“Service courses” are courses like college algebra and calculus that are taught by math departments to students not majoring in math, who take those courses typically to satisfy a major or general ed requirement. These courses are notoriously problematic, often with high drop-fail-withdraw rates or big gaps in student performance across demographic groups. Recently, I went looking for departments who are teaching service courses well. I found the math department at the University of Texas at San Antonio. In just a two-year period, the DFW rate (that’s drop-fail-withdraw) in their service courses dropped from 35% to 25%. That’s a huge improvement in student outcomes, especially for a department that teaches eight or nine thousand students each year.
I reached out to Juan Gutiérrez, professor and chair of mathematics at UTSA, to ask about the changes the department made that lead to this improvement. He very graciously sat down with me for an interview, and I am very excited to share it here on the podcast. Juan shares some of his rather amazing life story, his goals for students success especially for the Hispanic students who attend San Antonio, and the data-driven and highly successful changes his math department made to college algebra, calculus, and other service courses.
Juan Gutiérrez’s faculty page, https://math.utsa.edu/directory/juan-gutierrez/
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[00:00:00] Derek Bruff: Welcome to Intentional Teaching, a podcast aimed at educators to help them develop foundational teaching skills and explore new ideas and teaching. I'm your host, Derek Bruff. I hope this podcast helps you be more intentional in how you teach and in how you develop as a teacher over time.
As a mathematician in the field of teaching and learning, I am frequently asked to weigh in on the design and implementation of what are usually called service courses. These are the courses like college algebra and calculus that are taught by math departments to students not majoring in math who usually take those courses to satisfy a major or general education requirement.
These courses are notoriously problematic, often with very high drop fail withdrawal rates, DFW rates, or sometimes big gaps in student performance across demographic groups. It's all too common for a math department to have the lowest average course rates of any department because of these service courses.
Recently I went looking for departments who are teaching service course well. Thanks to a tip from a colleague on Twitter, I found the math department at the University of Texas at San Antonio. In just a two year period, the DFW rate, that's drop, fail, withdraw, in their service courses went from 35% to just 25%.
That's a huge improvement in student outcomes, especially for a department that teaches eight or 9,000 students each year and a great improvement With just two years of change. I reached out to Juan Gutiérrez, professor and chair of mathematics at UT San Antonio to ask about the changes the department made that led to this improvement, and he very graciously sat down with me for an interview.
I'm very excited to share that here on the podcast. Juan shares some of his rather amazing life story, his goals for student success, especially for the Hispanic students who attend San Antonio. And the data driven and highly successful changes his math department made to college algebra, calculus, and other service courses.
Thank you, Juan, for being on the podcast today. I'm excited to have you here and learn more about what you're doing at UT San Antonio.
[00:02:20] Juan Gutierrez: It is a pleasure. Thank you for having me today.
[00:02:23] Derek Bruff: So I've been reading up on you a little bit and it seems like you have quite a life story. Without telling the entire story, I would like to ask you about maybe a little piece of it, of your choosing.
Can you tell us about a time when you realized you wanted to be an educator?
[00:02:41] Juan Gutierrez: Oh, that's very clear in my mind. Although you could have not read that because I have not published that. It's part of a collection of a stories I'm preparing for my children. So they can see a different version of the world.
I was three or four. It's hard to tell. It's a very old memory. My mother was going through her purses, jackets, pants in between the cushions in the, in the sofa trying to find coins to buy two eggs for breakfast. Because we were poor and she didn't find any. My sister and I went hungry that day and I remember my mother telling us,
this cannot go on. She was a secretary in a very large government organization. She had a fourth grade education, although she didn't have a fourth grade intellect, she used to read a lot. So within a year, she completed her high school diploma, the equivalent of a GED. Six years later, she graduated with a law degree.
And she did that by going straight from work to school at night and then from school at night, she would arrive, I think because I wasn't awake, 11 pm or midnight to make food for her two kids. . So we would see her quickly in the morning before we went to school. We would come back to school, opened the door with the the key that I had hanging from my neck.
