 Extremely privileged to have a special visitor. So, Ulrich Treisman is the University Distinguished Teaching Professor at the University of Texas at Austin. And he's the founder and executive director of the Charles Dana Center. He's awarded many really prestigious prizes and recognition for his really seminal role in mathematics education at all levels. He's really one of the very prominent figures in this world. And I was extremely pleased that he agreed to come and spend a bit of time at PCMI and give us this talk. So thank you very much, Professor Price. I'm going to talk about tectonic plate shifts in education and their implications for equity, fairness, and so on. So half of my life is professor of mathematics. Half is professor of public policy. I'm going to try to hybridize those two fields for you. But first, about equity. Over the last 45 years or so, whenever things felt like they were going backward in our society, I understood that progress isn't linear with positive slope. But I never felt before the possibility that all the gains of the last few decades would be reversed. So this, for those who care about equity, this is a particularly challenging time. But there are, I am an optimist because I work in the real world on the inner planets, not the outer planets, like some of my colleagues. So I am always searching for assets, strengths, positives. And I want to talk about some of the work I'm doing to reclaim the mathematical lives of a million students a year. So just a few things about equity. As mathematicians, whenever an issue is confusing, we often start by saying, what is the definition? And addressing equity in that way reveals a lot. When I started, it was called affirmative action. And affirmative action was built on the theory of compensatory justice. The idea was that certain groups were systematically denied opportunity by law. So it was plausible that law should enable them to have some preference in higher ed admissions and other opportunities. In a few years, the counter to that movement, the fact that there were many other groups marginalized, really took the day, and the civil rights community broadened the term to diversity. That term was intended to be more inclusive, but it quickly ran into trouble when challenged by the courts. The claim that higher ed made and progressives made was that diversity is necessary for preparing people for tomorrow for the reality of our society. But if you read the court cases, it was pretty clear that university presidents could not give any examples of the practical or productive use of diversity. I can in my classes, but institutions couldn't. So we had yet another transformation in language. The one that your institutions are probably using, inclusion, inclusiveness. The problem for equity advocates is that each formulation, oh, by the way, when it became about inclusion, no one ever asked inclusion into what. There was no reference to any e pluribus unum. So what happened was each reframing had a different set of beneficiaries, and no one could keep track of who they were in each generation. So it's a fraud term. For those of you on the progressive side of the balance as I am, we have to recognize that the word equity never increases the constituency for fairness or social justice. We've become so tribalized as a society that when people hear the word equity, they decide which side they're on. And one of the challenges for equity social justice advocates is coming up with a language that broadens the base for fairness and that has enough robustness because it's anchored in the best parts of our history that we're a nation organized around not blood, but beliefs and ideas. We need the poet laureate of the United States to help us with this. Well, what does it have to do with math reform? Well, mathematics is in the spotlight. In my day job, I'm the distinguished senior fellow with the Education Commission of the States. That means I meet with governors, policy advisors. I meet with House and Senate education chairs. I testify on behalf of funding for universities and mathematics. In my 45-year career, mathematics has never been in the spotlight the way it is today. And it's in the spotlight for some good things. We'll start with those. And for some pretty awful things that we need to put up on the wall and look at every day. What are the good things? The first is mathematics is incredibly powerful, unnaturally powerful, and essential to the modern economy. I'm not going to go through why you all know that if you're in this room. But the economy depends on mathematical expertise. Now, teachers, I start every fall calculus class by asking, and the high school teachers I work with do this, by assigning these National Academy of Sciences documents. And the first assignment of all students is find three things in mathematics that knock your boots off. Mathematicians, physicists, love to tell their students things that are probably not even going to be turned out to be true. Culturally, don't tell students unbearably beautiful things unless we think we can prove them to them. Bad educational practice. So I start with these. Every week, Siam News. And we start by helping students understand what a precious legacy they are about to inherit if they join our community. The second thing that's important, and I'll explain this one in a minute, is that in the year 2000, there was a structural change in the economy. People of my age typically advanced if they were upwardly mobile in one industry cluster, as economists call it. After 2000, that shifted radically, disruption, cuss point. And now most people who are upwardly mobile cross industries. So what skill is most important if you're going to cross industries? Mathematics, because mathematics is about generality. It's not just about solving particular problems, but whole classes of problems. So it turns out that HR directors and company presidents