 Today I'd like to welcome somebody who really needs no introduction, so one of our own, Daryl Young. So Daryl, let me say a few words. He's a professor at Harvey Mudd College. He received his PhD in applied mathematics, and he's the founding director of the Claremont Colleges Center for Teaching and Learning. He's really a longtime member of the PCMI community and a really valuable one. So I'm very grateful to him for all that he's done for our teacher program and just being a general part of this. So he's been a strong advocate for effective teaching, effective methods for inclusion and diversity in mathematics education, and I'm really pleased that he's agreed to give this talk today on equity-mindedness in the teaching of mathematics. Thanks, everyone. I have a few disclaimers and instructions for all of you before we get started. The first thing that you should know is that I'm going to ask you to interact with me and with other people at some point. So if you're sitting by yourself and you're feeling brave, would you sit with somebody? Even if it's somebody you don't know, it's okay. Ideally, you'd also have something to write with and something to write on. So I'll let you get settled while I get started. The first thing I also want to say is that the backdrop for this talk is that we live in a highly inequitable society in which racism, sexism, and other forms of bias and discrimination just pervade. It's the air in which we breathe, and that sort of motivates a lot of what I do personally, professionally, and is part of the reason for this talk right now. Now, you can't expect that we'll be able to make a significant dent in that issue in the next 60 minutes, so I don't want to get your hopes up, but I just want to let you know that that's sort of the reason why we talk about all of these things. The second thing is that this is a cross-program talk that's not about math, so I hope that the title already gives you some sense of that. If you were not expecting that and you want to leave, that's totally fine. You're not going to hurt my feelings. I'll also just make a comment that talking about equity is really tricky. Honestly, what can be accomplished in 60 minutes, not a whole lot, but what I'm hoping to do is to give people some things to think about, not just for this time, but for beyond this time, that you'll have some ideas to take away in your own teaching practice that will help you to be more inclusive and more equitable. Another thing to keep in mind is that I don't know many of you, you don't know me, and it's difficult to go deep in any kind of equity kind of talk because that work is very personal and it takes a lot of internal work, and so this is something that you'll have to judge for yourself. The degree to which you take up these ideas will really be up to you, so I'm going to mainly give you some ideas to think about, but then you're going to have to do all the hard work later. Finally, some of the hard work that comes with dealing with equity and inclusivity are really internal ones, so I don't know if you were here at the cross-programmed last Friday, one of the questions that the panelists who were sitting here were asked were, what are some of the barriers to greater inclusivity and equity? And I'll add that one of those barriers I think are internal ones. They have to do with our own ego, our own compassion or lack of compassion for ourselves, so you might hear people say things like, I'm not racist, I don't need to listen to this, or I know this stuff already, I'm a person of color, so those experiences that we all have are very unique to ourselves and so we can't assume or impugn any kind of things about each other just because we particularly have a certain set of experiences and I'll just say also that it's important that we give ourselves compassion because if we can't make mistakes in an environment that's safe like this, I'm not sure where we're going to be able to make mistakes in our lives, so if we can have some grace for ourselves right now and over the next few weeks, I think that will go a long way. Okay, so through with all of the disclaimers, before I get to the talk, I should also just tell you a little bit about who I am and also that you'll know where I'm coming from because the experiences that I have are obviously different from the ones that you'll have to, so I am a faculty member at Harvey Mudd College, which is a part of the Claremont Colleges, there are seven institutions that are all together. Harvey Mudd is a very small liberal arts, STEM-focused institution. We have only about 840 undergraduates all together, so it's a very small place. I've also taught for a year in LAUSD and for the last two years, I've been the director of our Teaching Learning Center, which is basically an outfit that's supposed to help faculty enhance their teaching learning at the Claremont Colleges for all seven institutions. And in addition to those experiences, I work very closely with Math for America, Los Angeles. We're celebrating our 10th year of being in existence. We have about 150 teachers who've been through the program or are in it right now, and currently we have about 80 or so. It's just a quick plug. We just got a new grant for computer science teachers, so if you happen to know people who teach math and computer science and are computer science in the LA area, please send them my way, or you can tell them to go to mfala.org. Okay, so as a result of all that work with teachers and with faculty members, I am in a weird situation where I read a lot of education literature, both at the higher ed level and at the K-12 level, and it's really