__amzn.to/2AOLGTI__
($16, which is actually cheaper than I could get them from Yale at author discount!) It’s also the same price as paperback.

p.s. Here‘s a review from MAA reviews that really gets what I was trying to do with the book.

#Math4HF

]]>So, I decided to make bookplates for a special event: the paperback edition of * Mathematics for Human Flourishing* releases this week, on Tuesday February 2!

The bookplate features one of the most popular pieces of art in the book, from the opening page of the chapter on Beauty. The art is titled 'Beauty' and was drawn by my friend Carl Olsen (see his other work at carlolsen.net). A few weeks ago, I asked folks on Twitter to vote for their favorite artwork from the book, and this is the piece that won. I love the reflective nature of the piece, with a figure standing and reflecting on the beauty of stained glass window that is reminiscent of a Sie

So, for this week only, I'll send a signed, personalized bookplate if you (pre)order the book for yourself or a friend and send $1 through __Venmo__ or __Paypal__ to cover costs. (For U.S. residents only, through Feb 5, or while supplies last.)

Sign up here for the bookplate: http://bit.ly/Math4HF-bookplate

You can find the paperback at your local bookstore or on Bookshop (which supports local bookstores, https://bookshop.org/a/8982/9780300258516) or Amazon (https://amzn.to/2NKPRK1).

Feel free to tell others about the bookplate offer, along with why you like or are interested in the book. (Tag me, if on social media.)

Let's change the way people think and talk about math!

]]>Christopher Jackson and I were awarded the Mathematical Association of America's Euler Book Prize for *Mathematics for Human Flourishing* at the 2021 Joint Math Meetings.

Good memories around this day. Exactly one year ago today the book came out and 4 years ago yesterday I gave the speech that became the book.

Chris was especially thrilled. Although Chris would not have been able to accept the award in person, we were planning on his mother coming to accept the award on his behalf, if the meetings had not gone virtual.

Here's the citation and our personal responses.

#Math4HF

]]>(1) The combined birthday and book launch party that my wife threw for me in January was so meaningful to me, because Natalie put such care into it, with purple table cloths and thoughtful activities for the guests. It made me feel really special, since I never had birthday parties as a kid. Plus, the book came out and seeing it on the shelves at the bookstore was thrilling and terrifying---I had put so much emotional energy the two years before that into trying to get the message right, and now I was opening myself up to critics and scorn. But I also had the potential to change the way people thought of themselves and each other through the book, and that felt gratifying. I read a few excerpts from the book at the party and I couldn't keep myself from crying. Little did we know that would be the last time we saw most everyone in 2020.

(2) Seeing N being born in July was scary and amazing. He had such a big head that he face was bruised from passing through the birth canal. Having a baby during the pandemic made everything about the experience harder and more stressful. Wish I could tell you stories. But N is healthy, and big in every way (95+ percentile by weight and height), which means that even at 6 months, his old parents find it hard to lift him. He has a killer smile and he melts our hearts, which means we will cuddle and hold him even if it means our backs give out. Being present at home to watch him cross various milestones was a silver lining of the pandemic.

Almost everything else about 2020 has been challenging. Here hoping 2021 is better. May we all be kind to ourselves and one another in the new year.

Francis

]]>Chris and I correspond regularly. He was excited when the book came out, and together with some other mathematicians, we worked on a __research project__ that stemmed from one of the puzzles in it. We've also been hoping the book would draw some attention to his case and the plight of many who now have sentencing disparities. (If you read the book's epilogue, you know that the First Step Act in 2018 reduced harsh sentences for the kinds of crimes he was convicted of, but not retroactively--he'd be free now if it had.) So far, there has not been relief, either in legislation, or in the courts.

Chris has been doing okay, keeping safe from the virus (not an easy feat in a prison). When the pandemic hit, we talked about how those of us on the were experiencing their own "mini-incarceration" (as he put it), with the long isolation and loss of associated freedoms. Of course it's not real comparison. Now picture what that would be like for 32 years---starting as a teen---and you get might get a picture of his plight.

Although Chris does not have access to the internet or regular e-mail, the prison has a limited e-mail system and I've been approved by prison administration to use it. This allows me and Chris to send messages to each other easily.