see mathematics as a proxy for general problem solving ability. Now that may be a little bit of a conceit, but there's enough of it that's true to make a profound difference to your well-being economically. So governors and policymakers know that. That's why math is in the spotlight. We need a lot more people who are quantitatively literate. Even the most anti-hire ed legislators will grant that mathematics is worthy of support if we frame it properly. Well, that's the plus. What about the minuses? I don't know how many of you actually look at the news about your institution to know about your budgets, but this is the biggest crisis in higher ed in two generations. Enrollment is dropping precipitously across the United States and many states. Missouri in five years had a 30% drop in the number of freshmen. Illinois is close to that. That means institutions bond ratings are going down, and that means that it's harder and harder to support universities as they were. Second, for the first time in most states and majority of states in the US, the public no longer believes that higher education is a public good, but they see it as a private good, which means that tuition should be a bigger role of revenue, which works against those who don't have money. Also, in my state, Texas, 63% of voters believe that higher ed is no longer a useful social force for society, and in about half the states of the country, it's half of voters who no longer believe we are useful. That's why we are getting funding crises in our institutions and why Georgia and state after state institutions are consolidating and why you see a massive increase in math majors, UCLA, Austin, but no increase in faculty lines. Just to finish the economic benefit, there's so much enumeracy in the society. Every meeting I go to, someone says that the fastest growing sector of the economy is the jobs that require a master's degree, and they look at these Bureau of Labor Statistics jobs. Yeah, but the base is really low. Mathematicians know this. Where are most of the jobs? These BLS estimates are quite good, actually. Whatever negatives of an economist, these are almost always spot on. Almost all the jobs in the next few years do not actually require even a high school diploma to execute. They may need a high school diploma to get the job, but there's no evidence that you need the skills you learn in high school to do it. So why is this important? Because there's increasing competition for the jobs that pay a living wage. So for example, what are the jobs for low income people that allow them to do the best? Nursing, business accounting, and IT. That's why immigrants typically go for those particular positions. But who actually gets those degrees now from community colleges? 62% are people who started with community colleges with a baccalaureate degree. 7% of all students in the country who go to community colleges already have a baccalaureate degree, because they can't get jobs. They had a biology degree from Duke. They worked at Starbucks for two years, and then they decided they needed to actually grow up, and they went to nursing school. And advantaged whites and Asians are getting all those jobs because the number of jobs that really require something is actually very small. But mathematics is increasingly important for getting them. Now, enrollment crises. You probably look around you in your classes, not math classes, and you see that enrollment, you can see the decline from 2010, and it's about 55, 45 women to men. But who's actually in that lot is changing very quickly. We're seeing an increase in Hispanics, African-Americans, Asians, and a significant decline in whites. And I don't have the projections to 2027 on here, but whites drop like a rock as a proportion of the population. We're gonna get to why this affects mathematics in a minute or two. Who actually completes degrees? This is from the Census Bureau. This means the date is clean. Break the college-going population into four quartiles of income. 77% of the people in the top quartile of income get a baccalaureate by age 24. 9% of people in the bottom quartile of income get a baccalaureate degree. The population that's increasing in higher ed are the populations at the bottom. The poverty is increasing in our society. We are getting better. There are increases in the proportion. This is also originally from the Census data. You can see growth in the number of black, Asian, Latino, white students getting degrees, but the number of proportions are extremely small, still, for students of color. And the rate at which they succeed in college is so low that that is threatening the stability of institutions and the economy. So what we see in state after state is the funding formula is now geared to outcomes, including degrees completed. And that is a harder and harder bar for institutions to meet. So let's just see how math comes into it. Your mathematicians, so when you think of how many, look at enrollment across the whole United States in math courses. You think complex variables. I was reminded of Henry Helsen, my courses in harmonic analysis when I looked at that last talk and how far harmonic analysis has come. But all the upper division courses in American higher ed in math departments are about 8% of enrollment and that includes sophomore differential equations in linear algebra. In other words, the courses that we see as mathematics are round off errors in the enrollment of higher ed. College algebra and below, about two thirds of all enrollment. Now calculus, you think is a college course? Two years ago was the first year with three times as many students start calculus in high school as started in college. So really, when you go back to this chart, calculus is now really a high school course. I taught 120 freshmen in honors calculus. I only had 11 who did not have fours or fives on the AP or BC exam. And some of those had IB and