 So very welcome to all of you to the seventh review talk of this conference. The talk is titled, Teaching Mathematics in Ways that Disrupt Patterns of Inequity, Predominant in Classroom. And this talk will be given by Professor Deborah Ball. It's my immense pleasure to introduce her for many, many reasons. And in some sense, Deborah doesn't need any introduction because many of us are close to some of her ideas. But in some sense, we need to introduce her because there are many aspects to her work. So Professor Ball is the William Pine Ecology at Professor of Education at the University of Michigan. And she's also Tharna Professor and the Director of Teaching Works. She has taught to elementary students for 15 years. And she does the same every year in every summer. She teaches to fifth graders or sixth graders. She's an expert on teacher education. And her current work focuses on the how to improve quality of beginning teaching. She just completed her 11 years of dean at the University of Michigan School of Education in June 2016. She has authored, co-authored more than 150 papers and had made lecture and got many awards. So one to mention is the recent Felix Klein Award, which International Commission of Mathematics Instruction honors, gives in the honor of the most meritorious scholars within the mathematics education community. It's given to Deborah Ball in 2017 in recognition of her outstanding contributions and her leadership role in deepening our understanding of the complexities of teaching mathematics and in improving the practice of teaching and of teacher education. She has many affiliations right now, other than being the faculty at the School of Education. She is the President of American Education Research Association, which we generally called as AERA. She's also the member of the Commission on Future of Undergraduate Education, appointed by the American Academy of Arts and Sciences since 2015. And since 2013, she's the member of the National Science Board of the US, which was appointed by President Barack Obama. And since 2006, she's been Spencer Foundation. And right now, she's the chair of the board of the directors in Spencer Foundation. So this is a brief introduction to you, Deborah. And now I hand over the platform to you. Thank you very much for doing this. So you have roughly 40 minutes, 40 to 45 minutes. And then we'll take some questions at the end. Thank you. Thank you so much, Feta. It's really such an honor to be invited. And I'm so sorry that I'm not able to be there with you. How is the sound? Can you hear me? Can you hear me OK? Yes, it's very clear. The sound is very clear. Wonderful. I'm very pleased to be able to speak with you this morning. And I look forward to your questions. I do want to say that here this morning, it's Sunday morning here, 7.30 in the morning. And outside, the temperature is about 27 degrees below zero Celsius. So it's very, very cold here. So I'm happy to be sitting inside in my house talking to you. The title of my talk, as Shweta said, is teaching mathematics in ways that disrupt patterns of inequity that are predominant in classrooms. And I hope that as you listen to my talk this morning, you can think about how the issues that I'm raising here apply within the Indian context and where they are different. And I look forward to your comments about that. I'm going to start with a rather dramatic question. So if you can advance the slide one to the next slide. Before I think about mathematics education and mathematics teaching and classrooms, which are very much inside of classroom work, I want to connect the work of teaching and schools to a much bigger question about our globe, about our world. So can you advance to the next one? This is a question that one of my colleagues here in the US posed to me and my colleagues recently. She was noticing the large spread of violence in our country and also around the world, often very much associated with hatred and bigotry. And she reminds us that education is the social institution that we have hopes for changing our world. And she encouraged us to be thinking about how the work that we do with children inside of schools all over the world needs to keep in mind that our biggest purpose is to educate the next generation of citizens of our world in ways that they respect differences, that they know how to work with people who are different from themselves, that they understand that hate and killing are our past and cannot be our future. And I want you to be thinking about this very profound question while I talk about very detailed issues about mathematics teaching. And I think it might be useful to be thinking about this question as you watch children talking about mathematics with other children in school. How does that work inside of a classroom relate to this question? So I hope we can come back to that at the end. So next, we're going to talk a little bit about a bit of mathematics that I want to explain so that you can understand what the children in the first video that I will show so that you can understand what they're doing. So some of you might have seen this before. This was developed by a Belgian mathematician named Georges Papier. It's called a mini computer. It's actually not a computer at all. It's just a piece of cardboard divided into four squares. And as you can see, there are four colors, brown, purple, red, white. On the right-hand side of the slide, I listed some of the mathematical possibilities of this, but I'm going to briefly introduce how the mini computer works as a mathematical environment for working on mathematics with children. I have found this particular environment interesting for a very long time because one can make interesting and challenging problems for children from age five all the way up into secondary school. We will be watching children who are about 10 years old, so about the middle of that range, but perhaps your imagination will be stimulated about problems that are both more simple as well as more complex. So the way the mini computer works, you can see three disks below the mini computer, one yellow, one red, and one with an upside-down V. So if you take one of the colored checkers, the yellow or the red, there are also blue checkers. If you take one of those and place it on the brown square, the value of the entire mini computer that's represented is eight. So wherever you put the checker, effectively you are multiplying that checker times the square that it's on. So I took the yellow checker and placed it on the purple, the value of the mini computer would be four. If I place it on the red, the value would be two, or if I placed it on the white, the value would be one. The color of the chips or the checkers doesn't matter, but the color on the board does matter. It gets more complex. For example, I could place two of the disks on the brown and then I would have two times eight or eight plus eight and the value would be 16. If I put one on the eight and one on the one, I would have eight