Thanks for checking out the video! 

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! :-)

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! :-)

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.

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! :-)

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. 

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.

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! :-) 

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! :-)