some were foreign. That's probably true in your institution. But if you're poor and you go to community college, you're taking these courses for the first time. So this is what legislators look at and they ask me every time I testify, why the hell are we paying for this stuff twice? Is all of these, if you're lucky enough to go to a reasonable school, almost all the mathematics taught in our colleges and universities, you could have learned in high school. And most mathematicians don't have a clue about this. And if they don't in the future, they're gonna be in deep trouble with their budgets. Now, why does knowing mathematics matter to graduation? This is again, this is the Oregon data set. It looks exactly like the national aggregation. Oregon is in the middle, it's the mid in this distribution. So 100% of people start, that's the rate of the proportion enrolled two or three, four, five years later, depending on what math course you started in. So the students who do not start in a college credit course, very small percentage of them complete and that's a growing majority of students. So these are structural problems of our society. If you look at DeVed courses, remedial courses, if people start at level one, 11% of them ever pass a college credit math course. That's several million students a year. And I'm going to talk about them. And our beloved discipline is a burial ground for their aspirations. What about, this is a large sample from the California State University and Community College System, right? About 210,000 students. What about college, what about college credit courses? Well, for African Americans, 41% of them pass their first college credit course. And about 60% of white students pass their first college course. College algebra has a 45% DFW rate, which we call Texas grades. Massive failure rates. Because we're gonna talk about implications for equity, we gotta start with numbers, that's what we do when we're unsure. We go to the numbers. Here, we're looking at the completion rate of a baccalaureate degree when you look at level of math proficiency on national exams. And you notice that income matters profoundly as does race. They're not the same. But if you take a low income, bottom quartile of income, in the top quartile of math performance on the SAT and exams like that, they do as well as the high income students with mediocre grades. So we have structural inequality and opportunities to complete quality of education. If you go to Harvard, they don't let you fail out. Although professors love to say they have a right to fail. Well, you have a right to fail if you're rich. If you're poor, your right to fail means you'll have student debt forever. And that explains this. In 10 years, virtually every state now ties its public higher ed funding to number of degrees completed and they're moving in the direction of what you actually get out of the degree, not just the degree. This is the evolution of American higher ed. In the 60s, we broadened access. Now we're focused on completion and states are beginning to worry about what do you learn in that degree. And when you look at this data, the three highest failure rate courses in American higher education are all in mathematics. And pretty careful and econometric analyses show that we are disproportionate major factor in limiting opportunities for people of color, low income whites and Asians. The Asians is a silly, Asians, I really should say the universe of ethnicities that make up the Asian box on American check forms. All right, so what do we do about this? Well in 2007, I went back and started revisiting the work I had done at Berkeley 45 years ago that was the basis of my MacArthur. I went out, moved into the dorms, interviewed 20 African American students for 18 months, followed them on dates, went to their parties, learned Cantonese, still addicted to the food and studied as an anthropologist. How students succeed or fail to succeed in college and recognize that the whole enterprise was built on someone's ideas of students weaknesses and built models based on practical knowledge of their assets and hopes. So in 2007, I started to do that with the idea of can I actually as a teacher reclaim the mathematical lives of a million students a year, which I think I've now done. I'm going now for two million. But what was the work? And how was it the intersection of my life as a mathematician and my life as an educator and public advocate? Well, first, in 2007 and eight, I visited 50 community colleges. And when I visit, I learn that you learn nothing unless you go in and teach classes. When you speak to presidents or department chairs, every institution sounds the same. They all use the same buzzwords. When you're actually in a classroom, you know a lot about that institution and the teacher. Some institutions feel like community centers, students ask them the names of their professors, what they're teaching next semester. Other places feel like a gas station in the Midwest at midnight. So I was interested in figuring out how could this failure be possible? Because the students who make it, even if they're poor and go to shitty high schools, they're the best in their high school. And if you're the best anywhere, you should be the best wherever you're going. I strive to be. How can we account for this magnitude of failure that we are share responsibility for? This is our discipline. So what I saw, first of all, was every day, everywhere, good people, faculty members and staff were rolling up their sleeves and doing everything they could to help their students. The problem was they were working in a bad system. So what did I see? California, I did first. In 2007, there were more than 25,000 California college students who repeated a remedial math course for five or more times. Their problem ain't persistence. The legislature introduced a law limiting it to four allowable repeats. How's that for