plus one or nine. So if we go to the next slide and we go slowly through it, I will give you an opportunity to try. So here's the mini computer again and right now we're only going to look for a moment at these three checkers and more. The upside down V checker is worth negative one. So effectively this is a negative checker while the colored checkers are positive checkers. So if I put the negative checker on, let's say, the purple, the value is negative four. Okay, so let's try some examples. Can you put up the next, just click once on the slide? Yeah, so take a minute and see if you can figure out what amount, what value is being represented on this mini computer. Hopefully you are figuring out that the total here, can you click once? Can you click on, yes, it's 12. And you could figure it out in different ways. For example, you could see one on the eight is eight, one on the four is four, so eight plus four is 12. And then you might notice that negative on the two is negative two, but then you have one plus one, which is two positive and negative two plus positive two equals zero. So you'd still just have 12. But you might have added up the checkers in a different order. For example, you might have done eight plus negative two, which is six. Then you might add the four, which is 10, and add the one plus one, which is two, and get 12 that way. There are many different ways that you might get the total. Here's another one to try. Okay, click again. So this is negative four, and let's try one more. So here you can see eight plus eight is 16, or two times eight. And then you can see that the four plus negative four equals zero, so you still have 16, plus two is 18, plus negative one, 17. Okay, so hopefully now you have a bit of a sense about the environment, and we're going to turn next to talking about a particular child in a classroom. So here's a boy that we're going to be learning a little bit more about. His name is Vershan. He's African-American. In our country, rising fifth grader means that he is just about to enter fifth grade, which is in our country, 10 and 11 year olds. So I'm going to tell you about a problem that the children in his class worked on. Can you go to the next slide? So the children were introduced to the mini computer, and they worked on this problem. What numbers are possible to make on the mini computer with exactly two positive checkers? I'll give you one minute just to think about this yourself. What numbers are possible? What numbers are not possible? Maybe turn to somebody next to you and tell them if you see any numbers that are not possible. Okay, let's keep going. Please go to the next slide. So the children figured out that, and you probably figured this out too, that seven, 11, 13, 14 and 15 were impossible with exactly two checkers. So the teacher presented them with an extension. Can you click again? The teacher, click one more time please. The teacher introduced the negative checker for the first time and asked the children, if you can use this new negative checker, you still have to use both the positive checkers, but if you can use one negative checker as well, might you be able to make seven, 11, 13, 14 or 15? If you click again, you'll see what Vershan wrote in his notebook. Please click again. Vershan wrote in his notebook on this day. I think the negative checker is awesome. So Vershan was very interested in the negative checker. We're going to turn next to see a very short clip of video in which Vershan goes to the board and tries to prove to his classmates that 13 is impossible. While they're getting the video out, I want to comment about this, which is before you play it, can you just pause for a moment? That proving that something is impossible in mathematics is a very special kind of proof. It's an existence proof. And often young children like these don't have opportunities to prove that something is impossible. So I want you to think about what's important about the opportunity to learn that in mathematics some solutions are not possible and that capability as a child or as a mathematical thinker to prove that. Too often children think when they cannot find a solution to a problem, they think that they're not smart or that they don't know math and there must be a solution. So when you think about learning to prove that something's impossible, there's something very powerful about this. So I hope that you'll enjoy watching Vershan as he tries to prove to his classmates that 13 is not possible. Okay, you could play the video now. Can you explain how you proved it? Can you come up? Talk clearly to the class, please. Because A plus. Everyone give Vershan your attention, please. Because A plus A equals six, then you don't have then. The purple is a four, the red is a two and the white is a one, so you couldn't do it without another negative number. Why? Because... Talk to the class, please. So you have 16 and what is it you need now? Need subtract three. Okay, and why can't you do that with one negative checker? Because this is a four, this is a two and this is a one. So what did you conclude from that? What did you decide? But if you had another negative number, you could have had it because you could have put one on the red and one on the white. Can someone explain what Vershan just showed? Why is 11 impossible? Can someone explain his proof? How did Vershan try to prove it? Will Vershan listen and see if they understand your proof? How did he try to prove it? I think what you did was you tried all the ways to do it. None of them match with 11 because you tried, like the problem said. Is he trying to make 11 or 13 right now, Zion? 13. 13, okay. Yeah, he didn't match up to 13. He tried all the ways, he said you only have two positive checkers and you have to use those and only one negative checker that can only be used if it's needed. So really he tried all those ways to use them and it didn't work. Vershan, did Zion repeat your proof right or do you have anything to change about what he said? He proved it right. Okay, do you wanna hear one more person say it? Sure. Okay, who else would like to say how Vershan tried to prove that 13 is impossible? Can someone else explain it besides Zion? What you tried to do was try to put two on eight and try to go up one more and then make 13. Vershan, is that what you said? Yeah. You tried to put two on eight and add up one more but you couldn't because you didn't have a third checker. So you tried to put two on eight and one on negative one on one and it didn't work and you tried all of it and it didn't work and you couldn't make one and make 13. Can you say one more time what you said to the class? Say it one more time clearly Vershan. You put two on the eight and then one. You put two on the eight, so that equals 16. Then you can try to see 16 minus four. It goes 12, so that's not right. Then 16 minus two, two equal 14, so that ain't right. Then 16 minus one equals 15, that ain't right. Cassie? Sorry, go ahead. So you will need another negative