Teaching and Mentoring Portfoliocrodelle/teachingPortfolio.pdfCrodelle Teaching/Mentoring Portfolio Page 2 1 Teaching Experience Instructor Linear Algebra, Courant (Spring 2019, Fall

Teaching and Mentoring PortfolioJennifer Crodelle

This document contains detailed information regarding my teaching and mentoring experience,as well as future directions in both teaching and mentoring.

Contents

1 Teaching Experience 2

2 Evidence of effective teaching and mentoring 32.1 Summer 2019: Mentor to an undergraduate research student (Courant Institute) . . 32.2 Spring 2019: Instructor for Linear Algebra (Courant Institute) . . . . . . . . . . . . 42.3 Fall 2018: Instructor for Ordinary Differential Equations (Courant Institute) . . . . 52.4 Summer 2018: Mentor to an undergraduate research student (Courant Institute) . . 62.5 Summer 2016: Instructor for Undergraduate Research Seminar . . . . . . . . . . . . 62.6 Summer 2015: Instructor for Calculus II . . . . . . . . . . . . . . . . . . . . . . . . . 72.7 Spring 2013: T.A. Calculus II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.8 Fall 2012: T.A. Multivariable Calculus and Matrix Algebra . . . . . . . . . . . . . . 8

3 Potential Undergraduate Research Projects 93.1 Individual neuron dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Population dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Data science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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Crodelle Teaching/Mentoring Portfolio Page 2

1 Teaching Experience

Instructor• Linear Algebra, Courant (Spring 2019, Fall 2019)

Students in this class learned how to set up and solve matrix-vector systems. Topics includeGaussian elimination, determinants, Cramer’s rule, vector spaces, basis and dimension, lineartransformations. Eigenvalues, and eigenvectors. I lectured twice a week for 1 hour and 50minutes, as well as created the quizzes, worksheets, homework, and exams.Class size: 46 students, both semesters

• Ordinary Differential Equations, Courant (Fall 2018)Students in this class were introduced to ordinary differential equations, learned how tofind analytical solutions to these equations, and were introduced to basic modeling. Topicsthat were covered include: first-order equations including integrating factors; second-orderequations including variation of parameters; series solutions; systems of linear equations; andnonlinear dynamics including phase-plane description. I lectured twice a week for 1 hour and15 minutes, as well as created the quizzes, homework, and exams.Class size: 47 students

• Multivariate Calculus III, Russell Sage College (Fall 2016)Students in this class learned the calculus of vector functions, partial differentiation, multipleintegration and advanced infinite series. I lectured once a week for 2 hours and 50 minutes,as well as designed the quizzes, worksheets, homework, and exams.Class size: 6 students

• Calculus II, Rensselaer (Summer 2015)Students in this class were introduced to techniques and applications of integration, polarcoordinates, parametric equations, and infinite sequences and series. I lectured five daysa week for 1 hour and 15 minutes each day, for 6 weeks, as well as designed the quizzes,homework, and exams.Class size: 22 students

Teaching Assistant

• Methods of PDEs of Mathematical Physics (Rensselaer, Spring 2016)My duties as a teaching assistant for this course consisted of creating the solution manual forthe homework, grading the homework assignments and exams, and holding office hours.

• Ordinary Differential Equations and Dynamical Systems (Rensselaer, Fall 2015)My duties as a (part-time) teaching assistant for this course consisted of grading the homeworkassignments and exams.

• Linear Algebra (Rensselaer, Fall 2015)My duties as a (part-time) teaching assistant for this course consisted of grading the homeworkassignments and exams.

• Calculus II (Rensselaer, Spring 2013)My duties as a teaching assistant for this course consisted of running four 50-minute recitationsfor which I designed and graded weekly quizzes and reviewed material for the course.

• Multivariable Calculus and Matrix Algebra (Rensselaer, Fall 2012)My duties as a teaching assistant for this course consisted of running four 50-minute recitationsfor which I designed and graded weekly quizzes and reviewed material for the course.


2 Evidence of effective teaching and mentoring

I received the Ralph Ernest Huston Teaching Prize as a graduate student teaching assistant atRensselaer for “unusual promise and ability as a teacher.”

The following pages include summaries of evaluations from courses, as well as comments fromtwo summer research students at Courant. The surveys were all distributed at the end of eachcourse and collected and summarized by a third party. I’ve included a few student comments aswell.

