The teacher’s got it. He’s got it
over there, but I don’t have it. There’s a growing support for a growth model of intelligence, which is a much more malleable vision, which suggests, and we’re learning more as we can look at
MRIs of people while they’re solving hard problems and people growing dendrites and all kinds of things, which is what intelligence is really based on is all those neural connections in your brain
and all the dendrites that grow. If you accept the notion that intelligence is actually something that is influenced by what you do and how you go about it and the opportunities you have and how hard
you work, then if you start having trouble in mathematics, there’s a whole other mindset that comes in. In fact, the book my Carol Dweck called Mindsets really is about this idea of changing the way
we think about how smartness happens. And so I want to plant the seed that this maybe has something for us in education. It has to do with a student’s willingness to persevere, their confidence in
tackling a problem because if I believe that if I work hard, maybe I can get this and I will be smarter as a result of it, then that’s very different from thinking I’m not one of those math
people. And in fact, what we’re learning is that the activities that a person engages in and the ways in which they struggle through those activities, the tasks that they’re given, actually
changes intelligence. Now that’s really a pretty dramatic statement. The idea is not just that I know more now than I did yesterday. It’s that in fact there’s maybe some new neural connections
that have been made and actually I am smarter today than I was before I did this thing. That’s huge because guess who gets to determine the activities that our students do? Now there’s a heavy
responsibility, isn’t it? It’s both exciting and terrifying to think about the fact that the decisions I make about what activities you’re going to be doing, what tasks you’re going to tackle
in mathematics, those decisions have something to do with how smart you’re going to be. Now, the good news about that is you don’t have to just assign the rote, mechanical problems that are going
to reinforce someone’s notion of low-level thinking. And some of those problems may be important, but as a model that may not be our best model. So instead it can be that we can give students things
that they can wrestle with. We can give them the right kinds of support, the right kinds of scaffolding. And I want to come back to that a time or two. And we can help them learn and grow through the
process. AUDIENCE MEMBER: [inaudible] talking about the actual curriculum? CATHY SEELEY: I’m talking about the tasks a student does in class. In other words, the nature of the mathematical problem
we give them and the way we structure that. AUDIENCE MEMBER: Which emanates from a curriculum that’s already preselected. CATHY SEELEY: Yes and no. The word curriculum -- we actually are having a
series of meetings in the Dana Center to figure out what we mean by curriculum. So it means many things to many people, but if what you mean is the textbook we use or the instructional materials we
use, then that influences it to some extent. But I would argue that the teacher selects from those activities. And, in fact, that I’ve actually been in classrooms using -- I’ll use connected
mathematics as an example. It’s a curriculum at the middle school level that has rich, wonderful tasks, but a teacher can take those tasks and make them not rich at all. AUDIENCE MEMBER: [inaudible]
conceptual-based program, particularly in math, versus a more [inaudible] advocate of it. So I think that plays a part in the kind [inaudible] versus a more conceptual problem-solving. So I just
wonder what kind of impact that has in selecting a curriculum in teaching mathematics. CATHY SEELEY: Well, and that’s why I say you can take a rich conceptual curriculum and you can teach it in
different ways. And I’m going to argue for balance. I’m going to argue that you need conceptual mathematics, but you also need procedural skills and you also need to be able to apply what you
learn in problem situations. So we’re going to keep coming back to those kinds of themes. But I also believe if students have strengths -- or have difficulty with conceptual mathematics, but are
okay in computation, we better give them more experiences to do the conceptual stuff because they need to develop that. So a couple of quotes for you related to intelligence or the nature of
successful people. This is by a nutritionist and health writer named Anne Dunev. I have no idea who this woman is, but I found this on the Internet, so I figure she’s an expert. So anyway, I thought
it was kind of interesting. She wrote, I suspect that the current popular scientific theory that we’re merely a genetic roll of our parent’s dice or an amalgam of our brain chemistry keeps us from
truly exploring our human potential. Imagine if we were not so busy diagnosing new mental diseases and convincing people that they have weird and incurable conditions. We might find out how amazing
each child can be. I only half-jokingly say that ever since I found that I have ADD, I’ve been acting like it. That’s actually true, by the way. But I do think that we end up with a lot of labels.
And in fact, labels to me are some of the biggest disguises that students wear. The labels that we give students, whether it’s special education or ADHD or English language learner, whatever those
labels are give us a mental picture of a student and what he or she is able to do. And if nothing else, I hope you come out of this questioning our use of labels in particular, and especially acronyms
for labels, which are sort of the worst of the worst to me. I actually hear people dealing with English language learners who refer to their ells and their non-ells. And that’s E-L-L, ells. And
speds, as in special education students. This makes me crazy because the label is bad enough and the acronym compartmentalizes it even more, where we stop -- so be descriptive instead of labeling.
This is a student who has these kinds of issues that we have to deal with, as opposed to this is that. All right, the other quote that I wanted to give you is from Malcolm Gladwell. I really do know
who this guy is. Malcolm Gladwell wrote Tipping Point and Blink. He’s a fascinating man, a very, very smart man. And the book called Outliers is particularly interesting along these lines because he
looks at sort of the prodigies, the great geniuses that we’ve recognized in the world, whether it be Bill Gates or Mozart, all different kinds of people. And at the very end of his book, he looks at
their lives and how they got to where they are, what they bring to it, and he says, superstar lawyers and math wizzes and software entrepreneurs appear at first blush to lie outside ordinary
experience, but they don’t. They’re products of history and community, of opportunity and legacy. Their success is not exceptional or mysterious. It’s grounded in a web of advantages and
inheritances, some deserved, some not, some earned, and some just plain lucky, but all critical to making them who they are. The outlier in the end is not an outlier at all. The idea is that, yes, our
students bring certain things to us and they bring to us a life of experiences, however short that time may be. A lifetime of experiences that we have no control over. Those experiences continue
outside of our control, but we do have control over a piece of it. And we can understand that the piece that we contribute to the student’s life history is huge in terms of being able to influence
where they go. All those factors that you listed at the beginning about why students may not achieve their potential, I would ask the question, which of those things you mentioned mean that a student
cannot achieve high goals in mathematics? And when you start thinking about it, well, the student lives in that kind of a neighborhood, or there’s low expectations, or there’s peer expectations,
or there’s poor teaching. If you think about any of those factors and think, well, yeah, so that student’s not likely to succeed, the truth is that we can find some student somewhere who dealt
with that and has in fact reached high levels of achievement. And I would argue that when you find that student, there’s usually a teacher or more than one teacher right behind or next to. So this
whole discussion is to shift our conversation about issues why students have difficulty with mathematics -- and in fact, we’re finding more and more people looking at blaming mathematics for
students’ difficulty even in staying -- making it through school, that mathematics is one of the biggest stumbling blocks that many, many of our students face. And so we have to be thinking about
what is that? Is that -- it’s not all about teaching. It’s not all about curriculum. It’s not all about the students themselves. It’s about all of these things. And so we have to tackle the
parts that we have something to do with. All right. I mentioned that there are also some insidious factors that keep students from reaching their potential. A lack of opportunity, someone mentioned
whether or not they have an opportunity to learn. We know there are, from research, that there are less qualified teachers in the highest needs classrooms in our country, especially in the high
poverty students, urban centers, students of color, English language learners, high needs students of all different kinds in terms of the teachers who are most effective in working with students. We
also know that we have huge unequal access to technology, to textbooks, and to instructional resources. We know that we have schools and classrooms that are physically unsafe, let alone emotionally
unsafe for students, where they’re unstable or falling apart and simply just not a good place for students to be. And we have that whole plethora of unintentional low expectations of all different
kinds, which leads me to tell you a story on myself. One of the things that you may or may not know about me, I can’t remember if it was in the introduction or not, is that after 30 years in
education, I decided to follow a dream I’d been thinking about for some time and I joined the Peace Corps. And I taught mathematics from 1999 to 2001 in a country in West Africa called Burkina Faso.
