NSF Awards: 2021161
2022 (see original presentation & discussion)
Undergraduate
In this video, we will share preliminary findings from an NSF project that investigates the ways in which mathematics research projects, conducted early in students’ mathematical careers (as early as pre-Calculus courses) and around questions that the students themselves pose, can spark students’ engagement and interest, with a particular focus on students who have been historically excluded from mathematics majors.
Emmanuel Nti-Asante
Kudos on this project. I look forward to reading more.
Rebecca Lewis
Terrance Pendleton
Terrance Pendleton
Assistant Professor of Mathematics
Thanks for checking out the video!
Amy Alznauer
Lecturer
Good morning!
I teach mathematics at the university level, so you had me from “I’m taking this class because I have to” and the frustration that engenders on both sides of the learning equation: the students only work because they have to (which is an essentially frustrating experience) and the teacher daily contends with the gap between their own inspiring experience of mathematics in their personal research and the dull grind they witness in the classroom. BUT, the real trick is how to bridge that gap. Often the work mathematicians are doing is too abstract, too advanced, requires too much prerequisite learning, and yet you have found a way to take real contemporary questions, help the students develop fairly sophisticated models to investigate these questions, and then bring them to a place where they can say “I am happy!” You offered a list of questions which came out of your work with students, but I’d love to hear a little more about how you took one of these questions, successfully modeled it, and managed to bring a student (with maybe only pre-calculus knowledge) to the point of understanding and developing this model and collaborating with you in the investigation. Could you say a bit more about the context in which this is taking place? Is this incorporated into the classroom? Is it an optional research program outside of class? Do the students work in teams or individually? Do they work on their own question or on a question chosen by a group from a list of candidates? And finally, I’d love to hear how you are or how you plan to measure the impact of this program on students traditionally excluded from mathematics fields. Can’t wait to hear more!
Oh, and I was struck by the similarity of one aspect of your project and the Mindhive project. You both asked students to generate questions that are of contemporary interest and impact their lives. Check out their project here: https://videohall.com/p/2479
Terrance Pendleton
Terrance Pendleton
Assistant Professor of Mathematics
Hi Amy, Thanks for checking out the video!
This is an optional research program outside of class. In fact, many of these students have yet to take a math course at Drake University. Many of them were recruited from our Crew program which is a group of Drake students of color who stand together to support each other's success, academic excellence and leadership growth. I'm the faculty director of the first year CREW program and so I pitched the idea to this group along with all of our PreCalculus and Calculus 1 classes. I have done the program both with students working individually on a project and in teams. I based this from their survey responses prior to the first meeting using the question "If you could mathematize anything in the world, what would it be?" If I can find a common thread, I place those students in a group and together, we brainstorm potential research ideas. From there, I work with each student or team to try and develop a research question that can be answered through the power of mathematics. For the modeling process, I try and mimic the same process I use when working on a novel modeling problem--that is, I take an existing modeling framework and I try to think about how I could adjust it to help me answer a problem that I'm trying to solve. We first construct a framework by making appropriate assumptions and defining variables of interest. From there, we think about how we may want to relate the variables together. Almost everytime, someone will inadvertently (or perhaps purposefully) use a "math" term like optimize, combine or interact and I use those moments to show them how they can use math to connect these ideas. Once we have a game plan in mind, I walk them through a module in compartmental modeling and linear programming--sophisticated tools that do not require any knowledge of Calculus. In the event that Calculus knowledge becomes necessary, I teach the parts needed to help them on their journey. I also promote and advertise taking these math classes as a way to inform their thinking on a project (so now they have a reason to take Calculus 1 or Applied Differential Equations). There is also a programming element that usually appears in these projects as a way for students to simulate projected solutions from their models without having to explicitly solve the equations associated with the model (since perhaps they don't have the math tools...yet). It is the hope that these research experiences will serve as a gateway to taking more math courses (and even becoming a math major or minor). This is one way for which we can measure the impact of this program and its potential to help broaden participation in the math community. I hope this answers your questions and please feel free to follow up if you have more! Thanks again for your great questions and thoughtful feedback! :-)
Amy Alznauer
Andee Rubin
Senior Scientist
Kudos here from another math educator who has been trying to make math authentically intriguing to students for many years! Like Amy, I'd love to hear more details about one of the questions students asked, how they approached it, how you supported them and how "satisfied" they were with the answer they eventually arrived at. I'm especially interested in how you decided what mathematics students needed to know to begin to answer their questions. Did you then introduce that math to the entire class or just to the students whose questions clearly needed that mathematical approach?