social progress from a creative legislature? Arizona, I went to a community college that prepares firemen. More than half of all the people in the program did not complete their fireman's license because they failed college algebra. They passed all the physical requirements, all the science. They wanted to be firemen, and college algebra got more than half of them have prevented them from entering that job. College algebra, factoring trinomials in creative ways, not something that firemen need every day. That doesn't mean that algebra isn't incredibly important, but its misuse in these courses is unconscionable. North Carolina, I always start the meetings with faculty by inviting some students to speak about their experiences first. I was started as a landscape architect, so I was trained in design before I became a mathematician. You always start with your client. You don't build a garden before you watch where people walk. You don't build structures on weak foundations. You listen to the people you're serving. In North Carolina, the first guy who got up was about 40 years old, and he said I lost my job, I have three kids. I need the college education. I've cashed in my 401K to go here. Can you promise me that if I work hard, I will get what I need? And the department chair was sitting next to me, he said he was in tears. He said this is not some anonymous student from some other community, this guy goes to church with me. Right, our families, our friends, our kids go to school together, and I can't look them in the eye and tell them that these crappy sequences of courses that he has to take have any chance of helping him live a better life. So it was very emotionally wrenching. But for the educators in the room, I saw something much more challenging. What were faculty doing to fix the problem? All their solutions were one-dimensional solutions to many-dimensional problems. You figure that would cross the mind of a mathematician, something might be wrong there. So there were a whole bunch of people who thought the problem was content. Get rid of algebra, teach them statistics. If we change the content, that's really the issue. They don't need algebra. I was one of the early advocates for algebra for all. I didn't realize when I did that that it would become algebra forever for millions of students. But it bothers me that the reform community underestimates the beauty and practical power of algebra. Sequence structure. Students were enrolled often in five courses before they got to a college credit course. Even if they had pass rates of 70 or 80%, almost no students would complete that sequence. Another example of exponentiation, guys. Long sequences of courses will not produce success. Delivery. The problem, let's make it more convenient, use online instruction. This is what I call using modern technology to deliver bad instruction cheaply. Thousands, tens of thousands of students sitting in front of computers pressing buttons with no math, it's a carnage. It's an insult to mathematics, what they're doing. Student supports, fix the student. Right, teach them productive mindsets. Help them cope with a corrupt system. Or let faculty teach with new methods. If faculty only used active learning, this problem would go away. These are crazy hypotheses. Each of these solutions has value as part of a broader system. But the idea that faculty are gonna improve their instruction, have any incentives to do so, and actually have the skill and commitment to do it, they don't get the teaching, actual teaching is a bitch. It's just as hard as doing anything else well. So you had these crazy solutions and then sometimes you'd have a successful pilot in a randomized controlled trial, but they'd never get any students because the dipshit university down the road wouldn't count it for credit. So these course innovations occur in a policy environment, which means that even if you succeed here, and even if you understand that randomized controlled trials are a very bad tool for studying innovation, you're not gonna get scalable success. I went to an award-winning community college. I spent a week with the faculty, math faculty, and I asked them to put up on Butcher-Plocke every pilot project, an innovative thing they could remember in the department's history, 83 innovative projects. Then I asked them how many of them had become normative practice in the department? How many do you think? Yes, zero. So one of the lessons of actual organizational change is that pilots, even with good evidence from randomized controlled trials, never scale. We teach students RCTs, but we don't teach them that there are virtually no examples in social science or international development where anybody ever implements them, largely because by the time they're finished, the project has evolved. And at the end of the trial, it's not like a drug trial. Trials involving society require complex solutions. So what did we do? My friend Tony Breik became president of the Carnegie Foundation for the Advancement of Teaching. We started by interviewing students and identifying why they really were there, what their real hopes were. And what we found, and this has been replicated in large-scale studies, more than 80% of community college students wanted to get advanced degrees. The problem is that some of the letters they gave didn't correspond with actual degrees. So what they were saying, some of them knew, but many were saying, I want a life that I get through education. High aspirations, many of them to get, the poorest kids to get to college have paid a pretty heavy price to get there. So we took these developmental courses, we eliminated them, and we asked, which students could we help with just in time rich instruction, modern social-psychological supports, first-rate advising. And the first thing we produced was the stat way and quant way. Extremely sophisticated evaluation, this is Tony Breik who