I was one of these key latch kids. And we would see her the weekends. But that sacrifice paid off because we left poverty. That made a profound difference in her life, my life, the life of my sister. And that's when I, I realized the power of education is infinite. It can lift people, it can change life trajectories, improve people's lives.
And that's I, I think that's, that has been the driver. It might have been a too long of a story, but you asked.
[00:05:09] Derek Bruff: That's amazing. It's powerful and I can see why that would shape kind of who you are today and, and what you, what you've devoted your life to. And that actually leads me to my next question cuz I, I don't always see a mission statement on a cv, but I saw that you had one on your CV and it says, have the face of success match the face of society.
what do you mean by that? And what does that look like at at UT San Antonio?
[00:05:37] Juan Gutierrez: It's a perennial struggle of humanity. I believe. There are many mechanisms in all societies in the world by which certain groups gain power and advantage and they try to keep it at the expense of others. In the United States, it has taken the
the face of racism particularly, but there are other other forces that shape these dynamics. And what we observe, particularly in the US society, more pronounced in Texas and very true in San Antonio, is that those who hold power might look nothing like the people that form the communities. And I have to take something back because in San Antonio actually
the face of power matches the face of society in in a very interesting way, and this is something that has been increasing throughout the years. I became aware of San Antonio in one of the national meetings of the well, American Mathematical Society, mathematical Association of America, the joint mathematical meeting, one of the entry points for the Henry Gonzalez convention center is a long hallway, and if you pay attention to that hallway, you will see plaques for different years holding the names of the city council from probably the early eighties, if not late seventies, all the way until very recently. And you see the, the change in the names. There were very few Hispanics at, in the first plaques on the wall.
But at the end you see many, many more names of Hispanic origin. This is important because an Antonio is a region that has a 60% Hispanic population. So you would expect if the system were cleaned to observe a similar participation in the structures of power in the city, and San Antonio's going that way.
But let's look at the university. we have less than 20% Hispanic faculty, and this is replicated throughout the nation, except in a very few places in which representation of faculty who look like the students really match what is happening in society. So that's, that's what it means that people who succeed, who make it to positions of leadership,
probably should look like the community and the society they are serving. Nothing sends a stronger message of you do not belong here as having those who are decision makers and role models looking nothing like you. In fact, one of the first observations from a gigantic data analysis of students here at U T S A indicated that there is a nearly linear correlation between the amount of Hispanic faculty
and success for Hispanic students. That is the more Hispanic faculty they enter in contact with, the more likely they are to graduate and make a progression through, through the end. And that's fascinating is we have heard this as an aspirational claim. Say, well, students should be reflected in their in their faculty.
Well, now we have the proof. Indeed, it makes a difference.
[00:09:17] Derek Bruff: So let's, let's talk about math instruction. According to your department's website, you, your department teaches about 12,000 students a year 12,000 seats in courses. And I mean, the reason I got connected with you is I was looking for examples of math departments that were doing.
what are sometimes called service courses really well, so the, the, the math courses that are taken by non-majors that are often required for general education or particular program requirements. And I imagine you have a lot of students who take those courses. A lot of those 12,000 are probably not math majors.
And I saw that your drop fail withdraw rate, the DFW rate, which is something a lot of administrators and educators pay attention to, was I think 35% in fall of 2019 and it dropped to 25% in the fall of 2021. And if folks haven't looked a lot at at DFW rates, that may not seem like a lot, but that's a lot more students who are not dropping, not failing, not withdrawing from these, these courses.
How did you go about doing that? Because that's a big change in a, in, in just two years.
[00:10:31] Juan Gutierrez: It is a big change. And even though we only show two semesters as means of conveying the information, we have data going back to 2014. So I know that between 2014 and 2019, they averaged D F W was 38.5%. And if you see the number of students, that is very, very substantial.