Raise your hand if you’ve ever heard of it. Okay, a few of you. It’s actually a country called Burkina Faso. It’s in West Africa. It’s surrounded by Ghana, Cote D’Ivoire, Mali, Niger, Benin,
and Togo. It’s about the size of Colorado, has 14 million people, and it’s the fifth poorest country on the planet. And it was an amazing two years, absolutely amazing, powerful, wonderful, all
the things you would expect it to be, challenging. Well, actually, I knew I needed to get back to the classroom for a little while and I figured it was too hard and too political here, so I’d go
someplace easier. So that actually sort of was true, too. So my classes had 75 students in them. I had this particular group of students. The first year, I had a middle school group of students and
three groups -- three classes that were about a level of algebra 2 of geometry. And then I followed those high school groups the next year because they ended up with more hours a week the second year
because they were moving up through high school. And so on. So anyway, this is one of my high school math classes. And actually, I had classes that were in the math/science track and I had a class
that was in the non-math/science track. And if you look at this picture, you can actually tell me which one that is if you think about it. And the reason is there’s a bunch of girls in here. It’s
about half girls, so therefore which track is it? Non-math and science track. Unfortunately, there are some universal truths that we deal with. And in fact, young women in Burkina Faso, when they
finish a day of school, they go home to clean, take care of the brothers and sisters, fix dinner, and take care of whatever other things need to be done at the house. It’s a huge challenge for young
women to go to school. In my two math and science tracks, out of 75 students, each of those classes had four young women in it. This was about half and half. All right, so my story is that we missed a
lot of school while I was there for my two years. And we actually missed about a third of each school year. We -- it was a French educational system. I actually taught math in French. This was quite
an experience for me. But we missed school because teachers went on strike. That’s the French thing to do. We missed school because students went on strike. And we missed school -- this is my
favorite. We missed school when the government closed school so nobody would strike. This is a true story. Because there was an anniversary of a politically sensitive event coming up and they said, oh
my gosh, there’s going to be trouble. Close school, then there won’t be strikes. I don’t get this thinking. But anyway, so we missed a lot of school. So the second year is rolling around. We
haven’t really finished the first year. The teachers had refused to fill out their grade cards. We’re drifting into the second year. It’s about October and I’m working on the program. I have
to write down and plan out what I’m going to teach this year. And because we’re behind, I’m having to make some adjustments. Now, like a good Peace Corps volunteer, I was in a very large school.
It’s 2,000 students and 50 faculty and I was the only non-Burkina faculty there. And so, like a good Peace Corps volunteer, I shared my program with my colleague, Sela, a well-educated man who was
going to be their math teacher the final year they were in high school. And it’s actually called terminal. Doesn’t that sound awful? Their terminal year in high school. And because he was going to
be the one preparing them for the really big test. And if you think we have test pressure here, the bac that they take in French in France and in French-speaking -- French educational system, this
test takes days to administer and you have to pass each section of it before you’re allowed to progress to the next section a couple of weeks later. It’s a huge test. And the math part of it only
has a few questions, but they’re nested, deep questions that are so challenging that it’s really, really hard. So anyway, Sela is my colleague. He’s going to have them for their final year. And
so I go to present my program to Sela, make sure we’re on the same wavelength. And so I say to Sela, I said, so I’m going to do this and this and this and this with this group of students, but
I’m not going to do delta. Now delta is how we do quadratic equations, okay? Which by the way is using the formula for those high school teachers out there. Nobody outside the United States uses
factoring as a way to solve quadratic equations, just so you know. But anyway, so I say I’m not going to do delta. And Sela looks and me and he says, well, you have to do delta. And I say, well,
Sela, you don’t -- you know, I’ve got to make some choices. I don’t have time for everything, so I’m not going to do delta. And Sela looks and me and he says, well, you have to do delta. And I
said, Sela, you don’t understand! I say, it’s really hard. They’re not going to like it. They’re not going to get it. And really, do they really need it? And Sela looks at me and he says,
well, you have to do delta. So I’m thinking, oh my gosh. I was thinking maybe there will be a strike before we get there, you know. I decided, okay, you know, don’t want an international incident
or anything, so I decided I’d do delta. And so, as we go through the year and we’re getting to the place where it’s time to do it and I pull out my best problem-solving teaching and I’m giving
them all kinds of good problems to work on and thinking about functional relationships and stuff. And we’d been on this for a couple of weeks and I give them a problem to work on. And I’m walking
up and down between their desks like that. And as I’ve given them this problem, I’m hearing things like, well, yeah, we could use that function to represent it, but I think that if we do that, you
know, I think it’s going to get bigger instead of smaller. Maybe we should try a negative number over here. And all of a sudden, I think, my gosh, this is the kind of mathematical conversation that
math teachers live for. And I think I even did this. Oh my gosh. As I sat there and thought, what did I almost keep from these students? Now we went on and they worked through -- when we finished
dealing with delta, dealing with quadratic stuff, we celebrated. They knew they had done something hard and that they had done it. Now, whether any of those students ever use delta after that math
class or outside of school is highly unlikely. Only 1% of the population goes to college. And very few of the students are -- and these were the non-math and science students. But that’s not even
the point. The point is they knew they could do something hard in mathematics. And yet that was something that I almost withheld from them, not because of their limitations, but because of my
assumptions, my old habits, my beliefs. Now you got to understand, I see myself as the queen of high expectations, okay? When I was at the State Department in Texas, I was one of those people back in
the heart of our educational reform time, saying get rid of those low-level classes at high school. Our kids can do more. Raise the bar. But when you come face to face with real students in a real
situation, it is so easy to be pulled back by our old, innate thinking, and not by the students themselves. So that’s my story on myself. And I just encourage you to think about high expectations in
terms of challenging our habits, our beliefs, setting those high, challenging standards, but then doing whatever it takes for students to actually achieve those standards. And it’s about never
thinking in advance that we know where those students are headed. When I first started teaching, which has been a very long time ago now. I realized it’s been 40 years ago this coming -- well,
actually just finished 40 years ago that I started teaching. We used to think that there were college-bound students and non-college-bound students. Wait a minute, we still do, right? The point is
we’ve been wrong both ways a whole lot of the time. Students we assumed were going on to college may have gone to college to start with, but maybe they started building computers in their dorm rooms
and became billionaires instead. Or maybe students who didn’t choose to go to college, five years later, they’re out there in the world, they’re maturing a little bit, they’re dealing with a
family, and they say, wait a minute, this isn’t cutting it. I need more education. But we haven’t prepared them for that because we didn’t think they were one of those kids who were going to go
to college. So we cannot assume just because those are the kids in the non-math and science track, just because these are kids in the fifth poorest country in the world, we can’t assume that those
students don’t need what we’re giving them because part of what we’re giving them is irrelevant to the content. Part of what we’re giving them is the opportunity to be challenged, to wrestle
with ideas, to think about things and to move through them. And it's about making sure that every student gets to deal with that struggle and succeed with it which is huge. All right, so there's
actually a picture of a teacher there. So the question is, does teaching matter? And obviously that’s a rhetorical question. So in terms of teaching, I would argue that the adult’s view of
intelligence is just as important as our student’s view. My colleagues at the Dana Center work on a really exciting program called Academic Youth Development. It deals with eighth grade students
rising to ninth grade, kids who have not been accelerated into algebra, but they’re taking algebra for the first time in ninth grade. Hand-picked kids, not the remedial kids, not the accelerated
kids. The ones who are sort of social leaders. And putting them through, with their teachers, a three-week summer experience in which they spend half the day each day doing an in-depth, extended math
activity. It’s on forensics or something like that, takes three weeks in the mornings. And then the afternoons, they do things like studying about brain research and learning theory and how -- what
intelligence means and social stereotypes and why we get messages that some students aren’t smart and about leadership and all the social factors that go into understanding and being successful in
school. And in doing so, then the students are sprinkled in the classes of these teachers who have been through them with them, and there seems to be a huge impact not only on the students themselves,
but on their classmates. And unexpectedly, their teachers’ transformation seem to be at least as dramatic as the students themselves, and have as much influence potentially as what the students see.
