What I did on my summer vacation

Wow, pandemics suck. Pandemics combined with financial insecurities and your neighborhood being bought up by the state and evicting everyone also not so great.

Like most folk out there, when the pandemic hit many things in my life changed. I don’t want to get too personal here, but there was a lot of job loss in my family and many Covid-19 scares this summer. My neighborhood was also bought up by the state so we were forced to move in the middle of all this mess. On the bright side I now own a house AND it has a gas line for my beautiful gas stove.

So my May and June were dominated by waiting to hear if my husband and I got to keep our jobs and if we’d get to afford the house we were trying to buy (terrible timing, I know). But once that whole thing died down I got to focus on better things.


I was awarded a grant to research this summer! Early in May my research group submitted a paper based on our work last summer. We then spent the summer exploring other questions we hadn’t answered yet. My collaborator, Maila, discovered an interesting way to look at our question that boils down to solving a diophantine equation. So now I finally have a research project to work with my friend Eva on! We had wanted to find something when we were both at Smith, but, alas, that did not work out then.

We’ve met each week to discuss what we’ve learned and what the data says. Like a lot of research, it full of a lot of failure until it’s not. But I’m excited because there seem to be so many ways we could approach this problem. And so going into the fall I am motivated to keep tabs on it.


I was invited to run an hour and a half workshop on Gender and sexuality for Math Swagger. I was able to get to know a (now ex) colleague better because of this session. I felt woefully unprepared to discuss this topic since I only have my life experiences to work off of. But after talking with her (a researcher in Chicanx and gender studies) I felt more prepared.

I reread works that had been shared with me and reached out for more material when I felt I was lacking information. I learned a lot more about Queer Theory and how we can use that framework to think about mathematics classes as a whole. For example, we should challenge things in a math classroom that we see as a “norm.” Is there only one way for a student to communicate mathematics in a classroom? Can we find ways to use more creative ways for a student to explain what they know and how they know it? I don’t know, but it’s worth exploring. The session was wonderful, and my attendees really made it worthwhile. I’m so glad they shared so much with me and helped me to understand more perspectives.

Years ago, I added myself to a list of 500 women scientists. An aspiring mathematician reached out to me through the site and asked if she could ask about my experiences as a cis-woman mathematician. Some of the interview can be found here.

Diversity and Inclusion

After George Floyd’s death, my department reached out to our students and tried to give space for student to express themselves in zoom sessions. We did not want to stop there, as the protests have made it clear that the country is not going to suddenly be more inclusive if we wait long enough. We wanted to be more proactive. So we began a summer department workshop that will hopefully continue into the fall semester.

We discussed different readings on the research behind culturally relevant as well as assessment of past math reforms, like Common Core. We then talked about things we’d like to do this coming semester from what we learned. We each shared things about what we can do on our first day to get more connected with our students, and what changes we can make in the syllabus for it to have a more universal design.

Three actions I read that were more concrete were:

  • Valuing our students and making sure they feel ethnically and culturally validated.
  • Have high expectations for student success.
  • Have students experience connections with their teachers, classrooms, and school.

Because of these sessions, I learned more about what my department is already doing. I also was encouraged and was able to refine some of what I was doing in the classroom before. I also learned more about ungrading, and more actions I can take to support my students. Because of these workshops, we were able to get a survey out to the students on inclusivity and belonging. The students will be discussing the survey and other suggestions at our faculty retreat on Monday. I am excited to see what my colleagues will do with the information.

My college also had several session on race and racism and these session prompted me to finally read So you want to talk about race by Ijeoma Oluo. There was so much information here, and I took lots of notes. One thing I’ll be thinking more about moving forward is on intersectionality. Some questions she recommended asking yourself:

  • How might race, gender, sexuality, ability, class, or sex impact this subject?
  • Could the identity differences between me and the person I’m talking with be contributing to our differences of opinion and perspective?

What I didn’t do on my summer vacation:

I have not gotten better at writing, and I have not been socializing often. So teaching’s going to be an adventure this semester for so many reasons. I also did not solve the Riemann Hypothesis. Drat. Maybe next year.

Emergency remote online teaching

This semester started off so great. My students were developing their group work skills and would have such great conversations with little prompting from me. The project for calc 2 was interesting and most of my students had pulled together a nice intro to what happened during the Gulf of Mexico oil spill. My abstract algebra students were about to wrestle with quotient groups (which has been the hardest concept for most of my algebra courses), but many were really starting to understand cosets.

