## The Grant Cycle Diaries: Grantastination and Broader Impacts

“Piled Higher and Deeper” by Jorge Cham www.phdcomics.com

“Piled Higher and Deeper” by Jorge Cham
www.phdcomics.com

Dear Diary,

July 22 is the due date for this cycle’s NSF CAREER grant. This is nine days away, and I have nine full days of stuff that I still need to do. This is stressful. I take partial blame for my plight—it seems I cannot do today what could be done tomorrow. In January, I was thrilled to read this article about the creative benefits of procrastination. It turns out that in some situations, you will have more creative ideas if you let your mind wander for a while before getting down to work on a task. As a natural procrastinator, it was great to have behavioral psychology cut me a break for once. However, there is no denying that procrastination makes many if not most situations in life much more difficult. Through great effort I have managed to moderate my procrastination to some degree, to trick myself into starting important projects appropriately early, and to generally be a somewhat productive member of society. The struggle continues every day.

But I really did start early on this grant application! My favorite trick for getting started is to sign up for some kind of structured (and hopefully social) program. With that in mind, this February I attended re:boot Number Theory, a grant writing workshop/bootcamp at Duke University, aimed mostly at female number theorists. We spent 3 full days working on our own proposals, as well as learning about NSA (National Security Agency) and NSF (National Science Foundation) grants from previous applicants and representatives from the agencies. Although I had applied for the NSA Young Investigator grant twice, I had no idea how many additional aspects were involved in the NSF grant. The workshop was incredibly helpful because it provided

1. All the official information you could possibly want about the programs.
2. Great, patient people to answer the ridiculous number of questions that arise in working on one of these.
3. Structure and dedicated time for getting started on each aspect of the application.
4. Moral support from other people who are also attempting this same difficult and discouraging task.
5. A useful guilt trip—we were all asked to pledge that we would applying for at least one grant in the 2016 funding cycle as a condition on our attendance.