2.1 Summer 2019: Mentor to an undergraduate research student (CourantInstitute)

I was a co-mentor to Paulina Czarnecki, an undergraduate student who participated in the AM-SURE program at Courant during the summer of 2019. Paulina used the Hodgkin-Huxley modelformalism to develop a novel model for the complex calcium dynamics of a cell in the superficiallevel of the skin that mediates light touch. Below are a few comments from her end-of-summersurvey.

I appreciated the individual mentorship and the ability to hear about other students' and other people in the department's work.

My mentors put in a lot of time and effort into mentoring me. They were easy to communicate with and responsive, their instructions and expectations were clear, and were always available if I had questions or was stuck on something.

Charles and Rob were great at coordinating the program. They were careful listeners at the program meetings, coordinated social activities, and provided advice for our projects, grad school applications and anything else I had questions about.

The project I was assigned was interesting and Yt in with my background so that I could be productive and still learn something new.

What aspects of this experience were most useful or valuable?

Which aspects of this experience were least useful or valuable?

Tell us about your experience with your research mentor (e.g.,communication, responsiveness, teaching skills, expectations, etc.)

Tell us about your experience with the program coordinators (Charlesand Rob)

How was the project you were assigned?

Summer Research Experience Survey https://docs.google.com/forms/u/1/d/1QVjF6lJ42ybvfAqeT6Wph...

3 of 4 8/9/19, 4:55 PM

I appreciated the individual mentorship and the ability to hear about other students' and other people in the department's work.

My mentors put in a lot of time and effort into mentoring me. They were easy to communicate with and responsive, their instructions and expectations were clear, and were always available if I had questions or was stuck on something.

Charles and Rob were great at coordinating the program. They were careful listeners at the program meetings, coordinated social activities, and provided advice for our projects, grad school applications and anything else I had questions about.

The project I was assigned was interesting and Yt in with my background so that I could be productive and still learn something new.



Tell us about your experience with your research mentor (e.g.,communication, responsiveness, teaching skills, expectations, etc.)

Tell us about your experience with the program coordinators (Charlesand Rob)


Summer Research Experience Survey https://docs.google.com/forms/u/1/d/1QVjF6lJ42ybvfAqeT6Wph...

3 of 4 8/9/19, 4:55 PM


2.2 Spring 2019: Instructor for Linear Algebra (Courant Institute)

The students fill out an anonymous survey with the option to include comments. Each question isout of 5 total points.

Selected student comments:

• “Dr. Crodelle is an excellent lecturer that knows how to teach!”

• “Best math instructor I’ve had since high school.”

• “Please continue with the clarity and high standard of the lecture notes you have presentedto your students thus far, they are helpful.”

• “She is a really good instructor. She cares about the students’ understanding and would takeout extra time for office hours to accommodate students if they can’t make it to the originaloffice hours listed on the syllabus.”

• “Class is pretty hard, HW pretty long, textbook not great in my opinion. Great professorthough!”


2.3 Fall 2018: Instructor for Ordinary Differential Equations (Courant Insti-tute)



• “Love her style of teaching.”

• “Best professor ever.”

• “Professor is nice to talk to.”

• “She was very good.”


2.4 Summer 2018: Mentor to an undergraduate research student (CourantInstitute)

I was a co-mentor to Taylor Meredith, an undergraduate student who participated in the AM-SURE program at Courant during the summer of 2018. Taylor modified a model of the calciumdynamics during muscle contraction to incorporate realistic input from a motor neuron. She usedthis model to simulate muscle weakness that presents for patients with a neuromuscular diseasecalled Myasthenia Gravis, as well as the return of muscle force generation under a drug treatmentprotocol. Below are a few comments from her end-of-summer survey.

08/02/2018 21:36:06 3

Why did you choose to participate?

Try research out, Learn/try something new


I think both the report and the presentation were the most valuable aspects of this experience, as they served as great examples of what actual researchers accomplish, in terms of writing papers and giving talks. I really appreciated the feedback from my mentors, peers, and program coordinators. I believe that by writing the report and giving a short talk on my project, I was able to absorb much more of the information I've been learning all summer.


I would say that probably afternoon tea was the least "useful" aspect of this experience, just because less and less people attended the tea towards the end of the summer. However, at the beginning it was nice to meet new people and talk to the professors and other students in my program.

Tell us about your experience with your research mentor (e.g., communication, responsiveness, teaching skills, expectations, etc.):

My research mentors were extremely helpful throughout the whole process. We met usually twice a week and they provided me with great advice and guidance on how to move forward in my research. Meeting with them multiple times a week was a great way to ensure that I kept on track and made progress with my project. They explained concepts very clearly and were very responsive to all of my emails. They always made me feel welcome and comfortable enough to ask any questions I had. Overall, I could not have asked for better mentors! They are passionate about what they do and they genuinely support me and want me to succeed.

