Will Bachman is hosting a conversation with Jamylle Carter, a member of the Harvard and Radcliffe class of 1992. Jamylle graduated from Harvard with a degree in mathematics and went on to complete a PhD in math from UCLA. After UCLA, she also held a postdoctoral fellowship at the Institute of Mathematics and its Applications in the University of Minnesota.
Math Think Tanks and Researching Algorithms
Will and Jamylle had a conversation about math think tanks, in which Jamylle described her experience. She had spent four years in a math think tank at a university, and then another four years at a Mathematical Sciences Research Institute in Berkeley. Jamylle fell in love with the Bay Area and decided to stay, working as an adjunct professor, running a Math Circle and working at a science museum in San Francisco. She has been a math professor at Diablo Valley College since 2009. Jamylle explained that a math think tank is a place funded by the National Science Foundation and other private funders for mathematicians to leave their university appointments and focus on their research with other people in the field. Jamylle’s research was applied math, and it was for image processing. Jamylle was researching a new algorithm to solve a mathematical problem. The problem was related to blurring or noise in an image, and the goal was to approximate the original picture as closely as possible. She was looking at optimization methods, which are mathematical techniques that can find the best answer to a problem.
Teaching Math in the Math Circle Program
Jamylle then went on to explain a math circle she organized for middle school kids. The math circle was inspired by a program from Eastern Europe that was designed to expose kids to higher level math. The math circle would also give kids a chance to struggle with a problem and get excited about learning. Jamylle learned more about the program while at the Mathematical Sciences Research Institute.
In 2007-2008, the MSRI sponsored a Berkeley Math Circle for the children of professors and wealthy families. Seeing the need for a Math Circle for a different demographic, Jamylle proposed an Oakland Math Circle for black middle school students in order to challenge the idea that black people can’t like math. With the help of the Exploratorium, the Institute for the Advanced Study of Black Family Life and Culture, and the Museum of African American Technology, she was able to get grants totaling $8,000 to run the Oakland Math Circle. The Math Circle ran hands-on activities to engage students, teaching them that it was okay to be both black and like math.
She taught all the modules, did the recruitment and covered topics such as rocket science, probability and music and math. She also mentioned that in minoritized spaces, students tend to work alone, which can be due to racism, fear of being too nerdy, or fear that they won’t be seen as capable due to their race. Carter’s motivation for starting the Math Circle program was to provide a space where Black kids could come together and enjoy doing math without such pressures.
Designing a New Math Curriculum
Deborah Hughes Hallett was a Harvard graduate student who eventually became faculty in the Harvard Math Department. She never earned her doctorate, and unfortunately the math department still never treated her like real faculty. She was also at the forefront of the calculus reform movement and wrote textbooks to help teach the subject. Deb was an important figure in the Math Department, providing guidance and support to students in need and advocating for reform in the subject.
Jamylle and Will discussed math education and its importance. Will then asked about how to build a high school math curriculum from the ground up. Jamylle believes that everyone should have a solid background in arithmetic, such as fractions, decimals, and percentages. She also suggests introducing courses on probability, statistics, computer science, and using spreadsheets. Additionally, she wants to focus on dimensional analysis and number sense in order to help students become more comfortable with math. Finally, she believes it’s equally important to teach math in a way that avoids creating math phobias and traumas, and to make sure teachers are supported and not overworked.
Jamylle talks about the courses and professors that have had an impact on her life. Carter starts by talking about her undergraduate advisor Deborah Hughes Hallett, who she credits with helping her to graduate. A class that stood out was music 51, a year long music theory course.
08:24 Investigating Mathematical Methods for Image Optimization
11:15 Analysis of Total Variation Method for Image Processing
15:50 Optimization Problems and Finite Time Solutions
18:13 Image Enhancement Technology
20:00 Math Circles and Problem Solving
31:46 Intersecting Racial Identity and Mathematical Affinity
40:13 Comparing Experiences at Harvard and a Historically Black College
48:19 Supportive Mentorship in the Math Department
52:58 Music Theory and Performance
1:00:59 Exploring Equity in Mathematics Education
Will Bachman, Jamylle Carter
Will Bachman 00:00
Hello, and welcome to the 92 report conversations with members of the Harvard and Radcliffe class of 1992. I’m your host will Bachman and I am delighted to be here today with Jamel Carter Jamil. Welcome to the show.
Jamylle Carter 00:12
Well, thank you so much for having me. And thank you for doing this. It is a labor of love. But it is also a gift to our Harvard classmates and to anybody else who wants to learn about us. So thank you so much.
Will Bachman 00:27
That is very kind of you to say and maybe even someday their kids are kids, right. 1020 years from now, it’ll still be out there. So Jamil. Tell me about your journey since graduating from Harvard.
Jamylle Carter 00:41
All right. At Harvard, I was a mathematics concentrator. And I struggled with that immensely. And upon graduating, I did the logical thing, which is to go get a PhD in math from UCLA. So I dove in, I went straight to UCLA. I spent eight and a half years there, I graduated, I earned my degree in 2001. But I in 2000, I started my first postdoctoral fellowship at a math think tank at the University of Minnesota. It’s called the Institute of mathematics and its applications. So I started at UCLA for grad school, went for my first postdoc at the University of Minnesota, which is where I actually completed my PhD.
Will Bachman 01:40
Okay, I’m going to ask you one thing. You’re going in and out a little bit. Oh, okay.
Jamylle Carter 01:45
Okay, let me do this. All right. Okay, is this any better?