From my own perspective, I saw a different commonality among the questions students asked: many of them could be seen as data questions and approached with statistical reasoning. Did you introduce any statistics concepts to students as a way to use mathematics to answer real-life questions? And more generally, do these students eventually take a course in statistics in their college career or is that a different academic path? As a data science educator, I have to admit to having a soapbox: I believe that statistics is as important for most students as calculus, yet it has a very different academic status. We require calculus as a prerequisite for college admission and students "have to" take calculus-related courses to major in science. Yet, my bet is that most scientists spend at least as much time with data as they do with calculus. Do you have any thoughts about this issue?
Terrance Pendleton
Amy Alznauer
Terrance Pendleton
Assistant Professor of Mathematics
Hi Andee,
Thanks so much for checking out the video. To your first question, I've experimented with introducing math to the entire group in hopes that they will find ways (if possible) to incorporate some of the techniques introduced to them in their own research questions and I've also introduced certain math concepts to different groups based on conversations that we have. For instance, for one project a group of students mentioned trying to understanding how music goes viral on social media and "viral" made me immediately think about SIR models and so I introduced the SIR model to that group in the next meeting and before I knew it, students in that group were incorporating similar techniques to try and mathematize their own problems. In other group, "optimize" came up and so I decided to show them how linear programming could become a useful tool for helping them see how they could minimize the use of a material subjected to several constraints. For the problem of COVID replication in the body, I turned to exponential growth models. Regardless of the approach that we study, all students are work under same guiding principles of mathematical modeling:
1. Identify a problem of interest to study.
2. Identify variables of interest and make assumptions that help relate the variables to each other (if possible). This is where the mathematical approaches start to materialize.
3. Use mathematics to establish a relationship between input and output variables.
4. Analyze and assess the solutions (making any adjustments as needed) using either exact solution techniques or numerical approximations.
5. Report the results.
This past semester, two research problems (home ownership equity and the pay gap problem) allowed us to tap into a rich repository of data sources as a tool to develop mathematical models. One group has started working with linear regression while another group is using data to help with the parameter estimation aspect of their own compartmental model. The students that were working on the housing problem started out as a pre-law major and a pharmacy major. At the end of the semester, the pre-law student has decided to go into data analytics and the pharmacy major has decided to go into health analytics. The ability to analyze data is so important to an applied mathematician (this may be my own bias speaking but I stand by this statement) that we have a yearlong statistics sequence that we strongly encourage (and will eventually require) applied math majors to take. We also have pathways that make it easier for students to major in both mathematics and data analytics (I'm hoping that data analytics will serve as a gateway for the two students mentioned above to consider adding on a math major or minor to their degree programs. I've incorporated data analysis in almost every math course that I teach (still thinking about a way to do this in Real Analysis!) and our Industrial Math Capstone requires the use of some data to guide the process of mathematizing some kind of industrial problem. I anticipate that as this program grows, the lines between mathematics and data analytics (and computer science!) will continue to blur and students will tap into each of these fields to realize their full potential as mathematicians.
I hope this answer your questions! :-)
Andee Rubin
Senior Scientist
Thank you for such a detailed answer, Terrence - it sounds like you're having a significant impact on many students - if only more students understood how useful and consequential (my favorite word) mathematics is, math would have a much better public image. I wish more people took your approach. What I particularly appreciate is that you listen carefully to students and take their interests and curiosity seriously - those are the hallmarks of a great teacher, no matter what the topic.
Terrance Pendleton
Theodore Chao
Love this work. I'm interested in what sorts of forums students have to share their initial ideas about mathematics and to also get feedback about it. In my own work, I've found that children often put a lot more effort into creating a math strategy if they know that someone will read it or listen to it carefully. I'm wondering about the power of having an audience to share initial math ideas to for your students, particularly from actual mathematicians, in ways that help the students think, "Hey, I can do this too!"
Terrance Pendleton
Terrance Pendleton
Assistant Professor of Mathematics
Hi Teddy!
I love this idea about having students share their initial ideas with a broader audience. I focus so much on the end results (like giving a talk at our student research symposium or some local math conference--which we have done!) but as of now, students are really only presenting their ideas to me during the seminar. I don't know if this counts, but most seminar sessions are either record or attended by Sarah Sword or Anne Marie Marshall and so in a sense they are aware that they are presenting their ideas to someone other than me but I would like to broaden this opportunity even further. Thanks for the idea! :-)
Amy Alznauer
Lecturer
Thank you, Terrance, for this fuller picture of your work! I love that you use this program to "serve as a gateway to taking more math courses (and even becoming a math major or minor)." It would be really fascinating to build a program that begins with this optional research program and then includes a year or so of classes (maybe the calculus sequence, maybe a statistics sequence). Years ago at the University of Illinois in Champaign-Urbana I taught in a program called the Merit Workshop. It was a 6-hour per week replacement for the standard 2-hr per week calculus recitation. All the students went to the same 300-person large lecture. Our model was collaborative, the instructors acting only as facilitators. The students worked on problems, argued, went table to table to get advice from other groups, etc. Only occasionally would we offer a nudge to get the class out of a rut. But what grew up in every class was a thriving community and a group of students, almost entirely for students typically excluded from STEM majors, who went on to major in mathematics or engineering. I think your research program would have been an incredible addition to what we were doing.