So: I'd like to assemble a Christmas surprise for him: a collection of notes of appreciation from readers of the book. (Yes, it's a surprise since he has no internet.)

**If Chris' writings have meant something to you, would you be willing to write him a short note? **

You can send your him your thoughts on this __Google Form__ or use the comments section here. I'll collect all responses that arrive by the night of December 23, and email them to him on December 24. Or, you can send him a physical letter at this address:

**Christopher O. Jackson 59433-019**

FCI COLEMAN LOW

FEDERAL CORRECTIONAL INSTITUTION

P.O. BOX 1031

COLEMAN, FL 33521

Thank you for sending him a word of appreciation and encouragement.

Francis

]]>How silly. That is a surefire way to squelch the desire to write. It's way too much pressure.

And then the pandemic hit. Just trying to keep on top of the mad rush to pivot to online teaching, I had no energy to do anything additional. Then summer came, I had a baby, and... you know how the rest of the story goes.

I finally had some time to come back to it, but scaled back my plans. Instead of a series of blog posts, I assembled 100 questions about mathematics (that extend the ones you can find in an appendix to the book), and I put them on the Math4HF webpage:

These questions are tied to the themes of the book, but many of them don't require one to have read the book. So you might find them useful as starting points for a discussion, or as prompts for an essay. As I've written about earlier, reflection questions are great ways to think more deeply about __the virtues of mathematics__ and __recognize the larger goals of learning__. For teachers, such questions are useful formative assessment that can help students see that you value more than just specific skills, but that you are developing them into *mathematically-minded human beings*. In the pandemic era, they can provide meaningful ways to broaden what you assess.

On that page, I've also assembled some further readings to explore, related to each chapter. One of the gems there is a list of "__actionable references__", compiled by my friend Ben Braun, that contain concrete ideas for actions you can take to make the themes and aspirations in Math4HF a reality. I've heard from who are doing book discussion clubs or are using the book as a text for a course---if you develop reading lists, I'd be happy to consider linking to them as well.

And in case you missed my tweets earlier, I also made another webpage containing __the endnotes from Math4HF__, with clickable links, so you can dive into the references as you read.

Enjoy,

Francis

]]>My college (Harvey Mudd) is a school of science, engineering, and mathematics. Because writing is an important part of every discipline, the college shows its commitment to that idea by having every department contribute faculty to teach the college-wide writing course that every first-year student takes.

For me, teaching writing was a chance to think more deeply about how to improve my own writing. I taught this course for the first time in 2018, and as it happens, was also writing a __book__ for the general public at the same time. The old adage "you teach what you want to learn" is really true. Every lesson I taught my students was also being put immediately into practice---the best kind of learning, for sure. The second time I taught the course in 2019, I compiled a list of parallels between the process of writing and the process of doing math.

Here's the list:

- Both involve reasoning and making convincing arguments.
- Both involve creative choices about what arguments are most compelling.
- Both cause anxiety among some people.
- Everyone can improve with practice and encouragement.
- Both benefit from mastering technical skills as well as cultivating an overarching vision.
- It is unreasonable to expect an argument to pop out beautifully the first time.
- More often, getting good involves a process of repeated revision and creative choices to make arguments clearer and more compelling.
- Doing them well can bring great personal satisfaction.
- Clarity of communication is essential, and intertwined with clear thinking.
- Both build virtues that will serve you well no matter what you do in life.

(You can see more ideas, contributed by others, by clicking the tweet above.)

I wondered: if there are so many parallels between math and writing, then **how can teaching writing inform the way I teach math?**

For instance, if I really believe point #1, **then right answers are not as important as the right thinking that produces those answers**. This means in a math class, I should devote time honing students' abilities to make convincing arguments to their peers, and giving them opportunities to do so through class discussion and peer feedback, as is normal in my writing course.

If I believe point #5, then I'd realize that **helping students see the big picture is just as important as teaching them specific techniques/recipes/algorithms for doing things**. This mirrors what happens in writing an essay, where writing, grammar and sentence structure are technical skills that should be mastered, but they are not sufficient for writing a great essay, which also needs to have an overall vision.