Will Bachman 01:51
I think so. So you’re just going in and out. So let’s keep going.
Jamylle Carter 01:53
Okay, sorry about that. Okay, sorry. So, was at this math think tank for a couple of years, extended that through the university for a total of four years, then went to another Think Tank math think tank on the west coast in Berkeley, called the Mathematical Sciences Research Institute. And essentially, I’ve been in the Bay Area ever since that’s the very short version. The slightly more extended version is that I fell in love with the Bay Area. And even though I was only intending to be here for a semester, you know, it’s been what since 2005, so it’s been 18 years. And I actually declined a tenure track position on the east coast to stay. Stay in the Bay Area. Yeah, I did. I did. I just, I just loved it here. I just, I just loved it. And so I just made my life work. I extended my postdoc again. I started teaching adjunct at San Francisco State. I founded and ran my own Math Circle, which is an after school math enrichment program for middle school kids and in Oakland, and I worked at a science museum in San Francisco, and did all of that for about four years and then landed a tenure track appointment at a local community college. So I have been a math professor at Diablo Valley College since 2009. And, yeah,
Will Bachman 03:36
all right. Okay, I got a lot a lot I got to ask you about here. So first of all, okay. And I, I really loved math in high school. And I was like a math kind of math geek a little bit. It was math team state math team. Oh, yeah. But I kind of, I kind of pretty much ended my math career in. Math, applied math. 105. A and B. That was pretty much it for me. Yeah. So I’ve recently opened one of those books and actually, I didn’t even remember not like I didn’t remember how to do it. But it didn’t even remember ever knowing how to do it. Like what? So like, so first question is what is a math Think Tank? I’ve heard of think tanks, Brookings Institution, etc. But what is a math Think Tank?
Jamylle Carter 04:20
Yeah, it is a place funded often by the National Science Foundation, in addition to other other private funders as well. But it’s really a place for mathematicians to leave their typical university appointments typically, and come and focus on their research together with other people who are in the field. The when, when I did mine, when I did my first postdoc, the fee the workshop, they I think was imaging. My research was applied math. And it was for image processing. And so, so people were brought in from all over the world to talk about different aspects of, of using mathematics to enhance images. And so at the think tank is really a place for people to focus on their research and to collaborate with potentially new collaborators. So of course, my dog is on
Will Bachman 05:36
cue podcast very Tay. What’s What’s What’s your dog’s name? What’s your dog’s name? Frankie seeing Bambi the backyard. Maggie has things to say about image processing. So, okay, so let’s dial it back just a little bit. So, tell me it seems that math is one of the maybe the hardest areas to understand when, when you ask someone, okay, what did you do your PhD on? If it’s in? I don’t know if it’s in English or something. And they say, Well, I studied the letters of John Donner’s. Okay, you can imagine reading those letters or even if it’s in chemistry, well, but Matt, tell me, so tell me, tell me a little bit as much, you know, in laypersons terms, what what did you do your, your, your PhD on?
Jamylle Carter 06:23
Yes, I actually was really glad to choose this topic eventually, because I wanted something applied. And I wanted something that that everybody everyday people could understand. So if you have a picture, let’s say it’s a black and white or grayscale image, and maybe it’s blurry, you know, the camera got moved, you know, when you when you took it or whatever. Ideally, you’d like to remove the blur, and restore the picture to what it used to look like, before it got messed up. Now, you know, with today’s technology, you do this with the click of a button. But in 2001, which is when I got my doctorate, there were and still are mathematical procedures, that will remove the blur or remove the noise. And, and restore the picture too, as as I won’t say to its original format, but something as close to the original format as possible. So, so I was really investigating the one of the algorithms, I’ll say, for doing that process. My research was around solving the mathematical problem in a different way than it had been solved before. This is not, you know, a typical algebra 3x plus five equals seven where you know, there’s just one standard answer, it’s, it’s a, because of the noise or the blur is something that is unknown. You’re really making the best approximation possible to the original picture. So I was looking at some different mathematical methods, called optimization methods for for getting as close to the original picture as possible.
Will Bachman 08:24
Okay. Can you dial it up, dial up the technical level, like one or two degrees in, you know, we got a sophisticated audience here, right. So okay, awesome. Awesome. So okay, yes. Tell us a little bit more about how that would work. Because you don’t know, as a computer know how it got blurred? So how do you kind of? Yeah, so how do you is how do you recognize when it would be, you know, sharp because that information isn’t? You know, you don’t have absolutely,
Jamylle Carter 08:51
absolutely, absolutely. The I, the images that I focused on were images that had and of course, this is the dog needing some attention. So just in case you hear a squeaky toy in the back, that is the dog that has Maggie doing her thing, having a bit of good upstairs, so she’s not quite as distracted. So my, the images I looked at were images that had what we call sharp edges, really clear distinctions between black and white or between grayscale and so, what the algorithm would do is to get to an area in the get to an area in the image and determine based on some user input based on sort of a attuning if you will look at the surrounding pixels and decide based on the surrounding pixel values. Is this something Where an edge should be preserved? Or is this something where it should be actually kind of smooth. In other words, the constant color. And the process for doing this. It really comes from computational fluid dynamics. And I know that’s, that’s dialing it up quite a few notches. But it really has to do with like a weighted sum or weighted average, between the noise level in the image. And the preservation of these edges, the preservation of the boundaries between black and white. So it is, it is somewhat of a guessing game. Because like you said, you don’t know originally, what the image is. But this particular process, it’s a total variation method and go into details about that. But the process really kind of does a weighted average of, you know, is this supposed to be a flat region? Or is this supposed to be a region that actually has a sharp boundary between black and white? So let me dial it up a little bit more.