Thinking about the fact that teachers actually make dozens, I would even argue maybe hundreds of instructional decisions daily that influence student learning, and really teaching matters because as
you give students those challenging tasks and expect them to do some work on their own and actually to figure some things out for themselves and to persevere and we support them in the right ways,
which is a very delicate decision about not over-scaffolding to the point of spoon feeding, but actually giving them the kind of support that lets them go a little bit further without necessarily
telling them what to do. So I want to share with you what I’m calling some compelling comparisons. These are from a book called The Teaching Gap, published in 1999 by Jim Stigler and Jim Hiebert.
And it looked at -- and so this is a little -- this is 10 years old now, or plus, but it’s basically looked at some of the international studies that were done in the late 1990s in which not only
did we have the tests given to students that splashed the headlines across the newspapers about where the United States falls and how far behind we are and stuff, but it also included some other kinds
of study as well, including looking at -- observing classrooms, eighth grade classrooms, in several countries, in particular Germany, Japan, and the United States. So I just want to pull two pieces of
this data out and share with you -- well, this one’s going to be tricky to see because the screen is washing -- well, mine -- that’s really interesting. The graphics are disappearing. There we go,
okay. So there are two questions that I want to pull out from that study. One is the whole idea of whether or not the mathematics that was being taught was important, or low-level mathematics like
mechanical stuff, sort of medium-level mathematics, or very challenging, conceptual, complex, important mathematics. In Germany, they discovered that the observers noted that it was pretty well
balanced between low-level math, medium, high-level math. In Japan, it shifted a little more toward the medium and high level. You want to predict what the United States one looked like? Okay, the
observers noted that in the classrooms they visited, 89% of the mathematics they saw was low-level mathematics.11% they categorized as medium. And yes, that’s a non-existent bar on the right for
high-level mathematics. Now the first thing you got to say is you can’t generalize from an observational study. You can look to see if patterns seem familiar to you and get insights that way. And,
of course, this was 10 plus years ago, so, you know, it’s probably different now. Well, what the observers noted was -- what the observers noted was even in classrooms where teachers had challenging
tasks to offer students, and they saw those, even in those classrooms, because of the nature of the instruction, teachers basically, without intention, dumbed down the task. And here’s what we do.
And I have done it and I can see myself doing it. We start with this good task, the hands shoot up. Miss, Miss, I don’t get it. I don’t know how to do it. What do we do first? And in some form, we
end up doing something like, oh, you’re having trouble? Had you thought about? And remember you know how to? And don’t forget to. And by the time we’re finished, there’s no complex thinking
left. That’s what the observers noted as they reflected this one. And the partner piece of information is about developing new knowledge. And that’s the idea of whether or not content is just told
to students. They call it stated, whether it’s just stated or told to students, or whether there’s some development, either by the teacher or the students, of conceptually why this makes sense,
where this comes from, what you’re going to use it for, that kind of development. In Germany, they saw about three-fourths of the material was developed in some way. About one-fourth stated. In
Japan, a little bit more. And you can already predict what the United States looks like. It’s exactly the other way around. So not every single classroom, but there is a pattern in the United
States, which I’m going to talk about in just a minute. There’s a pattern in the United States where we tend to see our role as math teachers -- this is how I learned to teach, was do a really
clear presentation, prepare well and do a really clear presentation. And if you do it with enthusiasm and charisma, then your students will be with you. Well, it turns out, as we realize now, that a
lot of times the students are entertained, but -- I wonder where she got that. I wonder how you do that. I’ll never be able to figure that out. I think struggling is absolutely critical. Sometimes
math problems are hard. And our kids -- high school people know this. You give your kid a hard problem, they say, you never taught us that. I don’t know how to do it. They’ve had 12 years of
training, 13 years of training in some cases that said, hey, we’re going to tell you. Here’s how you multiply fractions. Here are some word problems. Guess what you’re going to use to do these
word problems? Oh yeah, that thing you just learned, how to multiply fractions. Oh good, this is a straight across thing, okay. I know how to do that. Sometimes math problem are hard. And
mathematicians, we all know at the extreme some of them take careers to deal with math problems, or certainly years or certainly long periods of time. And in business and industry, problems are not
solved instantly. But American students, and this is unique to the United States -- there are probably some other countries out there that are right there with us, but many of the high -- most of the
high-performing countries are very different this way. Our students tend to give up because they think, I can’t do that. I never learned it. And they want to believe that I have to have learned
every particular kind of problem if I’m going to be able to solve it. And, by the way, their parents really believe that, right? So if you try to challenge your students and give them things that
you haven’t taught them how to do, parents get upset. And if we have textbooks that don’t give clear examples of every kind of problem we think they’re supposed to do and then you give them
something on the test that’s not on there, everybody gets upset. So we got issues to deal with for sure. But the other part of it is we are compassionate people. I went to Burkina Faso, we had these
Burkina teachers who were helping give us our training. I was the only actual educator in my group of 30 volunteers, so these young mathematicians and scientists are there. They’re going to be
teaching math. And our Burkina teachers say -- the first thing they say to us is American teachers are soft. You don’t expect anything of your students. You act like that around here, they won’t
respect you. They say you have to be harder. Well, there’s somewhere between being really hard without actually teaching all the things you need to do and being soft. Somewhere in between there,
there’s a reasonable approach to teaching, which really is -- says, okay, so yeah, he’s falling behind. That doesn’t mean that I slow it down, help him a lot. It doesn’t necessarily mean that.
It may mean I find a different kind of support, I find a different kind of approach to this, I find a different activity or task to give this student. I put the student in a different kind of a group.