If I believed points #2, #4, #6, #7 and #8 then I'd **give my students opportunities to revise their work, to improve the arguments they are making, so that they can ultimately be proud of the final product.** In much the same way, when writing essays, a finished product doesn't pop out beautifully the first time. Instead, good writing is a process---it begins with a rough draft and in-progress ideas that grow through revisiting those ideas and revising them.

Amanda Jansen has a helpful new book, called * Rough Draft Math*, in which she makes and develops this idea very effectively. She's pushing back against the (unfortunately common) way of teaching math at the K-12 level that primarily expects students to memorize or compute things, and makes no effort to connect to the ways that students are beginning to make sense of the ideas. Rather than being affirmed for starting the journey of understanding, students are often shamed for wrong answers. Students who learn math this way grow inured to the idea that their thinking doesn't matter.

Of course, this is exactly the opposite of what learning math should be. Thinking is *everything* in mathematics. Thinking is where joy is to be found, when you *truly grasp* an idea and understand it. The process of learning is just that: a process. To grasp an idea is to start with an unfinished, possibly incomplete, understanding and, through exploring more and more examples gradually understand it better and better.

In fact, this is how mathematicians do math. When I am doing research, I start with an incomplete picture---a guess, a conjecture about something I've noticed. Then I explore more and more---doing examples, trying to reason about why something might be true, until I arrive at a more complete picture of an idea. Moreover, that picture is always being revised as I learn related ideas and place this idea in context. If this is really how math is done, then why isn't it taught that way at every level?

This is where I really appreciate Jansen's framing of encouraging what she calls *rough draft thinking*. As she defines it:

Rough draft thinking happens when students share their unfinished, in-progress ideas, and remain open to revising those ideas.

There's a lot packed in this. A math class should be an environment where students feel free to share their thinking, and feel no shame about brainstorming. They are encouraged, as Jansen says in her book, "to use language that makes sense to them...even if the language is not mathematically perfect." They are aware their understanding is limited, and look forward to revising their understanding as their thinking expands. Again, as I read this in Jansen's book, it reminded me of the way that research mathematicians work when they first start to work on a problem together. Often, when I work with a collaborator on a problem, I marvel at how imprecise our language is because the ideas are still fuzzy, and yet somehow we still communicate. Our language tightens and improves as our understanding grows. Doing math is a process.

How does one encourage rough draft thinking? For teachers (or parents), there's work to be done to create a welcoming environment where such thinking can take place. * Rough Draft Math* is filled with ideas about how to do this at the K-12 level: establishing a culture, and designing rich tasks that allow for communication and revision. Teachers of mathematics will find a lot they can use in this book, and I highly recommend it.

As a college professor, I'm challenged by Jansen's ideas to think about what rough draft thinking would look like in a college math course. The traditional non-interactive lecture---in which a professor recites polished proofs of important theorems and students take notes---doesn't allow space for rough draft thinking. It is the college-level equivalent of asking students to memorize things---in this case, Some Famous Person's Polished Proof. I remember seeing many such Proofs presented when I was in college. Although I'd be awed by the elegance of such a Proof, I often felt like: how would I have ever thought of that myself? That can be demoralizing.

So, what can a college math professor do? Here are some ideas. Many of these can be done in almost any kind of class, but the more interactive your class is, the easier it will be to implement some of these strategies.

**Award partial credit on homework problems when students suggest strategies**, even if they are not ultimately able to solve the problem.

**Publicly affirm any student that offers an idea in class, and build upon it.** In almost any 'wrong' idea there is some right idea that you can build upon to solve the problem. Or, you can pursue the idea, and then discuss what you learn by going down that path---perhaps it is an insight that affirms that this approach will not work. You are inviting students to see how you take a 'rough draft' idea and learn from it, inviting conversation about it. This may mean abandoning what you planned to do in class in favor of going down a path that a student has suggested.

**Encourage students to openly discuss with other students strategies they tried to solve a problem that did not work.** In one class, I made this a requirement: to earn participation points in a class, students would, over the couse of the semester, have to present 5 'productive failures'---things they tried that didn't work and what they learned from it.

**Discuss your own rough draft ideas with your students.** For instance, you might openly discuss in class your own journey to understand a concept: "when I first learned concept X, I used to think that it meant y. After a while I began to realize that Y was not sufficient to capture the idea, because of this example." Or, you might explain a research problem you are working on, and how some of the ideas you are thinking about are still in rough draft form.