created hierarchical linear modeling. This is not studies done by education amateurs. Very high-end modeling. What we found in reasonable sized populations is that we could take students, equivalent students, and triple their success rates in one year over what historically took them two years to achieve. Well, we were all full of ourselves. Then in Texas, we learned from the first experiment, this is data from a randomized controlled trial, so we didn't pick these students, right? An independent actor selected the institutions and the students. We showed that we could quadruple success rates. The problem wasn't bad teaching or caring, it was essentially a structural problem. And this will be one of the big points of this talk of the next generation of working on fairness if we actually wanna produce the next generation of mathematicians that looks anything like the diversity of our society and our world. So we thought like we were the only geniuses on the block. And then it turned out that some state systems looked at what we learned. They didn't use our materials, but they took our ideas and they organized them for use at scale. No pilot. Ivy Tech in Indiana was first. They went from a 29, 30% pass rate to doubling 64. Doubling 64, this is Tennessee complete population, not a sample. Tennessee is a state where everyone takes the ACT. So you could see in one year, getting rid of a corrupt system and putting in place a modern carefully designed system, the students that everyone believed basically didn't have the skill or talent to succeed were succeeding in courses. Good studies have shown that they persist at high rates and we have now, these are often in statistics and quantitative reasoning, we've used ASA instruments and show these students are actually learning stuff, the equivalent of traditional courses taught to majors in these subjects. So what have we learned from this part of the work? That improving education, especially if you care about fairness, is not about individuals teaching better, although that doesn't hurt. It's about systemically looking at the structures of our instruction, which we didn't really design, we've inherited it. It's like a Buick engine, we're trying to keep alive from a 1954 Buick. These systems can be redesigned in modern ways to dramatically increase success and help students learn better mathematics. So let me just say that a lot of people said, yeah, well, statistics is easier than calculus. In Tennessee and Texas, students who would have failed college algebra get A's in statistics and then they go back into calculus and they succeed. It turns out that having a success in a math course is just as important as having the prerequisites. Who'd have thought? The students work their butts off so once they believe they can do it in a real course with real content. And I'm like talking rigor. What is mathematical rigor? When I went to these departments, they said mathematical rigor is college algebra. And I'm thinking there's a matter, what does matter like, right, tell us, what's rigor? Rigor is a check on our unfettered enthusiasm. If any mathematician, that's why we need rigor because we have great imaginations and deep hopes. Rigor is the most central thing in any mathematics course. Some institutions put in courses that were easy to pass, that is betrayal of our mission as scholars, as professors and as mathematicians if we ever allow that to be a solution. The deepest betrayal to our discipline and to our students. Well, we've shown that people can take real courses but it requires work at many levels of the system. Some problems you can solve in the classroom, some require the department, some require the profession, some require the institution in the system, some require the culture. And what we've put together with a cross-section of leading mathematicians is a system to bring this about in these gateway courses. What we've learned, it's not just about teaching, that what you do if you wanna have more equitable outcomes and better mathematics is you have to organize the courses around your students, who they are in practical terms. It has to be faculty and staff driven. It has to be supported in practical terms by the leadership. It has to be policy enabled. Stupid barriers and rules that prevent change have to be addressed. And it has to be culturally enforced by leadership. People say that this will not change until you change the culture. Well, human beings don't like, the only human beings who like to be changed are infants. You don't change cultures, you culture change. And the way you culture change is by looking at the internal architecture of culture, which is routines, rituals, and structures. And what we did in redesigning these courses is we systematically looked at the structures, routines, and rituals, and introduced beneficial viruses in them to change them. Now, what about calculus? It drives me crazy that people say students, they can just take statistics. Many students just need a good course in statistics, but if they're gonna continue in statistics, they need to know a lot more mathematics, and we have to build bridges back into analysis for many of them. The idea that this stuff's not important, I can't imagine how anyone mathematical would think that. All right, so the cultural reinforcing. So my colleague, Philip Griffiths, IAS, I think Rafe called him the older generation, fairly, maybe two generations older than you, but a towering figure in our field. Eric, who is the past president of AMS, Jim Gates, first black winner of the National Medal of Science, mathematical physicist. Mark Green, IPAM. Atara Home and me, now Karen Sacks, formed volunteer groups working with the 17 mathematics professional societies. To legitimize these efforts and to develop standards of responsible practice in our profession, right, for modernizing mathematics instruction. And what do we think is important to do