Harvard Mathematician Prof. Wilfried Schmid on K-12 Standards & Results

Please excuse typos.

[00:00:00] Cara: Hello listeners. Welcome to another edition of The Learning Curve. It is your Wednesday, which means it’s time for Gerard and I to shoot the breeze. Talk about education and interview somebody really cool. Gerard, how you doing today?

[00:00:43] GR: I’m doing well in wet, wonderful Charlottesville. When we spoke last week, I believe it was in the eighties.

[00:00:49] I was working on my tan and that is not what I’m doing today, but glad to be with you always, it’s always a sunny day, one way or another. Yeah.

[00:00:58] Cara: You always bring [00:01:00] sunshine to my day. It’s rainy here too. I have to say though, lately I’ve been thinking we must both be really old. Cause we liked talking about the.

[00:01:09] Do you realize I’m like, can I talk about the weather? Like the first thing I do in the morning is like, Hey, Google, what’s the weather today. used to always like criticize my father for watching the weather channel constantly. And now I get it. So kind of scary. Oh, Google’s talking to me.

[00:01:25] I just want everybody to know if you heard that in the background she answered. We’re not even going to cut that out. have a question for you as I open this week, given your vast experience. I would like to know how much stock you put in these things called us news and world report rankings, whether it’s rankings of schools, rankings of colleges, , where do you stand on the rankings

[00:01:54] GR: business?

[00:01:55] In a scale of one to 10, I put an eight [00:02:00] because I know deans at different professional schools who use that as a. To figure out what they can do to go up one or two points. So personally I have seen it make a big difference for me. When I was looking at grad schools, it made a difference. And then third, I take an example from Northeastern university I had a president several years ago who moved the school, like 40 points. Of the U S news world report ranking. And there was an entire story on it because the president decided to be a data-driven person. So for me, it’s an eight for others may be.

[00:02:39] Cara: All right.

[00:02:40] Okay. Yeah, I know. I mean, it’s sort of controversial, but I feel like in my opinion, so, you know, folks that use it, but I feel like the public sort of wakes up to this stuff too. So whether we think that the rankings are fair or not, or we like the algorithm that the user, whatever is. It’s something that gets a lot of attention.

[00:02:57] And I think that that’s important. And I bring this up because [00:03:00] this morning and the Boston globe is an article about the fact that the 2022 rankings for the best high schools in the country is out. And I got to tell you, was drawn immediately to it. I texted our producer, Jamie gas early in the morning.

[00:03:14] Cause I was trying to think of like, of all the stories that can talk about this week. And this one for me brings together some stuff that had been thinking about both nationally, but also. Going to get a little Massachusetts centric for a minute. So in this article, it highlights that the states with the best high schools, by many measures, right, like performance and, , AP access and all these things are of course, number one, let’s always pat ourselves on the back.

[00:03:37] We are Massachusetts. Connecticut and number three, which drum roll Massachusetts people. Don’t like to hear Florida just consistently. And I’m sure it’s because you were chief there at one point. But th you know, Florida is this state that doesn’t matter what ranking you’re looking at.

[00:03:55] There are a couple states that are consistently moving up in these measures, [00:04:00] right? Here’s the same, of course, being who I am. I home right in on Massachusetts. And I want to see, so what are the best school districts? What are the schools that really stand out? Gerard? It’s not going to surprise you to know, but boy did it really make me angry to know the best high schools in the state of Massachusetts break down along these lines.

[00:04:23] And I’m talking here top 20 broad-stroke. Don’t worry. I’m not going to go through all of them. They are the exam schools in the Boston public schools and kiss your brain. Cause I’m going to talk about, I’m going to rant about that in just a minute. They are number two. Charter schools in Boston. Mainly there are a couple that are not, but charter schools just predominantly factored into these best high school ratings.

[00:04:48] And they are wealthy suburban districts, which in Massachusetts, Maine, they start with a w usually because it’s Western and Wellesley. Actually [00:05:00] Lexington made it in there, but here’s the thing that really gets me Gerard. So in people listening, who are in states with magnet schools and exam schools, I’m not saying that they’re a bad thing.