number, so I'm in another negative checker so you can put one on the two and one on the one. And what would that give you then? That would equal 13. Okay, take a moment and talk to somebody nearby. What did you notice about Vershan's effort to prove it over the three minutes or so that you were watching the video? And while you're doing that, if you can put the slide back up, that would be great. All right, let's continue. I want to step back now and talk with you a little bit about Vershan, Vershan's prior experience in school before this class. Vershan, on the day that you watched him, was trying to do something very complex and you could see him discussing in front of his classmates, listening to what they were saying and improving his argument as he listened to their efforts to repeat what he said. And as I said earlier, being able to prove that something is impossible is mathematically complex. In fourth grade, though, Vershan did like to share his ideas with other classmates and he also really liked to write, but unfortunately, he was often in trouble. He was often sent out of the room to the principal's office. He wasn't doing well in math. In some ways, it's not surprising that he wasn't doing well in math because he often wasn't in the class. He was often sent out to the hall or to the office because the teacher was scolding him or finding him to be misbehaving. So I want you to think about that now and I'm going to go back one week, not to the previous year, just one week before the day we just watched. So we watched Vershan trying to prove that 13 was impossible. But now if we go to the next slide, I'm going to tell you a story about Vershan one week before that day. On this day was the very first day that the children learned about the mini computer and none of them had ever learned about it before because this mini computer was not being introduced in the school that they were in in fourth grade. So this was something completely new to every single student. So can you click again? I'm going to tell you what Vershan was doing during the six minutes that the teacher was introducing the mini computer. So you remember when I was introducing the mini computer to you about 10 minutes ago and you know you have to pay very careful attention in order to learn how the mini computer works. But if you can just click, I'm going to show you Vershan. So to click once. So here's Vershan, a close up of him. Maybe you can see what he has in his hand but maybe you cannot. So if you click again, I'll tell you what it is. It's a paper airplane. He's making a paper airplane during the lesson and he's paying very careful attention to the paper airplane. Click again and you'll see a little bit more photographs of him building the airplane. Click again. And here you can see he's also taking the finished, go back once please. He's taking the finished airplane and putting it on this head. So go forward now and click again. Oh sorry, go back. Go back one, I'm sorry. So, oh sorry, back to the cloud. I apologize. Yeah. So if you stop for a moment and think how might the teacher interpret Vershan? After all, it's a math lesson and he's building an airplane and he doesn't look like he's paying attention. And in many of our schools in the United States it's extremely common for children to be disciplined for not paying attention during class. You'll have to tell me if that's common in Indian classrooms. But we also have a pattern in our schools that in particular African American children and especially African American boys are very frequently, as he was in the previous grade, often in trouble. So I think it's quite likely that what might happen next is that the airplane will get taken by the teacher. Perhaps the airplane will be ripped up and thrown away. Perhaps Vershan will be asked to go out in the hall until he can listen. But that's actually not what happens. So if you click forward I'm going to tell you what does happen instead. So one minute later the teacher says, you know what Vershan, I'm going to need you to come up here closer where you can see it here and won't be distracted. So click again. And you can see Vershan there on the left walking up to the front of the room and click forward. Over the next minute Vershan is raising his hand. You can see I put a circle around it and answering questions. He does have the paper airplane with him however. Go again. So at 11 27, one minute later the teacher says, okay I've been introducing the mini computer but now I'm going to call on the student to come up to the board and make a number on the mini computer and then call on other children in the class to do that. And Vershan you get to be first because you're sitting close to the board and you can come up and make a number and then you can call on people to see if they can figure out your number. So go forward. So at 11 28 Vershan takes on this role of being kind of like the teacher and you see he still has the paper airplane with him. Can you click forward? So a question is what do we think about Vershan now? Is he paying attention? Is he not paying attention? Should he be getting disciplined for having the paper airplane? He's using the paper airplane kind of like a pointer at the board. So I want to step back now and talk a little bit about patterns that produce inequity in our schools and I'm looking forward to you telling me how this relates to your schools. Go forward please. So what shapes or influences how Vershan's teachers might understand him? So one thing, go forward please. Teachers are making decisions all the time about how to read or interpret a student and the decisions that we make as teachers based on what we think the student is doing or thinking are all tied to how we read or interpret students. A second thing, you can click again, is that we all as educators have opinions or views about what it means to be engaged or paying attention or what it means to be on task or off task. A third element that might shape the teacher at her view of the student might be preferences about how children should behave in class. For example, in the United States, many teachers have a preference that students sit very still and look at the board and listen. Maybe that's not the preference of teachers in India but in the US, many teachers prefer that and so a teacher might be annoyed with Vershan for paving the paper or airplane. And finally, as I already mentioned, that Vershan is black, is African-American, makes it still more likely that his teacher might interpret him negatively. Go forward please and I'll talk a little bit about research on bias. We're finding an increasing number of studies that show that teachers' views about race and also gender influence their perceptions and their interpretations and their interactions with students. So for example, if Vershan was a white girl, it might be that the teacher might interpret her for the very same actions might interpret her differently. Might interpret her as creative or able to do more than one