Will Bachman 11:15
So it’s looking for things that it thinks should be a sharp boundary? And then it it’s kind of saying, Okay, well, what adjustments? Let me try a bunch of adjustments and see what adjustments would make it be a sharp boundary? Yeah, something like that. Pretty much. Okay, so how does one, do this kind of work? Do you know, I was in physics, we would always try to take sort of the edge case, the symbols gets to do so do something like, Okay, let me just take sort of a four pixel by four pixel image and see what happens with that. Yes,
Jamylle Carter 11:44
that is exactly what I did. I think I started with, I think I probably started with like, three by three, three by three pixels, or four by four pixels, or something like that. And of course, you know, when you’re doing these algorithms, you always start with the original picture in mind, because you’re testing it, right, you know, what the answer is supposed to be? So, so yes, I think I started and, you know, and I was, you know, doing all the code myself, so I coded in MATLAB, and, and, you know, just writing these, writing this, this optimization code, basically, to see, you know, can I preserve an edge that on this, you know, four by four, image, it’s really, it’s amazing, actually, you know, our human brains are so incredibly complex, and the things that our brains and our eyes can do. I mean, even now, you know, technology is fantastic, but it’s not better than the human brain. So I wouldn’t be doing all of this work, you know, on these simple tests, you know, four by four, five by five images, and I’d be so proud of the work I was doing. And then I would scale up to, you know, 64 by 64, or 128, or whatever. And I would be so proud of my work and, you know, look at the edge, and everybody around me would be like, we’re still blurry, you don’t understand all the work it took just to get this far. So, um, so yeah, yeah, started with, with our simpler test images. And, and really, a lot of the, a lot of the research is really about the, it’s really about how quickly the code can work. The method I was using was kind of slow. And so you know, looking for ways to speed it up without sort of degrading the quality at the eventual image that it would pop out.
Will Bachman 13:46
Knowing when I tried to imagine the postdocs at the math Think Tank doing the work. This is a lot of pencil and paper solving equations, or is this primarily using computer methods to kind of do just the, you know, just problem solving brute force with computers, and you’re kind of sitting there and some kind of MATLAB all day long, or what is the what would I see if I walked around like seeing the researchers?
Jamylle Carter 14:17
Ah, yes. So the researchers, such a great question, the researchers for my field would eventually be coding. I think that talking amongst each other, we would be maybe trying to debug each other’s code or you know, run it with various you know, software systems and various test images. Definitely a lot of coding and a lot of reading about different optimization methods. These These were, you know, for the folks that that hadn’t, you don’t have a tap to have a STEM background and understand this, these were what we call optimization problems. So we were looking for the minimum of something or you could call the maximum, you’re looking for a sort of a minimum energy, which is, and, and so these optimization problems, this is a whole branch of mathematics, right? This is beyond, it’s the general idea for those of taking calculus is the general idea of, you know, you find where the derivative is equal to zero, and then you, you know, run some sort of first derivative or second derivative test to tell whether it’s a maximum or minimum, generally speaking, it’s that type of work. But it’s much more involved and engaged because of the number of variables and because of just the format of the problem.
Will Bachman 15:50
Now, I’m imagining that in, when you get to those sorts of, you know, more sophisticated levels of math for optimization problems, give me an example, I bet there’s some that would be Kanak take till the end of the universe to you know, it, they’re infinitely time to, you know, get a full perfect optimization of something, but you can kind of get a sort of 8020 Answer, like a pretty good answer, where you’re saying, Okay, well, we haven’t optimized it perfectly, but it’s pretty good. And, you know, maybe a finite amount of time, are there problems like that?
Jamylle Carter 16:27
Um, I would really say almost any of the images that we see, you know, with, with our, with our phones, you know, the, the phones are giving the best, the best image possible in a finite time, but I suppose you could always make it even more crisp, right? Or even more, have the comp the contrast colors could be even more distinct? Or perhaps another, what would be another example of something where it’s good enough? Really, it’s the kind of thing that we do all the time as humans, actually, you know, certainly, physicians are excellent at, you know, this is what they’re trained to do, right? They look at MRIs, and they look at X rays, and they look at the ultrasound, and they look through all this stuff that those of us who are not trained, cannot see, but they can see through it, right. And they can say, well, you know, we’ve got to, I’m pretty sure that this right here is, you know, a mask that we want to take a stronger look at, right? It’s what we do all the time. I, when I first got into this field, some of the mathematicians and scientists were really excited that they thought that this research could be so helpful for physicians and you know, this can help you do your work. And the physicians were like, Yeah, not really. Our eyes are way better than what your what you think your computer’s can do. But, you know, they were they were, I think, kind enough to give some funding, but you know, not not too impressed at the time, they might be more more impressed now.
Will Bachman 18:13
So the kind of image enhancement, deep blurring kind of work that you did, is that something that is now built into a lot of, you know, phones, or at least maybe not your algorithm that someone’s algorithm, like, if we take a picture with the iPhone or our Android? Is that already kind of automatically happening those sorts of calculations to?