[00:05:09] I think they can be a great thing, but here in the city of Boston, as I’ve talked about previously, and we had a good friend, Charlie Chippewan to talk about this as well, we have been just trained to bang the drum about these huge disparity. That exists within the district. Right? So this got me to thinking, I’m going to pull up the M cast results in that’s our state test for what was cited as like the best high school in basically the country, but certainly in Massachusetts.

[00:05:38] And that is the Boston Latin school, which has been around since obviously the beginning of time. And it’s a very, it’s a very Boston Romany school, but this is a school, as I’ve said in the past, a lot of people will send their kids to private. pre-K. through five schools and then try and get into one of these prestigious Boston exam schools.

[00:05:56] And if you look at the results for a school like this, right, [00:06:00] an M cast scores, the students at these schools who are meeting or exceeding expectations , in Boston’s premier exams. You’re up in the 78%. You’re up in the 83%. Like these kids are knocking it out of the park. Gerard, if you look at our Boston high schools, meaning the schools that kids either they don’t test into, they get some degree of choice, but they’re mainly assigned to kids are scoring in the 28 30 range in terms of the percentage meeting or exceeding expectations.

[00:06:37] On our M cast scores. And this ties into something that I’ve been wanting to talk about because we’ve been banging the drum and saying, how can it be that there are these huge disparities within one district? And the vast majority of kids are shoved into these schools that are just drastically underperforming?

[00:06:55] Well, part of the reason is because. Oftentimes when folks say like, look [00:07:00] at the Boston public schools, they’re so great. What they’re doing is they’re factoring in the wonderful M cast scores from some of these very high performing exam schools. And Gerard, if you can’t tell this just gets under my skin to know and use this platform to talk about it again.

[00:07:20] And again. And so as much as I do appreciate us news and world report rankings, and I think that they can shine a little light on something. I think the big takeaway for me here was, wow, here. You’ve got a couple of really wealthy districts and by the way, charter school, Which are serving kids who are not coming from backgrounds, like the ones in these very wealthy districts where homes are probably the average home in a lot of these places is close to, if not above a million dollars Gerard, yet they are getting similar results in here.

[00:07:51] We are not only with charter schools on the rails. You know, we talked about this last week, not going to get federal start-up funds and stuff, but Massachusetts loves to [00:08:00] hate charter schools as well. So I just want a little bit of a. Shout out or I don’t know, just a shout maybe is what I’m doing.

[00:08:07] Some of our education leaders here in the Commonwealth to say pat yourselves on the back for some of these rankings, but pat yourselves on the back for having really excellent charter schools. And please, please, please. Can we take a hard look at the disparities within that are right in our backyard in BPS.

[00:08:22] So dread I am done. I invite you please to rebut anything that I have.

[00:08:30] GR: Question. So if Massachusetts first, Connecticut, second Florida, third where’s Virginia.

[00:08:36] Cara: Oh friend. I didn’t look that far.

[00:08:40] GR: Ah, here’s the point look that far. So let me start with a few points. What I think about rankings of high schools?

[00:08:49] I always think about my American enterprise Institute colleague, Nat Malpass and he identified that if you look at the top performing traditional [00:09:00] public schools, magnet schools, charter schools. Exam schools, others. They have a lot of things in common. One in particular is usually that one. Percent of the students are taking AP courses.

[00:09:13] So there’s already something built in, in terms of having an AP course. I mentioned that because last fall when I had an opportunity to go to a Gibbs’ national education conference in Florida, I moderated a panel that focused on looking at issues of equity and we had the current. Interim CEO for education trusts, who made a really good point, really several points.

[00:09:37] But she was saying, what are the challenges that schools that serve low income students have is they often don’t have access to a lot of AP courses. Even if the student’s bright, guess what your GPA and your transcript will look less competitive to a college. And so she was bringing in an aspect of AP we overlook.

[00:09:56] So what I think of us news and world. I think of Matt, but I [00:10:00] also think about the eight peak components. So that’s number one, number two, it’s not a shock that the best schools tend to be those that focus and work with talented students. Remember as much as people say that charter schools are public, they overlook the fact that public exam schools.

[00:10:20] In fact, many of them have tests to get in. A lot of charter schools, in fact, do not have a test to get in a number of magnet schools have a test to get in a number of charter schools do not have a test to get in. So in some ways, charter schools are actually more democratic than some of the exam and magnet schools that we compare them to.