culturally in our field? We have to narrow the gap between mathematics as used in the workplace, and mathematics as experienced in our classrooms. But we also have to narrow the gap between undergraduate mathematics and tomorrow's doctoral programs. The ecology of new knowledge production in mathematics has changed profoundly. Given the role of industry, it's not like the old, we do all the research and they translate it. It's humbling to look at where mathematics is actually produced today and what role we as higher ed people play in it. We need to serve as an essential partner to all quantitative disciplines and to take broader responsibility for quantitative education across the curriculum. You're a chair, you know that every other, there's more math taught outside of math departments and it's adversely affecting us and we're not playing a leadership role in it. And if we don't, we're gonna pay dearly. And then last, understand that post-secondary math is a potent resource for students' upward social and economic mobility. If we, tomorrow's mathematicians look like us, it's gonna be harder to build public support for the central discipline that we are. All right, so what did we do to bring this about? Took two years, organized faculty task forces operating under the aegis of governance to lay out the standards and rigor of these new courses and programs, starting in Georgia with my friend Doug Olmer and Malcolm Adams, moving on to Oklahoma, Ohio State Chair Louise Cassian and all 33 department chairs in the state met for two years, redesigning courses. This has to be done by us. We don't want legislators, as they are now doing, redefining college mathematics, executive order in California, legislation in Connecticut, Florida and Texas. If we don't design it, someone else will design it for us. And now philanthropy, the Gates Foundation, Kresge, the Logis Foundations have come together to support this. I chair their expert advisory board. No more pilots, we've learned shit, let's use it. I think that would be a great PCMI t-shirt, by the way. We've learned shit, let's use it. In so many contexts, is that relevant? All right, now a few words about high school. When faculty see this, they say, I can't do anything about it, the problem is high schools. And you've all heard, the high schools say it's the middle schools, the middle schools say it's the elementary schools. The elementary schools say, you know, if only they had better children, it's the in-laws. Everyone can go back in an infinite descent. So this chart that we do poorly in international comparisons, not actually true when you look under the data, but this terrified Americans. Policy makers wanted to terrify Americans because they thought that only a Sputnik-like entity would get people mobilized. Social scientists have found that whenever you tell policy makers about international comparisons, they believe that nothing can be done. It actually has exactly the reverse effect that you'd think from a rhetorical position. What they never showed you was that many states qualified as countries in these studies. This appeared in no newspapers, but it's in the data files. So look at mathematics. Yes, Korea did extremely well with high social costs to their population, by the way, and massive spending on extra out-of-school mathematics. But you know, Massachusetts and Minnesota do roughly, they do statistically as well as Japan. North Carolina does better than Quebec, which is supposedly the greatest North American example. And places like California, which is historically quite weak, big surprise, they're somewhere between Italy and New Zealand. Alabama is between Armenia and Romania. Not a good place to be, by the way, in this. Science, not one newspaper reported the science results by states, except for Singapore, which really kicked butt, Massachusetts outperformed every country in the world on the Thames, science. So what's the point of this? The negative rhetoric has backfired. What used to be a symbol of hope in our society, public education, has become a symbol of government failure. And when we go about reforming higher education, we must not fall into that same trap. We have to know what we're doing well, which is a lot, and we have to have strong evidence for it, or we will get killed in political debate. They also didn't note that there's much greater variance in student performance across U.S. states than across internet countries. 10 points on NAPE is a year of learning, roughly, a quarter of standard deviation, about a year of learning. By the eighth grade, Massachusetts, Texas, and someone else, New Hampshire, have three years more of knowledge than poor kids in California, and this is not only true on federal testing, it's true on commercial tests as well. So instead of learning from Finland, we have a lot to learn from Massachusetts and other states that actually got their shit together. Now, a little about solutions at K-12, and where I see promise. The standards movement is now pretty much over. It went through its policy cycle. The common core is the last gaps, and it did not do what we hoped. We hoped that the common core would be a tool for equity, and what we're seeing, because of income inequality, is that in virtually every district, save maybe San Francisco. The poor kids get the common core and the rich kids get the AP, so caring isn't enough here. Trying to design equity solutions without sophisticated analysis and checking your results. I'm looking back for it, but notice when the standards movement started, it introduced an innovation. The innovation was that scores were disaggregated and the lowest performing group gave you your school rating. So schools for the first time had incentives to work with the kids who threatened their rating. That had an enormously positive effect. In fact, by 2008, certainly by 2011 nationally, black and Latino students did better than white students in 1990. So this is not about the kids. All black students are doing better than white students used to, and in some states, it's a 10 year gap. In other states, it's a gap that's never been closed. When we focus on equity, we have to focus on ways that we can improve it. There's always gonna be vertical gaps because of income inequality. Now, a word about this. College algebra, college credit course. If you're going to be in a math intensive field, you have to take linear algebra. Almost everyone has to take linear algebra in differential equations. And what's the lowest grade that means you know stuff? To you, it's probably A, but let's say kind and say B. I don't know any of us who have gotten to B in these courses, but let's just say, if you had a B in those courses, you could plausibly become an engineer. 