I work with him in a different kind of way. I believe that all students need to constructively struggle, and they need to be able to get to the good stuff. Your student who has trouble with basic
computation but who can do fractions is a perfect example. And if we have time at the end, I’ll tell you another story related to another student like that. But we know that there are students who
have difficulty with chunks along the way in their mathematical development. But it may be that if you take the assumption that they’ve got to learn all their computation first before they can get
to the good stuff, you’re never going to know if they can do the good stuff if they have this big stumbling block in computation along the way. So I’m going to argue that even if we’re talking
about calculators and other kinds of things, or saying to ourselves, you know, she just doesn’t have her multiplication facts yet, I’m not going to forget that, but I’m going to go on to
something else, where she’ll maybe use the multiplication facts. Where am I in my process of things? Do I have time for that story? No. I’ll come back if I can. Okay, so to get to the good stuff.
Often in a United States math classroom, we see the idea that we demonstrate, we assign similar problems, we give homework, whereas in Japan, you’re much more likely to see, not always, but often,
that a teacher might give a group of students a problem without first telling them all the things they need to know to solve it. Then have the students work on that problem individually or in small
groups. Then talk about how do they approach it, what did we learn from that, which ways actually led to a solution that makes sense. And from that, you draw out the mathematics that you want students
to learn. And as you compare and discuss that, the teacher’s role becomes very different. It becomes one of facilitating and noticing what students have done and making connections among this thing
and that idea and this one over here, and filling in spaces if students don’t get to the mathematics that you want. And that’s very, very different. And then getting to the homework and so on. Now
the good news to me is this model on the right that we’re labeling as the Japanese model, that’s showing up in a whole lot more American classrooms now. And that’s very exciting. It’s
reflected in many of the newer curriculum efforts that have been done in mathematics in the United States. And it’s reflected in the ways that more and more teachers are learning how to teach. And
it’s really hard to do well. Really hard to do well. I mentioned the connected mathematics project earlier. If you look at that program, it’s very hard to teach it well. You need lots of
professional development, lots of support. You need strong mathematical understanding yourself. That can come as you learn how to use the program itself, but it becomes really, really important to
build up teachers’ mathematic knowledge for all of us to recognize that we can learn more mathematics. I have a math degree from an engineering institution, but I never learned anything about
proportionality until I was in a professional development experience a few years back. And as I’m sitting there, looking at how proportional relationships develop and how they start in elementary
school and look at patterns in the multiplication table and they move up through the understanding of scale drawings and similarity and percent and so on, and eventually they build you a foundation
that goes right into algebra, I never got that from a pure math degree. So even if we have strong math backgrounds, there are ways of thinking about mathematics that we can continue to learn. And if
we don’t have a strong math background, that’s got to be the foundation to start with too. AUDIENCE MEMBER: I work with student teachers, and we’re teaching that [inaudible] in Japan. And they
struggle because of the way they learned it. [inaudible] to teach this way and it’s totally, totally [inaudible] very, very hard. It didn’t seem hard [inaudible] teaching it this way. CATHY
SEELEY: I think that’s exactly right. Okay, it’s -- basically what I call this model is instead of give the rules and then give the word problem, it’s give a problem that lets people sink their
teeth into it, and then pull the mathematics from it. And it is very hard. And the other thing is we can succeed in teacher education to some extent, but then the schools and the situations in which
we send the student, young teachers, have to be ones that will nurture and support that model as well. And that’s -- finding the combination of those things is often extremely challenging. All
right, so upside down teaching is what I call it, where you go through this model that we’ve just described. So I want to look very briefly at two classrooms that give us a sense of this. And I
found a wonderful video of a kindergarten classroom in Hawaii and I asked if I could borrow their short video to share with you. And then I have a picture of a 12th grade -- a video of a 12th grade
classroom for this course that I’ve been working on -- we’ve been working on at the Dana Center, which is an alternative to pre-calculus. It’s a course that’s about -- it’s a rigorous math
course with an algebra 2 prerequisite, but it deals with statistics and finance and lots of modeling and applications and so on and so forth. It’s a really cool course called advanced mathematical
decision-making. So let’s take a peek at these. And I just want you to get a sense of the nature of the questions and so on. The kindergarten one’s very different because it’s a very small group
So now in this high school video, the lesson -- this particular lesson is from the beginning of the course. There's some numerical reasoning that's going on, and so the
teacher’s doing a lesson on if we change the size of your tire -- if you change the tires on your truck, what would happen in terms of other things on your car, your mileage, your speed, different
kinds of things like that? So here’s that particular video. [VIDEO BEGINS] STUDENT: Gas mileage is going to suck more. TEACHER: Okay, so you think your gas mileage is going to be terrible. It’s
going to affect your gas mileage, right? Okay, what else? STUDENT: [inaudible] TEACHER: So you think you’re going to use ratios? And you think -- you said something else. You said how many what?
STUDENT: RPMs to speed. Speed is going to slow down. TEACHER: Okay, so speed’s going to be affected, okay. You’re giving a lot. Let’s let a couple other people get in. Okay, what else? Anything
else that’s not listed here that you said that might be -- that you thought might be affected? The whole truck? So what do you mean by that? STUDENT: [inaudible] TEACHER: This is saying the height
in inches. I’m noticing you have the same answer here and here. STUDENT: Because the diameter is -- so the whole is the same as the height. TEACHER: Okay. I think on this they’re wanting just
this, just that part [inaudible]. STUDENT: So the diameter’s 16. Yeah, and we’re trying to get the circumference. Okay, but remember we can’t use the diameter because that’s just the rim
diameter. You have to do the whole tire. Do you know what I’m saying? [inaudible]. Both, so both sides. [inaudible]. STUDENT: The tire’s height is 70% of the width, and so I put X over 245 because
that’s what the width is. And then I cross-multiplied with 70 over 100. TEACHER: And how did you get 70 over 100? STUDENT: Because that’s 70%. TEACHER: Okay, but you did something different.
STUDENT: Well, I just did .70 times that. TEACHER: Okay, now how did you think -- I mean, what did you think of? So you thought of this as a ration. This is to this as 70 is to 100. And you thought of
it as what? STUDENT: As a percent. TEACHER: As a percent. So what did you say? You say those words again. You said that this -- STUDENT: 245 x .70. TEACHER: Is going to give you what? STUDENT:
[inaudible] TEACHER: Okay, and your answer is going to come out in what when you take this and multiply it by .7, which is what you said? What will your answer be? STUDENT: Millimeters. TEACHER: Come
out in millimeters. So then what did you do to get the 6.7? STUDENT: Divided by 25. TEACHER: So you did it just with the quick division and you guys did something cool over here. What did you do?