[00:10:38] But I’m glad that. have exam schools. I’m glad we have specialty schools, but those schools are going to do well for a long time. You bring up something. We often overlook and that’s wealth and household income. The number one school choice program is where you choose to move and buy a house. And where you choose to buy a house.

[00:10:58] It’s going to impact where you go to [00:11:00] school, approximately 83% of the students and the public school sector go to a school that they’re zoned for. And so there’s a correlation between zoning income and outcomes, but let’s also give a shout out and I’m glad you gave a shout out to charter schools. Let me also give a shout out to a school in Virginia.

[00:11:17] It’s called Richmond community school. I’ll start it in the 1970s. It is the only public high school in Virginia, and one of few in the country. Dedicated to taking. Gifted students. Many of them were African-American and many of them who come from financially challenged backgrounds, you and I’ve talked on this show about how many gifted students find themselves overlook.

[00:11:41] The assumption is if you’re a gifted, you’re great. Of course everything’s made for you. We know that’s not the case because a number of gifted students also find themselves with an IEP, a 5 0 4. And we also know that many of them get lost in the shuffle. There are many gifted students who found themselves in juvenile justice facilities, as well as in [00:12:00] prison.

[00:12:00] But you have Richmond community school, which has a great college going. The number of alumni who are doing great things are wonderful. And it’s a school that proves that you can take smart students who are low income and do well. But this program also shows we look at high schools like charter schools that take students who are qualify for free reduced price lunch, but are amongst the best students in the state.

[00:12:26] It just goes to show that poverty doesn’t have to be a proxy for destiny, but we can’t overlook the. That at the end of the day, this is a game of Thrones. And depending upon who you think you are and what family you belong to, we’ll decide who’s going to serve throwing. Who’s not.

[00:12:45] So your story also get me pretty excited and I’m glad to see it out there. There are people who will say all kinds of things about it, but I tell you what, when families are looking to buy a house, they go to places like this. [00:13:00] So let me give a shout out to U S news and world report and for all the drama.

[00:13:05] For having the audacity to rank schools.

[00:13:08] Cara: There you go. Game of Thrones.

[00:13:10] GR: So my story is a little different. We’ve talked a lot about the pandemic and the impact that it’s had on teachers. We know a lot of teachers are not doing well either because of lack of support, own personal professional challenges.

[00:13:24] But one thing we don’t talk about. Is a term in the education space or we talk about contract uh, And then we, we don’t talk about it is we often don’t get into the nuance of teacher licensing. So this story is from Texas. There is a teacher who’s a second grade leader. She joined the profession six years ago and she joined the teaching profession.

[00:13:52] She’s elementary school teacher because she wanted to help students. Well, for the last two years, She’s like, wait a minute, I’m going to be teaching [00:14:00] online for quite some time. And so Stacy decided, you know, what. I’m going to do something different. I’m going to actually lead the profession and I’m going to pursue something else, but she decided I’m going to wait until the end of the school year to leave.

[00:14:17] Is that because she didn’t want to leave her students behind possibly. Is it because she didn’t want to put her principal in a bad spot? Possibly. Is it because she’s got a great. Education program to end the year, and then she will see that done. And then she will leave the professional altogether possibly.

[00:14:34] But one thing she also said is that if I leave in the middle of the school year, I may find my license revoked. And so she’s like, I’m not going to do it. But Stacy is one example. At the same time, she decided to stay in the profession, guests. Over 500 teachers have decided to leave. And in responsive being in the middle of the school year, there’ve been at least [00:15:00] 471 claims filed with the state board of education certification in Texas to say, My teacher left in the middle of the school year.

[00:15:10] He or she broke their contract or contract abandonment. But what does that mean? Well, at least in the state of Texas, they created in 1995, a state board for educator certification and the legislature actually created it because they want it to recognize school educators. As professionals and they wanted to grant educated, the authority to prove and move forward with standards.

[00:15:35] The board has 15 members, 11 are voting members appointed by the governor to six year terms for our classroom teachers. One’s a counselor to our administrators and for citizens, there are four non-voting members who also serve on the board. The governor appoints a Dean of education and a person who has experience working with.