thing at once. And the studies that are tracing the effect of racial and gender bias are very dramatic in the United States. They show for example that black children and brown children are much more likely to be in special programs for children with difficulties or disabilities. They're much more likely to be disciplined including being expelled from school and they're much less likely to be selected for special programs for advanced learners. Even though they don't have a higher incidence of disability, they are extremely talented at similar rates to white children and they're being suspended from school for the same infractions that white children are exhibiting but are not being disciplined. So these studies help us to understand that there is strong effect of racial and gender bias in how teachers read students. So I wanna think a little bit about the segment that we saw about Vershan and think about my question that I opened my talk with today about how teaching can actually affect justice in our world as well as mathematics. So please go forward. I wanna ask the question, how can teaching have a bigger purpose about justice? And if we think about in and vision, can you click forward? Can you click again please or is it not working? Thank you. Debra, you have to repeat. Debra, hello. Yeah. You might have to repeat a couple of lines back because you were frozen on the screen, yeah. Okay, so in thinking about how teaching can adjust this, there's both invisible world and then. She can't hear me anyway. Debra, we are going to disconnect you because you're like the frame is stuck and we'll call you back. Hello. Hello. Yes, you are coming back. Yes, you're back. So. Does it seem better now? Yes. Yeah, please continue. So you said how can teaching work for justice and from there you can actually move. And so then there's invisible work and visible work that has to do with this question. So let's talk about invisible work first. Can you click? Thank you. So in one way the invisible work that we were seeing in the story about Vrushan is that, and you can click again, that the teaching is trying to interrupt patterns of racism and gender bias in several ways by believing that an African American boy could be smart and understanding that Vrushan is interested in being a leader or a teacher. The teacher is also imagining that Vrushan might really be listening even though he's building a paper airplane. The teacher is making some choices about how to interpret Vrushan and what to ignore about his behavior and what to pay attention to. And the teacher also has to trust that Vrushan will respond if she asks him to come up to the board and make a number. But those are all specific things that the teacher is trying to do to change the pattern in which black boys are often being disciplined or sent out of the class. But there are also other things that teacher is doing if you click forward. The teacher is using a routine of giving children the role of being the teacher for a minute and as a way of engaging children more in the work and distributing the work so that the teacher is not the only one presenting ideas in class. But it's a routine with definite routines and structures for how to do that. And finally, the teacher also chooses a problem that has many different entry points. So making a number on the mini computer, there are many ways you can do that problem. And so the choice of choosing a problem like that is also part of the invisible work that we don't see, but if we think about it, we can notice. But there's also visible work if you click again. We know that the teacher invited Vrushan to be the teacher. The teacher was supporting him to present skillfully so that he could be successful. She oriented other children to pay attention, to watch him, to listen. The teacher expected the other students to be listening when Vrushan spoke. And she gave them opportunities to say what did they think that Vrushan said. That's different than the teacher repeating what Vrushan said. Instead, the teacher asked class, who can say what Vrushan just said? And then the teacher also puts Vrushan in the position of being able to listen to his classmates and determine whether they understand his idea. And that is different than the teacher being the one to validate his idea. So these are all examples of how teaching can work to change patterns in classrooms. Please go forward. So I'm claiming that teaching can be a force for justice as well as for high quality mathematics. Please go forward again. I think you can click again. I think some of you are familiar with the diagram that we call the instructional triangle. I put the reference on this slide. This shape or this diagram is intended to show, can you click again please? That the work of teaching is built together inside of classrooms. Please click again. In much broader social and political environments, historical, economic, cultural, all of these outer environments are shaping what children bring to school, what teachers think they're supposed to be doing, the experiences that teachers have had themselves with schooling and all of those things are influencing the classroom. But if you click again, it's also important to understand that teaching is being constructed by the ways in which teachers interpret their students, interpret the mathematics, interpret what teaching and learning mean. And so at the micro level inside the classroom, teachers are making a very big impact on the experiences that students have with one another and with the content. Even though the larger environments are also an important factor. So a big question for my talk today, this evening with you, is on the next slide. And I'm claiming that the work of justice lives directly inside the work of teaching. Of course I'm not arguing that in order to achieve justice in your society or in ours, that it only happens inside of schools. I'm only claiming that there is important work to do in teaching that can change and disrupt patterns that have repeated inequalities and inequities inside of mathematics teaching. So if you click forward, I'll try to explain this. This is based on work I'm doing with several people here, including Lindsay Mann and Amber Willis. One piece of the work is to understand one's own identity and role as the teacher and to understand that when we do things, we're often repeating larger forces of oppression. For example, if Vershawn is scolded for his behavior, it's important to understand that I as a white woman scolding a black boy and repeating a pattern that in our country has been persistent and has led to very large patterns of oppression and bias. But it's not just about one's own identity, it's also about knowing what typically happens for a student and being conscious of realizing that we have the power as teachers to sometimes do things that are very different than what typically happens. A third is knowing that it's crucial to be seeing the strengths mathematically of each student and learning to hear what students are thinking and saying and building on their strengths. And finally, it's actually inside of the mathematics as well or science by thinking very deliberately about what counts as mathematics and what's important for students to be doing mathematically. For example, learning to prove that something is impossible is a sophisticated mathematical skill. But the teacher needs to know that by opening up mathematics in that way, the teacher creates new opportunities for children to be inside the mathematics rather than excluded. We can go forward again. Do we have, what time, how are we doing on time? Shweta or Savita, do you want me to try to finish up or do one more example? I know we started late. Yeah, you have, I think, 20 minutes. 