interesting to see where some ideas get taken up in one sphere, but not in the other and vice versa. And it's cool because I get to be at the nexus of those two things, and so when I hear my teacher friends telling me about this awesome idea, I get to pass it over to my higher ed colleagues, and likewise when I hear some interesting research in the higher ed world, sometimes I can take it back to my K-12 friends too. So today I'm going to be sharing some bits about both from both worlds, and I'm going to start here. So if you saw the top title in the PCMI app, there's probably something completely different, and that's because when Rafe asked me to do this a few weeks ago, I kind of made something up. I'm sorry, Rafe. But by the time I heard the equity panel discussion last Friday, I really decided to scrap the whole thing and start over again. And so I'm starting here with a definition of equity-mindedness from one of my favorite scholars, Estella Ben-Simone. She's a faculty member in the School of Education at University of Southern California, and also the director of the Center for Urban Education. So I'm going to read you three sentences from a paper of hers that defines equity-mindedness. So here we go. Equity-minded faculty and teachers focus intentionally on the educational outcomes of different groups of students and are able to understand any inequalities in the context of history of exclusion, discrimination, and educational apartheid. Equity-minded faculty see their institution and now add, and themselves as bearing primary responsibility for eliminating those inequitable outcomes rather than making students responsible for overcoming deficits, which may be lack of knowledge or skills or qualities. And finally, most importantly, equity-minded individuals are far more likely to understand that the beliefs, expectations, and actions of individuals influence whether minority group students are construed as being capable or incapable. So the reason I share all of this with you is because what I find so attractive about this definition is that it reverses the locus of the usual conversation about equity in many places, which is that it's about these students are coming to us with deficits and we're going to help to make that up in some way by putting them in these programs or we're going to give these things to them or we're going to administer these tests and put them in these special sections. And all of those things can be helpful, but they always put the locus of concern on to the student. The student is the person, the group that is somehow deficit and is needing to be fixed in some way as opposed to thinking internally about my own practice, my institution's own practices to think about how I can become a more inclusive place. I can talk a bit more about that later, but that's the basic idea. I'm going to get to how we implement this idea very practically in a classroom setting, but first I'm going to take a little detour and tell you about what this has to do with belongingness. So if you all remember taking an intro site class from college, you probably learned about Maslow's hierarchy of needs and very briefly this theory has to do with the things that motivate us to do whatever, to live, to breathe. So why do we do the things that we do? According to this theory, which is pretty well established, there are a hierarchy of different needs that humans have, and what we do is we operate in a way to meet those needs. The needs are organized in a hierarchy because according to this theory, which may or may not be true, this part, is that if your needs aren't met at a particular level, you don't even perceive the needs higher in the hierarchy. So for example, at the lowest level, humans have a need to breathe and sleep and eat and have water. If we don't have those needs met, then we may not even be concerned about our safety, but if we do, then assuming you have those needs met, you'd be concerned about your physical safety, your emotional safety, and once you have those needs met, you care about longing and receiving and giving love, so on and on and on. So I mention that as a very general theory for what people do, but let's turn that around and think about how that might play out in your classroom. So students have needs, and each of these categories can translate to the right into something that has to do with your teaching practice. I left off the bottom most category of physiological needs, but I should say that for many of us, these are still important concerns. They're just maybe not ones that we have direct control over. So for example, when I taught in LAUSD, many students came to class hungry, and if you're hungry, you can't learn very well. It's pretty basic. At Harvey Mudd, most of my kids have food to eat, but they often don't sleep very much. That often prevents them from learning. So these are basic physiological needs that you have to make sure your students have met. But above that, so safety might translate into the classroom as emotional and intellectual safety. That has to do with whether or not you feel like you're going to be ridiculed for something, for being different, or maybe for giving the wrong answer in class. Love and belonging might translate into a sense of belongingness to the classroom, to the school, and if you're a teacher who puts students in small groups, then belongingness to that small group might also be a factor. So this is sort of a general concept map that we can put a lot of things on. And what I would like us to do is to spend the next few minutes doing a little bit of quick writing to tease out the importance of belongingness. And