Jamylle Carter 18:34
I believe it is, I know that there is a mathematical software package. And I think it’s, it’s either Mathematica or it’s MATLAB. It’s one of the two, where they’ve got some image processing, like toolbox or capabilities built in. And one of them does actually reference the type of the type of Deibler and the type of de noising that I was working on. So I just made them there’s certainly lots of other people, but But I remember, because I discovered this, oh, maybe back in 2015 or so. And I was thinking, wow, you know, 14 years later putting us earlier, when I was working on my dissertation, like it would have been, in a way it would have been kind of cool to have this but it also would have had a different dissertation to write about, as well. So I’m not I’m they’re different formats. Mine was more sort of an optimization format. There’s some people that take a statistical approach. There are other folks that take a more functional analysis kind of wavelet approach. So I’m not exactly sure what the phones are using. But I do know that for this particular this particular math gadget, and I just can’t remember was Mathematica or MATLAB that they were using We’re
Will Bachman 20:00
now at the think tank, beyond your work on imagery when people get together, kind of in front of a whiteboard or at the lunch room and chat, totally random stuff. And was there, that kind of, oh, let me problem let’s problem solve on your random other problem.
Jamylle Carter 20:17
Yep, yep, yep, people would have their offices, and there’s lots of whiteboards in the offices and also in the common spaces. And yes, people will be standing around and sitting around, you know, writing out ideas for proofs or for theorems or for just whatever, whatever the topic is at hand. So typically, it’s kind of a quiet environment until they have a workshop where they, you know, bring, bring in mathematicians and scientists, you know, from all over the world. But when there’s not a workshop going on, excuse me, it’s typically Yeah, typically, folks are coding or they’re there. Yep. Small groups. Not too dissimilar from what’s what happened. You know, what happens in colleges all the time in office hours? It’s just that there’s not necessarily one person who knows the answer. The professor. Everybody’s kind of trying to figure it out together.
Will Bachman 21:23
Let’s talk about the math circle that you set up for I think you said middle middle aged kids. Middle School.
Jamylle Carter 21:31
Yeah. Yeah. Yeah. So started with the, one of the, the, one of the final think tanks that I worked at, called the Mathematical Sciences Research Institute. They had sponsored a Math Circle, which I believe these, these things started in Eastern Europe, excuse me, Russia in particular. And the idea is to expose kids to higher level math, university level math, that they would not get in the classroom, to give them an idea of what it means to struggle with a problem, to really get them excited about trying to figure things out and trying to do things beyond what they were doing in class. This is really a big part of how the Eastern Europeans would sort of find the next generation of mathematicians, really by so I learned about this in the think tank that the acronym is MSRI, for Mathematical Sciences Research Institute MSRI, sponsored a trip of a lot of us to Russia. So we could, we could observe the math circles. And and they were in the process of they had already been sponsoring a Berkeley Math Circle, whose participants were mainly the children of professors at UC Berkeley, and the children of other pretty well established well off families. And MSRI decided that they wanted to do a Math Circle that would focus on other students. And they were just kind of toying with this idea. And I was like, Well, what about Oakland, because Oakland is right next door, and it has a pretty different This isn’t cheap. At the time, it was 2005. That’s a lot of Oakland has a pretty different demographic. And they said sure, yes. You know, yes, let’s do it. And it ended up that I ended up doing it myself. So, in 2007 2008, I got three grants, and for a total of $8,000. And I ended up running the Oakland Math Circle, which was focused on black middle school students. And it was hands on activities for the students to do this is all beyond the math that they were doing in class. The idea was that it’s okay to like to be black and like math, it’s those those are not. Because in that ideas that should be separate, then you can’t be black and like math is okay to do. And so it really ended up being a collaboration among the Exploratorium, which was the Science Museum where I had another postdoc and talk about that later. Where I got a lot of great ideas. I was working in a Teacher Institute, which was doing professional development for middle school and high school teachers, math and science teachers and the so the employees there and then the faculty and scientists were super helpful with ideas for what The kids might be might enjoy doing after school. So the exploratorium helped a lot. The fiscal agent was a long title, the Institute for the advanced study of black family life and culture. They served as the fiscal agent. And the location was the Museum of African American technology, which was a museum in downtown Oakland, sponsored by the northern chapter of black professional engineers, I believe this was, and they had a museum in downtown Oakland, who, which everywhere was paintings and posters and books and hands on toys by and about black scientist. So, so yeah, I did this while I was teaching adjunct at San Francisco State. I was teaching calculus and maybe something else. And then I was also doing my postdoc at the Exploratorium. But we ran this 2007 and 2008. I ran it and taught all of the modules did the recruitment. I mean, it was just kind of everything. And but we did topics from rocket science to probability to music and math. And we did something else. I can’t remember because it was it ended in 2008.
Will Bachman 26:33
Do you recall any of the specific exercises or math problems that you covered in that? Anything stand out?
Jamylle Carter 26:43
Oh, yeah. The main one that stands out comes from a book called The math explore math explore. And it’s published by the Exploratorium. And I think it’s, I think it’s called Rock something about bottle rockets or something like that. It essentially is this, the students make paper rockets, they launch those paper rockets up in the air, using a PVC pipe connected tape to an empty, empty soda bottle, and they blow into the pipe and then jump on it. And so that so that the rocket goes into the air, and they use these income inclinometers, which are these handmade, little survey tools to determine how high the rocket goes. So they, they find the angle of inclination, and then they, you know, translate that and they graph that angle on to a grid, and they, you know, do the do the arithmetic for that. So that’s the one that stands out the most. Because the kids get such a kick out of, you know, making their instruments and of course, jumping on the rocket jumping on the bottle launcher, and who can, you know, get that rocket Quetico the highest and it’s a fantastic activity. That’s fantastic.