So let's start first at the high levels. What happens when we have high DFWs? Let me start with the number of students that we received for the fall semester. 6,000. Nearly 6,000 here at U T S A. It's a very regular freshman class for a university that serves 35, 34,000 students. Yeah, our graduation grade being an urban serving institution
is about 50%. That means that of those 6,000, 3000 might never graduate. Now, if the average income of a person with a high school diploma is about a million dollars less than a person with a bachelor's degree over a lifetime. 3000 times 1 million is 3 billion removed from the regional economy in average year after year after year.
And the problem is not the money that we do not collect in taxes. The problem is that we are saddling people with debt and binding them to poverty. That's the real issue. And that goes back to the story that I remember of my mother struggling to make ends meet and how education was transformational.
It's a human tragedy when we allow this to happen. When we look at data, what are the, the main factors that contribute to a student attrition to a student? Failure? Math is the single largest influence. After math reading. So as the joke goes, and it's a joke. It's, it's not that grammar, it's a joke.
English is important. But math is important-er. In a quantitative sense, you could say, or you could say that math is the largest eigen value in this system, twice as important or as in terms of correlation as compared to English. Now, when a student fails math in those introductory courses, which are
close to 97% of all the credit hours that we serve. Because if we serve 12,000 seats, our majors is less than 300 . So you can imagine that the vast majority of what our department and all deparments of math are doing in the nation is serving service courses.
[00:13:18] Derek Bruff: This Is college algebra?
[00:13:20] Juan Gutierrez: Exactly. Precalculus, calculus. Calculus, 1, 2, 3. Exactly. Those courses, the, the STEM core, the backbone, all the education in stem, well, not only stem. If the students are going to sociology or music, they have to pass the core curriculum, and the core curriculum has a quantitative component, and that component is going to be college algebra.
Now, we don't teach one single version of college Algebra for everybody. We have a college algebra for liberal arts college, algebra for social sciences, college algebra for stem. and they have different requirements different approaches, different pedagogical needs. So we try to serve those populations.
But when you put 12,000 seats, this certain number of students are seats because some students take more than one course per year. But that's the number of that is the capacity that we have to install. It's probably of between 8,000 and 9,000 students, which is still a lot. It's close to one third of the university going through our department every year.
Once you put that number of students in these introductory courses, you see why we have such a large footprint and we know that if a student fails an algebra course, pre-calculus, calculus one, et cetera, they're much more likely to change majors. There is nothing wrong with sociology and psychology.
That's not what we're we're trying to say, but people should not end there because they fell off some other wagon. People should end there because that's what they want to pursue. So by creating a mechanism to keep people in those tracks, we might be able to match students with their greatest contribution potential with their passions.
And that's where this becomes very, very important for the trajectory of so many students. So definitely mathematics is the gateway to social mobility.
[00:15:26] Derek Bruff: I've talked to other math departments that have struggled with these service courses. And with, you know, similar DFW rates that are just really problematic.
And I often think about lots of different levers that a math department could pull. And I don't think there's one lever that solves this problem, right? I think you have to operate at multiple different levels. What are some of the levers that you've pulled at U T S A to, to see that change? What are some of the changes that you've made structurally or pedagogically to math instruction that have started to, to see more student success?
[00:15:57] Juan Gutierrez: Very well. So now that we have defined the importance and the size of the problem, let's see, how did we go about attacking this problem? It was a multifaceted or multidimensional strategy. First of all, is the community, the community of instructors. We have to create that sense of community. How did we do that?
Well course coordination. We have for each one of these fundamental courses, the STEM core that are courses, some of them have 20 sections with multiple instructors. All instructors meet at least once a week. At least, and they discuss the topics for the week, the homework problems, the student learning outcomes, and how are they mapped to homework problems and test problems.
Since we have so, so few opportunities to measure the performance of the students with assessments, homeworks, tests, et cetera, every question should be very intentional. , it's because we want to measure something very specific that within the students need. Now, course coordination seems natural, but it was also identified through data analysis.
And I have to mention the importance of doing data analysis for institutional transformation. We studied 5.5 million credit hours, 86,000 students, five years . It's a gigantic dataset. That was absolutely essential because we could, for example, measure and visualize the standard deviation in DFWs for every single course, and it was very evident that a course with a D FW between five and 85%.