One more thought (inspired by Andee's line of questioning), have you considered (or maybe you do already) collaborating with a statistician? Compartmental modeling and statistics are both powerful ways to get at the types of questions the students were raising and it would be fun (maybe) for the students to see alternate pathways to approach the same questions.
Terrance Pendleton
Terrance Pendleton
Assistant Professor of Mathematics
Hi Amy,
Thanks so much for watching the video! The Merit Workshop sounds pretty amazing and would definitely complement this program. I have a bit of a statistics background from grad school and we've dabbled a bit in introductory statistics (especially for the last two projects--please see my comment to Andee's question) but I do think that collaborating with a statistician (and possibly a computer scientist) will allow for an even more diverse pool of ideas and strategies for tackling a variety of problems. As more students from the project consider majors in these areas (and hopefully in math too of course!), they will already have a great contact in those departments to help them navigate their academic journeys.
Amy Alznauer
Lecturer
Beautiful answer to Andee's question above. And I absolutely love the blog link you shared below in answer to Brian's post. You (and your alter ego Lamar) are a phenom! My only concern about this program and all of your incredible work is that you will run out of steam! I sincerely hope you can build a team of folks around this project so that it will be sustainable going forward. The students who encounter you as a professor are truly fortunate, and I am sure you have and will inspire many, many students to pursue mathematical fields.
Terrance Pendleton
Brian Smith
Professor/Associate Dean of Research
Thanks for doing this work, Dr. Pendleton! I have a 17-year-old who was doing great in math but decided not to continue high school calculus. She just couldn't see the relevance of math in her real life. I tried to explain it, but I'm her dad....you can guess how that went ;-)
Yet she *did* complete an AP Statistics course. I don't know if that had any real-world relevance either...unless you're oddly curious about the probability of picking blue and red balls from a bag. Andee mentioned this in an earlier post. Like her, I'd love to hear your thoughts on the kinds of math we might want people to learn to see its relevance. The questions your students posed were so data-centric. I wonder if there are ways to introduce modeling and simulation ideas and tools as part of their work? Is it helpful for them to understand how to represent change in a spreadsheet vs. or along with formal derivatives?
Also, what kinds of things are you doing to help students of color feel safe in math classrooms? I'm guessing you have some great ideas here that we could all learn from!
Terrance Pendleton
Terrance Pendleton
Assistant Professor of Mathematics
Hi Brian,
Thanks for watching the video! I know that I've touched on some of the more statistical aspects of some of the projects in a comment above but I do want to mention that in problems that we have tackled in this project, data is primarily used to help estimate parameter (unknown constants) that help relate two variables together. From there, students are introduced to numerical simulation techniques (using Octave or Matlab) that allows them to obtain a graphical solution to their problem without having to solve the problem analytically (which is usually not possible in any case). The math topics that I tend to bring up that do not rely on prior knowledge of calculus are compartment modeling, linear programming, functions, data analysis (in particular, regression), and difference equations. When appropriate, I do introduce ideas from Calculus to help further a project along...and to motivate the need to take Calculus as a way to help students advance their research projects.
As far as helping students of color feel safe in the classroom, the only strategy that I can think of effective is that I try to humanize the process of learning mathematics and navigating the research process as much as possible. For a more complete answer to this question, please feel free to check out a blog post that I wrote which reflects on ways that students are supported in authentic mathematical inquiry. (https://blogs.ams.org/matheducation/2021/06/24/...
I hope this answers your questions! :-)
Andrew Jackson
We recruited students for MSEIP at the Freshman and Sophomore levels with the idea that they would be with the program longer and grow academically. What criteria did you use to select your student participants?
Terrance Pendleton
Terrance Pendleton
Assistant Professor of Mathematics
Hi Andrew,
Thanks for watching the video! I tend to recruit and select students that are at the earliest stage of their mathematical careers, that is, they are taking our lowest level math courses (PreCalculus, Calculus I or Business Calculus). I also recruitment heavily from our Drake Crew program which is a program that supports students of color on campus. Some of these students (from CREW) have not taken a math course at Drake (yet!). I try to accept all students who are interested in participating in the program and so there is no criteria around academic performance. For interested students who have taken at least Calculus II, they are placed in the Applied Math Group at Drake which runs in a similar fashion to this project.
I hope this answers your question! :-)
Further posting is closed as the event has ended.