**Before presenting the proof of a theorem or a solution to a problem, invite student discussion to generate ideas about how it could be proved.** Here's an example. In one class I teach (Galois Theory) there is a deep theorem that is hard, and the proof is quite unmotivated. Every time I've lectured on this theorem, I've just presented the Proof of Famous Theorem. And I've never been satisfied with that. So last time I taught it, I decided I'd ask students to brainstorm strategies for addressing this hard proof. Two students volunteered their ideas. Neither would work, but we talked about why---and then I showed them Famous Proof, and what was neat was how both of these strategies actually appear in some form that proof. It made everyone pay more attention to the proof because the class had come up with the strategies themselves.

**Give students opportunities to revise their work for a higher grade.** For instance, in my analysis course, on the first 3 assignments, I allow students to revise and resubmit after getting graded feedback. This incentivizes students to pay attention to the grader comments and improve their work.
It also tends to level the playing field, since students enter my course with vastly different backgrounds, and revision allows students some time to adjust to my __Guidelines for Good Mathematical Writing__.

**Incorporate peer feedback in your course.** For instance, have students swap homework assignments, and offer helpful critique on how to improve each other's writing. You should coach students on what good feedback looks like. They could use the Guidelines (linked above) as a start, but you should also explain how to offer feedback in constructive ways.

**Design a final project in which a student takes some bit of work they've done earlier in the semester and revises at the end of the semester.** For instance, they could choose a solution to one of a selection of difficult homework exercises. In addition, ask them to offer a reflection on how they've grown in their thinking and communication.

So much of doing mathematics is really a process: of starting with an idea and improving it. As Jansen reminds us: we can make sure our teaching reflects that.

Wishing you all the best in your pandemic teaching adventures,

]]>But as James Tanton reminded us __recently__, we can shape what it becomes.

After weeks of forced "emergency teaching," I am now in more of a place of equilibrium, and it feels liberating now to actually *plan* some changes. Among them: what kind of questions I'll give on my final exam.

I speak often about how mathematical teaching often overemphasizes teaching specific facts or procedures, while underemphasizing all that goes into building *mathematical explorers* who have the habits of mind and confidence to solve problems they've never seen before.

In other words, we often overemphasize building *skills* rather than building *virtues. *

Virtues are aspects of character like: persistence, curiosity, imagination, a disposition toward beauty, creativity, strategization, and thinking for oneself. Any mathematician will tell you these are important qualities for a mathematician to have, and *better yet, they are important for any other profession as well.*

Both skills and virtues are important in mathematical problem-solving, but the latter is often shortchanged. It's usually only implicitly hinted at in teaching, if mentioned at all. One reason is that skills are easy to measure, but virtues are much harder to assess. This is why K-12 standardized exams focus on skills, and at least at the K-12 level, standardized exams unfortunately drive too much of what we teach. But if you talk with employers about what they are looking for in a mathematically-trained person, it is more often the virtues that they ask about. Can a student think? Are they creative? Curious? Do they have imagination? Moreover, the skills needed from math will change in the future, but the virtues needed from math will not.

Are these in the messages we explicitly send to students (and parents) about what a mathematical education is all about? Do we explicitly tell students: "*One of my goals is to grow your mathematical persistence"?* Or: "*I want to give you a taste of sublime mathematical beauty*." Or: "*I am building in you habits of mind that will serve you well in tackling problems you've never seen before."*

So even after writing a __whole book__ about the way the proper practice of math can build virtue, and even after aspiring to teach math in this way, it dawned on me that these virtues have not appeared much in my student learning goals or the way I assess student learning. A standard college math exam usually looks like this:

Solve these N problems in this fixed amount of time.

Eek... that's what my exams usually look like. How do these exam questions show that I value the building of mathematical virtues? Of course, I always choose problems in which students will display persistence, creative thinking, and curiosity as they solve them, but do my students realize that these virtues are part of the goals I have for them if my exams just ask them to solve a bunch of problems? Why not have some questions on the exam where these virtues are explicitly called out?

