Maisie Gholson - Your knowledge ain't like mine....

[music] [applause] DEBORAH COCHRANE: Maisie Gholson is going into her third year as a doctoral student at the University of Illinois at Chicago. Maisie entered into mathematics education as a career change from patent law in the electrical and mechanical arts where she is certified before the United States Patent and Trademark Office. She graduated from Duke University with a degree in electrical and computer engineering. Her research interests are still forming and varied, but include: black students' thinking and reasoning in mathematics, particularly in algebra; pre-advanced placement and advanced placement mathematics classes as racialized spaces; teacher use and implementation of standards based curricula with black students. This Spring, Maisie received a fellowship from the National Science Foundation graduate research fellows program. Her proposed research is about how classroom talk in 9th grade algebra classes develops African-American children's sense of self, racially and academically, and affects students' participation patterns and mathematics acheivement. Please welcome Maisie Gholson. [applause] MAISIE L. GHOLSON: So thank you Deborah for my introduction. I also want to thank Swapna and Ann for inviting me here. I count this as a great privilege and opportunity to just talk with you and share with you some of the things that I've been thinking about. Then I also have to thank Swapna and Brian for hosting me. They've already treated me to Portland. I'm a fan already. I'm trying to figure out how to get here again. But it's a beautiful city and I really love it here. So thank you. Thank you for having me. So this presentation attempts to articulate my journey in developing my own definition and theory of learning. I'm finding this increasingly important in the current political and economic environment where education is under siege. I don't know if you feel it, but I feel it. Education is under siege and learning is being commodified. We're trying to figure out how we can benefit and profit off of learning. And so I want a clear understanding of learning so that I have a principled stance, not only in my research, but just in my educational politics. And so that's what I'm going to share with you today, is my evolution of what I'm learning; how I'm considering and developing my definition of what it means to learn. And this is important because how we as educators, administrators, students, etc. define learning, how I define learning, determines how we set our gaze in a mathematics classroom. What do we see? What do we give primacy to? What do we hold as important? And I've titled this talk "Your Knowledge Ain't Like Mine: Embracing Sociocultural Approaches to Mathematics Learning" because I believe we must begin to embrace ideas of culture within the mathematics education community. As Deborah said, we often think mathematics is apolitical; it's neutral; it's genderless. And so how can we start understanding how culture really comes to bear. Which means we have to set our gaze on the child, on the teacher and on our humanity in order to move the field forward. And so before I begin dicussing sociocultural perspectives... So I'm going to be very clear: I'm absolutely biased. I believe sociocultural perspectives are the way to go. But before I go there [laughs] I would like to share with you a set of images that I think really capture to me the common view of learning. Now these images... most of you will be very familiar with... were taken from a well publicized documentary, "Waiting for Superman." And they weren't talking specifically about learning in this portion of the film, okay; rather, they were discussing the bureaucratic nature of education and how it impacts teaching. But I'm gonna argue that these images provide a common view of learning, generally, and about learning mathematics specifically. So let's take a look. Okay, so here is what we do as educators. We crack open students' heads and we take knowledge that's in a nice carton and we pour it into this empty vessel of a child. Right? And oh, wow, look, he's full of knowledge and he grew wings. He is now an angel and look how happy he is. He can fill out his worksheet. Great. This is what you guys do every day, right? And so...or what you want to do every day. And here is the teacher again. She opens the child's head, pours the knowledge in, and this child also sprouts wings and then looks at this poor kid. Oh, no. The teacher is so bogged down with educational bureaucracy that she can't pour correctly into the child's head. And this poor child will never have wings. He won't be able to fill out his worksheet. We're very, very sad for him. Look at him. And of course it's the brown child. I know, I'm kidding. Ha-ha. Okay. [laughter] So I'm suggesting that this is the common view of learning. This is the common view the greater public has about education: why can't you teachers just pour knowledge into our kids' heads? If our teachers could just pour better, and if we didn't have unions getting in the way of teachers' pouring ability, we could be like Finland and China. Or if we could just unhinge and open their empty minds, or if children would just let us unhinge and then open their empty minds, then they could be filled with knowledge and become angelic, because you're only angelic when you get filled up with the knowledge that we want you to have. And they could sprout wings and be able to complete their assignments. Now of course, I'm making a caricature of learning. And I'm highlighting this cartoonish nature of this depiction. But I would argue that this view of learning is not a far cry from cognitivist views of how children learn mathematics. It really isn't. So, in a cognitivist view there is the "Universal Child," who for the most part is just an empty vessel; that is, we do not need to attend to issues of race, gender, ethnicity, language...perhaps age, because we're concerned about developmental issues. Perhaps age. But very little about who the child is. Very little about who the child is... In fact, gender, race, ethnicity, etc. are considered noise in our data. There's an underlying assumption that the child is a child is a child. Secondly, cognitivist views see learning as transmission and reception. So in our cartoon image, this is the act of pouring and the child acting as the receptacle. In this sense, learning is about acquiring stuff. Okay? It's acquisition; it's acquisitive. So in this case, the learning is about moving knowledge which is external to the child to the internal as if knowledge is separate from who the child is; as if the child has no knowledge at all. And also teaching and learning is about these "disembodied" moves. And what I mean by this...it sounds kind of amorphous, disembodied moves. If teachers were just able to make the right moves, or if students were just able to do the particular set of moves, then learning would take place, regardless of who the people are making the moves. In other words, best practices can be divorced from the people who are doing the practicing. Okay? And