Will Bachman 28:05
That is bringing back memories. That is so cool. I don’t do bottle rock didn’t do rockets. But what you’re talking about the inclinometer reminds me of fifth grade, we we had this thing on trees, this unit on trees. And we measured the height of the tree by Yeah, a little Protractor with the angle and a little like, yeah, lead weight. And you measure the distance between you and the base tree. And I just thought that was the coolest thing that you could that’s it? Yeah, absolutely.
Jamylle Carter 28:33
Absolutely. It’s all of this, you know, chicken nama tree that’s coded into it, right? Yes. But you’re learning it, you know, real time, you know, without these fancy words like cosine and sine, but you’re doing it. Yeah,
Will Bachman 28:45
that is very cool. I still remember that. I mean, I mean, I don’t remember a lot else from fifth grade, but that tree thing, you know, measuring the trees. That’s great that you did that. Now, you mentioned about, Hey, it’s okay to be black and like math. Just say a little bit more about that.
Jamylle Carter 29:01
Yeah, well, I’m certainly what I experienced and I’m not alone. arry Treisman has done lots of research about this terms turns out that in racially minoritized spaces, one of the effects of being one of the few black or brown students is that students tend to work alone. I certainly made this mistake at Harvard there were a couple of times when I worked with other people, but not as many as I should have and not as many as I wanted to. And a lot of times it’s a combination of things. Sometimes people feel like you know, it’s liking math is too nerdy. You know, you don’t want to sort of show the world that you actually really like it. Other times. There is is really just too much racism in the classroom from the other students, or there’s more, there’s so much of the effect of the stereotype threat where, you know, a student might say, a black or brown student might say, well, you know, I don’t want to show everybody else that I don’t understand everything completely, because then they will think that I am, you know, just a product of, of, you know, my race, and they think negatively about my race anyway. So I don’t want to give them more ammunition for it, therefore, I’m going to keep my mouth shut. And I’m just going to study on my own, and that it doesn’t work. It doesn’t work. These college courses are not designed for students to progress and do well, by working by working alone, it just doesn’t work. It’s well documented. So part of my reason for starting the Math Circle, was to provide a space where black kids could just be together and enjoy each other and enjoy doing math together, and really start to find a community that might not exist in their classes. And hopefully, you know, continue that process through their, through their careers. But yeah, getting the message early on, that there’s no need to separate the different parts of your identity, your racial identity, and your mathematical affinity are not exclusive spaces. They’re not mutually exclusive spaces, they can they do intersect, they can intersect and they should intersect. And so I wanted the kids to have a positive experience around them.
Will Bachman 31:46
Can you share anything about your own experience, you know, being, you know, getting a PhD and postdoc and lifelong, you know, math Yeah, so forth. And
Jamylle Carter 31:58
Absolutely. My, my mother is a retired mathematics professor at Alabama State University in Montgomery, Alabama, where I grew up. I had very strong math, background teachers, all of that got to Harvard figured that I should at least minor in math, so that I could get a quote unquote, good job, whatever that meant. And, but my initial concentration was African American Studies, Afro American Studies was called at the time. And so that’s what I started out doing. I was an frm, major, or concentrator, whatever, math minor. And, but this was, you know, where the class of 92 so in sophomore year, so this was would have been spring, fall of 89, spring of 90. That’s when the Afro American Studies Department started to crumble. professors were literally dying and leaving literally dying and leaving. And the university was really trying to shut it down. Of course, Now, fast forward 30 years, you know, Skip Gates has been brought on board. The department is flourishing in all kinds of ways. There’s nobody’s thinking about shutting it down, I’m sure. But that wasn’t the case. At the time, Skip Gates hadn’t yet arrived. And I’m setting the stage for all this because I had to decide whether I was going to stay an frm major, I was afraid that the department was not going to exist by the time we graduated. And my parents made it clear that they did not have more than four years of money or loans to people clear. So I was like, I gotta graduate. So I knew I was already a math minor. I was like, let me just bump it up to a major. So that’s what I did. junior year, I became a math major. And I got I was already getting my behind kicked anyway, in my math classes, it was so hard. Now looking back, I understand that a Harvard math class is really a graduate prep school. It’s what really what it is, but at the time, I didn’t understand that. So So I struggled. I struggled gold a lot. And I, but I ended up doing a summer program. Generally they’re called our II use for short research experience for undergraduates. And these are summer programs to introduce introduce college students to research in various disciplines. One of my friends from home, Dana Willis Henderson had gone to Xavier University in Louisiana, which is a historically black university and she knew all about these summer research program. She had been exposed to them and she’s like, Oh, it looks great on your resume and you get paid to do research. I was like, what you get paid. So, so I ended up applying and I went to a program at UC Santa Barbara, the summer between junior and senior years, and I met Professor Ken Mallette, who really changed my life, quite frankly, he changed my outlook and my perspective about mathematics. We worked on a completely different topic not we worked on knot theory, which is its own its own