So below are a few questions I am considering for a final exam. Notice that **all of them are reflective questions that attempt to explicitly assess the development of virtues**, like the ones I mentioned earlier: persistence, curiosity, imagination, a disposition toward beauty, creativity, strategization, and thinking for oneself*.* There are plenty more (developed in * Mathematics for Human Flourishing*)... but let's just consider these.

And they are **all questions that can be used with untimed, open-book exams.** During a pandemic, students are embedded at home and are not in environments where timed tests can be distraction-free. I don't think the pressure of timed exams will serve students well in these conditions. Why not try something different? And if you do have time restrictions, I encourage you to give out these questions beforehand. Students will appreciate the time to reflect and will give better answers.

**Take one homework problem you have worked on this semester that you struggled to understand and solve, and explain how the struggle itself was valuable.** In the context of this question, describe the struggle and how you overcame the struggle. You might also discuss whether struggling built aspects of character in you (e.g. endurance, self-confidence, competence to solve new problems) and how these virtues might benefit you in later ventures.

**What mathematical ideas are you curious to know more about as a result of taking this class? **Give one example of a question about the material that you'd like to explore further, and describe why this is an interesting question to you.

**How has your mathematical imagination been enhanced as a result of taking this class?** Give at least three examples.

**Consider one mathematical idea from the course that you have found beautiful, and explain why it is beautiful to you.** Your answer should: (1) explain the idea in a way that could be understood by a classmate who has taken classes X and Y but has not yet taken this class and (2) address how this beauty is similar to or different from other kinds of beauty that human beings encounter.

**Give one example of a mathematical idea from this class that you found creative, and explain what you find creative about it.** For example, you can choose an instance of creativity you experienced in your own problem-solving, or something you witnessed in another person's definition or reasoning.

**For any problems you cannot solve on this exam, suggest a strategy you might try to tackle the problem, and show what happened as a result. **Describe any strategic gaps you were unable to bridge, and list 3 helpful insights that may help another person trying to tackle the problem. Doing so will earn you up to 1/2 credit on the problem.

**Choose one interesting problem from the text of medium difficulty that was not assigned. Describe why you find it interesting. Then either solve it, or find a solution online and work through it, using your own understanding to critique that solution and improve it.** An alternative to this question might be: Write 10 true/false questions that illustrate a variety of ideas from this course that you might put on this exam if you were teaching the class. Give a key, explain the answers, then explain why you chose these particular questions and what you hope they will assess.

I teach mathematics at the college level, so you may have to adapt these questions to your own context and grade level. But these types of questions are appropriate at any grade level. You might be wondering now: how to grade such questions. I encourage you not to spend too much effort wrestling with that. The notes with each question suggest a natural rubric (e.g., 'describe 3 examples...') and I'd suggest, and announce, that you'll give full marks for very thoughtful answers where mathematics is correctly described.

You can see more examples of reflective questions that I've used before on ,,__this MAA blog__. One thing I love about reflection questions is that they are much more fun to grade. And you'll see how your students think, which is one of the most important parts of teaching well.

Hang in there, everyone. I hope you are staying safe.

*- updated 4/26 at 11pm to correct a few typos and fix some omissions.*

But as the __reviews__ come in, and I see how the book lands with readers, I'm beginning to re-live the choices I made and the emotions I felt as I wrote the book: the debate over what to say, and how to say it; the struggle over the choice of a word or a phrase; the balancing act needed to reach multiple audiences; and what the book would communicate in its overall feel---whose voices I would amplify, the artwork I would choose, and kinds of stories I would tell. And now that people are hearing about the book, I often get this question: "what's your book about?"

I've found that question surprisingly difficult to answer in one sentence. Some reviewers of my book said the same thing: "this book is hard to categorize". And maybe that's because I had multiple goals for the book. I'll describe here the goals I had in mind while writing. You can debate whether I succeeded. :-)