[00:15:55] Alternative education programs, the commission of education appoints a [00:16:00] staff member from the Texas education agency, their state board commissioner of higher education appoints a staff member as well. So they make the decision when they receive a claim from an independent school district, they say, you know what drawer left the profession is.

[00:16:16] The middle of the school year. And he did so without cost or better yet with good calls now in the state of Texas. Good cause means you can leave the profession without punishment, meaning loss of your certification, if it’s for health reasons, or if the spouse is getting a job in a different city, or if you’re even going to transfer schools within the state.

[00:16:37] But if you’re leaving for as some teachers. Health challenges. Some are leaving because they’ve gotten fed up with the way things are going, right now that does not fall under the good cause claim. And so you have attorneys who are working in Texas, who said, they’ve, haven’t seen in number of years, this many people leaving the [00:17:00] profession and some of them are leaving nor are they going to lose their license.

[00:17:04] Which means at least in Texas, if you lose your license, there’s the least one. Where you can’t teach and if you do so in the middle of the year is a good chance you can lose one academic year and half of the other. But according to the reporter, some of the teachers said, I simply don’t. I’m not coming back to the profession, I’m fed up and I’m leaving.

[00:17:24] So there are a couple of takeaways for the listeners. Number one, if you want to learn more about contract abandonment and reasons why people are leaving the profession, in this case, your. State board of education certification in Texas is one example in other states that information or that authority is under the department of education.

[00:17:46] So take a look there because when people are leaving and they’re leaving for different reasons, number two, if state legislatures are thinking about ways of. Keeping a teachers in the profession. Maybe we have to give some thought [00:18:00] to what includes good costs do we put in frustration? Well, maybe not.

[00:18:05] that’s a contractual challenge, but maybe we should broaden the definition to give teachers an opportunity to say, you know, I’m going to leave for a year, but I want to come back and I’d like to come back and teach, but I just need time off. So, one of the few stories, we’ve had an opportunity to talk about regulation and law, but it’s something that I found interesting and interested in getting your thoughts on.

[00:18:27] In fact, I should mention this as well. You could also have your license suspended and not taken away. So there’s also that option. I’ll stop

[00:18:35] Cara: there. I would just say real quick, Gerard, that, what’s amazing to me about this is in a time when everybody’s thinking, oh my gosh, oh my gosh, teacher pipelines, what are we going to do to attract teachers?

[00:18:46] And some are thinking about retention, but most of the new laws we’re seeing are all about pipeline and growing new teachers. And I love this idea that we need to think about making the profession more sustainable for people and. [00:19:00] Troublesome that it took a pandemic to get us there. we could go on about this for quite a while, but you know, Gerard, we’ve got a phenomenal guest actually waiting in the wings for us here.

[00:19:11] So we are going to be talking really quick, coming up with Dr. Wilfried Schmid and he is the Dwight Parker, Robinson emeritus professor of mathematics at Harvard university. So let’s try and put our math caps on. Mine’s not very big, Gerard. It’s not, it’s going to be. Anyway, coming up right after this.

[00:19:53] Learning curve listeners, please help me welcome Dr. Wilfried Schmid. He is the Dwight Parker Robinson professor of mathematics [00:20:00] at Harvard university. He’s a leader in the representation theory of light groups and gave the first construction of the discreet series, improved Blattner conjecture in a minute.

[00:20:09] He’s going to, I hope. Tell me what all. Professor Schmid’s work on Hodge theory has produced wide ranging applications. In 1960. Schmid entered the undergraduate program at Princeton university, graduating with an AB in mathematics. He received his PhD in mathematics in 1967 from the university of California at Berkeley.

[00:20:29] After three years, as an assistant professor. He became professor of mathematics at Columbia university. He moved to Harvard university in 1978. In addition to his research interest, became involved in K-12 mathematics education after a disturbing incident in his daughter’s second grade class professor Schmid went on to play a major role in the drafting of the 2000 Massachusetts mathematics curriculum framework and served on the U S national mathematics advisory.

[00:20:58] In 2008 [00:21:00] Professor Schmid, welcome to the Learning Curve. We’re very happy to have you. And I am curious to know about the experience with your daughter that led you into drafting the mathematics standards for Massachusetts, but let’s, start with you first because you grew up in Germany and you have obviously had a remarkable academic career here in the U S could you talk a little bit about your interest in mathematics at a young age and how you were taught math in German schools?