And, and, and a very good distribution is not like these are two extremists and everybody's concentrated. No, it was a uniform distribution in that range. That is the signature of lack of course coordination. And indeed, I interviewed faculty and they were telling me, yes, every instructor select their own homework and they can select the level of difficulty and they do as many tests as they want or not.
And it was the wild West. Lot of independence.
[00:18:19] Derek Bruff: Lot of independence. But if I'm following you, a lot of very different outcomes. So some sections might have a very low DFW rate. While others might have a very high dfw. And it was kind of evenly distributed there, so there was a lot of variance by the
[00:18:34] Juan Gutierrez: Exactly. And one of the arguments in favor of this variance was, well, academic freedom, , to which I responded to all my faculty, academic freedom in the STEM core means nothing. You can go and deliver your course in whichever way you want, where in whatever you want, but you need to be consistent because this is a sequence of very strict, a very strict chain of co-requisites.
If you want academic freedom, send a grant proposal to the National Science Foundation about galactic commerce, teach a graduate level course, and then if you get students registered for that, teach it as you want it , but not in the STEM core. The STEM core has to produce a, an outcome that is homogeneous because too many things depend on that.
It's not that people take calculus for the sake of it. In in, in stem, there are a number of courses that depend on that knowledge and they need the students coming with a baseline of knowledge, and the subject is difficult, that we make a lot of effort just to guarantee a baseline. It has to be homogeneous.
So that's how we approach this. We have to do coordination because we need to produce homogeneous product. Then I asked our faculty in college algebra. Since we know our list of lessons, we have a lesson planned for every course. And by the way, this was also very important. Not only list in one paragraph, the objectives of, of the course, not only one paragraph.
Give me a table with the list of lessons one by one, mapping for each one of those lessons. What is the student learning outcome? Why are you teaching this lesson, and what are the prerequisites for this particular lesson? So this led to the creation of a network of about 1,960 something student learning outcomes throughout the mathematics curriculum.
Then since we have this list, I commissioned every course coordinator. Please produce the top 10 from this list. Top 10 student learning outcomes that students should have coming into your class and the students should acquire leaving your class. So we aligned and compare what happens from college algebra to precalculus.
From precalculus to calculus one, calculus one to calculus two, and so on. And. To the surprise of some, and not to the surprise of many, they did not align. What the instructors of, let's say, precalculus thought that students coming from algebra should know, should master, didn't coincide with the greatest emphasis placed by the instructors of Algebra.
And we're talking about very competent faculty here. I have to give credit to our community here at U T S A , our instructional faculty, they're fantastic. They really know how to teach they . We have a very experienced, very stable workforce. We have very low rotation of personnel. , it's a very good community.
There are personal connections, professional connections. It, it's a very healthy community. And having all these professionals who know what they're doing. Who have experience, who were convinced that they were delivering the, the, the best that they could just to realize were misaligned. That was transformative because then it elicited conversations across different courses.
Now we're, we're having college algebra talking to Precalculus. I have started stimulating a rotation of faculty. So those teaching college algebra should go to precalculus and vice versa and pollinate those communities so they sit and experience how these students make the progression.
So that was part of, that was the other component. We call that the vertical alignment of the curriculum because we ensure that topics. Have the enough emphasis so that the skills that are essential in the next level are truly developed in each one of these courses. That has been transformative as well.
So, so far we have course coordination. , the identification of a student learning outcomes and the mapping to individual lessons. The vertical alignment of the curriculum, and I believe that this is, these are the main factors that contributed. Now there is one more, and that one more is also coming from data analysis.
There was a very clear cluster in well quantitatively and very easily seen in a graphical representation of faculty who were serving too many students. And those faculty were having a high level of DFWs. And the way we visualize this and how we identified is we created a table with total number of students served and average levels of DFW for every faculty.
And when you put that in a plot, what you have in one axis, dfw, and then in the other access number of students served, and then you put a bubble for every faculty member you find that find this cluster. This cluster has very large sections, two hundred or so. 11 instructors were producing half the revenue of the department.