20? Yeah, is that right? Okay, then we can do one more example, I think, if that's okay. Yeah. Would you like to do one more? Yes. Okay, so let's go forward. Here we have two more children. They're not in the same class with Varshan, but it's a similar class. They're also rising fifth graders. The girl on the left is named Anaya and the girl on the right is named Tony. And as you can see, they're both black girls. If you go forward, I'll explain the problem that they are working on. It might look very simple to you, but it's not so simple, because the children are just learning now that fractions are numbers on the real line. In the United States, many children learn about fractions mostly by looking at parts of holes, like what is one third of a pizza or what is one half of a cookie? But they don't always learn that fractions are really just numbers that are points on the line. So the children were asked very early in their learning to look at this diagram and to name what number is at the point on the line where the orange arrow is pointing. Yes. Okay. I'm going to show you a video in which, very, very short one, and I'm going to ask you to think about what the two girls know. Maybe while we're getting the video out, you could think to yourself, you know that the answer should be one third, but what do you think are other answers that children might give for that diagram if they're just learning that fractions can be numbers on the line? What answers do you think they might give? Okay, let's watch now. And remember that I'm asking you to think about what can Anaya and Tony each do and what do they know? Who'd like to come up to the board and try to tell? And you know, it might not be right. That's okay, because we're learning something new. I'd like someone to come up and sort of be the teacher and explain how you are thinking about it. Who'd like to try that this morning? Okay, Anaya, when someone's presenting at the board, what should you be doing? Looking at that person. You're trying to mark what you think this number is and explain how you figured it out. Listen closely and see what you think about her reasoning and her answer. But one seventh, because there's, yeah. Because there's seven equal parts, like, one, two, three, four, five, six, seven, seven. Before you agree or disagree, I want you to ask questions if there's something you don't understand about what you did. No agreeing and disagreeing. Just all you can do right now is ask Anaya questions. Go ahead and question for her. Okay, Tony, what's your question for her? What? Go ahead, it's your turn. Why did you pick one seventh? Thank you. Let's listen to her answer now. That was a very good question. Can you show us again how you figured out that, why you decided one seventh? Okay, let's go back to this slide. And remember that the question I'm asking you is what do Anaya and Tony know and what can each do? Can you click forward two times? Thank you. So I'm going to tell you what many people in the United States say when they see this video. It might be different from what you would say, but it's very common. And I'm telling you this because this is related to my question to you today. How do we make teaching a force that can interrupt patterns of injustice and inequity? Please click. Can you click forward, please? Thank you. So about Anaya, I think you can guess what people say. Click again, please. They say that she has the wrong answer, that it's not one seventh, it's supposed to be one third. And about Tony, you can click again. They say and you can click. They think that she's basically just being unkind and impolite to Anaya, that she's making fun of her, that she's trying to embarrass her. And what's interesting about this and also very troubling is that, again, like for Sean, Tony is often being interpreted as doing something wrong, but that might not be the way we can choose to read Tony or understand her. And it's also might be important to understand that there's a great deal to understand about what Anaya is doing, even though her answer is not right. So if you click forward, I want to pause for a moment to talk about why it's so important to help teachers learn to see the mathematics of their children's work as a force for mathematics teaching and learning and also for disrupting inequity. So click forward. Often find that at least people who are learning to teach and often teachers can ask this question. They can say, why is it so important to not notice the things that children are lacking, to not talk about deficits? Why are we supposed to always talk about their strengths? If you're a good teacher, aren't you supposed to be identifying things that children don't know and helping them learn things that they don't know? So I find that it's helpful to tell people three different reasons from research about why it's so important to learn to see what children are doing instead of what they're not doing. So the first one, please click, is that we know from theories about learning that the way human beings learn is by building on what they already know. That is how we all learn things. The second reason that's important is that we know from research on developing children's identity and their sense of confidence and competence that it's important to develop those in order to boost the way they learn mathematics. We also care that students come from school feeling capable and confident. So paying attention to students' strengths helps to build a strong academic identity. And third, there is considerable research that shows that students who are members of historically marginalized groups, in our country that would mean Hispanic children, African-American children, Indigenous people, that they often suffer from what the research calls a stereotype threat, which causes them to be nervous and anxious about their performance in ways that interfere with their actual capability. And it's important, therefore, for educators to be aware that the way they read students who are members of these groups can change that pattern. So if you click again, we try to help teachers understand that focusing on children's strengths is effective, is important for both very good teaching and as a force for justice. So I want to think now about