I pledged to apply for the CAREER grant. If you are annoyed by this kind of thing, you may find it upsetting that CAREER is treated like an acronym but it definitely doesn’t stand for anything: the official name is the Faculty Early Career Development Program. Coming to terms with the non-acronym is the first and least difficult step of the application process. The CAREER grant is for non-tenured Assistant Professors who are in tenure-track positions. It is a 5-year program, with a minimum award of $400,000. This should support both an extensive research program and an educational component, which helps to provide “broader impact.” CAREER grants are very competitive, so I almost feel like I’m overreaching by applying, but I hate even writing that, because I hate the idea of one of my students or colleagues feeling that they are “not good enough” to even apply for something. Ugh! So much tangled impostor syndrome and negative thinking there. Also, people are 100% right when they say “the one [blank] you definitely won’t get is the [blank] you don’t apply for.” This is not what I want to hear when I’m looking for an excuse not to do something, but it is true. Also, I want women to receive a fair proportion of these grants, and it seems likely that a larger percentage of female applicants would result in a larger percentage of female awardees. Starting out, I felt ready because I had all the materials from my NSA grant application. I worked hard at the bootcamp, worked on the application a lot more through the spring, got in touch with my University’s and College’s research offices, made a budget, patted myself on the back for being ahead of the game, and then… ARGH! It’s nine days before the proposal is due and I am nowhere close to done! Almost nothing is all the way finished! I still need to get letters from 10 different collaborators attesting that they will work with me if I do get the grant. I still need to address several important questions in my proposal, like how I will evaluate the educational component, and why 5 years is the right amount of time for the proposed work. Why? Why didn’t I do these things earlier? I console myself with the fact that I really did do many things early, but I had many other things to do, and there are just many, many pieces of a grant application, which take an extraordinary amount of time to assemble. And I know that because I care about these projects, I will keep putting time in until I am satisfied with everything, which will never happen, so in some sense it is actually impossible for me to be done ahead of time. Working up until the last minute doesn’t always mean procrastination—sometimes it just means going overboard. I will be working hard for the next week to get everything in order, but even if I had more done, it would still take me all week to do the rest. Right now I am working on polishing up the educational/broader impact components of my proposal. The following slides, from a November 2015 NSF talk about the CAREER program, give a general idea of what they say they are looking for in education/broader impacts. Many people that I talked to had a very easy time outlining their research plans but struggled to come up with broader impacts that they found exciting. My experience with this was different: I found thinking of broader impact ideas to be incredibly fun, and couldn’t stop once I got started. I had a list of ideas much longer than I could use and had pare down to a realistic and cohesive plan. It seems important to match your real educational interests, to integrate the education with the research component, and to propose something that will not take a ridiculous amount of time away from your research and the rest of your regular job at your institution. At the workshop, we brainstormed some more specific activities that could meet these criteria. Here are just a few of the more popular ideas that people had: • Run a speaker series, potentially focusing on women or other underrepresented groups when inviting speakers. • Organize a conference, coordinating with/making use of an existing meeting (like the Joint Meetings or a regional AMS meeting) if possible. • Contribute to an existing Math Circle, or start your own (many people at the workshop pointed out that starting one can be a lot of work, but could work for you if you are passionate about it!) • Organize or give a talk in a science pub lecture series. • Write expository articles/introductory notes on advanced material in your research area, especially if there is no introductory textbook available. • Write a great math blog. • Contribute code to an open source software package like Sage, or make contributions to online math resources like the Online Encyclopedia of Integer Sequences. I had better get back to working on the actual application now, but I’d love to hear how other people are doing with their grant applications, and any other great ideas for broader impacts or not procrastinating. Posted in grant proposals, research | | Leave a comment ## Painless Inquiry: TIMES Curriculum I wrote a lot about my linear algebra class last fall. While many things had gone well, I was a little disappointed in some of my attempts at developing inquiry based activities for my class, and wanted to work on polishing (or completely re-making) a lot of my material before I teach it again this fall. To that end, I signed up for a minicourse at the joint meetings run by the TIMES (Teaching Inquiry-oriented Mathematics: Establishing Supports) project. TIMES has pre-made curricula for linear algebra, differential equations, and abstract algebra. The activities I saw in the minicourse lined up very well with the way I like to teach: not straight up Modified Moore-style IBL (which works great for some people, but doesn’t really seem to fit me or my students), but more structured and supported. Through these activities, groups of students will get an intuitive sense of what it means for, say, two vectors to span a space, before the definitions are introduced. Each of the three subject areas has student curriculum, notes for the instructors, and even videos of the activities in action so you can get a sense of how the classrooms work. For a more thorough explanation of the goals of the project, a list of references, and details on how to access the password-protected parts of the curriculum, read a post by the three PIs of the project, Estrella Johnson, Karen Keene, and Christy Andrews-Larson, over at the AMS Teaching and Learning blog. I enjoyed the minicourse and planned to implement some of the activities in the fall, so when the organizers invited me to apply to be a TIMES fellow, I went for it. Last month, we had our training workshop at NC State. Our (admittedly somewhat uninspired) divisions. We began with an icebreaker that I am definitely stealing. Normally this is my absolute least favorite part of a workshop, but this was pretty fun and a good way to encourage a lot of questions. In groups of four, we had to design a set of axes based on some yes-or-no criteria – do you have a dog? are you an algebraist? – in such a way that each group member ended up in one quadrant. We did this on our group whiteboards, which I’d used back in my K12 teaching days but hadn’t even thought about carrying over to college. They’re just showerboard, cut to size at the hardware store, and way, way cheaper than typical white boards. It comes in 4×8 foot sheets for under$15, and they’ll sometimes cut it for free if you’re nice.

The rest of the workshop focused on exploring the content of the curriculum, and how to effectively implement it by encouraging small group work and facilitating larger class discussions. We had surprisingly deep conversations about nuances of linear algebra which none of us had ever really thought about before, even though we all thought we knew the subject forwards and backwards. We talked about how to help students adjust to this different style of teaching – which I’m actually finding easier and easier as more K12 schools start adopting these techniques. And we talked about how to mitigate the dreaded effect on teaching evaluations (which seems to be negligible, possibly after an adjustment period).

I’m really excited about implementing this curriculum this fall, and not just because it will save me the work of designing something new from scratch. This community has a ton of great ideas on how to improve teaching and learning, and I’m looking forward to our weekly discussions. Oddly, I’m also looking forward to getting videotaped and having my own teaching critiqued. I haven’t been recorded since my very first lesson as a Teach for America teacher almost 15 years ago, and while I know the experience will be pretty painful at first, it will certainly improve the way I run my class.