STUDENT: Dimensional analysis. TEACHER: Which is really important. I want both of you to hear that. You know what I’m saying? So it’s nice that you guys need the dimensional analysis and that gets
you lost. You can just see it and divide it. Wouldn’t it really frustrate you if I stood up in front of the room and said, you’re just going to multiply by .7 and divide by this? You would be
lost. You would be lost if I said we need to do dimensional analysis. STUDENT: Yeah, like my algebra class. STUDENT: This is our first part and this is going to be the height. Or not the height, the
width of the tire, which is 245 millimeters. And how we got the height, we got the width of the millimeter -- or width of the tire and divided it by 25.4 millimeters to get 9.245 [inaudible]. TEACHER:
So you turned it into inches first. STUDENT: Correct. TEACHER: Okay. STUDENT: So then we found out -- or we know that the aspect ratio is 70%, which is basically 7 over 10. TEACHER: Now what made you
pick 7 over 10? What I want to know is there anything like a specific something that you guys did different than what’s up here already? Okay, this group over here, just have a couple of you guys
come up and just tell me in words what did you guys do differently, point it out, and let me know why you did it differently. STUDENT: Okay, well, when we were finding the height of the tire, the
first -- most people, they took the width of the tire and turned it into inches. What we did was we just took what they gave us and made a ratio out of it. So we did -- so for this one -- TEACHER: And
you can write it on the board. Is obviously one tire’s circumference is larger than the other. So what I’d like to know is how do you think that’s going to affect how the odometer or the
speedometer, and how do you think that’s going to affect how far that tire has to travel. So conversations you’d like to have. [VIDEO ENDS] CATHY SEELEY: Okay, I think that that last video gives
you a really good idea of a very different kind of teaching from what we usually see. And by the way, I have to tell you a story. The last little group of three big guys that got up front, the story
was -- I wasn’t in the classroom, but my colleague who was there while they were videoing, the bell had rung. The students were in the hallway, ready to come in for the next class, and those guys
said, no, no, Miss Flick, we have to share ours. We have to share ours. So they barred the door and she said, okay, come on up real quickly and share yours. And you saw that they wanted -- they had
gotten into the habit of wanting to present their point of view. And I love it because at the high school level in particular, and I think we can develop this all the way from elementary school, is
notions of what we’re now calling college and career skills of investigating to find out an answer, and then presenting and writing reports and actually doing the in-depth problem solving. This is
something that’s absolutely critical that most of our students don’t get before they leave high school, whether they’re going onto college or a technical training program or straight into a
workforce with a career path. So the kinds of things you heard Kelly saying is, say what you just said again, or say more about that. And then what did you do? Or, well, what does the one represent in
your solution? How did you know to -- and what made you choose seven? What did you guys do differently? That was her one at the end there. And what if -- you know, that’s kind of interesting. Now
what would happen if? And then what would be different then? These are just some sort of general questions that you can ask. So -- and by the way, that video is very public. It’s posted on the
website for that math course, and so we -- the website was shown there, but again, if you email me, I’ll be happy to connect you to it. It’s utdanacenter.org/amdm for advanced mathematical
decision-making. All right, so I want to -- the last section of what I want to do with you today is to think a little bit about democracy and what it would really look like to be reflecting a
democratic value -- the democratic values in our mathematics classrooms. And so to start with, to me, in today’s society math and science are absolutely essential for tomorrow’s citizens in terms
of their ability to go on to further education, their ability to get good jobs, and just to be good citizens. The kinds of things that you -- if you realize what voters vote on today, think about the
issues and the quantitative and scientific basis to the issues we vote on. Climate, energy, the economy, health care. All of these have financial and quantitative and scientific foundations. And so to
have our students prepared to make wise decisions, understanding things, knowing what it means to back up your point of view with evidence, understanding what research is all about, and the kinds of
skills we can develop in mathematics class, I think those are huge. We have reports from all kinds of folks telling us what needs to happen in our schools today. The World is Flat -- whoops, which
I’ll get to in a minute, in which Tom Friedman talks about this notion of a flattening world. Time Magazine looked at 21st century skills. I notice that’s a theme in this conference as well. Where
I pulled a quote out of there that I -- the article from -- it’s been a few years ago now when they were first talking about these 21st century skills. And Time Magazine, the article that they wrote
about, it said, you know, this is about the big conversation that we’re not having about education, the conversation that determines not just whether some fraction of our children get left behind,
but whether an entire generation of kids will fail to make the grade in the global economy if they can’t think their way through abstract problems, work in teams, distinguish good information from
bad, or speak a language other than English. Really a broad vision of education. And if you think about what that means in terms of mathematics, it has to do with how we organize our classrooms, how
we teach, and the nature of the mathematics that we give students. And so the message we’re getting from all of these different places is Tom Friedman talks about a flattening world, meaning that
the playing field is getting leveled. And the other -- another part of that message is no longer do you have to get access to information hierarchically. You don’t have to -- only certain people
have to report to your bosses or get information from people above or go to certain kinds of files and places to get information. More and more people can get access to information. More and more
people can use that information to do things. Even some of my colleagues and students from Burkina Faso have almost as much access to information as students in this country because they can get
community Internet cafes or some at the university. They have some access to information that is unprecedented. In addition to that, we could ask the question, how well are we leveling the playing
field in this country? We know people in other countries have more access to not only information, but jobs. As we see Dell Computer is setting up plants not only in India, where we have heard about
that for some time, but recently in Poland and Brazil. Well, Brazil is a rising economy, but Poland? That one really struck me as interesting as we find out that people in all different parts of the
world can have access to the global marketplace. We’re also hearing that workers of the future have to be adaptable and have to be creative and able to learn quickly, that we need more well-educated
STEM workers, the whole idea of science, technology, engineering, and mathematics. Hot field right now. I was doing some work with the state of Washington a couple of years ago and a woman from
Microsoft was on our state standards committee that they were working with. She told us that at that moment in time, Microsoft was poised to hire 5,000 mathematics PhDs if they could find them. And
for every one of those that they could find, they would build a team around them that would have people with other levels of education and expertise, all the way from skilled high school students
through students with degrees in business and problem solving and mathematics and science and the social sciences. And all these people with all different kinds of training, but all related to the
STEM fields and all of the common foundation and problem solving and collaboration. But I would argue that even the non-STEM workers need way more math, science, and those 21st century skills than
ever before. If you have to make decisions about your personal finance, about credit cards -- I shifted my credit card recently to one from my credit union. And I was struck the first time I looked at
my online bill because I had some number -- I always pay my credit card off every month, but on this particular bill it said if you make the minimum payment, you will pay this bill off in -- I can’t
remember how many years it was. It was like 35 years or something like that. And you will have paid 10 times the amount that’s on there altogether. So understanding those kinds of financial
implications is huge. And the bottom line on all the message is always that we need to overhaul the education system. And because of time, I’m going to -- so if we think about this kind of an
environment, we come down to the mathematics that students need. And now I’m going to come back to the discussion we had earlier about conceptual versus computational. And I’m going to argue that
when I was in elementary school, which you can gather was quite a long time ago, we -- I took the Iowa test of basic skills. Yes, it was around at least that long. And we -- they reported my scores to
my parents in terms of computation, problem solving, and concepts. And I would argue that those are still the big three. Now, we know a lot more about them and about how they interact with each other
and about how to develop them better, but basically we want students to understand math, to be able to make sense of it. We want students to be able to perform the skills and procedures to know that