I think it's easy to say that belongingness matters in the classroom, but I think it's something that's so deep and that has such impact that we often forget. So if you wouldn't indulge me, why don't you get something to write on? Or if you don't, that's okay. You can just think of these questions. Let me see my slides. Okay. All right. I want you to think about your teaching over the last year, or whatever, the last time you were in the classroom, and you had a substantial interaction with a group of students. So number one, think about one student in a class who you perceive to feel a strong sense of belonging in that class that you're thinking about. And write about an interaction that you had with them that gives you that perception of why you think they felt like they belonged. And then think about a student who you perceive to feel a lack of belonging in that class and write about an interaction that you had with them that makes you think that way. Just 90 seconds. Okay. I don't have a lot of time. Okay. So just very briefly think of two people for one and for number two. Okay. That's about 90 seconds. And I apologize if you're not, if you haven't been in the classroom recently or you're a student and you might have to think about a similar experience, maybe tutoring or maybe you can put yourself in the shoes of being the student in that situation, whether you feel like you're belonging or didn't belong. Okay. Two more quick questions for you to consider. Okay. Can I get a thumbs up? Are you all ready? Okay. Good. Thanks. Okay. Three. List some teaching practices that make your class unique or that set you apart from other instructors you know. So I'll give you an example. For me, I use standard space grading in my classes and that means that students have a limited number of redos for their quizzes and they can take them at any point in the semester. This is one aspect that is a little bit unique about my class. Okay. And then number four, what is one thing you wish students would do more of in your class to succeed? So I'll give you another 90 seconds just to write thoughts down for both of those things. It's about 90 seconds. All right. So here we're going to go, we're going to connect the first two questions with the second two questions. You see where I'm going with that? Okay. Here we go. I'm sorry that red isn't showing up super well, but okay, think about those teaching practices that make your class unique and that sets you apart from other instructors. How did those two students that you talked about first, how did they respond to that thing, or to those things? You can just think about it. You don't write anything down. Just think about that. Did they respond well? Did they not respond well? And on the bottom, what is that one thing you wish students would do more of in your class to succeed? For me, I wish students would come and ask for help when they're stuck. I just wish that. It's a lot of students don't do that. They think that they are too embarrassed or somehow. Anyway, what did those two students that you were thinking of earlier have to do with that thing? Did they do that thing that you wished or did they not do that thing that you wished? Okay. Let's just maybe we'll take a quick poll here. So that thing that you wish students would do of, more of in your class to succeed? Student A, the one who belonged. Did that student who belonged, did they do that thing? Raise your hand if they did that thing. Okay. Look around the room. Now let's see. Student B, the one who didn't belong. Did they do the thing that you wanted them to do? Raising your hand if they did that thing. The student who didn't belong. Oh my goodness. I didn't realize it would be this dramatically different. Did you look around the room? That's pretty strong. So I've actually never done this before in a group. So I was sort of taking a risk. I didn't know how I was going to turn out. But it's pretty amazing if you think about it. That one thing that you think is so important that you want them all to do, why is it that certain students aren't doing those things? It really matters, doesn't it? Okay. So the next thing we're going to do now is we're going to sort of unpack equity-mindedness in the context of this stuff, belongingness in all of these things. And what I would encourage you to think about is that I think going to teaching talks often it's easy to walk out of the room with like these are the five things that you should do. Check, check, check off the box. You know, like I'm going to blah, blah, blah, and blah. And I think those are helpful. But what I'm advocating more is beyond just taking away a list of things to do, inculcating a practice of habit of mind, of thinking in a certain way as to be able to uncover those things continually for yourselves. And here's an example of what I mean by that. So how might we embed equity-mindedness in our practice? So for any instructional choice that you make in your class, in your teaching, whether it's the thing that makes you so special or the thing that you wish students would do more of, whatever it is that you do, these are some questions that you might continually ask yourself to know if you're doing a good job at being equity-minded and inclusive. So how might that thing affect who feels included and who does not feel included in your class? How might that thing affect who would benefit and who might not benefit in your class? How might that thing affect who would have access and who would not have access in your class? And then the last one is kind of a crucial one. How would you know if you had to intervene in some way, given