then finally, in the cognitivist view, knowledge is well-defined stuff. Because we know all there is to know out there in the world, and we can package it, and in this case it fills... it fits into a nice little milk carton apparently; everything that we need to know. So again, this assumes that we know exactly what students should know, and exactly how it should be packaged. And in this case, knowledge is material: something that you can have. However simplistic and over-simplified, I would argue that these are some of the basic tenets of a cognitivist view of learning. Okay? So I am, I am agreeing, for the cognitivists out there, this is an over-simplified view. But I think I've hit some of the major components here. And so the question is, and what I ask myself, is this view of learning detrimental? Can this view of learning hurt? And if so, who does it hurt? Who does it impact? Okay? So I'm going to give you a simple example. And I think this is a fairly typical question for an elementary age middle school children. In fact, this problem...I'm going to read it to you in a second... comes from a correspondence from Dr. Bill Tate, who he wrote to Gloria Ladson Billings. And it's a simple, simple example of how this view of learning can hurt. So it says: "It costs $1.50"...and I want you to do the math with me. Cause we're math people, right? "It costs $1.50 to travel each way on the city bus. A transit city "fast pass" costs $65 a month." "Which is the more economical way to get to work, the daily fare or the fast pass?" Okay. Do you all mind doing a little bit of math today? You don't mind? Alright. So, work it out for me. Which is the best way? Y'all say the fast pass. Can somebody...we're like family here. Tell me why you think the fast pass? Did you do the math? [people talking; very faint] Alright, okay. So everybody has an answer, they have an answer. And so, my answer is, my answer to the question is, whose knowledge are you talking about? Whose knowledge? Students responded to this question differently. White, middle class students responded in one way; black, lower socioeconomic status students responded another way. For white, middle class children, let's take a look. For a "9 to 5" suburban commuter, who only travels to and from work: I pay $1.50, I go one way. I go the other way: that's times two. That's $3. I multiply that by 20 which is five times a week, four weeks a month. That gives me $60 a month. What's better for me? [people talking; very faint] Pay the daily fare. For urban public transportation user, for our black children or latino children who live in the city, who travel to work...perhaps have multiple jobs... and use that fast pass recreationally within their community, look at how the problem changes. We can even suggest that the mathematical rigor of this problem has increased. It went from an arithmatic problem to an algebraic problem. So now I've got to figure out how many times, how many trips I can take before I can figure out if the pass is economical for me. Right? Whose knowledge are we talking about? I'll give you another example. Here's one: circle the independent and underline the dependent variable. Seems simple. This is an exchange from a colleague of mine, Wendy, a wonderful teacher. She had an exchange with her students, and this is a common problem in the state of Texas, where I originally taught. And we test children on their understanding of independent and dependent variables, obviously. And we give a pair of words and students are asked to identify in some way which is independent and which is dependent. Okay? So think about it. Which one's independent and which one's dependent? Which one determines which? Okay? You got an answer in your head? Got an answer? And my answer is, guess what? Whose knowledge? Someone who says, "Fill 'er up!" They say "fill 'er up," what do they do? They go to the gas pump and they pump their car full of gas and then they look at the pump...the other day, I looked at the pump and oh my gosh, it said $56 and I drive a Beetle. [laughter] And so then I go and I pay that money. So the amount of gas that I put in my car determines how much money I pay. But what about the person... when I was growing up I was taught things were a little bit different. And Mom would give me a twenty dollar bill and she would say, go give this to the gas attendant and tell him we want $20 on pump 3. So how much gas was in my car was based on the amount of money that we had that week. Right? So again, it's whose knowledge. Whose knowledge are we talking about. And so the point that I'm trying to make here is that context matters. And if context matters we cannot assume that the child is the child is the child. If we cannot asssume there is a universal child, and that knowledge is not well-defined, then how do we understand the process of learning? How do we do that? Okay? So I believe that we have to take an uncommon view of what it means to learn. I say uncommon because this is not often how we think about, talk about or consider learning. To, to share this view of learning I'm going to use the practice of Double Dutch. And the image that you see here is a painting called "Double Dutch" by Rhinold-Ponder. And we're going to watch a bit of video together. And it may not be apparent at first but the children in this video are learning. And the learning, as we witness it in the video, is also how children learn in mathematics classrooms. They are not different. Okay? So I'll play the video a couple of times, but this is...hopefully this will...alright. [VIDEO CLIP] [Percussion and bass heavy music] GHOLSON: Ooh! Get it! [laughter] [faint sounds of children laughing and chanting] GHOLSON: Watch her this time. She's getting it! [children applaud] [END VIDEO CLIP]
 GHOLSON: Okay. So I can play the video again, but I want to focus on what did we see. What did we see? We saw a group of children that were black and female in a neighborhood, in a particular time, playing Double Dutch. Another way to say this is we saw a community of learners engaged in practice that we know as Double Dutch. We saw varying levels of participation. We had watchers, we had jumpers, we had rope turners, we had singers. We saw some experts and some novices. And based on how the children were participating, we know that these beautiful black girls identified as a particular member in the community. That is, these girls had an identity that allowed them to participate in particular ways. So if I'm not a good jumper I might be a good rope turner. If I'm not a good rope turner I might be a good singer. But in any shape...in some shape or form, these girls took on an identity and they acted it out and they participated within their community. Another way to think about it: one girl may have thought, I'm not a great jumper yet, but I'm going to become a great jumper by trying this move out. Right? We saw the first little girl, and I'll play it again, in the white t-shirt, she wasn't there yet, but she was really trying to show out. She was trying. And we can assume that over time the girl's identity changes and they begin to participate in