the episode with Anaya and Tony and let's think about what they do know and what we can see. Please click forward. So what do they know? Let's take Anaya first, please click. She knows a lot, you can click again. She knows a great deal. For example, she's using the definition of a fraction to explain her answer. She identifies the whole. She makes sure that the intervals are equal, something that many children do not do. She's counting the intervals, not the little marks. And she knows how to write one seventh. Furthermore, she produces a very good mathematical explanation and she presents her ideas very clearly. So let's think about Tony. What can she do? Well, let's click again. She's listening very closely to her classmates' presentation. She's using the definition of a fraction to ask Anaya to clarify, how did you decide on seven? And she asks a very pointed question. So the teacher has a choice. Should the teacher pay attention to Tony's laughter or to her question? And that choice is important. Maybe Tony is laughing because she's a little bit nervous. Maybe someone on the other side of the classroom said something silly that made her laugh. We can choose to interpret Tony as serious and engaged, or we can choose to interpret her as being rude. Similarly, we can choose to interpret Anaya as simply having the wrong answer. Or we can recognize the many things she does know and build on those to move forward. In fact, the only thing that Anaya doesn't yet know is that on the number line, we always consider the interval from zero to one as the whole. That's only one small part of the whole concept. So let's go forward again. I'm coming to the end of my talk because I want to be quite concrete about what this all means for teaching and for teacher education. Please click forward. So if you think about how can teaching actually work, let's think about the invisible work first. So when you think about what was going on in this video, there are many things like we saw before that are invisible. The teacher has to look at all of the student's work before she decides who to bring to the board. Before she chooses Anaya, she has to see what all the other children have so that she can pick Anaya on purpose. She also has to think about which child in the class should have the opportunity to present her ideas, just like Vershan. And like in the episode with Vershan, the teacher is also changing patterns of gender and racial bias by understanding how capable Anaya and Tony are and can be by trusting them to be learning and to be engaged and to be making very deliberate choices about how to read the children and what to pay attention to, exactly like we saw with Vershan. There's also visible work if you click again. So the teacher is supporting Anaya. Instead of focusing on error only, the teacher is focusing on other parts of what it counts as being mathematically capable. And you see other things on this slide that the teacher is also doing to help build visibly what it means for these children, these girls and their classmates to have access to complex mathematics and to be seen as competent rather than deficient. So I want to connect now, if we click one click at a time to a set of ideas that my colleagues and I have been working on that we call high leverage teaching practices. And we think these are very important because they help to make visible how we teach teachers to do this very complicated work of teaching mathematically carefully and in ways that disrupt patterns of inequity. So if you click once, one practice is eliciting and interpreting students' thinking. This means asking children questions to help them explain their thinking. Leading group discussions like we saw on both videos. If you click again, building relationships with the students and with students with one another, expecting students to listen to one another, to be respectful, and the teacher also treating students with respect for their thinking. Another is establishing norms and routines for how we go to the board, how we talk in class, how people get turns. Another one is modeling and explaining mathematical content very carefully and precisely. Another is specifying the kind of behavior that students should engage in and reinforcing that. Each of these is what we call a high leverage teaching practice. So I'm going to conclude now by just explaining briefly what these practices are and also what they are not. Can you click forward? So first, what are they? Can you click forward? So they are the integral tasks and moves that teachers make all the time in their classrooms and that beginning teachers, early teachers, need to be able to do right away when they start teaching. A second thing that high leverage practices are are important parts of the work of teaching that put children at risk educationally and socially when teachers do them badly. For example, if a teacher leads a discussion in class in which children are humiliated or embarrassed, children might not try again to do complex work in mathematics. So a badly led discussion can lead to children excluding themselves from mathematics. A third part is that these practices are specific ways in which beliefs and commitments about equity can be enacted in everyday practice. For example, specifying behavior and deciding what to value is part of disrupting equity and it's also part of teaching children ways of learning and ways of being in school. And finally, high leverage practices are things that you can actually teach teachers to do that it can be learned. You don't have to be born as a natural teacher. You can learn to do these things well. Someone can coach a teacher or help a teacher to do them better. And one can also assess whether teachers do them well. So what are they not? Let's go to the not column. The high leverage practices are not disconnected from the relational work of teaching. They're also not content free. So for example, leading a discussion in science is not the same as leading it in mathematics and yet there are some common skills to learn. Leading a discussion in an Indian classroom is not the same as leading it in many different kinds of United States classrooms but there are some things in common. High leverage practices are not natural or obvious. They have to be learned. Often they're different from what adults would do if they were not trained as teachers. And they're not disconnected from the imperative to attend to questions of social justice and equity and to disrupt racism. So they are the main things teachers do and there are also things that can make a huge difference for content teaching as well as for equity. Please go forward. Can you click again please? Thank you. So I conclude my talk by saying teaching can be a force for justice and let's click forward two slides now, okay? So there's some things we need to ask of our society of Indian society and of the United States society and really of our world in order to achieve this goal. So what are they? Let's talk about them for a