My department began talks about how we would shift to online courses before the spring break even if our college did not make the decision. Then during our spring break Covid-19 was declared a pandemic. We got the email the next day. We would delay opening the college for a week, and when we’d get back we’d be all online.

Many of my students spent the week moving out of dorms, figuring out how they could make rent, deciding if going home was the best option. All in all, my courses were not going to be their priority. I read so many blogs that week about teaching online and expectations I should set for myself. They mentioned that I should only really worry if I was teaching core classes. Given that I was teaching Calc 1, 2 and abstract algebra which are all core classes for the math major and many other stem majors this did not alleviate my stress.

I’m still wrestling with the morality of grades in this situation. Many of my students have more pressing problems than can they take an integral? Many of my students wifi is spotty if not non-existent, most don’t have cameras, some told me about how they did not time manage well in online courses, can’t make rent. So what does an ‘A’ mean in this situation?

Transitioning to online/remote learning

I decided to still hold class sessions and record as much as possible for my students that needed to have a schedule (and for myself because I need routine to function). I uploaded videos to youtube and shared them with students if they couldn’t attend. Most of my students are using Khan academy; I am thankful for all their professional videos. My college is a Microsoft campus, but I made all my decisions on what to use before I had enough training to be confident I could use Teams. So I didn’t use Teams.

I chose to have class in Zoom, and use Slack for my breakout sessions and for students where Zoom wasn’t working. I was lucky to already have a document camera from experimenting with it last year. So it hasn’t been hard to share math with students in this way. I then would take pictures of my notes and post to Slack.

My students would break up into groups and work on activities through the bulk of class. Ideally, they would then respond to polls or post their work, or ask questions. In practice, I worked through a lot of examples in most class because they weren’t comfortable/familiar with sharing their work in this format.

Many of my calc 2 students adapted to this format fairly well and many participated in the Slack channels. They would have good conversations and questions and would encourage me to go more in depth on certain ideas. Their project also changed to modeling Covid-19, and those have been real interesting reads.

Abstract and Calc 1 have been more quiet during our classes, but many students are still turning in the work and dming me on the regular for help with the assignments. I think I will try to adapt using a chat room like this one for regular in person classes because I think more of my students that didn’t engage as much before found it to be a better way to engage with the class. I wonder if Canvas has an easy to use chatroom feature?

Plus side

My cat has never been happier. She loves having both of us home to spend time with her.


Juno is so content.

Animal crossing is awesome and has been a fulfilling quarantine activity. I even got to have a birthday party through animal crossing. Complete with piñata!Screenshot 2020-04-28 12.23.11

Reflecting on my first semester using SBG

Last semester was my first semester being a full time assistant professor. As it was my first year in the job and my department said they wanted me to experiment with teaching I decided to implement some of the things I saw at MathFest and modify them to work for me. I decided to teach my calc 1 and discrete course with Standards Based Grading using inquiry based learning textbooks. I also saw a great panel on metacognition, so I implemented one activity that they had shown as well in hopes that I would gain student buy in for IBL and SBG. For those unfamiliar with SBG, I recommend you go to Kate Owen’s Blog on her experiences implementing SBG. It is not something new, as gk-12 teachers have been implementing the system for awhile. It was just new to me.

What I tried:

For Discrete, I tried a to do a full standards based grading system, where they would have almost daily “learning targets” and many chances to make up the 20 learning targets my coteacher and I had decided on. They also had a semester long project to create a proof portfolio (thank you NExT fellow who shared their resources with me!) that would focus more on proof techniques and latex skills.

For Calc 1, I was teaching on my own and didn’t want to do daily quizzes, so instead I implemented a bin system that some of my colleagues had been testing out. Each type of assignment I gave was assigned to a bin, and students had to score a certain amount in each bin to make the grade they wanted. I had a bin for webwork (their daily homework) in which they had to score above a certain threshold for me to qualify it as passing; a written homework bin where they had 2 chances per assignment to turn in an almost perfect draft of their work (only then would it count as passing); a project bin where they had to turn in an almost perfect project at the end of the semester (they had many draft deadlines prior to the final deadline for me to lead them to the bar I had set); a bin for the midterm where they had 2 chances to score about a 70 on the exam, and bin for metacognition reflections in which they had to watch videos and read articles on things related to how students think and learn and write me 3 one page essays (they just had to do turn an essay in for a pass).