thing. But he, Professor maletto, can went to MIT for undergrad. And then he went to Wisconsin Madison for grad school, he understood how much I was struggling in school, he got it. He got it because he had gone to MIT. And so I had any he told me this, he actually shared his undergraduate transcript with me. At the time, I think I was the only person who had seen his transcript. And I was shocked because his grades were worse than mine. Like what? Oh, my God. And he’s like, Yeah, I can’t believe I’m showing you this. And then he showed me his transcript at Wisconsin Madison, which was stellar. And he was just trying to show me to me, you can do this, you can do this. So I got my confidence back. And I. So that was summer after junior year. So starting senior year, I actually was at the I spent it, quote, unquote, a brighten up abroad in terms of presented a different school. It wasn’t at Harvard. I went to the Atlanta University Center, fall semester of senior year, because I wanted to have an experience of attending a historically black college or university. So I enrolled at Clark Atlanta University. But I took classes at Clark at Spelman College and also at Morehouse College. And it’s important because not only just for the environment, but Spelman College in particular, is just a powerhouse in terms of churning out undergraduates who go on to earn PhDs, their math department is renowned for that. So I was in this environment where, you know, all of these women were, you know, applying to these PhD programs. And, you know, I found this wonderful mentor, Dr. Negombo Shah, who, you know, didn’t really know me from Adam, but you know, ended up writing all these all these letters of recommendation for me for graduate school. And I just was like, Yeah, I’m gonna do this, I got and I fight back, I got my, you know, my confidence back. So got back to Harvard, you know, finished up senior year of spring semester, graduated, excuse me, and then went off to graduate school, with the intention originally of coming back to Harvard and showing folks how to teach. That was my original goal. Nevermind that, you know, I, there were some issues with the teaching, for sure. There were also some issues with my maturity as an undergraduate student, but you know, that’s neither here nor there. So yeah, went off to grad school, and prove to myself with a lot of hard work, a lot of hard work, I really could do this mathematics thing I really could dig in and, and figure things out, you know, had a great fellowship from the university. And so I did that that first year, I did really well on my qualifying exams. And then I had to decide, is this something I want to do? You know, now that I can’t not now that I know that I can do it, do I want to do it? And I never really got the answer of yes, this is something I want to do. Even though I ended up completing the degree, I ended up getting the PhD, but it was always a struggle, because my heart really wasn’t in it. I was doing it to sort of prove a point, but not necessarily for the love of the discipline. So I had a couple of changes in terms of my, what I was focusing on, I’d started out focusing on algebra, and then decided didn’t want to do that and switched to applied math, but I didn’t have the Applied Math backgrounds. I had to start over and then I got a new thesis advisor to start over. So So I had two sort of major changes in my program, each of which added at least an extra year to my program. But initially, I was just like, just let me get out. I just, I’ve been here too long. I just need to get out. I just need to be done. And so the first postdoctoral appointment was really a way to force the powers that be to to get me out. You know, when you take a postdoctoral position, the idea is that you are post your doctorate So, fortunately, the faculty at the Institute for mathematics and applications were extremely supportive, and really helped me to finish the finish up. How to
Will Bachman 40:13
experience different at all, if at all, when you were taking that fall semester, at historically black Oh, yeah, yeah. How would you compare that versus?
Jamylle Carter 40:28
So, um, socially. You know, it was all black folks. I probably, I think that was my first college boyfriend and or maybe first, yeah, first college boyfriend. And so socially, it was just, it was just sort of rich and, and, and fun. And I was in the south, you know, was I was in Atlanta, it was a two hour drive to Montgomery, I had a car, you know, in hardware, it didn’t, I didn’t have a car. So socially, it was, it was phenomenal. And just such an IO. And it was, it was such a relief to be in an environment where you don’t have to think about racism. When you when you think about it all the time, you don’t realize how much of a of an issue it is, wait, it is, until you don’t have to think about it anymore, then there’s plenty of other isms. There’s plenty of other isms. There’s colorism and there’s homophobia, and there’s classes and then all of that, that’s very real. But you don’t have to think about racism. And so in that sense, it was a relief. On the other hand, academically, certainly, from my math classes, you know, my math classes at Harvard, were kicking my behind. And I was doing very well. In the classes, pretty much really all my classes, but in particular, my math classes. They were slower paced. They were paced, you know, at a, in a way for us to actually understand the material. So it was actually kind of a shock to me, quite frankly. And this is not this is not to say anything negative, I think it’s actually a positive, when you’re in an environment where you can actually learn the material and not have it, you know, go so fast and so far above your head that you’re just sort of, you know, trying to catch up all the time. So I think it’s a positive, but it was, but yeah, it was definitely a reprieve. I would say it’s a reprieve in many ways.
Will Bachman 42:36
You mentioned how it was comforting to be in an environment where like, race was not an issue, and there wasn’t. What did you experience either overt or sort of, you know, kind of covert in some way, racism at Harvard would tell me about that experience.