[00:21:30] Dr Schmid: Well, there are some significant differences between German and us schools beginning in grade five. There were three different school types in Germany, the least ambitious, and these prepared students continued to go to the same school that had attended before for an additional five years in the middle.

[00:21:51] We’re students who went into professions that required better preparation. They attended separate schools that [00:22:00] went up to grade 10. If I recall correctly. And the top level schools were staffed by teachers who taught only two or three subjects for a total of 13 years of schooling. These top level schools provided preparation, FireEye education.

[00:22:16] Teachers at these top level schools were trained at universities, followed by a period of two or three years as apprentice teachers and even teachers at the two lower levels of schools tended to be better prepared than beginning teachers in the us, all my male teachers, and most of my teachers were indeed male.

[00:22:37] I had returned from world war two and prisoner of war camps. That experience tended to make them more tolerant of dissent from students. I certainly argued with my teachers in ways that would not be tolerated by us teachers. My father was a professor of Latin and Greek, and so I attended to school. [00:23:00] That emphasize the teaching of Latin and ancient Greek mathematics was very much an afterthought, but nonetheless mathematics was taught well, in general, one of my parents’ neighbors was the most prominent mathematician in Germany at that time.

[00:23:17] And , when he heard that, I did not think I learned enough mathematics in school. That mathematician gave me private lessons that was truly a remarkable, most prominent German mathematician, volunteering to offer mathematics lessons to a high school student. To some extent I became intensely interested in mathematics as a result of that experience.

[00:23:40] Cara: That’s really quite amazing to have such a prominent mathematician as a tutor. So you’ve got , your own international experience, but you have taught here at Harvard and other. Universities. And you’ve already given us a hint as to the differences [00:24:00] between the system you grew up in and the American system.

[00:24:02] I think it’s really interesting that you could dialogue with your teachers in Germany and didn’t have the same experience here. Can you talk a little bit about. Comparatively at a place like Harvard, for example, what you see in terms of preparation, academic preparation, coming from students from other countries versus the students who are by every definition, elite who were admitted to Harvard.

[00:24:25] Can you talk about the differences in what you see?

[00:24:27] Dr Schmid: first of all, you mentioned Russia and I believe their school system was similar to the Germans. Thing report did an excellent job in teaching students, by making teaching a revered and very well paid profession, the Singapore ministry of education and trust that the writing of textbooks to the most experienced teachers and those Singapore textbooks are ex.

[00:24:54] By tradition in China. Teaching is a deeply valued [00:25:00] profession. Indian society is highly stratified and the Indian students we see in the U S typically come from has that very, that value of education.

[00:25:11] Cara: it’s fascinating that you can locate those differences. Now I mentioned at the outset that you had an experience at your daughter’s school that prompted you to really look at. K to 12 mathematics standards and curriculum. I would love for you to describe for our listeners what that experience was.

[00:25:34] And then can you talk a little bit about the experience of, I mean, this is in the year 2000, so Massachusetts was sort of on the leading edge of states that were even thinking about curriculum standards. This was new at the time. states had them, they certainly weren’t putting them to good use. So I’m curious about how you got there, the experience that led you to this work, and then what the work itself was like.

[00:25:55] Dr Schmid: Well, at that time I lived in Lincoln, [00:26:00] Massachusetts, my wife and I chose to live in Lincoln in part because the Lincoln school. At the highest per capita student spending in Massachusetts, it was also politically liberal.

[00:26:15] GR: My wife and I

[00:26:16] Dr Schmid: assumed that these attributes would make for good schools to some extent that was the case,

[00:26:22] GR: but not in math.

[00:26:24] Dr Schmid: In grades K through five, the Lincoln schools had chosen the program called. Investigations in numbers, data and states that program, the stand, the learning of what are called number facts purposely admitting the teaching of wrong addition and multiplication algorithms and relied heavily on so-called manipulatives.

[00:26:49] That means tiles measuring pictures, measuring tapes. I should say that I was dissatisfied with the Lincoln schools, [00:27:00] mostly because of the K through five mathematics program, the Crimson, the Harvard student newspaper published an op-ed piece that I had written in which I criticized the teaching of math and the Lincoln school.