Our department produces in credit hours about in tuition, about 20 million per year, and they were producing $10 million, 11 instructors out of 60 with an average salary of 28,500. Okay. Which is an absurd quantity. Was. 2019. With data, with the numbers, it was relatively easy to go to the upper administration that in the provost and say, we have a problem.
Yeah, we need to correct this. So we corrected the situation. We less than halved the classroom size. So now our largest classroom size is 60 something and we're trying to bring that down. Most of the classes are under 40 and 50. Okay. And we doubled the salaries of those faculty who were underpaid. And guess what happened?
Suddenly those faculty don't have to go and Uber at night. They don't have to overextend themselves teaching all over the city. Now they can focus and the quality of life has increased because now there is no a slavery of go and grade 200 tests. Once you put all these things together, the transformation was very quick, I mean, and, and this is from 20 20 19, and the pandemic, of course, introduced noise in the system.
So by the end of, by the beginning of 2021, , we were already at this level of 25% and since we have had seven semesters with an average D f W of 25% and we want to keep it dropping, we know because we're looking at data, what can we tweak? What knobs should we turn to continue this optimization? So this has not ended.
We will keep doing it. But what we have created at U T S A is I hope something that can be transplanted, can be replicated, and I hope it will become a model for the nation. This is the San Antonio math model nobody else has been able to do in the country, to the best of my knowledge. This mapping between every single lesson for the entire math curriculum, and we have it and it's database driven and it's all open source.
[00:26:41] Derek Bruff: So I have lots of thoughts. So one so I'm a teaching center guy. I think about faculty development all the time. I'm curious, you mentioned, I mean, there's a level of course coordination here that makes a lot of sense. But there's also a lot of these course instructors are, are now talking to each other on a regular basis.
Cuz you haven't talked about pedagogical change, right? All of that was structural. It wasn't what's happening in a particular classroom. But I have to imagine that what's happening in particular classrooms is changing as these instructors are talking to each other and coordinating their work on a regular basis.
Are, are you seeing evidence of that as well?
[00:27:27] Juan Gutierrez: Yes. Anecdotally, and I know because I have witnessed some of. Coordination meetings that there is pollination, there is an exhibition of ideas from multiple sources and structures are acquiring the practices that actually work. And somebody come and says, Hey, look at, I tried this and this was the outcome.
And other people say, oh, terrible, or, oh, that's great. Let's replicate it. So it's changing the community. As I mentioned earlier, we have a fantastic workforce of instructional faculty. I have to keep them credit there again, they're very, very, very good. They know what they're doing, so it didn't take a lot of training to teach 'em how to teach because all of them know how to teach.
It just took a little bit of effort to facilitate the conversations. And what has happened naturally with a little bit of incentivization and catalysis is that the, the best actors, the most cooperative have become the course coordinators. The course coordinators are selected by their peers.
They're not appointed by the chair of the department. And at that moment, the chair of the department, I just have to say, okay guys, it's all you. You decide, you plan, you do it. I'm out of it. The only thing that I have to ensure is that this is happening, and, and that's my job, is just get to the point of giving you what you need to do your job.
That's what I tell the instructional faculty. More interesting is the non-instructional faculty or Well every, all faculty are instructional. The tenure track faculty. Those conversations are occasionally on rare occasions, a little bit more difficult. I think that we're also very lucky because we have very good tenure track faculty who are passionate about instruction giving students
the best of themselves, the best opportunities. But on, on a few occasions, we have had faculty with whom hard and difficult conversations have happened. When I had to tell somebody, I'm very sorry. You cannot keep teaching upper division because you're hurting our students. You're gonna go and teach in a lower division with a coordinated section, and you have to follow the lead of the course coordinator, which is a non-tenure track faculties.
You're, you're gonna have a we call this faculty instructional, faculty, fixed term track faculty. as opposed to tenure track faculty. I think that the, the number of non-tenure track is a misnomer. We should not define people, but what they don't do, we should define them, but what they do or the nature of their contract.