different ways. And then I want you to watch when I play it again, there's a little girl standing with her legs crossed, and we can imagine one day that she will begin to see herself as a jumper, or a rope turner, after seeing a more knowledgeable girl show her the way. These girls are learning, but no one is transmitting anything to them. What they need to know is not well-defined. Somebody define Double Dutch for me. Define how to do Double Dutch with style. How do you define that? That knowledge is there but it's not always well-defined stuff to know. And yet we can argue that they are learning. So would you mind watching it again with me? [VIDEO CLIP] [drum and bass music] GHOLSON: She's trying. Novice. Novice. Here's someone who's at a different developmental level. You see the little girl I'm talking about? She's, she's watching. Learning, learning. Here she is. She wants to be, she wants to be a superstar. Look at her. And then you have your expert. You have your singers. People finding ways to participate in the community of practice. [laughs] [END VIDEO CLIP] GHOLSON: So what I want to suggest here is that in the sociocultural view, first we consider the child-in -context. We consider them in their environment, in their community, with all of their attributes. That includes their race, their ethnicity, their gender, their language. We do not divorce the child from their context. We don't take away from the fact that these little girls are black, that they're in their neighborhood, and they're doing Double Dutch. We have to consider all of those things together. Learning is considered experiential and transformative. Learning is about appropriating cultural practices and meanings or being apprentice in a particular practice. Learning changes who you believe you are and therefore what you should be doing. If I'm a rope turner and I think I can become a jumper then that's who you become. That's what you try. That's how you begin to learn. And so finally I want to emphasize this point. I've used the word "experiential" twice, but knowledge is experiential. Knowing is not about what I've acquired but what I do and how I do it. Knowledge is a process. It's not a product. Knowledge is not material. We have to get...we are so consumed in this country, and probably everywhere else, with stuff. And so knowledge becomes stuff that we acquire. College degrees become stuff that we get, and it doesn't begin to change who we are. It doesn't become transformative. It's just a thing that we have that we can hang on the wall. But I'm getting preachy so I apologize. So if we, if we put these two views up next to each other we see some stark contrasts. One sees a universal child. The other sees a child-in-context. Another sees transmission and reception; the other sees experiential and transformative. Notice that in the cognitivist view, learning is somewhat passive, and in the socioculturalist view, learning is an active process. In the cognitivist view, knowledge is well-defined "stuff." And in a socioculturalist perspective, knowledge is experiential. It's not material; it's an experience that we have. And I will offer that cognitivists set their gaze on knowledge of that well-defined "stuff." In some cases, mathematics education. Or in the case of, excuse me, mathematics education, we set our gaze on the math content. That's where we look for learning. On the other hand, socioculturalists set their gaze on the child-in-context, and they believe if they do this, then how the child positions themselves will tell us about what and how the child knows about math. Right? So, I'm saying a lot there, but what I really just want you to walk away with from this slide is cognitivists set their gaze on knowledge: on mathematics content; socioculturalists focus on the child, on this humanity of this child. What is this child experiencing. And so before I go any further I want to make the point about where we set our gaze is a political question. It is not without value. It is not a neutral thing. It is not just a luxury for us to be able as researchers to say, I'm going to focus on content or I'm going to focus on the child. It's a political thing. Within the mathematics education research community it appears... and I say that to soften it...but I would say it is a contested question. And I want you to consider the following. So this is an NCTM...I don't know if you're familiar... NCTM is National Council of Teachers in Mathematics, and this is in their flagship journal. They published a commentary that read: "JRME publishes research in which mathematics is an essential component rather than being a backdrop for another area of inquiry. I encourage readers to continue to examine articles with the 'Where's the math?' question in mind." What are they saying? I don't want to hear about your context. I don't want to hear about that. Mathematics has to be at the foreground. This is from the editor of the flagship journal of the National Council of Teachers in Mathematics. Consider this as well. This is a summary of a symposium held at the annual national NCTM conference in 2010. So this is like a session that they have, and it was a room three times as big as this that was filled to the max with mathematics education researchers. And the focus of the talk...and I went, just cause I wanted, I was nosy and I wanted to hear what they were going to say... And it says: "This session focuses on the role of mathematics in mathematics education research. In particular, the session addresses a growing concern among many mathematics education scholars, who will remain nameless, "regarding the lack of attention to mathematics in much of the current work in mathematics education." I don't want to hear about your context. Keep math center. And notice the title of the talk: "Keeping the Mathematics in Mathematics Education Research." Okay? This is a political thing. So in response to these concerns, I'm very lucky to be at UIC, where the, the status quo there is to push back on these things. And I was lucky enough to co-author a piece with my advisor, Dr. Danny Martin, and also Dr. Jackie Leonard that... we wrote this article that pushed back on where we should set our gaze as mathematics education researchers. And I hope you don't mind but I'm going to read to you a little bit more. And this is what we argued. We argued that "questions such as "Where's the math" represent political stances and are symbolic of larger power relations in the domain" "They are not neutral and we find it necessary to ask whose interests are served by these political stances. What intellectual territory and spaces are being claimed or reclaimed by such concerns?" "Mathematics education, as an enterprise, benefits from a variety of research perspectives and approaches. Nevertheless, mathematics should not be the gatekeeper for the production of knowledge in the field." And so, in other words, gate setting in mathematics education is not a zero sum game. It should not be a matter of whether it's content or context as these diametrically opposed or competing approaches, but there must be room within mathematics education research for culture and context and for the child to take primacy. There has to be room. So very simply, we argued that context just imply produces different knowledge. It produces different understanding. It examines the lived reality of children in their totality, and it attends to the understudied and under-conceptualized issues of power, identity, language, race, gender, etc. And I would say most importantly is this last bullet. It says "the focus of context through sociocultural approaches challenges deficit-oriented constructions of children. As Deborah was mentioning in her opening remarks, that we look at all this test data and what does it say? There's an achievement... [audience faintly responds] I like you a lot...