[00:27:15] Then the New York times published a very long article in K through 12 education that also mentioned my disagreement with the Lincoln case were five schools that brought me to the attention of other mathematicians who are interested in K through 12 mathematics education. At the time, , the Massachusetts mathematic standards.

[00:27:38] Which is a document that describes what should be taught in various grades, where to be a revived. The committee of Massachusetts teachers had written a first draft in line with the ideas of the so-called reform curriculum, including investigations and numbers, data.

[00:27:59] [00:28:00] Start ski at the deputy commissioner of education. And to a lesser extent, the Massachusetts commissioner of education, David Driskell were unhappy with the drops. They contacted a Stanford mathematician, James milligram, who had been very heavily involved in the California. Which proceeded the Massachusetts not force.

[00:28:28] you suggested that start ski and Driscoll contact me. They did. And it asked me to revise the first draft of their Massachusetts curriculum frame.

[00:28:38] GR: Well, let’s take the math wars discussion, just a step further. So when you were working on Massachusetts state standards at this time, We’ve got to remember that there were very unique features about mathematics standards in that state that not only led the state to being a national leader on NAPE going back to [00:29:00] 2005, but it also became really the only state that globally could compete on an international level as related to science and math testing, including Tim’s and PISA.

[00:29:11] Talk to us about the math wars, both sides of the fence. How you were able to help Massachusetts achieve global success?

[00:29:20] Dr Schmid: Well, to be fair to the math education reformers, whom I oppose the school system in the U S had not been successful in teaching math, but it would have made sense to look at other countries that managed to do well in math education and try to emulate.

[00:29:40] Instead the reform has tried to homegrown untested ideas. It’s true that Massachusetts was doing better in mathematics teaching than other states. However, the Massachusetts state standards are only one reason by the state. That’s a, well, it’s a state with two of [00:30:00] the top us universities. And many top medical research facilities.

[00:30:05] These institutions attract a lot of domestic and foreign talent. And then in particular towns to whom education is very important.

[00:30:16] GR: You mentioned. Boston really being a hope for what I would call brain power. When you look at magazines and other articles about the smartest states in America or the smartest cities, Massachusetts, or from a city perspective, Boston will often finish number one, just because of the number of people in the city.

[00:30:35] And yet when you look at Boston public schools math results, Really aren’t that great. And there’s conversation now about receivership, which my colleague Kara has written about recently, but let’s just use that state and even Boston, as an example, there’s a really big debate over why the American K-12 system is so unwavering and implementing true math reform.[00:31:00]

[00:31:00] Is it bureaucratic? Is it ideological? do you see is roadblock.

[00:31:04] Dr Schmid: I’m like in the science and medicine accurate Countrywide, comparative studies in education. Now almost impossible to construct because different states standards specify various times when various topics should be taught.

[00:31:22] The us K-12 education reform was were well-intended. But most of them did not look beyond us borders to see what works instead. They kept trying out various ideas that look new and exciting, but turned out not to be success.

[00:31:41] GR: idea of America looking beyond its borders, be it across the Atlantic or the Pacific ocean, or even going north and south has been a really big challenge. I know you have. Links to Germany many years ago, had a chance to travel to what was then east and west Germany shortly after the [00:32:00] fall of the Berlin wall to look at the K-12 and higher education system.

[00:32:03] And they talked about the apprenticeship program and they also mentioned the. The three things you had mentioned earlier, but the system really focused on the importance of thinking in mathematical ways, not simply to pass a test, but to be able to function in society. You’re at Harvard now Dr.

[00:32:21] Paul Peterson convened a group of scholars, domestic and international to come and talk about students. Well, I ended up meeting the principal of the highest performing math high school in China. And when I went to visit China, he began providing an opportunity to go to the school and meet people.

[00:32:37] Other countries are making this a priority and you identify some of the challenges as why we can’t. Well, let me go to my next question, because as much more fundamental, you’ve talked about algebra one being a gateway course to higher level math. And yet we have a number of students. Who find themselves going into high school without algebra or leaving without algebra [00:33:00] in 2008, you remember the prestigious us mathematics advisory panel, that interview, which reviewed more than 16,000 research, publications and policies on the topic.

[00:33:10] Similar question, even after the work you did at inmap, what can Americans do to really push the idea of teaching students, even basic mathematics?