Jamylle Carter 42:57
And I did. And I know that my experience is similar to to many other of our classmates. I certainly did. I, I know that’s well, you know, when we were there, the Confederate flag was being flown in, was it Elliot house, some river house, I think it was Elliot, I can’t remember. And then somebody at Cabot house, which is my house, you know, decided to fly it. But then when just sent to Townsend put up a swastika in her, you know, room, then, you know, the campus including completely out of control irate students, you know, went in her room and, you know, tore it down. And so that so the overall environment, I’m not going to say that every individual person was racist. I don’t believe that. But that experience was just one to say that I wasn’t really welcome. You know, when if the if the school allows Confederate flags, but doesn’t allow. And I’m not saying that either one of them should be up. It’s either both to be up or neither one should be and that’s what I’m saying. Right. So that type of thing. And I’m sure there are other experiences that that that I’ve blocked out. But I think it’s mainly for me. I guess just just overall sort of sort of lack of representation, which is, which is why frankly, I think that the friendships that I developed are still so close, and so tight. We really as classmates, especially as black women, classmates, in many ways, we had each other’s backs and we still do. I’ve I mean, I Can you imagine what my life would be like, much less my Harvard career would be like without my girlfriends? I just were so close. You know, we’re so close. I definitely had, you know, an experience in the math department. And I don’t, I don’t know whether this was it probably was racism. I mean, think about a year probably was so. So what I will say is a senior year, spring semester, you know, we always the Q guide evaluations, the faculty evaluations at that point, they were handwritten. And so I, my topology professor, emailed me and said, I know what you wrote about me in your cue guide evaluation. And that’s fine. If you said, you hate me or whatever, but you just needed to work harder. And he emailed me this email me, which meant there was clearly a record doing this. And I, you know, I reported into the game, I don’t know, whatever happened to it, but just the fact that a professor would read the faculty about the student evaluations, decide upon whatever logic was going on in that person’s brain decide that they wanted, you know, who the identity of the particularly valuation was, and then to context that student. I mean, it’s all kinds of ethical problems with that. It’s all kinds of thin skin on the professor’s behalf. And and I think I was the only black person in the class, I don’t remember. And it was inappropriate behavior. But, yeah,
Will Bachman 46:55
it does seem like a breach of security to me. While we’re talking about classes, maybe not topology class, but what, if any, were some of the courses or professors that you had that continue to resonate with you? And it doesn’t necessarily have to be math related, you know, could be anything that just stuck with you, and maybe shape your life in some way?
Jamylle Carter 47:24
Absolutely. I’ll start with the math related. The reason I got through the math department was because of Deborah Hughes Hallett who is who was my faculty, and now I believe, has a joint appointment with the Kennedy School, and the University of Arizona. I think she splits her time. She was my advisor, my undergraduate advisor, and she is the reason why I graduated. She got me through. Wow. And we’re still connected. We’re still close. I think I emailed her sometime last year. And we were talking about a lesson plan actually, that I had written that she wanted to use. So So Deb, just gets all the all my love, all my love and all my
Will Bachman 48:12
appreciation when you say that she’s the reason that you graduated, what was it that she did, let’s give her more of a shout out even Oh, even
Jamylle Carter 48:19
more of a shout out. Well, she was just so she she understood how difficult the Math Department was. She had started I believe, as a graduate students, and eventually became faculty. She did not earn her doctorate and the the math department just never read it really treated her like real faculty. Even though there was another math professor who was tenured, who didn’t have his doctorate either. Andrew Gleason didn’t have never got a doctorate either. He was a famous number theorist, and they had no problem with him, but, but she just was never treated fairly. She’s never treated her like real faculty. So she was the person I could go to, to say, I don’t understand, you know, this, this, this, this concept. And she would give me the encouragement to actually talk to the professor or talk to the TA you know, I could go to her office and cry, or trying to achieve, you know, wrote me letters for for graduate school. But she was just, she got it. She understood just how difficult that concentration actually was. And there were many other she eventually wrote textbooks on calculus she was part of the there used to be the sort of calculus reform calculus that ended up being calculus wars, but whatever. A different way of teaching calculus. She was really at the at the root, she really spearheaded that in many ways. is with your textbook. But at the time that I was there, she was the safe place to go. Her office was a safe place to go where I could just, I could just let it out, you know how much I was struggling and how it seemed like, it felt like, even when when I would ask questions in class, or what I would ask questions at the TA, I still didn’t understand what was going on. And of course, you know, I started to question my capability and all of that. And she was like, no, no, no, you know, there’s, there’s nothing wrong with you know, we, you just have to, we just have to try this a different way. But she just got it, she got it, because she had lived through it. She lived through it. On that, on that notion. Another class that stood out was music 51, which is a year long music theory course, that I took. And at the end of that course, we had to write a song. And my song was I’m coming home, guess what the theme was. But, but I’m really proud of that song I did. It’s a conversation between a mother and a daughter, the daughter is saying she’s leaving college and the mother is encouraging her to stay. I, it’s, I’ve, I’ve copy written it. I have not released it. But it is, I hope that it will be part of some music that I that I’m then working on recording and releasing. I hope that it’ll be finished by August. That’s That’s my plan. But, but yeah, that that class, not only the culminating project of the song, but in music theory, a lot of what we did was was to analyze songs, and analyze them by their chord structure. And it means listening carefully, and, and understanding how the chords relate to each other. Which means you have to listen carefully, and you don’t stop listening after you leave class. So all the music that you hear whether you want to or not, you start analyzing it, which on the one hand initially was kind of annoying. I remember, you know, we were complaining to the professor, like you’ve destroyed music for us, because we can’t listen to music anymore without analyzing it. But ultimately, it becomes really helpful, especially as you start to play more improvisational styles like jazz and gospel and funk and whatever. Because in that you’re a lot of most folks are playing in terms of the chords and the chord structure. Anyway, so it really was fantastic. Prep,
Will Bachman 52:58
and have you for continued to be a musician’s and you know, what do you what do you play? Do you perform?
Jamylle Carter 53:05
I do? Yeah. So I play piano, and I sing, and I compose songs I played for so when I was in Minnesota, I played for a church, a children’s choir at a church. And I think I did that for three years. Was it three, three or four? It was three years. It was always my dream to play for children’s choir. And so I did. And the choir was led by these wonderful, wonderful church volunteers. Nicole Foster was the the director and the the choir tripled in size. Well, well, while I was there, it was fantastic. I moved to California and started playing for for another church for my church, in this in Oakland, and I was the church musician. They’re one of the church musicians there for 10 years. Wow. So So yes, yes. I have continued to play and, and sang and compose.