**The book should feel human.**(Fitting for a book about human flourishing.) That means it should not look or feel like a math textbook. There should be lots of stories, to humanize the practice of doing math and to align with the basic human desires discussed in the book. The artwork should evoke math but also evoke humanness. (p.s. maybe we should re-think the way math textbooks are written, so that 'feeling like a math textbook' isn't a thing?)**The book should be more about being human than about doing math.**Math may be a primary character in my book, but it should always play a supporting role to what my book is really about:*the elevation of human dignity*. Thus, the book and its chapters should lead and end with human stories, and urge us all to be better human beings to one another. Thus I wanted my book to widen the lens around which all of us discuss mathematics, by stepping back and asking the question: "What makes us human?"**The book should be inclusive.**I attempt this in all sorts of ways. The book looks forward to the future of mathematics, and as such it should highlight a diverse set of people doing math, not just professional mathematicians. Teachers and math education researchers are often neglected voices in books about math. Students and non-mathematicians are often left out too. And the voices of very few women or people of color find their way into books about math. So, in quotes and in stories, I have amplified a diverse set of voices and I've positioned those often-neglected voices as people we may have the most to learn from.

**The book should be deeper and broader than the original speech.**The__speech__I gave as President of the Mathematical Association of America was centered around 5 themes ('basic human desires') and in a hour-long speech there is only so much I could say about each one. The book has 12 'basic human desires' that are the chapter titles, so there is lots of new content, but even the themes that were in the speech get a much more expansive treatment in the book. For instance, I actually said very little about Beauty and Truth in the speech, but I perhaps worked hardest on those chapters in the book because they were the hardest to get right.**The book should be accessible to a wide audience, and encourage or challenge all the possible audiences that encounter it.**It's not just a book for the math-anxious public, but it's also a book that can challenge professional mathematicians to change the way they think about math too. I also wanted to write the book in a way that could be used to generate discussion in a math class or a book club.**The book should still have real mathematical ideas in it, explained in a publicly accessible way**. Most of the reviews have focused on my attempts to tie human themes to math, but I also do try to explain some real mathematical ideas too. I use analogies to bring up ideas like these:*duality, invariants, axioms, linear algebra, game theory, proofs by induction and contradiction, mathematical modeling,*and a few other treats. I apologize: it was hard to avoid mentioning the Pythagorean theorem, but that is only because it is so well known and therefore a good launching point for connecting with readers. But there's plenty of uncommon mathematics in there also.**The book should be personal.**Some of the topics I discuss are contentious, and in such situations, I've found that telling my own personal stories can be disarming. I've leaned into that, uncomfortably at times, in the book. I'm grateful to my editor, who encouraged me to double-down on what others have often found most compelling about my writing. But it also means sharing a lot of my own vulnerabilities, and trusting the reader to treat them with care.**The book should start conversations about what we are doing with incarcerated people, and many others who are often forgotten by society.**Christopher Jackson, my friend who wrote the reflections as an official contributor to the book, is one of many remarkable people who remain locked away in the prison system with unduly long sentences after making mistakes as a teenager. If you know someone in a position of influence to change such harsh sentencing laws*retroactively*(the First Step Act reduces sentences, but not retroactively), both Chris and I would be very grateful if you would send them a copy of my book, and let me know so we can track of who's been reached.

In looking over all the goals I mentioned above, it strikes me that the unifying theme of all of them is the elevation of human dignity. So next time I'm asked what my book is about, maybe I will say this: "My book is about the elevation of human dignity, and how we are using math to raise people up or tear people down." If you have a better one-sentence description of the book, feel free to leave it in the comments.

Right now I am feeling gratitude for all the people who have shaped me and helped me along my journey in mathematics. After my own deep discouragement in graduate school, I never expected to be elected MAA President or to be in a position where I would even get to give a speech or write a book that people might want to read. So I took the responsibility seriously, and put forth my best effort. I hope you find * Mathematics for Human Flourishing* encouraging.

#Math4HF

]]>In the past, I've blogged only rarely, mainly because I'm a perfectionist. I like to choose my words carefully and artfully, and the breezy nature of blogging seems to run counter to this. Blogging feels to me like speaking off the cuff, rather than delivering something fine-tuned and profound. I also don't always feel I have anything interesting to say, and along with that, I fear that I'll say something completely off base. Taken together, this means I wait until I have something I'm really sure I want to say, which means I almost never post anything, and therefore I've only used blogs as a way of posting speeches or other things I'd spent a long time crafting, And now the pressure is on---since I'm surely going to disappoint you, if you have come to expect profound from me every time!