[00:33:20] Dr Schmid: if I recall correctly, it was Laura Bush, the wife of George W. Bush, who convinced her husband to make education a priority. And to a point the national mathematics advisory panel the members included psychologists interested in how children learn mathematics, educated.

[00:33:43] And mathematicians interested in math education. It would take far too long to enumerate all the conclusions of the tunnel, but that may numerate the main points. The importance of a clear progression off topics, typically in [00:34:00] us schools, mathematical topics would repeat it year after year in the stead, that kind of suggests.

[00:34:07] Each topic should be taught once with adequate depth in school, mathematics is a cumulative subject topics that were covered in prior years would come up again implicitly. And that makes the revisiting the subject really unnecessary importance of preschool. Again, that was one of the main points of the national math panel.

[00:34:31] The importance of preschool. To alleviate the difference between children of different backgrounds. And then there was the issue of adequate preparation of teachers, including in particular teachers in the early grades, a common misconception is the idea. I mean, a common misconception in the year.

[00:34:52] Is the idea that to quote, if you know how to teach, you can teach anything on the quote. [00:35:00] No, that’s just not the case. You cannot teach what you do not understand yourself. Then at the time of the panel, she pocket calculator that said become available. The panel strongly suggested that calculators should not be used in the early grades.

[00:35:16] Because that him, that the learning of what’s known as the number facts,

[00:35:21] us textbooks typically were far too long. And just related to the issue of with repeating topics. Yeah. After a year, of course, then the importance of national tests. at the time state assessment to us real common, but the quality varies greatly making it very difficult to compare the effectiveness of various state curriculum guidelines.

[00:35:48] I have to say that the conclusion of the panel, even though well-founded widely ignored, If I look at my Harvard colleagues, roughly half of [00:36:00] them receive primary and secondary education and other countries, that fact has surely several explanations. One of them certainly is the poorest state of us case with 12 mathematics.

[00:36:14] GR: Very good point about the international dynamic of those who go into the PhD program for mathematics. was just an Indian question for you. Title nine is 50 years old this year. Part of the push was to make sure that. Understood the role of gender, the role that women played in academics today, at least at the undergrad level, we have 2 million more women in college than men.

[00:36:39] We have more women who are enrolled in stem today than 50 years ago. And there are a number of stem teachers. We now have women, we look at. The PhD level for mathematics numbers moving in a better direction than 50 years ago. But surely not as high as we have for men. There’s also an internet, a domestic dynamic of trying to get [00:37:00] more American students to also pursue a PhD in education, independent of race from your years of experience, as a researcher, as an educator, and having looked at this subject uh, the K-12 level and beyond what a couple of recommendations that policymakers.

[00:37:16] Deans at colleges of arts and sciences ed schools. What should we be thinking about to make sure we have more women earning PhDs in mathematics, as well as American students doing the same?

[00:37:27] Dr Schmid: Well, and that’s a very confounding issue. I cannot really say why. There are so many more men in mathematics at American universities than women.

[00:37:42] I just have no excellent. But it is the case. And it is the case in spite of attempts to how should I say, get more women involved in academic mathematics? they are Harvard mathematics department. The vast majority of [00:38:00] members is men. And in spite of efforts that you’ve made to recruit.

[00:38:05] GR: Absolutely. Well, Dr. Smith, thank you so much for spending time with us. Continue the good work and know that you have a platform here in the future to get the message out about the importance of mathematics. Thank you. Take care.

[00:38:54] Cara: And listeners, we always leave you with the tweet of the week and this one [00:39:00] from, a former guest, Barry Weiss I mean, who isn’t talking about Elon Musk and Twitter right now, but she said. Free speech is the bedrock of a functioning democracy. And Twitter is the digital town square where it matters.

[00:39:13] Twitter gives me hives. I’m not going to say for a variety of reasons, but I think that this is a very important point listeners. Next week. We’re going to be speaking with Dr. Eric Hanushek. I think you might know him. He is at the Hoover institution of Stanford university and boy. Oh boy. He’s got a lot of accolades internationally.

[00:39:35] For his economic analysis of educational issues amongst so many other things until then Gerard take really good care of yourself. I can’t wait to be back with you again next week.

[00:39:45] GR: Sounds good.[00:40:00]