stuff. And we want them to be able to use the mathematics to actually do something, to solve problems, to get at applying what they’ve learned. And I would argue that we also need something that
I’m going to call just the new basics, the deep, transferable skills for what Tom Friedman calls -- he made this word up and I just love it. He says workers of the future will need to be able to
versatilize. Don’t you love that? Versatilize, meaning take what you know and put it in an environment that your job requires or your life requires right now. Because the truth is that many, if not
most, of the jobs our students are going into don’t even exist today. And the estimates are that many of our students will have three or four or more different careers in their lifetime. Not just
different jobs, but actually different careers. So the path that they may think they’re going may be nothing like the path they end up. And we can’t possibly give them all the skills they need for
whatever direction they’re going. So we have to come back to giving them sort of these deep, transferable skills like problem solving, critical thinking, being creative. Basically the math that
people need is the challenging, appropriate, relative math that’ll give them options once they get out of school. AUDIENCE MEMBER: I agree with everything you’re saying. CATHY SEELEY: There’s a
but coming. AUDIENCE MEMBER: It’s my own frustration. I was a former school principal and, as I said, now I’m working with student teachers, which is much easier. And I remember my last school, we
had [inaudible] which is conceptually based. And we had this debate among parents who had [inaudible]. And some parents were really, this is great. Others were like, well, you’re not teaching my
child how to computate. And so they -- now here’s my problem. My problem is that there appears to be a disconnect between what we’re doing in math -- because all of a sudden you get this rebellion
from some parents and political leaders who are saying you’re not teaching our kids how to do math with these conceptually-based programs. And yet all the research is everything that you’re
saying. So how do you reconcile with that? CATHY SEELEY: There’s lots of -- that’s a really important point and that is that there’s a backlash against some of the more -- I would call them
innovative, conceptually-based programs. And part of it is discomfort from people who never learned that way. It’s different from what people have been taught. And so it does get into all kinds of
political arenas, but it’s interesting to me that -- someone told me recently -- I could give you names. So basically two people who are on very different sides of this argument were in a situation
of visiting schools, in this state by the way, a few years ago. And they disagreed philosophically about almost everything on mathematics teaching. They never once -- they visited classrooms together
and they never once disagreed about an effective math classroom and a non-effective math classroom. And so I think part of it is giving people experience because I think we get stuck with the labels
again. And people make assumptions about what the labels mean without having a clear sense of what this classroom actually looks like, the nature of the mathematics that students are doing. And I do
also think that sometimes we get carried away with thinking that this new program means we’re supposed to throw out everything old. And that’s why I think this particular way of communicating to
people helps. I think helping people see that, you know, we still think, after all this time, that the three basic tenets of mathematics are critical. You have to have some skills in procedures. You
have to have conceptual understanding. You have to be able to use what you learn. And coming back to that and being descriptive about what’s going on in your math classroom -- and I would say if I
was in a school doing this new program, whatever the particular textbook you’re using, I would not be putting out the message that’d say, oh look, we’re using this program. I would be saying
Cedar Falls School -- this is the Cedar Falls School math program. We have resources from all different kinds of place, but this is the direction of the Cedar Falls math program or the Monument Park
math program or whatever it might be. And avoid using the labels and avoid talking mostly about the book and focus more on what’s happening with students. There’s no good answer because there’s
continuing to be disagreements, but I think we have to keep following what we believe in our heart as educators the very best. That’s why you’re educating teachers to teach that way. All right, so
when I think about democracy this way then, to me you got to start with -- and I know many of you deal with -- how many of you deal with special needs students? A lot of you. To me, special needs
students may be the most overlooked and underopportunized -- I just made that word up -- students that we deal with. But I would argue that every single student in a democracy needs to experience
rigorous mathematics and science, particularly mathematics since that’s what we’re talking about right here. All students need to be engaged in rich tasks. And I mean the ones that require you to
think, the kinds of things that students in both of the videos that we looked at were -- were not struggling with, were dealing with. And struggling in some cases. And that in fact all students need
that opportunity to think and to reason and to work together and to wrestle with ideas. And especially students that we assume can only do a piece of things because it may be that the student who has
difficulty computationally may be one of the best problem solvers out there. Maybe some of the students who aren’t fast on their multiplication facts are in fact thoughtful, long-term thinkers who
could deal with a problem that might take a couple of days. So we have to keep giving opportunities for students to develop. And maybe some of the students who are real fast need to develop that
ability to persevere through something hard that takes a little while. So to me, a democracy takes place in a safe, nurturing environment where every single student’s opinions, answers, and
strategies are valued. And all students would have access to high-quality teaching and resources. And all teachers would be expected to and supported in ongoing learning. In these budget days in the
state -- our state legislature is putting the final touches on slashing education to the bone. And it’s not the only state where that’s happening, I know. I was speaking to someone here yesterday.
So I know that we’re dealing with situations in which professional development is getting undercut, in which resources are even in scarcer supply. And we know that the students in many of the high
need schools are going to be many of the ones who suffer because of that. But I want to share with you a story about this -- in particular this notion of valuing all students’ input in this kind of
teaching. I want to talk about the best fourth grade classroom I ever saw. I was invited to a school district in central Texas. And I was visiting that day and the school was using one of the more
innovative textbooks and so on, and so I went into this classroom where I had been invited. And fourth grade classroom and I walked in and I sat down in the back of the room. And the teacher started
math class. And she stood up in front of the class and she said, okay boys and girls, let’s do our number song. And so all together the kids started saying two times two is four, two times three is
six, two times four is eight. And I’m sitting there thinking, what century have I gone back to? What classroom did I get sent to? Well, the teacher went through this for a while. The kids were all
with her. And it lasted three minutes. Then the teacher went on to do one of the most conceptual, interesting, engaging, hands-on lessons I’ve ever seen. It was about three-dimensional objects,
which were sitting on all their tables. They were in groups of four. And the students were making two-dimensional -- they were making nets for those of you who have dealt with this. They were making
two-dimensional models that would cover the different three-dimensional shapes, like a pyramid and a rectangular prism and all different kinds of things like this. And the language they used was they
called them jackets, but she said, you know, making a jacket for these things. I watched and I visited with different groups as they were working on stuff. And I watched the teacher and the kinds of
questions that she asked. And as she went to the different groups, every single student in that class was absolutely engaged. Every single student appeared to me to be successful. And I saw the
teacher at lunchtime and I was talking with her. And I commented, I said, that was an amazing class. What an interesting activity. And I loved how you gave the number practice, but you also went on
and did this other lesson. And she said, oh, and you didn’t even see. She said, after you left, she said there were two kids that hadn’t gotten it yet. She said, but by the time they left for
lunch, they did. She said, now I noticed that one particular group you spent a long time with. She said, did you know that in that group of four students, there was a gifted student and a special
education student, as well as two students who weren’t classified? And I said no, I didn’t know that. She said, I want you to tell me which was which. And I guessed wrong. Those students, every
one of those students, the special education student, the gifted student, the regular students, who are also all over the -- had a range like this, all of those students were engaged and successful in
that classroom, both in the sing-song number repetition part and in the conceptual hands-on part. And I guarantee you any parent visiting that classroom would have had no question about the issue that
you raised. So it’s all about balance and perspective and making sure that we communicate that -- you know, our own language traps us sometimes. I remember I was watching a video on our local -- we