that maybe you noticed something wasn't going right? How would you even know if you weren't paying attention, you'd probably just keep going the way you were going and things would be fine? So these are some questions that I'm going to keep bringing back over and over again in the next remaining maybe 30, 20 minutes or so. And I'm going to do them in two different contexts so that you get a sense for how you might embed these questions into your daily practice. Okay? All right. How are we all doing? I'm talking a lot. I'm so sorry. Are we okay? Does anyone want to pause and ask a question at the moment? Okay, we're okay. It seems like we're okay. All right, good. So I'm going to talk to you about two areas where these things might play. So one has to do with the instructions that we give students and the second thing has to do with using group working class. Okay? All right, here we go. So instructions in class. Let's talk about transparency in teaching. So this is one of those things that I learned in my higher ed readings. A lot of my colleagues at the K-12 world, they don't use this word a whole lot, but I think it makes a lot of sense still. And that has to do with the word, this idea of transparency. Transparency has to do with making clear all those hidden assumptions that we make and the expectations that we have for our students that we don't always verbalize. And often, when we ask students to read our minds, what we're basically setting them up to do is to get it wrong sometimes. And the students who know will be fine. The students who don't know how to read your mind will not get it right. And so many areas of our teaching practice connect with this idea of transparency. So let me just read you this quote from Mary Ann Winklemas, who is a researcher in this area. Transparency means teaching students about more than just the core subject matter. It means telling students about your rationale for how and why you've chosen to shape their learning experiences. Okay, so let me tell you about a brief, very briefly about a research study that is pretty exciting. So here's what these researchers did. What they did was they found about 1,150 students over a bunch of different institutions, 1,180 students. These were across seven different institutions. 35 different faculty were involved in this study. And what they did was the researchers taught the faculty members in this study to revise their assignments to be more transparent. And I'll tell you in a second what that means. But all they did was they basically went to some training and then they took their assignments that they were already using in their classrooms. And they just made them a little bit more transparent, a bit more clear, okay? And then they were asked to go back to their classrooms and have the same class using the same old instructions, the same old assignments, and then to teach the same class with the revised version of the assignments. That's the only difference in the two classes. And what they found is that across all of the institutions and the classes, all of the students in the intervention group, meaning the students who received the more clear instructions, reported self-reported gains in confidence, belonging, skills mastery, compared to the control group, control group, just meaning the students who received the as-usual assignments. And not only that, historically underserved students, meaning students who were first-generation students and students of color, reported even higher gains than the majority students did. Sort of amazing. So everybody tended to do better, but the students that were marginalized did even better. And then in a follow-up study, what they did, this was just at the University of Nevada, Las Vegas. They took a whole bunch of first-year students, and what they did was they trained their first-year instructors in this transparent assignment thing. And they asked their teachers to keep track of the retention rate, and it turned out just by making the assignments more clear, the retention rate from first to second year went from 74% to 90%. Just doing that little tiny thing. It's pretty amazing. So let's kind of dive into a little bit about what they did by this intervention, I'll tell you more now. So what they did was they basically trained their faculty members to do these three things. Okay, here are the three things. How can you be more transparent with your students? Specifically with regards to assignments. One, whenever you give an assignment, just tell them what it's for. Why are we doing this particular assignment? What does it matter? How does it connect to your life? What kind of skills and content are you going to acquire as a result of doing this assignment? Two, tell them what tasks they have to perform to do the assignment. It sounds very basic, but that's basically all you have to do. Just tell them how to be successful, what might be the first step to take to perform this particular task. And then the third one is the biggest one, criteria. What does good work look like? How is success measured in this class? Those were the three things that they were trained to do in that particular intervention, and when they did those things, they generally performed a lot better. If you think about what was done, maybe the results in the study start to make more sense to you. For example, say I give you an assignment in intro site class. I say, okay, Andy, you have to write a paper about eating disorders. I want a 10-page paper with at least eight sources. Do Monday, go. So that's a very typical kind of thing that you might say to a student. But a beginning student in a