Tell us about your experience with the program coordinators (Pejman and Jason):

The program coordinators were always willing to help and answer any questions we had. They helped us with coding problems, and they suggested ways to improve our models and numerical methods. They always seemed genuinely interested in everyone's project and presentation. They were very helpful during the editing process of our reports and presentations as well.


The project I was assigned was my first choice so I was very excited to work on the topic. As a math major and pre-med student, modeling the neuromuscular junction was very relevant to my studies and to the research I may want to pursue in the future. I had a lot of fun learning about this topic and just learning about research in general. Research was always something I've been interested in, and now after participating in the AMSURE program I definitely want to continue researching this project and other applied math projects as well.

How were the group meetings?

The group meetings sometimes ran a little long, so not every person got the chance to present each week. However, I think it was nice to hear about what everyone else was working on. Many times, the

08/02/2018 21:36:06 3

Why did you choose to participate?

Try research out, Learn/try something new


I think both the report and the presentation were the most valuable aspects of this experience, as they served as great examples of what actual researchers accomplish, in terms of writing papers and giving talks. I really appreciated the feedback from my mentors, peers, and program coordinators. I believe that by writing the report and giving a short talk on my project, I was able to absorb much more of the information I've been learning all summer.


I would say that probably afternoon tea was the least "useful" aspect of this experience, just because less and less people attended the tea towards the end of the summer. However, at the beginning it was nice to meet new people and talk to the professors and other students in my program.

Tell us about your experience with your research mentor (e.g., communication, responsiveness, teaching skills, expectations, etc.):

My research mentors were extremely helpful throughout the whole process. We met usually twice a week and they provided me with great advice and guidance on how to move forward in my research. Meeting with them multiple times a week was a great way to ensure that I kept on track and made progress with my project. They explained concepts very clearly and were very responsive to all of my emails. They always made me feel welcome and comfortable enough to ask any questions I had. Overall, I could not have asked for better mentors! They are passionate about what they do and they genuinely support me and want me to succeed.

Tell us about your experience with the program coordinators (Pejman and Jason):

The program coordinators were always willing to help and answer any questions we had. They helped us with coding problems, and they suggested ways to improve our models and numerical methods. They always seemed genuinely interested in everyone's project and presentation. They were very helpful during the editing process of our reports and presentations as well.


The project I was assigned was my first choice so I was very excited to work on the topic. As a math major and pre-med student, modeling the neuromuscular junction was very relevant to my studies and to the research I may want to pursue in the future. I had a lot of fun learning about this topic and just learning about research in general. Research was always something I've been interested in, and now after participating in the AMSURE program I definitely want to continue researching this project and other applied math projects as well.

How were the group meetings?

The group meetings sometimes ran a little long, so not every person got the chance to present each week. However, I think it was nice to hear about what everyone else was working on. Many times, the 2.5 Summer 2016: Instructor for Undergraduate Research Seminar

An anonymous survey was sent out electronically to the students asking for feedback and commentson the instructor.


• “The instructor was engaged and prepared for each subject we discussed.”

• “The instructor worked with input suggestions.”

• “The instructor was very organized and gave thorough presentations on how to give mathtalks.”

• “Excellent instructor, I learned a lot.”

• “The instructor gave good illustrations.”


2.6 Summer 2015: Instructor for Calculus II



• “Lots of examples in class really helped me learn the concepts.”

• “Very example-oriented lectures. Expressed the material in a very understandable way.”

• “Clear and very informative.”

• “One on one teaching when necessary, inspired asking of questions, detailed study of conceptsbehind lessons.”

• “I liked learning from Ms Kile and she was very approachable and friendly.”

• “Amount of worked through examples was extremely helpful, daily quizzes helped keep ontrack.”

• “Keep being happy and loving math. It’s more fun when you are energetic.”


2.7 Spring 2013: T.A. Calculus II


Scanned by CamScanner

2.8 Fall 2012: T.A. Multivariable Calculus and Matrix Algebra


Scanned by CamScanner

Figure 1: Summary of evaluations, each out of 5. The department average for overall performancefor all calculus classes at RPI that semester was 4.82 out of 5.