[laughs] There's an achievement gap. We call it a racial achievement gap. There have been gaps throughout the history of, of US education. There's been literacy gaps. There's been elementary attendance gaps. There's been high school attendance gaps. But it seems now that we can profit from this idea of a racial achievement gap. There's some sort of profitability in that, in us constructing, constructing that idea. So as we noted in the JRME article, studies often talk about poor and minority children and how they enter school with only pre-mathematical knowledge. But it's unclear whether these researchers who report these findings understand even partially, even partially, the everyday lives of these children. There's no evidence of it. So, as I'm, as I'm working through this presentation, I want us to practice in gaze setting. We're going to do a bit of gaze setting practice together. And so the first thing that I would like to do is introduce you to a child. His name is Aidan. And then we're going to set our gaze on the math by looking at Aidan's understanding of multi-digit addition. And then finally we're going to set our gaze on Aidan as an 8 year old child in a mathematics classroom. And then we're gong to look at what we can learn from these two views, these two different views. Okay, so here's Aidan. And I'm going to read a little bit about him to you. So, "Aidan is a serious 8 year old middle class African-American child who attends a public school in the southern suburb of Houston, Texas." "Aidan lives with his mother and grandmother, and while technically Aidan is a child of a single parent household, his family network of great aunts, great uncles and aunt provide a cohesive support to him and his mother." "Aidan knows that...Aidan's mother knows that he reads beyond his grade level and has progressed to chapter books. This 8 year old kid, chapter books." "Aidan confirmed this report, citing two popular children's novels: The Adventures of Captain Underpants, which is on the 3rd to 5th grade reading level, and The Diary of a Wimpy Kid, which is on the 6th to 8th grade reading level." "According to his mother, Aidan is only allowed to watch one hour of television per week and often uses that to watch wrestling." [laughter] "For play, Aidan's mother notes he enjoys playing legos and building things, and typical of a child his age, Aidan's favorite things include watching television, playing video games, eating junk food, and he prefers not to eat vegetables and do his homework because he considers them boring." "Aidan is currently in a regular, second grade contained classroom; that is, Aidan has one teacher for all subjects throughout the day." "His mother noted that the racial composition of the classroom is split into thirds: a third white, a third black, a third latino. And on his last report card, Aidan earned a B in mathematics and A's in the rest of his subjects." "And despite his high grades Aidan confides that he does not enjoy school." And this is interesting: "His explanation concerning his distaste for school relates to behavorial disruptions of his classmates and resulting discliplinary action of the teacher." "Aidan reports of his mathematics class that he paints... Aidan's report of his mathematics class paints a picture of a traditional classroom, marked by a series of worksheets, problem or exercise modeling by the teacher, and then work stations." "Aidan mentioned partner work, which indicates that the students must also at least occasionally work collaboratively on their mathematics assignments." "And as discussed later, Aidan was also familiar with base 10 blocks, so his teacher appears to employ at least this manipulative during instruction." So here's Aidan, and here's a bit of Aidan's context. I just took some highlights. He's got, he's, he likes to read. He likes his WF. He likes video games. He likes Cheetos. Okay? And so here's some highlights. He's a highly literate child. He's a serious child. When I talked to him, he had adopted the "culture of schooling." He's African American; his family identifies as African-American. He's the child of a single parent home. And as I mentioned before, that signifier doesn't really...single parent home, what does that mean? He's got a whole network of, of people around him that support him and his mother. He's a middle class child. He's male. These are some highlights. So we're going to gaze at math, okay? So we're going to take a cognitivist perspective and we're going to see what we can learn and Aidan's going to compute 99 plus 96 for us. [VIDEO CLIP] GHOLSON: We're going to do a problem.... You ready? Okay, so here we go. I want you to work this problem for me. Can you do that? Have you done...here's a question...have you done problems like this before? AIDAN: Yeah, I have. I've done problems like this before, but I'm used to putting them on top and bottom. GHOLSON: Oh, well go ahead and write it on top and bottom. He just wrote a 5. Did y'all see that? AIDAN: I'm going to try my regrouping...can I do my regrouping? GHOLSON: Sure! He says "I want to try my regrouping." AIDAN: I want to put 9 right here but it's not right. GHOLSON: Okay. Why do you want to put 9 right there. Tell me that. AIDAN: Because 9... 1 plus 9 equals 10. And 10 plus 9 equals 19. And it wouldn't make any sense if you put the 1 so, so it makes sense for me to put the 1 and just add the 10. GHOLSON: Okay. Can we....okay. So, why don't you go ahead and put what you think should go on the paper and then let's work it with the blocks. Let's do that. Okay, so just 95. That's what you think? And do you think this answer makes sense, that 99 plus 96 equals 95? Okay, so we gotta figure it out, okay? [END VIDEO CLIP] GHOLSON: Okay, so I was not...I should have prefaced this video clip. I was not trying to abuse this child. [laughter] I know we were sitting there with these long pauses and long silences. This was a project for my class, and our job was to do a clinical interview. So in a clinical inteview, you're not supposed to do any prodding. You just let the child work the problem, and if...at one point he said, "I want to put a 9 right there." And then I, that gave me an opportunity to say, well, why do you want to put a 9 there? So this was not a situation where I'm trying to teach him. I'm just trying to see from this kind of cognitivist perspective what the child knows. Okay. I hope