## Writer’s Blargh (prompts for student writing, prompted by my own writer’s block)

Look, this adder-subtractor is totally working, not blocked at all (unlike my writing life right now)!  Image by en:User:Cburnett [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons)

Sometimes I love writing. Sometimes I hate everything I write: mathematical, recreational, shopping lists—sometimes all the words I produce just seem icky. Writer’s block is not something that should matter in math life, right? It’s not adder-and-subtractor block! Alas, I am becoming suspicious that writing might actually be the skill most central to academic life. I write lesson plans and assignments, I write on the board, I write comments on student papers. I write math papers and grant proposals. I write so many emails. I write endless reports on how I am doing great things and should get to keep my job. And of course, I write a blog. But right now writing is difficult, and I am trying to work out how to deal with that.

However, thinking about how much writing I do (and how I still struggle with it) strengthens my belief that it’s important to write in math classes, at all levels. Computational abilities are useless without conceptual understanding and the ability to communicate. Written communication is necessary to effectively convey understanding and justify reasoning in both academic and “real-life” settings. I believe that writing is also a tool to build understanding—by working to express concepts we come to understand them better, by working to express confusion we see a way to clarify. So writing assignments are part of almost all of my courses. However, creating these assignments (and grading the submitted work) is hard!

If I didn’t think that writing is really important I would have stopped there. However, I learned from this mistake and got some help. There is plenty of advice and guidance out there on creating and grading writing—a Google search on “writing assignments for college math” turns up many excellent resources. As a general resource here is a collection from the MAA, and here are a bunch of wonderful ideas from Annalisa Crannell. There seems to be a little less material available for more advanced classes. So I thought I would share some of the writing prompts I used for my Intro to Proofs and Modern Algebra courses last semester.

Note that these were designed to be blog posts, complementary to but very different than the formal proofs that they wrote. I wanted these writing assignments to be informal and not research- or problem-based.  Mostly I asked students to respond to something or explain something.  This may not be what you are looking for, but it has been a useful tool for my courses.  I should also mention (again) that whole idea of doing blogs in my math courses was inspired by reading this blog, and there are also some great prompts there. However, I originally used some of these as non-blog assignments in other courses and they went well. I created all of these prompts, but I do not claim that these are all my own brilliant ideas–some were inspired by colleagues or other sources. You can certainly blame me for the ones you don’t like, though. And of course, please share your good writing ideas and thoughts on these assignments in the comments!

For both classes, these first two prompts were always allowed:

1) Explain some idea from the class up to this point in language that a non-mathematician could understand.  You could pretend that you are talking to your grandmother or your art-major roommate.  Make your explanation as intuitive and non-technical as possible, while bringing across something actually cool about the idea.

2) Write about anything you found especially interesting or puzzling about the material or course so far.  Your classmates are your audience here–you can assume that your audience has a similar mathematical background to yours.

3) This was a popular and useful first week assignment:

Imagine that you are a famous mathematician and have written an autobiography.  Write a 200-500 word excerpt from this book, focusing on some aspect of your mathematical life up to this point.  Your audience is a general reader, at least somewhat interested in math but who may not have taken calculus.

4A) I used the following for Intro to Proof:

There are a ton of math blogs out there, with a huge range of goals and aimed at very different audiences.  Steven Strogatz is a professor and math writer who blogged for the New York Times.  He aims for a broad audience with the goal of entertaining while explaining real higher mathematics.  Here is a link where you can access several of his blog entries:

http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html

Read a couple of Strogatz’s blog entries and write 200-500 words on one of the following:

a) Critique a piece–what does he do well?  What techniques does he employ to make the mathematical idea clear to a general audience?  Are there any things that you think he could do better?

b) Write a continuation of his piece, using a similar style and expanding on what he wrote.

4B) For Algebra, I gave a very similar prompt but focused on this group theory post:

http://opinionator.blogs.nytimes.com/2010/05/02/group-think/

5) In Foundations, we were studying logic and sets, so it seemed worthwhile to bring up this guy…

Bertrand Russell (1872-1970) is one of the greatest figures of modern logic.  With Whitehead, Russell wrote Principia Mathematica, a nearly 2000-page tome that rebuilt the foundations of mathematics in terms of set theory.  He was also an important figure in philosophy, and generally a public intellectual in many arenas.  His personal philosophy led him to a highly controversial lifestyle.