Nevertheless, in the new year, I'm going to try to think of blogging differently, and try to blog more regularly. I'll still try to keep it interesting, but I won't kick myself if it's not the best piece of writing ever. I'm going to assume the best of my readers, that you are going to be gracious and not bite my head off if I say something foolish. Feel free to graciously push back against my ideas, though, in the comments section. I'll try to write a little more often, and not always about my new book (which by the way, I have a new book!), but it might be the case in the short term that I'll have stuff to say about my book that didn't make it into the book. The stories behind the stories, if you will.

I'll mostly blog here at francissu.com/blog unless for some reason it requires LaTeX and I need to use my Wordpress blog (__mathyawp.wordpress.com__). (This site was created with Wix—easier to use, but still no LaTeX plugin.) I'll mostly post about math or teaching, but sometimes I'll stray off the beaten path and post personal musings. I invite you to subscribe to this blog (use the ‘login/sign-up’ button at the top to sign up, which will also enable you to comment).

With that out of the way, I'll get to the main point of this first post. As you may know, I have some big news:

**I have a book coming out next week (January 7)!**

My book is titled *Mathematics for Human Flourishing*. If you liked my speech by the same name or my essay The Lesson of Grace in Teaching, you’ll like the book even more. The book has more themes than the speech did (‘basic human desires’—there were 5 in the speech, but there are 12 in the book), and I had more space to develop the ideas. Plus, I included some puzzles to charm the reader.

While most popular math books try to sell you on math by showing you what cool things it can do, I instead focus on how the practice of math can (or should) shape you as a human being.

In the book, I argue that exploring and experiencing math is central to the notion of a good life, a means of developing virtue, and vital for any society that cares about beauty, truth, justice, freedom and a range of other human desires. I also tell lots of stories, and the book is readable even if you don’t know much math. One central story in the book is my correspondence with a prison inmate named Christopher who taught himself math in prison—he’s added some of his own reflections to the book. Another is religious mystic philosopher Simone Weil, whose brother was a famous mathematician. Her journey in confronting her own feelings of inadequacy also provide a poignant frame to the book.

You might enjoy this early review of the book from Harvard Magazine. Here’s an excerpt:

As the review notes, I’ve made the book for everyone, and accessible to a wide audience, including those who are fearful of math but also those who know a lot of math—like math teachers and mathematicians. I’ve also worked hard to ensure that the voices represented in the book are diverse so that everyone can see themselves in the stories told.

The book launches January 7 (though word on the street is that it's already available on Kindle). Pre-orders are possible at your favorite bookseller or on Amazon. By pre-ordering at your local bookstore, you encourage the bookstore to stock more math titles. You might also ask that your public library order it to ensure it is accessible to all. And please tell your friends!

Here’s wishing you all a meaningful and flourishing 2020.

Francis

]]>After giving this talk, I had so many requests for the text that I shared it on Facebook. But Facebook deleted it. So I created a blog just for this. I hope you find it helpful.

It was the hardest thing I ever had to write: because it is deeply personal, truly me, and about my biggest life lesson... given at a conference in front of hundreds of people who, I'm sure, struggle with the same things that I do.

From weakness to wholeness, the struggle and the hope

**Francis Edward Su
**

**MAA Haimo Teaching Award Lecture**
Joint Math Meetings, January 11, 2013

An audio file is available: __bit.ly/W4gyD0__.
Published in print in the Princeton University Press anthology __The Best Writing on Mathematics 2014__.

"We know truth, not only by reason, but also by the heart." ---Blaise Pascal

I’m honored but I’m also really humbled to be giving this talk to a room full of great teachers, because I know that EACH of you have a rich and unique perspective on teaching. I had to ask myself: could I really tell YOU anything significant about teaching?

So: I decided instead to talk about something else, that at first may appear to have nothing to do with teaching, and yet it has everything to do with teaching.

I want to talk about the biggest life lesson that I have learned, and that I continue to learn over and over again. It is deep and profound. It has changed the way I relate with people. It has reshaped my academic life. And it continually renovates the way I approach my students.

And perhaps it will help you frame your own thoughts about teaching. The beginning of that lesson is this:

*Your accomplishments are NOT what make you a worthy human being.*

It sounds easy for me to say, especially after having some measure of academic ‘success’ and winning this teaching award.