you can see this well. So I'm going to zero in on a particular exchange because it reveals a common misconception that children encounter in multi-digit... those elementary teachers in the room know that children struggle with multi-digit addition, primarily because of regrouping; because they really don't have a conceptual understanding of what it means to form these, to form groups in base 10. So Aidan...I'm going to read the purple... so he writes a 1 above the tens column... this is after he tells me he wants to do his regrouping... and then he pauses for several seconds and then withdraws from the paper and he says, hmmm, I want to put a 9 right there...in the tens column, he's pointing. And I say okay, and we sit quietly for a few seconds and I say, well, why do you want to put a 9 right there? Because, hmm, 9, well, 1 plus 9 equals 10 and 10 plus 9 equals 19 and it wouldn't make any sense if you put a 1, so it makes sense... and basically he's saying it makes sense if you put a 9 but it's inaudible, really. Okay. So what I find interesting about this exchange is that this is a common misconception. You've got this highly literate child who likes school, who likes schooling, and he has this common misconception. And so what we find, if we're just focused on the math, is that Aidan shows proficiency with single digit facts. Aidan prefers the standard algorithm...did y'all see how he was like, well, I wanna write it one on top of the other? He prefers that standard algorithm. He didn't try to invent his own strategies. He's well-schooled. I have...my teacher gave me this strategy so this is the one I'm going to use. It don't matter if it don't make any sense to me. Okay? Aidan struggles with place value when making meaning of the sum "19." He doesn't interpret it as 190. He says, I know there's a 1 and a 9 in here somewhere but he has this common misconception. This is what we learn, or I'm sure some of you took away some different things and maybe we can talk about that during question and answer, but this is what I took away from it. And those of you math folks in the audience know that these are common things. There's...I don't know if I've found anything from that video clip. Perhaps we did. Okay. So now I want to set my gaze at Aidan. Okay? So I'm taking a sociocultural view. And so Aidan's going to describe his experiences in his math class. Okay, this is kinda the pre-interview and this is what will happen. [VIDEO CLIP] AIDAN: ...Math Mountain. And there are 12 levels and each person is on a different level. So everybody's not on the same level. GHOLSON: Okay. AIDAN: Some people are still on level 1. Some people are all the way... some, some people are all the way up to level 7. GHOLSON: Wow. And...I mean, how do feel about that, like, taking that test every week? Do you like it? AIDAN: No, it's very, very hard. It's very frustrating. GHOLSON: It's frustrating. Okay. And so, what's your goal? Do you wanna, do you wanna move up a level, or do you just do it cause you have to do it? AIDAN: We have to do it. We have to do it. If you, um, if you don't do, if you don't do the test then you get moved down two levels. GHOLSON: You get moved down two levels. Okay. And then, if you had to, like, make a goal for yourself, what level would you want to get on? AIDAN: Level 8. GHOLSON: Level 8, okay. If I asked your teacher what kind of math student you were what would she say? AIDAN: She would say...I have an 87 in math, so she'll say I'm okay in math. She wouldn't say that I'm, like, good, like, excellent in math, but I'm pretty good at math. GHOLSON: So you agree that you're, you agree that you're a little... do you agree with her? Do you think you're better at math? AIDAN: No, I agree with her. I need to, um, sometimes I, I just get, sometimes I just get, it just gets, I just get lazy and I don't wanna do it. And so that's why I'm in 87. But my goal is to get back to 90 because the first report card I was on 90 in math. GHOLSON: Wow. So you told me what your teacher would say. What would your classmates say if they asked what kind of math student you were? If, like, one of your friends, if they say, oh, Aidan, he gives me help, or he's a good math student. What would they say? AIDAN: Well, if we were partnered up they would say he was pretty, he's pretty good in math and he helps people. GHOLSON: Okay. So tell me...I've got one more...two more questions. Do you use math outside of school? AIDAN: No. GHOLSON: No? Okay. And do you think math is important? AIDAN: Yes. Math helps you get into a good college. GHOLSON: A good college... Is there any other reason that you learn math besides getting into a good college? AIDAN: Yeah, because we, because the teacher wants us to push ourselves so we can get better at math. And to, and to not give up. GHOLSON: Not give up? [END VIDEO CLIP] GHOLSON: Yeah, so there I was putting words in his mouth, but... So, this is the exchange I'm going to focus on. I'm going to highlight this exchange because it tells us about how Aidan positions mathematics. So he does not find mathematics useful in his everyday life. Wow. Right? But ironically, he considers it important. "I don't use it. It's not relevant. But it's important." And it's important because it helps him get into a good college. This child is 8 years old. Acquisitive nature of knowledge. It was also interesting listening to him discuss the Math Mountains problem. Didn't you find that interesting? "I'm on level 4, and so and so's on level 7." This weekly timed test has begun to shape his identity. Here's a kid who gets 87's, all A's, and he says, I'm kinda good at math. Because of...and I'm arguing here, and I would need more data to back it up... but I'm arguing that part of his identity is being shaped by this weekly test that he's taking, and it's positioning him in a way in which he feels that he's not capable. So it doesn't surprise me that when he's working a multi-digit addition problem that he doesn't feel capable. Right? Because of how he's position-, how he's been positioned in his classroom; through the culture in his classroom and how it's positioned him. So these are the things that I found, if we were to just focus on the experience. Aidan does not consider himself highly proficient because of a level attained on a weekly, timed math test. Aidan's conception of mathematics is confined to schooling and achievement. And that means that Aidan's conception of math does not relate to thinking or reasoning. Math is something that you just do. It doesn't really make sense. You know, it's just math. You do it at school. Okay? So we haven't connected with him about the relevance of mathematics. And so these are my wonderings. These are my wonderings. Which approach, or which gaze, provided insight into how Aidan has come to know mathematics? What did we learn from him doing that multi-digit problem versus me just asking a few simple questions that we would ask any... he's actually my cousin, but y'all...