So in this case, fixed term track. So I told our, some of our tenure track faculty, now your boss for instruction is gonna be a fixed term track faculty, and please be cooperative. And we have seen the transformation of some faculty. They have truly learned and now acquired a better understanding and a a heightened sense of respect for those other faculty.
In many departments, tenure track faculty and instructional faculty do not mix. They don't even know each other. I've seen this in many departments. You can put them in the same room they do. They wouldn't recognize each other, not. Here we have a mixture and, and we have ensured that everybody knows what everybody else is doing.
[00:31:03] Derek Bruff: So if you were, you know, if some department chair at some other institution was to call you up and say, I, I love what you're doing there. I'd like to get us moving in this direction. What advice would you give for a department leader who wants to start moving this way?
[00:31:19] Juan Gutierrez: Well, let's collaborate. That's what I would say.
And let's collaborate, not perhaps one-on-one. With the pandemic, we haven't had the chance to do all the things that we want to do, but I believe that there is an open conversation needed in the community. Going beyond the traditional discussions that get cornered into active learning and the discussion about individual courses.
We need to take a systemic approach, this Petri dish approach in which we take every course individually, and then you go and see the IUSE grants from the National Science Foundation. They're given for improvement of calculus one. Improvement of college algebra and that is nonsense. Why is the National Science Foundation doing this?
It's absurd. It's creating islands that are disconnected from what is needed, which is a continuing the curriculum. We don't want a collection of cliffs that is students have to face every time that go to a new course. We want a smooth ramp. We want an a function with infinite number of derivatives.
If anything comes over out of this conversation, Derek, is the need to change in the culture of our communities, the perception that we have to study islands and the need to switch to a systemic approach, we have to look at the system. It's tough in isolation, is meaningless and becomes an obstacle because the next thing that is happening, either next thing, the sequence or, or simultaneously.
Cuz many students take simultaneous courses, it is gonna be incoherent, disconnected and is not going to lead to success. And by success what I mean is students actually learn to do math and they learn it to you to be a tool for their development. And, and that's the the bottom line for us. Are we moving the needle for those students to make them better in whatever trajectory they're taking?
We should be doing that, but in many cases it's not happening. And it will not happen on a massive scale until we change this approach.
[00:33:32] Derek Bruff: Well, thank you Juan. This has been a really great conversation. I think you've given our listeners a lot to think about both in terms of their own teaching, but their position within the departments and programs and how they affect change.
So thank you so much for sharing today.
[00:33:44] Juan Gutierrez: Derek it has been a pleasure. Thank you. And let's share all this information with as many people as we can.
[00:33:52] Derek Bruff: That was Juan Gutierrez. Professor and chair of mathematics at the University of Texas at San Antonio. I am so impressed at his heart for students and student learning and student success, and I'm a little amazed at the systematic changes he's been able to implement in the San Antonio Math Department in just a few short years.
As much time as I spend helping individual instructors make more informed, intentional teaching choices in their own classrooms, I know that some of the challenges facing higher education can't be solved through individual course design. Sometimes we need changes at bigger scales to move the needle, and that's just what Juan and his colleagues at U T S A have done.
Over on the Intentional Teaching Patreon, supporters will find a bonus clip from my interview with Juan, where he has some strong words for departments that see themselves as gatekeepers for students. He doesn't think holding the bar high should be something departments pride themselves on, not if students aren't able to reach that bar.
Thanks to Juan Gutierrez for taking the time to come on the podcast. If you'd like to learn more about Juan's work or connect with him to talk about student success on your campus, please see the show notes for links. This episode of Intentional Teaching was produced and edited by me, Derek Bruff. See the show notes for links to my website, the signup form for the Intentional Teaching Newsletter, which goes out most Thursdays, and my Patreon, which helps support the show. For just a few bucks a month, you get access to the occasional bonus episode, Patreon only teaching resources, the archive of past newsletters, and a community of intentional educators to chat with. As always, thanks for listening.