Will Bachman 54:08
Yeah, question about math education. So if you are going to build high school, math curriculum from ground up, would you scrap anything and replace it with anything? And I’ll give my two cents just kind of tell you? And I see react to it seems to me, you know, and I loved math, right. I love math. I was a physics major. I love math. But seems to me that there are some things in math that are not taught in high school, which would be more valuable than some of the stuff that you get, like, I would probably think about including probability, including maybe some, you know, probability statistics, maybe put in some more computer science, maybe even just have a course on how to use a spreadsheet. And I have not really used trigonometry. Pretty much frankly, I had a year of it. And I mean, other than doing a little bit of sine cosine stuff in calculus. And I, just for most, you know, and I was even more relevant than most people, you know, Physics major as a nuclear trained submarine officer, so did all the math, but I have not used a lot of that calculus or a lot of that trigonometry. I’m curious what your thoughts are, are we teaching the right stuff to our kids? Yeah,
Jamylle Carter 55:22
I remember, you asked this. I can’t remember the guys name. But he’s a math teacher somewhere in in Ohio. I want to say his name is John Unger. Did I get it right? Yes, I remember that question. I was kind of prepped, I was kind of ready.
Okay. Got it. Yes, yes.
Jamylle Carter 55:39
Yes. So, um, so yes, there’s all kinds of ways that we need to improve not only what we teach, but how we teach it. And there is a significant movement. In terms of changing there, there are lot of students now that come to college, having taken statistics, and, and some basically a data science type curriculum. In high school. This is happening already. What I would love is for all students to have a solid arithmetic background, meaning I want everyone to be comfortable with fractions. I want everyone to be comfortable with decimals, and everyone to be comfortable with percentages. And knowing how to go back and forth between those three ways of expressing a number. I would love for everyone to have basic algebra, but a solid understand when I say basic, I’m talking about like elementary algebra, things like that. But mainly in terms of the skills that I would love for people to have dimensional analysis, you know, can you handle fractions? Can you handle you know, one, I’ll just give an easy example. You know, one half is equal to how many sixteenths right? It’s those types of skills that students are lacking. Students are lacking folks, according to calculators into computers, and don’t have number sense, you know, is one half bigger than three fourths? Or is it less than? How do I figure that out? But so there’s that there’s that that’s a subject matter. But equally as important, if not more important, is that the way that it’s taught, and so many, so many students have negative poor experiences in mathematics, you know, they get to us in college, and there’s all kinds of math phobia, and math, trauma, and math, anxiety, and all of these things that we have to address. Because people were dismissed, either, you know, the, and I don’t want to blame teachers, you know, k 12. Teachers are the real MVPs in my book. And they are often under supported, certainly underpaid, and been very much overworked. So I think that many teachers are doing the best with what they have. But they just don’t have enough support enough background in terms of overcoming their own math, phobias, and math traumas, so that they don’t pass it on to their students. And, and there’s also there’s this false notion that mathematics is neutral. The subject might be neutral, but the people teaching it are are inherently political. So I would love for everyone, regardless of race, color, creed, sexual orientation, all of that. And more disability all ability, I would love for everyone to have equal, not not just opportunity, but equal encouragement, equal encourage, my mom was a math professor, I could go to her. And I did go to her and say, I don’t understand why three fourths times four thirds is one. I understood why 1/3 times three was one that I could visualize. I couldn’t visualize it with the fractions. And even my mom would be would start what she was doing, which is either grading papers, or doing the books from my dad’s pharmacy because my dad owned and operated an independent pharmacy and she was the first bookkeeper had the books went to the accountant. So she was working, right. She was working, but she would stop what she was doing to help me so, so I had a place to go. And I always had, you know, great math teachers would, you know, I did I private school, whatever had great math teachers. And most, most students don’t have that. So, you know, if I had to, if I were able to design curriculum, it would, it wouldn’t just be what’s taught, it’s how it’s taught, taught with appreciation and taught with, with an appreciation for the inherent brilliance that students bring to the classroom, you know, that there’s a lot that our students already know, there’s a lot that they can teach us. And it’s really our job as teachers to be open to their brilliance, and to recognize it and to try to support it and certainly not to try to squash it, you know,
Will Bachman 1:00:59
yeah. Jamel Carter, thank you for joining for listeners that want to follow up with you or track what you’re doing. Where would you point them online?
Jamylle Carter 1:01:11
I would say LinkedIn is a good place. I’m also on Facebook. So either one of those LinkedIn or face Facebook, I use my real name. So it’s easy to find me either way,
Will Bachman 1:01:23
we will include your LinkedIn URL in the show notes. So if you want to catch up and reach out, send a connection request to Gmail, it’ll be there. Gmail, thank you so much for joining us as a lot of fun.
Jamylle Carter 1:01:34
Thank you Well, for doing this. It’s just it’s like I said, it’s a labor of love, but it’s really appreciated. Another important experience I had was with the Harvard Radcliffe cool and the singers. were started in 1974. Harvard students, Radcliffe students, students from the Boston area, black students to come together on a regular basis. It really ended up being a sanctuary for me and for many other students. So not only did we learn spirituals and gospel and African folk songs and contemporary music, but I learned that I was a soprano, not an alto. I cut my teeth as a student director, I became part of an acapella group within Colombo called Sisters. I really learned to direct I learned to arrange. I learned about choir dynamics, and I just found a family. So Khumba was really super important in my undergraduate career.
Will Bachman 1:02:46
Thank you very much.