[laughter] Someone that we would ask, we would ask any child: how's your day; how was school; do you like school? You learn about how they're positioning themselves. Which approach positions Aidan in his fullness, in his humanity? When I set my gaze on the mathematics it invites me to see Aidan inevitably in his lack, right? Why didn't he compute the multi-digit problem correctly? That's what I'm focused on when I look at the math. I'm only left with his lack. And we have learned when meeting Aidan that there's a great deal more to this child than how he carries out multi-digit addition. However, when I set my gaze on Aidan as a child, I see his relationship with the content, and how mathematics is purposed in his young life. And I learn about Aidan's knowledge of mathematics based on his experiences with mathematics. So here I'm not making any, I'm not faking any punches. I feel like the sociocultural approach, I've learned something about him. That's...I've learned something about Aidan. I've learned something about mathematics and the culture of his classroom. And I've learned something actionable, something that I can go in and I can do something about the culture in that classroom. Right? And so, this question of whose knowledge is really a question of whose experience. Aidan's knowledge about multi-digit addition is intrinsically intertwined with his experience in his mathematics classroom. And I argue when we focus solely on the mathematics as knowledge, we overlook the experience that produced that knowledge. So in short, knowledge is experiential. Knowledge is the experience. If you want to change what your kids know in your classroom, change the experience that they're having. Change the experience. And so, this is my final thought and I'll just read it to you. This is how I concluded my paper; this is my paper on learning. I said that "in conclusion, measuring and understanding"... I was trying to develop, again, this is my theory of what I believe learning should be in mathematics education; this was the charge that I was put forth me in this class. And I said, "In conclusion, measuring and understanding learning through a sociocultural perspective positions children in their fullness and respects their experiences and environment." "This is particularly salient to children of color; for example, African-American children, who are held against cultural norms of white children." "Child development in a sociocultural sense does not rely on the universal child, but acknowledges that learning and development are highly dependent upon the context and the experiential affordances granted by society." "With respect to issues of equity, sociocultural theories are essential to highlight all children's lived realities and maintain their humanity." To maintain their humanity. So, I want to thank you for your time, and I'll invite any questions or comments that you may have and happily respond. So... [applause] AUDIENCE 1: I know we're going to get into your lecture, but right off the bat I wanted to ask you to speak a little bit to what precipitated your shift in career from patent law to working with children. GHOLSON: [laughs] That's so funny cause we were talking about this earlier today, and I'll be very honest with you. It was very lucrative, but I was a functionally depressed adult who would have to roll herself out of bed, and sit in a room in front of a computer, and it wasn't an engaging environment. I wanted something where I could give back to my community. I wanted to feel like what I had learned really came to bear and had an impact on the people around me, but on myself! Why did I spend all that time and invest all that time just to benefit companies and corporations? It just, it, it stopped...it didn't feed me. Spirtually. Yeah. Yes, ma'am? AUDIENCE 2: It's refreshing to see someone with your kind of thinking. I mean, I'm in a school everyday and I see people everyday, and there's people out there with teaching degrees and teaching licenses that don't get it. And you do. That's refreshing. GHOLSON: Well, thank you. Thank you very much. But I would say that they don't get it because what they are taught is cognitivist theories. We're taught if you can do these best practices or how to transmit these mental representations and get them inside childrens' heads, and how to develop these analogues so that kinds can... so that's what they're taught. And I think that it's going to be essential in the mathematics education research community and in colleges for us to start pushing that and saying, we need classes that talk about sociocultural theories. We need classes that talk about people. And not just content. And those things need to be connected. The mathematics and who Aidan is are connected. And I would even argue that how he carries out the mathematics and who he is is connected. So I think it's a matter of just beginning to offer courses, and beginning to change the culture within the colleges themselves, yeah. Yes, ma'am? AUDIENCE 3: I wonder if you could talk a little bit about kind of the divergence between the cognitivist and the socioculturalist theories as far as what knowledge is and what it's for? GHOLSON: Mm. So, I mean, in the presentation I tried to make the argument that knowledge in a cognitivist perspective is stuff. That I would say traditionally is found in books. And a socioculturalist would say that knowledge is an experience, that once you have the experience then you begin to know. What knowledge is for, that's a great question... So I would say socioculturalists would say it's for participating in a particular community and being able to engage as a full member of that community. Whereas...and again, I don't want to paint such a stark... I'm painting a very stark contrast that is somewhat of a caricature... but we could say that cognitivists, it is about, just like anything in this world when we get stuff, it's about how we can use the stuff to move in particular ways and better ourselves. AUDIENCE 3: So like transactional [can't understand]? GHOLSON: Yeah. It's a transactional thing versus a transformative thing; how I can become a part of something. So, yeah, great comment...question. Yes? AUDIENCE 4: I have a question. I worked for the school district for five years where poverty was number one with all latinos, and how do you get parents on board? Because they would hold a lot of parent functions to teach them because we knew they didn't have much schooling so we'd teach them but it seemed like the children in our school would just never grasp on and didn't care because the parents were always like, it's the teacher. How do you get the parents to, you know, interact and participate? GHOLSON: So, I would say, and....I would say that the general public's view about what it means to learn is a very traditional and cognitivist view. And that if you were to ask parents, what do you want... do you want your kid to go to an alternative school where they're building things or do you want your kid...parents want their kids to be empowered and be positioned so that they are no longer marginalized. And if the prevailing view about what it means to learn means that you sit in the classroom, or you sit in a charter school, and you strip kids of their identity, and you make sure that