How this all worked out:

Pros: I really don’t hate grading anymore. It used to be the worst thing ever and my least favorite part of teaching. Most students I have taught never look at the comments my graders and I would put and they would continue to make the same mistakes on every assignment. Since students had to keep retrying things until they mastered the material, they read through my feedback and tried to improve. I also have a better grasp of what my students do and do not understand, because the more they did on an assignment the more it became clear what in the process was being misunderstood.

For Calculus, the students that passed my course very well were not just students who had calculus before, which had been my experience the other times I had taught calc. I also think for both courses it was a system that was more forgiving to students who had personal issues pop up during the semester that impacted their attendance and learning.

Since deadlines were essentially all at the end of the semester, a student who had an emergency midsemester still had the same opportunities to master the material as students that did not have sudden emergencies (albeit they had a less time so they had to be more on the ball with making appointments and coming to office hours).

The reflections in calculus got me the buy in from many of my students who hated my teaching and grading system at the beginning of the semester. Some said they still didn’t like it, but they understood why I was doing it and accepted that they would have to adapt.

Cons: Oh my goodness! Learning targets eat up so much time in class and out of class! We even had a file with learning target questions from the prior year and it still took us a little bit to put ones together for this semester. You need so many versions of questions for each target. Then you have to spend time in class giving a target. Since we didn’t want to grade every single day, we had students grading in class to learn how to assess their work. This was good, but also took a lot of time. So we ended up covering less material (which isn’t terrible for a discrete course, but there’s so much cool stuff we couldn’t do because of it). Then outside of class, we had to hold so many extra hours for students to come in and make up targets. We tried to control the workload by limiting students to only 2 a week and only holding hours on Thursday and Friday, but there were still several Thursdays that every hour I had a student coming in to work and talk through a target. There was no time to do anything else like prep for my next class.

Grading 2 versions over every homework assignment in a timely fashion can be difficult when sudden obligations pop up. For example, I’m behind on giving feedback Calc 1 and Calc 2 homework right now because I needed to finish reading applications for an REU last week.

Student buy in takes a little time, so many students would push back against my system over the course of the semester and some left scathing reviews in my evals.

Our grading system on Canvas did not like they way I graded in either class, so I had to constantly remind students not to look at the percentages in the grade book, but to see if the amount of completes they were getting matched my grading scheme. Some students were still confused at the end of the semester, as they fell between categories. So I had to find a consistent way to score these between category students that was as fair as I could be to all.

No deadlines till the end of the semester means the last day of the semester I get to grade all the late work, piles of it.

I wanted to do reflections again because they ended up working so well, but my Calc 2 students next year have almost all already had me, so they’ve already done this assignment. I did not figure out before the start of the semester how to make an assignment that would go in more depth.

Things I’ve changed for this semester

I decided against doing learning targets in abstract algebra as it would have been far too much work. Instead they have homework everyday, participation (measured in how often and how well they present the material), and a proof portfolio that will determine their grade at the end of the semester. I restructured the proof portfolio to have more drafts and less questions so students can get more feedback and a better idea of what I mean by an excellent proof. That way they are not all in my office the last week of classes concerned that they still haven’t written a perfect proof.

I will probably try learning targets again in discrete next year, but I will have less of them, so I can better manage the time for my students and I. I will also share more resources with my discrete students so they better understand the research behind this style of grading and teaching. I will also modify the proof portfolio here as well so students get better feedback. I’ll also structure the regrading in class differently, the first few we will do as a class with several students recording on the board their solutions and we will carefully critique them. Then for later targets, I’ll share solutions so they can grade outside of class and post their solutions.

For Calculus, I really liked reflections and doing multiple drafts of each assignment, so I’m keeping with that. I think for next year, I will write a more in depth reflection for Calc 2, so student who have had me before get a new experience rather than the same information as before. I think I’ll have them do more research on the things they read on their own, rather than use resources I found (which means they are prone to be my views and biases).

I have more firm deadlines now (they are still really flexible so there is still the pro benefit from above). If students want the more flexible deadline, they have to have extra credit points that they earn by engaging with the campus or the community through lectures of volunteer work. Then the deadlines are one month after the original assignment is due, that way I don’t have all the things to grade on the last day (just some of the things).

Things that have helped make these systems work for me

Canvas is amazing. All work my students do has to be uploaded as a pdf and I grade it on Canvas. This means I can have version control when I ask students to regrade their work.  I always have a record of everything they’ve turned in and what quality it was. This way it’s quick to keep track which versions of a learning target students have done.