moment. Of our society we need more people to understand the power of teaching. We need people to not assume that this kind of teaching happens by itself without help and we need to stop finding excellent teachers and holding them up as examples because this makes people think that teaching is about being a hero instead of being a skilled professional. We also need to ask some things of people who make a policy. Can you click again? So one thing we need is for policymakers to expect people to demonstrate that they're ready to take on the responsibility of teaching children before we let them do that and we need to also support teachers to develop and improve their teaching over time because it's difficult work. And finally there are things we need to ask of ourselves as educators. We need to be willing to unpack what teaching like this requires as I tried to do in my talk. We need to change the way we recruit people to be teachers and the way we make the teaching workforce in our countries. We need to figure out what kinds of resources and experiences help adults to become really good teachers. And finally we need to be more responsible for teaching people how to teach, how to teach mathematics, how to teach science and ensure that we don't simply ask people to do this work without providing the supports and resources. So let me conclude by reviewing the core argument of my talk. Please go forward. This is a quote from teaching can be a force for justice. No, let's go forward. We need to finish. Thank you. I would like you to read that quote. It's really beautiful and maybe we can read it at the end. So how can teaching be a force for justice? It can only be that if we act, if we do things. We need to make the teaching force diverse and reflective of our countries, of your country and of our country. We need to be able to see and challenge and disrupt practices that have made it difficult for children who are often marginalized to succeed. And we need to work together to develop ways to enact practices and policies that can change that normal. Let's go back now to the quote and that will be the end. Can you go back one more? This is a quote by a very beautiful one by an author named Maya Angelou. And I'm just going to read it out loud to conclude my talk. What does a teacher who believes and holds the aims that I've been talking about do? And she wrote, this is the value of the teacher who looks at a face and says, there's something behind that face and I want to reach that person. I want to influence that person. I want to encourage that person. I want to enrich, I want to call out that person who is behind that face, behind that color, behind that language, behind that tradition and behind that culture. I believe you can do it. I know what was done for me. So thank you very much. And I hope we have a few minutes for questions. The slides will be posted on my website so that you can get a copy if you would like. Thank you very, very much. I hope it was possible to follow this using Skype. Thank you very much, Jabra. This was a very detailed talk. So we'll take some questions. And like last time people can say their name and be a little slow and speak only on the mic. So anybody have questions? And also briefly, yes. You have question, Parveen? One minute. No, I just wanted to say that it's one of the most powerful talks that I ever heard on how and what kind of a powerful role a teacher can play in the classroom. Thank you so much. Thank you. There is another question, yeah. Can you say your name, please? This is Jyotsana from the Homi Baba Center. I wondered if you believe that all the things you said about, if a teacher believes, I should say, that all children have the potential, I won't repeat what Maya Angelou said, but there would be cases I imagine where a teacher probably needs to be sensitized to that. Would you agree with that? And if so, so then at the entry point, I mean, is that a requirement for, can one make that a requirement for a teaching position? Cause it may not be immediately obvious, but then you will see it in the classroom practice. It's such a good question that you're asking. And in the United States, it's one of our biggest problems because we find that many teachers who enter teaching often don't have that realization about students. And as I mentioned a few times, it's particularly a problem when we have teachers who come from one group in our country, more middle class, more white, and when they see children of color or poor children, they assume that the children are not capable. And we're trying to find new ways in our professional education to do two things. One, to recruit more people from more of the different groups in our society to become teachers. And the second thing is to change the training we provide to not just work on people's beliefs, to work on their beliefs, but also on their actions, so that they learn to see the strengths of the students. They learn to see that the students are capable and have a skill to build on them. But you asked exactly the most important question because you're quite right that at least in our country, that does not happen automatically at all. And I would love to learn more about how that comes up in your society. Subramaniam, yeah. My name is Noesisi Feza. I'm from South Africa. And your talk really touches mainly on what is going on in our classrooms in South Africa. It touches on the race. It touches on entitlement. It touches on exclusion. Now my question is, I think in the United States, you are moving towards a right direction after quite a lot of experiences. But in my country, we are a baby when it comes to a democratic space. Now how can one influence development of teachers itself when teacher development depends on the hands of people who've got biases towards the students they are training to become teachers first. So how does one influence those developers? These questions are so perfect. Your question is exactly right. And our countries, both South Africa and the United States, have long histories, that histories are different, but long histories of racism. And the systems in both of our countries reinforce those structures. So the people who are the policymakers in our country are very often also very privileged people who went to privileged schools and they make policy that reflect values of white people and of privileged people. So we have similar problems, even though the details of our histories are obviously very different. In some ways, they're also very similar. And these questions make me wonder whether we might not develop more capability if we worked on these problems more internationally than we sometimes get to. These problems are, as you said, very clearly. We face these in many parts of the world and they're crucial because these children whom we're talking about are the future of the world. And it's actually crucial that we find new ways to educate teachers. I think the main thing that my colleagues and I are really working on right