3 Potential Undergraduate Research Projects

In this section, I describe a few potential undergraduate research projects. In general, I am inter-ested in using mathematical modeling as a tool for uncovering mechanisms underlying biologicalphenomena. I am open to advising projects in the broad field of mathematical biology, but Ispecifically describe projects here in my research area of mathematical neuroscience.

3.1 Individual neuron dynamics

Several mathematical models exist to describe the membrane potential of an individual neuron.The most complicated of which is the set of Hodgkin-Huxley differential equations that includesnonlinear equations to describe each individual ion channel along the cell membrane. Investigationsinto the behavior of one cell in response to different input requires numerical integration (which canbe done via Matlab’s built-in ode45 function or a student’s own numerical integration scheme)and other simulation techniques to analyze the resulting behavior. Some potential applications ofmodeling an individual neuron could be:

1. to incorporate a variety of ionic channels into the Hodgkin Huxley model, potentially in-cluding stochastic components (e.g., channel failure), and investigating their effects of themembrane potential. Often, neurons in different regions of the brain are composed of differ-ent sets of ion channels. This project would include a literature search to find experimentalmeasurements of the membrane potential of these different neurons and matching the modelto those experiments.

2. to allow two neurons to communicate through either an inhibitory or excitatory synapseand perform an analysis on the observed behavioral changes that come with varying theparameters of the synapse strength and time scale of transmission. Depending on studentinterest, one could write a simplified version of the Hodgkin Huxley model (e.g., the Wilson-Cowan model) whose null-clines and phase portrait can be easily computed and analyzed.For different timescales of synaptic transmission, one might observe different steady-statebehavior.

In each case, depending on the interest of the student, we would perform in-depth literature searchesto find experimental behavior to check that the model is behaving as realistically as possible. Inaddition, one could introduce damage or disease to the model and use it to investigate differenttreatment protocols.

3.2 Population dynamics

Computational neuroscientists often model the behavior of a collection of neurons, rather than indi-vidual neurons, to understand the interaction between several regions of the brain. One can modelthe collective behavior of a population in terms of an average firing rate or average membrane po-tential. The resulting differential equations are often much simpler to analyze than those requiredfor individual-neuron modeling. Potential student projects might include analytically investigatingthe resulting dynamical regimes of these systems and understanding how varying the type of in-teraction between populations of neurons can affect these dynamics. Some potential applicationswithin this framework include:

1. modeling the interaction of populations of neurons responsible for sleep and wake dynamics.In particular, oscillations of varying frequencies often arise in the dynamics corresponding


to states of REM or nonREM sleep. Students can examine how changing parameters in apopulation model can affect this oscillatory behavior and relate that to different observedsleep dynamics.

2. simulating a decision-making task using mutually-inhibiting populations of neurons. Mod-elers have had success describing interesting sensory phenomena such as binocular rivalry(when visual perception alternates between different images) and auditory segregated input(when auditory perception alternates between different frequencies) using mutually-inhibitingpopulations of neurons. Students can work within this framework to understand how the in-troduction of noise or more populations of neurons (excitatory and inhibitory) might affectthe decision-making (alternating perception) properties of the network.

3.3 Data science

Due to the growing computational power and experimental designs, large sets of data can be gen-erated or measured in very little time. Mathematicians are in a unique position to deal with thislarge quantity of data by helping to design tools for organizing raw experimental data and extract-ing key information. Neurons are noisy objects where multiple recordings often lead to differentmeasurements. In order to extract key pieces of information (such as a preference for some sensoryinput), tools from signal processing are often applied, sometimes performing some averaging orsmoothing over large sets of neurons, resulting in the loss of important, detailed information. Apotential student project could be in applying different tools from signal processing to understandhow different techniques lead to separate conclusions about the activity of the cells. The studentmight pay particular attention to the oscillation frequency or synchronization properties of a net-work of neurons and try to develop some tools that can guarantee that the features we observe arerobust and not just due to the method of processing.

I have had experience mentoring students in simulating neuronal networks, detailed modeling ofsensory cells including calcium and mechano-sensitive ion channels, and modeling the resultingforce generated by a contracting muscle fiber. My own research spans topics from neuroscience,epidemiology, and data science of crime trends. I look forward to developing projects in any area ofapplied math where one can use equations (ODEs, PDEs, deterministic or stochastic) to describeand further understand interesting biological and physical phenomena.

Documents

Teaching and Mentoring Portfoliocrodelle/teachingPortfolio.pdfCrodelle Teaching/Mentoring Portfolio Page 2 1 Teaching Experience Instructor Linear Algebra, Courant (Spring 2019, Fall