My department really tries to encourage us to try new things in teaching and understands that this will come with growing pains. So when I get bad teaching evals from trying something new that did not work out as well as I hoped, I’m not punished for it. They also give me full control on whether I will give exams.

My classes are 2 hours each twice a week, so there is time for me to do things like learning targets and grade them in class and still cover new material.

Concluding thoughts

All in all, I will continue to try SBG (and IBL) over the next few years. My hope is to get better and faster at it so that they don’t take as much time. I want to have a better bank of questions to pull from for both learning targets and proof portfolios. I will also try to improve on the reflection assignment to better accommodate students I’ve had multiple times.

MathFest 2018

After a summer filled with conferences and a crazy move (we moved and had exactly one week to find a home, I don’t recommend this), I am excited to get to work in a new environment!


Juno hates road trips

I spent my summer expanding my knowledge in cryptography, arithmetic geometry, SageMath, and math education. I now have ideas to implement in classrooms and am more familiar with terms and programs my collaborators use.


Enigma machine! We got to play with it.

MathFest was another whirlwind of information and hanging out with friends. I learned more about implementing standards based grading from Kate Owens, David Webb, and David Bressoud. You can check out Kate Owens blog full of standards based grading here: Kate Owens Blog. I think the over view here is to know what the big questions are for your course and share those with the students. Then for each of the big questions, come up with standards you think would answer those big questions. Then give your students many opportunities to demonstrate their grasp or mastery of those standards.

Ed Burger asked us to focus on the 20 year question in our teaching from now on. That is to say, what do you hope your students will remember in 20 years from now and be mindful as you walk into your classroom each day on what you are doing to address that question. He also assigned us the homework of not referring to the problems we work on in math as problems anymore. We’ll see how that goes. His final advice was to not leave a failure in the classroom hanging. Always address it, so the students have a chance to learn from them. In that way we can practice effective failure.

Ed Burger was not the only one to discuss failure at MathFest. Laura Taalman discussed the process of failure in 3d printing and in mathematical research and the importance of sharing this process with students so they can recognize that mistakes are perfectly normal to make.

Here was her flow chart:

math research flow chart

Math flow chart. The woo part is important. Someday we get there.

Here are some of her designs that she has made: Mathgrrl. Turns out you can just send designs to folks and have them print it for you.

Eugenia Cheng gave us yet another mathematics that can be interlaced to social justice. She discussed category theory and inclusion-exclusion in mathematics. I really felt like I could understand category theory after her talk. She also related the generalized form of factoring to a way to think about privilege. She looks at the number 42 and finds a way to represent the factors as a cube, which visually is way more appealing than listing all the factors in a straight line.

factors of 42

Prime factors of 42 done up as a cube. It’s hard to draw cubes for me.

And if we’re thinking about how those arrows are pointing, this diagram seems to suggest that 6>7. Abstracting this cube on the right she looks at privileges for the set of  {rich, white, and male} and discusses what the implications are by drawing it as a cube.

category theory and sj

More of a rectangular prism than a cube to represent how having some privileges may lead a person to be better off than those from the same row.

The first thing she mentions about his diagram is that this demonstrates that privilege isn’t about being more privileged than everyone else in the diagram. This version of the rectangular prism helps us see that a person is more privileged than the person they are directly above. But being a rich, non-white, non-male vs being a non-rich, white male would be incomparable according to the arrows on these sets because they have completely different sets of privilege. I thought this was a good reminder of how complex privilege can be because of the intersectionality of our identities. Then it goes further to give us a mathematical means to think about our intersectional identities and how they can interplay. Here’s a version of her talk that she gave at MathFest: Inclusion-exclusion talk

There was so much more going on at Mathfest, so I’m a little overwhelmed. I will be spending the next few weeks synthesizing what I can into my courses before I forget all this useful information.


Panel on teaching Social Justice in mathematics

Another wonderful Joint Math Meetings has passed and I was quite busy at this one. I was able to see my friends and colleagues because I helped organize the special session on arithmetic dynamics. I also got to spend some time with new friends from Project NExT by running a special session on Social Justice in the mathematics classroom.

Lily Khadjavi, Karl-Dieter Crisman, and Aditya Adiredja made our session a success. I think one of the big things I learned is that I can work in small ways to start incorporating social justice and service learning in my classroom. For example, Calculus students can tutor at the local high schools in algebra, or I can carefully choose which examples my students can look at in class. As Lily Khadjavi said, the data speaks for itself.

I also learned that I’ve done service learning already in my classroom. Partnering my math for elementary school teachers students with a Hawai’i elementary students as penpals was a service learning project. I learned about the value of student reflection as well as making sure my students met with the community partner.