now is that somehow in addition to these big aims of believing in children and changing racism and sexism and class bias, that we need to equip teachers with actual practices, that when you work only on beliefs, that's good, but often then the practices turn out to be the same practices again. And so we somehow need new ways of developing what is a set of practices that we can actually teach teachers to use and help them see why they can be so much more successful when they use them. But again, I would like to say that I would really appreciate opportunities to find ways to work across our national borders more to learn from one another. I think we could learn things from South Africa. I think there are some things possibly that we might do that are useful, but I think these are not all completely separate, even though we need to respect the differences in our countries. I really appreciate your question. Thank you so much. Yeah. Yes. This is Ravi Subramaniam from the Homibaba Center. So thank you for a powerful talk and for illustrating in some detail how questions of justice emerge in actual practice. It reminded me of a work of an Indian sociologist and thinker whom I think in education we've not paid that much attention to. His name is Gopal Guru. He himself, he's a Dalit sociologist and thinker and as you know, structures of oppression in India operate often through caste and Dalit is one of the oppressed and lower caste in society. Gopal Guru has in a recent book in which he dialogues with an upper caste thinker, Sundar Sarukai. He's talked about this notion of humiliation and of self-respect. And I think that there's a lot of work and elaboration there. It's something that I think is very important for our work in education and probably we've not paid enough attention to. So just makes me feel after listening to your talk that we should pay more attention to this writing. And so thank you very much. I really appreciate hearing about that and I hope maybe you could send me the reference on email. It really would like to learn more about that. Thank you very much for connecting me to that. Okay, we have two more questions. I think you go first and then Jayesh ma'am. Hello ma'am. I'm Chitgala from Bangalore, India. And your talk was very, very inspiring. And it not only gives the context on how a teacher should handle the classroom to bring justice, it is also making me reflect on how I should, as a parent, adopt these strategies in upbringing my own children too. Thank you so much. But having been in this field, recruiting teachers over 15 years now, I have always had this dilemma when I had to recruit teachers to teach a particular subject. My weightage goes more on their subject competence and ability to deliver. So what should I use as a strategy to also evaluate a teacher who can bring up justice in her classrooms while recruiting? Yeah, that's a very good question. I wonder if there are some ways we could combine. I appreciated your comment about parenting also. I also think about that as a mother and as a grandmother now too. I think that we might explore some ways to combine what you were describing there with content and this valuing of children. For example, think about the videotape of Anaya and Tony. I wonder whether we could sometimes use a video like that where we ask teachers or teacher candidates or applicants, what do they see about the mathematics and what do they see about the children? I would be interested in knowing, I would be interested in a teacher who both is very inclined to see Tony as really serious and I would be interested in seeing a teacher who knew that Anaya has almost all the mathematics right because somebody who only sees that she doesn't have one third doesn't understand the mathematics really very well because there's a lot of mathematics in her answer. So I wonder if we could build some examples where we can get at those two things together because you're right. I mean, you can't see children's strengths when you don't understand the content. If you ask me to be in a high school science class and see the strengths of children in a physics class in secondary school, even though I have commitments to children I might not see as much as some of you would because my expertise is not in physics. And so I think the content does intersect these issues of justice very strongly. Thank you ma'am, you answered me to my satisfaction and I would practice that immediately and in fact as a recruiter as well I must see the positive side in the candidate who comes and that's another takeaway from your answer. Thank you. Thank you. Jai Sri ma'am. I'm Jai Sri Ramadas. I used to be at the Homi Baba Center. You know, of course I really appreciated your talk and I very much appreciated Noh Sisi, our colleague from South Africa, her comment about the biases that exist in teacher educators also. And these are something which really, I mean us being a group of teacher educators we need to look at very critically. And I think one thing which is important is that the educators, the teacher educators, the researchers, they set the language of discourse. Discourse about what this problem is about. And I remember that from more than 40, 50 years ago it has been about underprivileged. You know, that children are underprivileged. And so that is the word which is used and it used to be that another word called discrimination was not used at all because I mean people somehow found it too threatening and discrimination as a word did not occur. But in the intervening time, the literature on cognitive biases has really grown and now it is well established through a lot of research that cognitive biases of various kinds exist. And I think we should change our vocabulary from one of underprivilegedness to cognitive biases which puts the responsibility where it should be. And which is on us, you know, and yeah. That is so well said and a very interesting insight that so much of our language places the blame on the people, on the children and their families and their communities instead of on our systems. And part of my reason for wanting to give this talk is to remind ourselves that education is a very powerful social institution that can, as you said, and as the woman from South Africa said, can reinforce structures of racism and bias and oppression or we could leverage them on purpose and we could take that responsibility. But it is a challenge because as several of you have said, those biases are built into the people who have power to shape education. So it does take all of us determining that we're going to use this power to make change and that's not simple. But I think your observations about language are really wonderful. Thank you for sharing that. Okay. I think there are no questions. So Deborah, thank you so much. Let's give a hand again, a big hand for us, thank you. Thank you, thank you so much. I'm sorry I could not be with you today but I appreciate the opportunity and I appreciate your questions very much. Thank you.