Russell wrestled with some of the same issues of language and logic that we are working with in class.  For example, in the following piece, he replies to a reader’s letter regarding his use of the word “implies”.  He has used it in the strict mathematical sense we have been considering in truth tables, while the reader took it in the more informal sense that most people use in speech.  His reply is enlightening: http://www.users.drew.edu/~jlenz/br-on-if-and-imply.html

For further reading, here is a very large collection of Russell’s work.

Read Russell’s reply and let it influence you as you write 200-500 words on one of the following topics:

a) What is the difference between the mathematical use of “implies” and the usual use of the word?  Can you use this to explain what truth tables and logical equivalence do (and don’t) mean?

b) My favorite math joke:  Three logicians walk into a bar.  The bartender says “Do you all want a drink?”  First logician says “I don’t know.”  Second says “I don’t know.” Third says “Yes!” Why is this joke funny? Explain.

6) Pierre de Fermat was a French lawyer and mathematician who lived from 1601-1665.  He discovered many of the main ideas of differential and integral calculus before Leibniz or Newton, and developed many of the main ideas of analytic geometry before Descartes.  He often wrote mathematical ideas and conjectures in the margins of his copy of Diophantus’ Arithmetica (a 3rd century Greek text).  Later, mathematicians proved many of the statements in these notes, and also disproved a few, until at last only one remained unresolved.  This statement, known as Fermat’s Last Theorem, stood without proof for over 300 years, until the early 1990s when Andrew Wiles, with help from his former student Richard Taylor and others, finally completed a proof.  “The Proof” is a documentary about the remarkable process that led to this proof.

Your assignment:  Watch “The Proof” [PBS or BBC version].  It is approximately 45 minutes long.  After watching, write 500-1000 words on one of the following topics.

a) Mathematicians work in many different ways.  Often, popular culture and accounts of some very famous mathematicians give us the sense that great mathematics must be the work of lone geniuses, working alone, in isolation from the distracting outside world.  The account in “The Proof” in some ways fits that narrative.  However, Wiles was not able to complete the proof entirely alone.  Though he developed many of the main ideas, he needed others to carefully check his work, and Richard Taylor made many essential contributions to fixing the proof.  He also built on the work of many others who worked on the problem in the previous 300 years.

To what extent is collaboration necessary and useful in mathematics?  Is it important to solve problems entirely on your own?  What is attractive about working alone?  Working with a group?  How do you work on mathematics?  How do we know when mathematical work is correct?

b) You may have thought a bit about the difference between “pure” and “applied” mathematics.  Pure mathematics is often thought of as math for it’s own sake, while applied mathematics is done with an application (practical or otherwise) in mind.  One of the main areas of mathematics that arises in the proof of Fermat’s Last Theorem is the study of elliptic curves.  These are cubic curves, the points of which form a group under a nifty geometric operation.  These curves are also important objects in modern cryptography, the science of sending messages over public channels while keeping the content secret from eavesdroppers.  When people first began studying elliptic curves, neither of these applications were anywhere in sight.  Often, mathematics that initially seems uselessly “pure” finds amazing application as times and technology change.  What is your interest in pure vs. applied mathematics?  What kinds of problems do you find exciting?  Do you think that the division between pure and applied math is valid?  Does the idea that pure mathematics can become applied make it more or less exciting to study pure mathematics?

7) For Algebra:

The Rubik’s cube is an example of a game that can be understood using group theory. At the most basic level, every transformation of the cube can be accomplished by some combination of 6 basic moves and their inverses. In cube circles, these moves are often known as F, B, U, D, L, and R, and they correspond to turning the front, back, top, bottom, left, and right sides of the cube clockwise by 90 degrees. Thus the group of possible transformations of the cube is generated by these 6 elements. This group of transformations has order more than 10^19. However, through group theory, it has been proven that every cube can be solved in a sequence of at most 26 basic moves. For your blog entry, think of another game that relates to algebra in some way.  Explain the game and how we can view it through the lens of algebra. Explain what the objects in your set are, and the operation that combines them.  Though there does not have to explicitly be a group, you should explain why the group properties do or do not hold.

What I do when I can’t write anything good (gratuitous fishing with my dad pictures):