first-year class might have a lot of questions, like why eating disorders? Why am I chosen to give this particular topic? What are sources? What constitutes a source? Is Wikipedia a source? I don't know. Do they have to be in a particular article? Do I have to cite them in a particular way? What's the formatting requirement? Does it have to be double-spaced? I mean, all of those things that are kind of confusing, students often don't know. And who are the students who probably will know? And who are the students who probably won't know? We all know that in this society, students aren't equally trained to do school well. Since we've had a lot of experience with these sort of open-ended assignments and writing papers, they probably will be familiar. They won't have those questions. Students who do not know those things, who encounter the, quote-unquote, hidden curriculum of higher education, they're the ones who are going to have questions. And let's compound that with the problem of being one of a few in a class. If I'm a person of color and I don't see a lot of other people like me in the class, and I have these particular questions, when nobody else seems to have those questions, I might begin to doubt my ability in the class. I might begin to doubt whether I belong in this space, everyone seems to get it, I don't seem to get it, I'm not going to let anyone know, I'm just going to keep going, pretend like I'm okay. That's a very typical kind of reaction that you might get in a higher-ed class. But the same thing is true even in a high school class to middle school class. So another example I might give you is a more mathematical one. So all of us, I think, have been guilty at some point in our lives as teachers in using the word simplify. And you'll know that in the Common Core State Standards in mathematics, the word simplify never appears. Did you all know that? Raise your hand if you knew that, by the way. Yeah. It doesn't appear because the word is rather vague. What does it mean to simplify anyway? Sometimes writing something in factored form, even though it looks longer, is actually simpler because of the thing I'm about to do to that thing. And so even just eradicating the word simplify might help because it just makes your intention more clear. Students are less likely to have to guess what you mean and will know what to do. Now, at the same time, what you should realize is that when we are transparent with students, what we're doing is we're making our expectations clear with them. We're helping them not to struggle with the things that we don't want them to struggle with. There are things that I want my students to struggle with and I want to intentionally do that because I want them to, for example, grapple with the difficult problems. There are reasons sometimes to not be totally... not to totally lay things out on the table, but even in those situations, you can be clear about why you're doing that. For example, in the morning math class that we're subjecting the teachers into right now, you know that Bone and I, the instructors of the class, we generally don't answer any of your questions when you ask them of us and the reason why is, as we said to you on the first day, because we want to allow you to enjoy the joy of discovering the answer on your own. So there's a situation where I'm clearly being opaque in my answer to you, but I did that intentionally because I actually want you to be able to enjoy the discovery yourself. Another example might be the following. In a problem, you might give missing information or too much information for students to solve the problem. That's a good strategy. Sometimes being able to parse information is an important skill for students to learn. And so you might say to students, by the way, this problem may have either too much information or too little information for you to solve the problem. Just wanted you to know that that will happen. I did that on purpose because blah, blah, blah, blah. So that transparency is what I'm talking about. Just being clear about your instructional choices so as to not have students wonder why you did a certain thing or whether it had to do with them or their inadequacies. So the first idea has to do with transparency. And so in any piece of instruction you give to students, you can always ask yourself, who will have access to understanding that information? Is every student in this class going to equally understand and know what to do? If not, that might be something you can revise. And I'll give you one more pro-tip about transparency. The best way I've found to make your instructions and your things, your classroom materials more transparent is find a colleague who is not in your discipline and trade your work with them. They're going to read your work as a biologist or as a whatever, right? And they're going to have questions for you that they will like your students not know because they're not versed in your field. So many of us have been teaching in our field for so long that we swim in this information. It's hard to know what we know that students don't yet know and separating that is difficult. Well, just ask a colleague and trade with them so you can look at their materials and help them identify and cover those questions that maybe they were assuming students already knew what to do. All right, are we good? Okay, thank you for that. This is a very... I'm talking a lot. This is a quiet audience. Did anyone have any questions that they want to stop me with before I move on to the next topic? Yes. Yeah, yeah, that's a great question, Melissa. So, for example, if I say to you, oh, write a text...