they can fill out and bubble the sheet correctly, then that's, that's what they are going believe, because that's what our, how our culture positions what learning means. And so part of it is educating...and, and this is what I felt with... what I was trying to do is say that we have to start...that uncommon view of what it means to learn needs to become more common. And I don't know how you'd...I don't have, I don't have answers for how... AUDIENCE 4: It's just really tough because, like, they hold these functions for parents to come in and we have to do daily stuff that they wouldn't be doing at the grocery store; this is how you guys can, you know, interact with your children with children when you go to the grocery store, you know, do this or do that. But instead the kids would be, like, oh, we didn't do our homework because we sat in front of the tv and our parents don't care. Oh, we didn't do this because we sat in front of the tv and we went outside and it's just, like, how do you...it's hard to get parents involved. And that, like... GHOLSON: So I think parents are very involved. I think that's, again, if you look at how parents interact with their kids, they are giving their kids all sorts and all kids of knowledge. It may not be the kind of knowledge that schools value, and I think the question becomes how do we get schools to value what parents do with their children at home? Because I guarantee you that parents care and love and want the very best for their children. But the ways in which they do that are not valued by mainstream educational communities. Yes, sir. Yes. AUDIENCE 5: You mentioned the achievement gap just real briefly, and I went to other lectures where they talked about it. Have you ever, throughout your time traveling, doing these lectures, have you heard anybody define an achievement gap other than "the achievement gap," and like in a positive way? And, if I hear somebody talking about achievement gap is there a way I can step to them without offending them and being, like, positive about it? GHOLSON: Be positive about the achievement gap... So there are people.... [laughter] No. Well, there are people that say, should we acknowledge, should we acknowledge these ideas of racial achievement gaps, or should we not. There's an article about the achievement gap fetish Rochelle Gutierrez talks about. So should we pay attention to these gaps or should we ignore them and try to find other ways to redefine them? And some people would argue that achievement gaps let, show us the inequity that is, that is embedded in our system. And other people say when we talk about achievement gaps we're just re-substantiating and perpetuating these ideas of inferiority of black and latino children, and women. So those are two different takes. One thing that I would say, I can, if you email me I can send you this article that James Anderson wrote. And he talks about that achievement gaps are a part... GAPS are a part of US educational history. These gaps have always existed. It was criminal to teach African-Ameri-, black folk, to read. And cypher, as my grandma says. It was against the law. It was criminal. There were gaps in access to elementary schools. There were gaps in access to high schools. Black, black children that lived in rural areas did not go to high school because they were still trying to put food on the table, and that was a gap. There was a literacy gap. And all of those gaps have closed and we don't talk about that. And now we have this new gap, this racial achievement gap, and the question I would ask is who benefits from talking about a racial achievement gap. Right? Testing companies benefit because as long as there's a racial achievement gap, they can still, they can continue to test us. You know, who benefits from those things? So, I mean, I don't know if I'm answering your question. I'm just sort of vibing with you, but yeah, you know, I hear what you're saying. AUDIENCE 6: It's funny that you talk about testing because before I went to the school that I taught at that [can't understand] diverse. It has quite the achievement gap. I really thought I was walking into a school where kids could not read, where high school students didn't know what was going on. And I found such a different experience of really intelligent people. And I remember it took another person for me to see that, you know, "what's wrong with this," and she said, "what's wrong with the test?" Like that's what's wrong. And as I look over the shoulder of my kids while they're testing and all of these layers are imbedded into one question, I start to understand that. My question for you is: I was one of those girls that stared at Double Dutch [laughter] and I never experienced it. I was...maybe I tried it once or twice but I was never good. So I could always swing the rope, but I never, and I still can't get in there and Double Dutch. And so, in terms of my mathematics classroom, I can't still get kids to experience. To...they might, they might try a little bit, but I have... verbally saying the right answer. But in terms of actually trying to work out these problems, where I will sit with them alone; where I will do these things and their fear or their hatred or their whatever it is. But they will not experience it like I wouldn't. After a while I just stopped trying, right? And so I just wonder how to get kids, as a high school teacher, to re-engage? And try to Double Dutch? [laughter] Or solve two set math equations? GHOLSON: No, I hear that. So, part of what I was going to say in my talk, which I ended up taking out but I'll share now, is that it's all about identity. So that's what I'll say. It's all about how you view yourself and how... so, what I was going to share is that earlier this week I called, I called Brian and Swapna and I said, um, I was a bit frantic, a bit manic. And I was like, I don't think I can do the talk. And I was really, I was really about to just like, you know, Swapna would have killed me, I know she would have. But I was so frantic because I don't see myself as a lecturer. That's not who I am. I'm a teacher. I'm a student. You know, I'm a work-, I mean, I'm a worker bee, but I don't see myself as someone who gets up and talks, you know, who can tell people, "this is..." You know, that's not who I am. And what I would say is, that experience with them, it was a nurturing. "You'll be fine. You'll be great. I believe in you. I see you. You can do it." And I think that we have to become that for children. We have to become those identity shapers for children. And it's not just enough to say I'm going to work with you, but it has to be I believe in you, and this is who you are as a mathematics doer. And there have to be ways in which people can have entry points into those identity shaping opportunities. This is an identity shaping opportunity right now for me. And so how do we offer opportunities for kids to begin changing and shaping that identity. And I would argue that for some reason... I know maybe that Double Dutch thing was a metaphor, but there was some reason that you were not a member of that community. That someway, some