20 years ago, college algebra was really part of a path to calculus and engineering. But now we have complete data in three states. What percentage of students who got Bs or better in linear algebra in differential equations? I mean, any linear algebra, not just rigorous proof based, actually took pre-calculus or college algebra in college. What percentage have it on their transcript? Everyone pick a number. So we're looking at the universe of students who got Bs or better in two sophomore level courses. What percentage of them took college algebra or pre-calculus in college? Yell at your number. 0.7%. So we are teaching courses in our institutions. We say in the catalog it's a prerequisite, but the data says it isn't. As an ethical matter, we shouldn't be allowed to say that A is a prerequisite for B if we have no evidence to the fact that it is and we have counter evidence. These are the structural barriers to really working on equity. Now, let's just look at fifth graders who are in the top part of the performance distribution. Lot of black little class kids with college-aged parents do well in fifth grade math. This is the percentage of them by race who ends up in eighth grade algebra. How's that for societal discrimination differences? Not like I want to discriminate against you, but structural inequity. The most talented black and Latino kids almost never end up in honors classes unless their parents are extremely sophisticated. Now I'm just gonna give a, something I never say, a personal example. So I took legal responsibility for two kids, 13 year olds, one African American and one Latino. They both had very difficult lives, drugs, abuse, physical abuse. Every penny I had to get them through high school and college. They came as ninth graders to Berkeley and the deal was they would take algebra. And I, if you know me, I have black and Latino students, armies of them working with me. So they had perfect role models. So I never had children of my own. I send them to school Berkeley high liberal. And I get a note back, I'm so sorry they're not ready for algebra. We can't put them in it. So I said, no, put them in algebra. And they said, no, we're putting them in career math. So I wrote a note and said, I'm a new parent. Can you tell me which careers? Then I get a note saying, we're not putting them in. I don't care who you are, but you can come in and petition. So Sean and Julia were urban fierce. Corn rode hair, you scratch them, they cry, but a 16th inch thickness of urban toughness. So I walk into the school with my arms around both of them. And I had been at the governor's office before I'm wearing a good suit. And I wore my one good suit and I walk in and the counselor looks up at me and says, without me saying anything, I'm so sorry, sir, I'll put them right in algebra. I, the experience of taking responsibility for those kids taught me certain things that I could not know otherwise. I don't know how people understand these things, but I didn't even know what to do with the rage. So this stuff is real, but a majority of white adults now believes that it's whites who are discriminated in public systems. It's passed, it's about 70% of Republicans now. Why Republicans believe that whites suffer more discrimination than blacks in American society? Now, all right, this is a graph. Each dot is a high school in California. Blue is percentage of minority students, unfortunately, who drew this, sort of thought more carefully about the colors. Brown is Latinos and African-Americans. And this is the proportion of students in the school. The size of the dot is the size of the graduating class. And this shows you how many students on the vertical y-axis met the college board's college readiness standard, which means you have a 75% chance of getting a C in college algebra. That's the college board standard. 75% of getting a C in a course that leads nowhere. And you can see the distribution of effect in a very progressive state. In Alabama, it's like there are no outliers, like seven outliers. All right, I wanna end with some positive things and work going on here. But I wanna say that in 2008, this is for the high school teachers who work in urban communities. When we used to work in urban communities in the Civil Rights days, there was a hope. People were poor and felt oppressed, but they could see the future. Society had come to recognize that we needed inclusion and that people had certain rights. What happened in 2008 is a massive crash in black and Latino wealth in the US. So that the median wealth of white households is now 20 times that of black and 18 times that of Hispanics. This is, by the way, from the census community survey. This is not a political. So we need ways really of, we can't ignore these factors. So here's what's happening that's gonna be challenging for equity. Because of the new economy, advantaged parents around the world, this is not a US phenomena, unless sure that their children will have lives as good as theirs. So in the 1890s, kids were born with a silver spoon in their mouth, the rich used physical ornamentation