have a 24-hour Austin news channel that goes with our cable network. And so I’m sitting there one summer and I’m watching the news and I hear this teacher get on. She’s going to talk a summer
math program in the school district. And I get all excited and I hear her say there, she says, yeah, and we have these kids here and they’re doing all these really cool problems. She says, and we
don’t even care if they get the right answer. I went like this, I said, oh no, please pull those words back! And I think what she was trying to say was we’re teaching kids important processes. And
if they make a mistake and get a wrong answer, we’re going to work on that. But we can’t use language like we don’t care about the answer. We do care about the answer, but we care about the
process that you use to get there. And we’re not going to penalize you if you get the answer wrong as if you did nothing else right. We’re going to look at balance, at how it all fits together. So
I think there’s lots of things to think about in terms of how we communicate. But to me, one of the most important things we do in terms of a democracy is recognize that not all struggling students
should be treated the same way. Some students are struggling because they’re five minutes behind because they were looking out the window or glancing at their friend or, you know, a spider crawled
up their leg, whatever it might be. Some students are a few days behind, a week or two behind because they really didn’t get what was going on or they were absent or they were distracted or they
weren’t sleeping well or something was going on at home. Some students are way behind, a year or more behind. Some students are even farther behind than that. These students don’t all require the
same kind of attention. Some of those students may just need a little conversation in the ear as you’re walking by, and then they’re back on track again. Other students may just need a 20-minute
session at some point to figure out what it is they’re misunderstanding. And other students may need more intense kinds of interventions. But we need to be looking at personalizing the kinds of
things we do, and not just lumping all kids who are struggling into the category of struggling students. In a democratic math program, we would see that not everything depends on what came before, and
we would let all students get to the good stuff. Okay, and I’m going to take liberty and tell you the story I didn’t think I was going to have time to tell, so I’m going to tell it anyway. We
have till 10 and I’m going to try to let you out a little early, so we’re still good. Okay, so this is a story about -- in the late 1990s, before I joined Peace Corps, I decided I was going to
sort of dip my toes into the classroom again, so I volunteered to teach an algebra class for a year at my local high school. And it was in a heavily tracked system. This was sort of the middle track
of students. First day of school, I give my students a survey. I say, what do you like about math? What do you not like about math? And this one young woman that I call Crystal, she writes on there,
she says, well, I’m pretty good at some things in math, but I can’t do fractions. She said, I can’t add, subtract, multiply, or divide them. Don’t ask me; I can’t do it. She said, but I
notice when I came in this morning that in the back of the room, you have those little blue calculators. Well, the blue calculators are the Texas Instruments calculators that do fractions with
denominators and everything. She said, if I think I had one of those calculators, I’d be okay. And I thought, ooh, my first test as being a woman of technology and all this other stuff. And I
thought, what do I do? What do I do? And I decided, I said, okay. So I decided I would check her out one of the little blue calculators for the year. So we’re going through the year, we’re getting
into the heart of algebra. I give one particular test. We’re getting about November of the year. This is when we’re really getting into what equations are and how you use them to solve problems.
And so I give this one particular test and Crystal has done really, really well. And as I’m giving her test back, I say to her, Crystal, you must have really studied hard for this test. And she
looks at me and she says no. She said, I didn’t, but you know, I just kind of get it. Well, it turned out that Crystal is absolutely one of the best algebraic thinkers I have ever seen. The girl can
look at any situation, she can represent it algebraically just like that. Once she has an equation, she can solve it as long as she has her calculator. She can tell you what the answer means in terms
of the problem. She can analyze a graph and tell you what the slope has to do with where the numbers came from. She’s just a really good algebraic thinker who doesn’t do fractions. Whoa. Well,
that’s just the beginning of the story. That’s pretty impressive right there, though, isn’t it? Because the truth is that 10 years ago, 20 years ago, a student comes into my ninth grade class
not knowing fractions, I’m thinking there’s no way this kid can do algebra. And I’m going to give her a whole lot of practice on what? Fractions, that’s right. That’s going to help her,
right? Because she’ll be motivated this time and she’ll get it this time. Okay, well, the story goes on. So we go through the year and we’re getting toward the end of the year and I’m getting
a little nervous because I’m straight out of the state department of education and my kids are just finishing up the year. They’re about to go onto another math teacher and she’s not the only
one who has some computational deficiencies. But I’m not willing to stop teaching algebra because that doesn’t work either. There’s not enough time. And so I struggled with what I was going to
do about that. And finally the solution I came up with was I said, okay, you know, they’d done a couple of out of school projects during the year, really cool stuff using algebra for this and that
and the other. I said, so your last six week project is going to look a little different. And I gave them all a little arithmetic inventory, a little test. And after they’d done that, I said, okay,
so here’s your last six week’s project. I want you to pick something in arithmetic that’s getting in your way in algebra, something you’re not good at, and I want you to get good at it. I said
you can use the books in the back of the room. You can come meet with me before or after school. You can work with your brother or sister, your friend, your parents, someone who knows how to do the
thing you’re having trouble with, but I want you to pick something you’re not good at and get good at it. And I had something different for the kids who were really, really good at all the
computational stuff. And now the way they were going to get a grade on this is they had to come sit with me one on one at the end of the six weeks and they had to convince me that they had learned
what they said they were going to learn. So I gather up their papers about what they’re going to learn. And I get to Crystal’s and Crystal writes on there, she said, I’m going to learn how to
add, subtract, multiply, and divide fractions. I thought, whoa, a little ambitious here. Then she writes two of the great lines that students have ever written. She says -- the first one is the time
has come. I thought, all right, a little realization there. Then the other sentence she wrote -- because now you have to understand we were also using graphing calculators eventually, okay? But
graphing calculators then didn’t deal with fractions. So by now Crystal’s a two calculator girl, right? So the other line she writes is -- she says, I’m wasting too much time using my
calculator. Whoa! You mean a student can actually decide when it’s appropriate to use a calculator and when it’s not? You bet. All right, so the time comes for her to convince me that she has
learned what she said she was going to learn. She comes up, she sits down next to me, and as we start, I said, now before you start, I have to tell you something. I said, you know I go out and I give
talks for teachers, right? And she said, yeah. I said, well, you need to know I’ve been out there talking about there. I said, I call you Crystal because I don’t use your real name and I tell
people that even though Crystal doesn’t do fractions that Crystal’s one of the best algebraic thinkers that I have ever seen. And I went on for a while and she grinned and got all embarrassed and
thought that was kind of cool. And then she proceeded to convince me absolutely and positively that she had learned how to add, subtract, multiply, and divide fractions. Whoa, you mean doing the
high-level stuff can actually motivate you to learn the low-level stuff? You betcha. Your student who’s having trouble with the basic number stuff can get there if we’re using other kinds of
situations that allow them to develop other parts of their brain and see, oh, there’s a reason why this can make sense. The light bulb can go on. Well, that’s a pretty good part of the story right
there too, right? Well, last day of school, I give them one more survey and I pass it out and say, you know, what’d you like about class? What didn’t you like about class? What do you want me to
tell teachers when I’m out there talking to them? And I’m flipping through there and I get to Crystal’s and she writes on there, she says, tell them that Crystal can do fractions. I said, all
right! Well, so there’s a couple of epilogues to this story, actually. The first is that a couple of months later, after school, I was doing the kickoff professional development day for a large
school district in Texas. And they had decided that it was going to be math year, and so they decided the math lady in for everybody to be there. So in this large school district, we had bus drivers
and cafeteria workers and all the teachers and the administrators and the counselors and the aides in the classrooms. Everybody was there to hear the math lady, okay? So I thought, well, I better tell