I still want to create something big in partnership with the community I live in, but for now I can help incorporate social justice into my classroom by choosing good examples.

Some resources I heard about in the panel and Moon Duchin’s talk:

  • tinyurl.com/teachgerry
  • https://he.kendallhunt.com/product/just-math
  • Forthcoming: Lily Khadjavi and and Gizem Karaali are working on a “volume of classroom modules”— Mathematics and Social Justice: Perspectives and Resources for the College Classroom. I think that is what this one is called, but I didn’t get a chance to write the name, so I had to use googlefu to find it.
  • There should be a social justice issue of PRIMUS soon.
  • Link to slides and other resources from our session: JMM session


Notes from Analysis

I get to teach real analysis this year! So I’ve been making notes for my students. We are working from Rudin, and we began by building the real numbers using Dedekind cuts. Each set of notes has a rough learning objective at the top. You can find them here:

Lecture 1_sv

Lecture 2_sv

Lecture 3_sv

Lecture 4_sv 131

Lecture 5_sv_131

Lecture 6_sv_131

Lecture 7_sv_131

LEcture 8_sv_131

Lecture 9_sv_131

Lecture 10_sv_131

Lecture 11_sv_131

Lecture 12_sv_131 more compact properties

Lecture 13_sv_131 Connected and compact

Lecture 14_sv_Conv seq

Lecture 15_sv_131 cauchy conv seq

Lecture 16_sv_131 Completion

Lecture 17_sv_131 limsupinf

Lecture 18_sv_131_series tests

Lecture 19_sv_131 Absolute convergence

Lecture 20_sv_131 Continuity and limits

Lecture 21_sv_131_Continuity consequences

Lecture 22_sv_131_uniform continuity

Lecture 23_sv_131_differentiability

Lecture 24_sv_131_Taylor and Uniform convergence

Lecture 25_sv_131_Function convergence

This is what a mathematician looks like

I don’t know how many of you have gotten bored like me and done a google image search of things like professor and mathematician, but it’s results weren’t very surprising for me.

In fact the results have actually improved since the last time I did this search! Last time “professor” had only yielded images of Einstein lookalikes.

It was exciting (and inspiring) to be at MAA Mathfest this past week and get to interact with many mathematicians who don’t fit the stereotype. If I were to be asked what a mathematician looks like, I have no idea what I would draw! Maybe myself, maybe any one of the friends I just made, there are so many people that become mathematicians!

bluedots mathfest

Junior faculty learning math and having fun.


Equally inspiring was the session at Mathfest on the journey of how many of the women mathematicians I admire arrived at where they are. One of my many takeaways from that session was that mentorship matters and that I should learn more about finding mentors for myself and being a good mentor for students that might one day follow in my footsteps.

Programs like EDGE and Math Alliance were instrumental in helping these folks get to where they are today as well as groups like SACNAS. I’m glad to have heard more about some of these groups so that I can share these opportunities with my students and others colleagues who could not make it out to Chicago.



Future Conferences

Conferences I’ll be attending in the coming months:

  • Virtual: Rethinking Number theory (Oct 8-18th) 2020
  • Virtual: SACNAS (Oct 19-24th) 2020

Some recent past conferences I attended:

  • JMM 2020
  • Summer at ICERM, REU, 2019.
  • REUF at ICERM, 2019
  • Women in Sage: Sage days 103, August 7-9th, St. Louis Missouri (organizer)
  • AMS Western Sectional March 2019, Honolulu, HI.
  • SACNAS October 2019, San Antonio, TX.
  • MathFest July 31-August 4, 2018, Denver, CO.
  • IAS Women and mathematics program, May 19-25th, 2018, Princeton, NJ.
  • SAGE days 94, June 29-July 4, 2018, Zaragoza, Spain.
  • Latinx in the Mathematical Sciences Conference March 8-10, 2018 (invited speaker).
  • JMM 2018, San Diego, CA.
  • Women in Sage: Sage days 90, October 2017, Claremont, CA (organizer).
  • WIN 4,  August 13-18, 2017,Banff, Alberta.
  • MathFest July 2017, Chicago, IL.
  • AWM Special Session on Women in Sage Math at the 2017 AWM Research Symposium at the University of California Los Angeles (UCLA) April 8 -9, 2017
  • JMM 2017, Atlanta, GA.
  • West Coast Number Theory Conference, Dec 16th-20th.