to signal privilege. Now, advantaged parents put all their discretionary money in their kid's supplemental education. In San Francisco, where the district had the courage to eliminate tracking, they created a massive after-school industry in algebra courses populated with whites and Asians. So we now need to do this work in a period of insecurity in Shanghai. The average Shanghai family spent $6,542 a year in American dollars on their kid's education each year. That's more than the national average age of average wealth income of Chinese. Advantaged people are doing everything for their children. How are we going to also do something for everyone else's children? If we don't get this right, I couldn't find the modern chart. This is the chart before the last recession. This is the correlation between fathers' wealth and children's subsequent wealth. We talk about ourselves as a country fueled by the hope of upward mobility. We now are below Britain, basically in the US now, more than any other developed country, family wealth determines child's wealth. When the whole culture of American democracy is built on the idea that you can start anywhere and go anywhere. So we have a lot of work to do and we are better positioned than any other discipline to take this on. Now, what does this mean? Some of this in our classrooms, some of this in our departments, some of this in our colleges and universities, some in our professional societies and discipline, and some in our community. We are in a very bad place now where people have strange beliefs. Republicans believe that almost 40% of Democrats are black and Latino and Democrats believe that a quarter of Republicans make $200,000 a year or more. It's actually only 2% of Republicans make that. So we've gotten to a polarized battle where people have constructed images of each other that are false and dangerous to the polity. We're not only mathematicians, we are citizens, but we are the holders of the most powerful discipline for improving the world and for creating opportunity. As I said, we've learned shit, let's use it. Thank you. If what I'd like to do, I don't take questions, what I'd like you to do is each, speak with your neighbor and formulate the question that you think is most important for me to answer for this group. And I will call on people, not raised hands. So speak to your neighbor. What do you think are the most important question or two that I should answer based on this talk? Or reference that I could give or something of that sort? Do it, make believe you're in class. By the way, I haven't seen a piece of chalk in a long time. I'm gonna take it and put it with my slide rule. I want my grandchildren to know what this was. You think I'm figuring it out? Okay, somebody over here, good question. Over here. We wanted to know some practical suggestions for say like an average high school teacher, middle school teacher, just like somebody with not a lot of power, what can we do, maybe on a smaller scale to make things better for our students? Yeah, for high school teachers, I think the right first unit is your department. One of the things, especially if you teach in urban areas where you have a lot of new teachers, learning to teach in those areas is extremely difficult. Working for social justice in your classroom is even harder. But if you want to improve teaching and mathematical knowledge, it's much better if you have common norms across the school and high relational trust. So you gotta work at the level you can work at. Once you can work at the department level, then you could look at the district level. But always work where you are first. Build a constituency and start with data and don't start with only the negatives. If you're in a high school and you have a diverse population, figure out who you're teaching best. Start with your best successes because that's how you get the courage to expand the number of successes you have. And then join your professional associations where you'll have kindred spirits in other places. All right, question over here. Anybody here? No questions. Are you in it? Teachers know how bad that is. So we came up with a question. You said that students who graduated from engineering didn't have the algebra, pre-algebra prerequisite, but perhaps they came prepared with that and they didn't have to take it at the university. So how'd you get around that? No, no, yeah. What I'm saying is that most students who become math majors or major in fields that depend on us, like engineering, actually have had calculus in high school. And they've increasing proportions have it in the junior year of high school. So we have a problem. The problem is that students who go to poorer communities or weaker high schools don't have the opportunity, on paper it looks like they can make it, but the courses have become much more competitive. So we need to make sure that every student everywhere, that students' opportunity to pursue mathematics isn't the function of their zip code. We have to argue for good mathematics everywhere. We have to argue for exceptional resources for the students who fall in love with mathematics. They deserve special investment. And we have to make sure that everybody's children, not only our own, have a chance to do what we do. And we have to think about how we organize our professional lives to take care of everybody's children because that's what our country needs. All right, this may have to happen over beer. You know, certain things compensate for pedagogical weaknesses. All right, I hope this was helpful to you. I'm easy to find and I'll hang out for the people who want to get more information. But I will say, AMS, IAM, ASA, AMATIC, the education committees of those organizations who are on this, the professional communities are now ahead of the membership. We need to catch up, starting with our departments and our institutes. Thank you. Thank you very much.