cultural barrier. And the question is, how can we break down those cultural barriers. I don't see a lot of black women up giving lectures. Right? So that's a cultural barrier that has to be broken down or people have to nurture you into saying, yes, you can do this, and yes, this is part of your identity. So...yeah. Mm-hm? AUDIENCE 7: I just want to add that there's a lot of work around the African origins of science or math. And we're...unfortunately, we lost an expert here in Portland when [can't understand] left Portland and went to Washington DC, but... When I ran the Whitney Allen Learning Center for the Urban League, so many kids did not see themselves as mathematicians. But when I would bring Kamou [sp] in and he would do a presentation on the African origins of science and math, and they began to understand that math was a part of their culture... a part of their heritage, and a part of their genetic makeup, they had a whole different perspective about math. And then you start to see changes: in their interest level, in their participation level. I mean, I'm not saying it's the only answer but it, but it does help to begin to show children...and the same for latino, I mean, the Aztec. The Mayan. It's incredible, the math. So, I mean, it, it's a part of people's heritage that has been sort of stolen from them, taken away from them, and we need to give that back. GHOLSON: Absolutely. And if I could just piggyback on that, if there are math teachers in the room I would challenge your kids... just do it as a, as a warm-up or an opener... say "draw me a picture of a mathematician." People do this...I've...there's a couple of people, there's people who've done identity studies, and inevitably what kids will draw...one interesting picture... they'll draw a white male in a lab coat. One kid in one talk that I went to drew a white male with a magician's hat on [laughter] because that's what mathematics is! It's magic! Right? It doesn't make sense. You just, you know [hand gestures], and then you get the answer. So it would be really interesting for your kids to see what their conception is of who a, who a mathematician is. And I think that's absolutely right, like, part of changing the culture is changing who, who does math, where math is in me, and changing this idea that mathematics is not a part of our everyday; that it's only something that we use for achievement purposes or in schools. That it's part of our everyday experience. And so... More questions? Mm-hm? AUDIENCE 8: I think also we need to have teachers actually look at math at different ways. Like we are trained in looking at math one way, and that's the way we learned it, and that's the way we're going to teach it, and if the kid does it another way they're wrong. You're wrong. I'm right. I'm teaching it this way. If you don't get it this way, you're not right. And I think teachers need to learn how to recognize when the child... cause sometimes the child is right even if they're not doing it your way. They're getting it, and they're understanding math. And they're doing math. But they're not doing it your way, so that's not right kinda thing. GHOLSON: And that's what, when I'm saying changing children's knowledge is about changing the experience, the way in which most of us probably experienced math; in a very traditional classroom where we took notes, did homework assignments, took a test, got the test; that is not the experience you want kids to have. And if we think that moving the math community forward is going to happen by just reorganizing common core standards or... yeah, I said that, it's on tape...Oh my goodness. [laughter] But if we think that by repackaging content that that's going to change, we have to change the experience. Bottom line. So it's gonna be...and constructivists would say, oh, we've got to get kids to build their own knowledge. And I would say you've got to change the culture in the classroom. That, that's not an issue of construction, it's an issue of "what is the culture of mathematics." Okay, so I see hands, so... Two more? Okay. Yes, ma'am? AUDIENCE 9: I'm just kind of piggbacking on what they said up front. My son, he enjoys math. He really loves math and it just comes really naturally to him. But one day I got a call from the teacher, and she was concerned because he was being lazy in math class. And she was just telling me in front of him how he wasn't doing his work. And then eventually he just opened and say it's just too easy! It's just too easy for me and you're asking me to do all these steps that I don't need to. You know, I have it, and you want me to explain to you why I get to these points the way that...because she was expecting him to go to these, you know, final products in a way, but he wasn't doing it that way. He was doing it his way. And she was trying to make him go back and explain why, and he was just like: I'm done. I mean, It's just too easy and I'm not going to do the job. And as the mom I was, like, devastated because I'm thinking, okay, can you do something else? Can you work in some different homework, different assignments, something? And she's like: no. He's in this grade, and we're going to be working in this grade, and we can move on, because I don't have the time. I don't have the skills or the material to teach him at the level that he is. GHOLSON: Right. So, so, I hear you, and I'll stick up for the teacher a little bit, because I feel that teachers are also positioned within school districts and schools to be didac-, to be bad teachers, in certain ways... I don't want to call her a bad teacher... but to, to toe the line in ways that are often detrimental to children. And, so again, but there...she has a responsibility in her classroom, but school districts have responsibility to encourage teachers to be able to see kids in their fullness, and to provide for these different avenues for kids who solve things differently. But oftentimes there are professional developments that say: we're going to do this new math program called "blah." And we're going to have all the kids do this. And when teachers do that there are repercussions to it. So that may be the case. But she is not...I, I don't think she's doing that to pi-...Just to stick up for teachers. We've got to stick together, y'all. [laughter] She's doing that probably out of a lot of different kinds of pressures that relate to, again, the culture of mathematics and how we view it. Okay. Yes, sir? AUDIENCE 10: I think the biggest piece of what she just said is the fact that the teacher didn't have the time or resources to teach the child at the level that they're at. Teachers I feel are, at least in the system we have right now, are put inside a box and can only teach what's inside of that box. I mean, if that teacher was given even just a little bit more resources I believe that child would be getting more the experience that they need to be getting. Which kind of goes to changes at the administrative level as well as teachers [can't understand]. GHOLSON: I agree. [laughs] Amen. [laughter] Okay. Okay, well thank you so much. Wonderful comments, thank you. [applause] [music]