lots of stories, keep it engaging. So I told the Crystal story. At the end of the presentation, a young woman came up to me with tears pouring down her face. she was an aide in an elementary classroom
and she said to me, I know I was Crystal and nobody ever found me. Whoa. By then, I was crying too and I’m hugging her, I’m apologizing for the entire educational system. And all the way home, all
I could think about was, and how many others did I miss? How many others were out there that I didn’t notice or didn’t give an opportunity to? Well, the last epilogue, by the way, is -- oh, I
forgot this part. So, you know, it was a really good story. And I saw Crystal often over the next couple of years. She was a friend of my daughters and I kept thinking I should ask her, you know, how
she was doing with the fraction thing, you know, because I knew she’d learned them several times before, but here was one more time and I didn’t know was it just another quickie and then it was
gone again. And I kept wanting to ask her, but you know, it was such a good story I didn’t really want to blow it. So finally, two years later, I think I got to ask her. So I said, so can you still
do fractions? And she said, yeah, and you know, it’s coming in really handy in algebra 2. Well, she went onto algebra 2 and pre-calculus. Graduated high school before you had to have four years of
math in Texas, which you now do, with four years of good math up through pre-calculus. Went onto college in a nutrition program. And the last time I saw her at Linens n’ Things after she had
graduated from college, and I told her the story was impacting lots and lots of lives. And she said, well, I do what I can. And she was headed off to graduate school in a program in nutrition. So,
anyway, that’s my story about letting all kids get to the good stuff. And I just want to encourage you that math is not nearly as linear as we think it is. It may seem very, very much this and then
that and then that, and you can’t do this until you know that. And yes, we want to have mastery if we can, but we can’t use mastery as a weapon, as a barrier to hold kids back. We have to pay
attention to it, but we have to let everybody get to the good stuff. And I think we can be letting kids get to good, rich problems at every stage of their learning, even as they’re learning very
rote kinds of things. And I believe that if we were teaching in a democratic program that a lot of our students would get fired up about math and they would choose to pursue math in all different
kinds of ways. And some of them would become STEM workers. Some of them would become math teachers until they find out that we’ve been laying off teachers all over the place. But some of them would
become the kinds of people that we want to have them be. What I see in classrooms are something I call pockets of wonderfulness. I mean, people go and they do wonderful things in their third grade
classroom, but unless they’re working closely together with the fourth grade teachers and the fifth grade teachers, then what they learned and the operating procedures in that classroom if they’re
very interactive and very different and very collaborative, they go to the next year, if it’s something very different, then we’ve lost the benefit of that. And we have to look at building on it I
see teacher presentations and explanations, some of them are nice and clear and even enthusiastic. And I see some nice questions going out there. And I see the active involvement of some children part
of time, and a few children a lot of the time. I see helping or scaffolding that goes just a little bit too far. And I’ve seen myself do it. I’ve done it with teachers. I’ll be sitting there,
we’re doing a rich problem-solving activity at a professional development thing, and I’ll sit down and I’ll say -- and they’ll be wrestling through some idea and I’ll say, had you thought
about trying? And then I went -- because I’ve just taken it away. I’ve just robbed them of the opportunity to wrestle with that idea. It’s -- oh, it’s so easy to fall into that pattern. I see
in classrooms little or no wait time. I see some children wanting to be engaged, but just a little bit lost. And I see some children totally disconnected from what it is they’re there for. Teaching
for engagement means you have students discussing and thinking and justifying and writing and modeling and reflecting and wrestling with problems. And to get there, we have to have -- we have to
expect a lot, get rid of our bias, choose good tasks, talk less, and listen more. And navigate that thin line between scaffolding and spoon feeding, and ask questions that push the thinking. Not
things like, and then if I add three, I get? And then we subtract? Instead asking questions like, now what -- how might you decide what to do? And what happens next? And how do you know that’s true?
What makes you think so? Well, what if it wasn’t that way? And so on and so forth. And it means doing that for every single student, even the ones with labels on them. So -- and that includes
English language learners. I just pulled this because I really -- I liked what these folks said at a recent presentation that I went to. But the idea is that English language learners, where we have
all this -- or anybody struggling with reading, we have all this language around mathematics. The way we solve that is not by giving them naked computation. The way we solve it is by building
instructors -- may be having them work collaboratively in groups that always have at least one reader or something, where they can get into the mathematics and share their ideas and develop their
academic language at the same time. So the bottom line is that our students will not learn what they need to learn if we don’t give them opportunities to learn it. So when I see the words
achievement gap, it gets way too easy to think about that and just have those words roll off of our tongues, so I’d like to replace that thinking with untapped potential. And I’d like to argue
that untapped potential isn’t just about the kids at the bottom. It’s about raising the floor so, yes, everybody gets more, but once you do that, then it’s about identifying some new stars and
letting them soar. When we bring up students, we discover that there are kids who are successful that we didn’t expect. We can raise the ceiling, we can let them go. We can recognize that there’s
untapped potential within students, within schools, within districts, and beyond. And we can turn even untapped potential into unlimited potential. So even our best students benefit from that kind of
a classroom. And my last story is one about Ambucari. Ambucari, very, very bright young man in my math and science group came to me about two-thirds of the way through the first year of school and he
says to me, madame, I know that you like to solve -- have us solve all of these problems. But you know we have a program to cover, right? And he said, maybe -- I had a really strange schedule. It was
like five hours a week, but a two hour block, a two hour block, and then an hour on Friday. And he said, maybe you could do your problems on the one hour on Friday, and then we could use the rest of
the time to cover the program. And I said, thank you for your input, knowing he would never have dared speak to a teacher from Burkina Faso in the same way that he had just spoken to me, but my
students often reminded me that they understood Americans because they saw the soap opera Santa Barbara. But anyway, so this is a picture I took as I was leaving because Ambucari was not thrilled that
I was going to be following students into their second year, so we would be dealing with more problems. So he comes up to me as I’m getting ready to me and he has a sheepish grin on his face. And he
says to me, madame, I think I learned more mathematics with your problems than I would have otherwise. And I thought, all right! He actually did very well on a national math competition. So from
teachers, what it takes is, if we’re going to help them realize their potential, we’ve got to change our thinking about who’s smart and what we do. We’ve got to engage students, have them
struggle, and not always show them exactly what to do, not always ask them too many questions -- not asking one too many questions, where we just go a little too far. And we got to work together
across the grades. Even as we cover stuff, our commitment to doing what’s right have to overpower all the mandates, all the requirements, all the expectations that others are going to impose. So we
don’t have time for your questions or comments. That’s good. We had some during the discussion, so that’s good. All right, so there’s my email address. It’ll come back in just a minute. My
personal website, my Burkina Faso website, which is kind of cool, and then the math solutions website in which five of the messages from my book, including Crystal’s calculator, by the way, are free
for downloading if you go to mathsolutions.com. And Faster Isn’t Smarter, that’ll come right back. I just want to close by reminding us that the reason we do this is because their future is in our
hands. And as a friend of mine recently reminded me, our future is in theirs. These are the voters, the doctors, the tax folks, all the different people. And by their future, I’m talking about,
well, those are all of my grandchildren, several of my students, and a couple of other interesting kids I’ve met along the way. And I realize that I’ve used this slide for a long time, so I
decided to update it. So anybody who’s seen it, are you ready? Watch. Oh, my beautiful grandchildren, my students much older and successful, and the next generation of Burkina Faso up there. All
right, so at any rate, those are the reasons why I do it, why you do it, why we’re all here willing to think about the students that we serve whose future is in our hands. And I guess I’ll just
close by reminding you that as you go down the highway of life, that’s my license plate, that if you do math, you can in fact do anything. So I thank you for staying with me. We gave you a few
minutes extra to get to the next session. Have a great day.
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