But twenty years ago, I was a struggling grad student, seeking validation for my mathematical talent but flailing in my research, seeking my identity in my work but discouraged enough to quit. My advisor had even said to me:

“You don’t have what it takes to be a successful mathematician.”

It was my lowest point. Weak and weary, with my identity and my pride stripped away and my PhD nearly out of reach, I realized then that my identity and self-worth could NOT rest on whether I succeeded or failed to get my PhD. So *IF* I were to continue in mathematics, I could not do it for any acclaim that I might receive or for the trappings of what the academic world would call success. I should only do it because math is beautiful, and I feel drawn to it. In my quiet moments, with no one watching, I still found math fun to think about. So I was convinced it was my calling, despite the hurtful thing my advisor had said.

So did I quit? No. I just changed advisors.

This time, I chose differently. Persi Diaconis was an inspiring teacher. More than that, he had shown me a great kindness a couple of years before. The semester I took a class from him, my mother died and I needed an extension on my work. I’ll never forget his response: “I’m really sorry about your mother. Let me take you to coffee.”

I remember thinking: “I’m just some random student and he’s taking me to coffee?” But I really needed that talk. We pondered life and its burdens, and he shared some of his own journey. For me, in a challenging academic environment, with enormous family struggles, to connect with my professor on a deeper level was a great comfort. Yes, Persi was an inspiring teacher, but this simple act of kindness---of authentic humanness---gave me a greater capacity and motivation to learn from him, because we had entered into authentic community with each other, as teacher and student, who were real people to each other.

So when the time came to change advisors, I decided to work with Persi, even though it meant completely starting over in a new area. Only in hindsight did I realize why I had gravitated to him. It’s because he showed me grace.

*GRACE: good things you didn’t earn or deserve, but you’re getting them anyway.*

By taking me to coffee, he had shown me he valued me as a human being, independent of my academic record. And having my worthiness separated from my performance gave me great freedom! I could truly enjoy learning again. Whether I succeeded or failed would not affect my worthiness as a human being. Because even if I failed, I knew: I am still worth having coffee with!

Knowing my new advisor had grace for me meant that he could give me honest feedback on my dissertation work, even if it was hard to do, without completely destroying my identity. Because, as I was learning, my worthiness does NOT come from my accomplishments. I call this

**The Lesson of GRACE:**
** Your accomplishments are NOT what make you a worthy human being. You learn this lesson when someone shows you GRACE: good things you didn't earn or deserve, but you're getting them anyway.**

I have to learn this lesson over and over again. You can have worthiness apart from your performance. You can have dignity independent of achievements. Your identity does not have to be rooted in accomplishments. You can be loved for who you are, not for what you’ve done---somebody just has to show you grace.

You are worth having coffee with!

Now the academic world does not make it easy to learn this lesson. Especially when so much of academic success depends on achievement. Grades, PhD, publishing papers, getting tenure. And we are applauded for those achievements. We crave that applause! So it’s tempting to be drawn into this trap of needing my achievements to justify me.

So even now, as I receive this award, I must hold fast to this lesson. I must not cling to this award too tightly. It does not GIVE me dignity... because if someone showed me grace, I’d realize I already HAD dignity.

Don’t get me wrong... I’m not saying that achievement shouldn’t be rewarded. There IS a place for credentials in academia. We would not want to hear a talk by someone without credentials. We would not want to graduate students who didn’t have skills. But achievement, in its rightful place, is NOT where we should derive our ultimate sense of identity and self-worth, and we need to have a healthy separation between achievement and worthiness.

If I could really believe this then it gives me great freedom! I can do math SIMPLY because I enjoy it, not because I have to perform. I don’t have to be “the best”. I can stop being so hard on myself. I can have a healthy ambition without competition: striving towards goals, without having to compare myself to other people. I can be happy for another person’s success. I can be appropriately open and authentic---I don’t have to fear showing weakness. Because my worthiness isn’t earned, there’s no need and no room for pretense. I can stop worrying about what others will think of me, if I believe the lesson of grace.

*Grace gives people dignity they don’t have to earn.*

Grace seems simple but it is such a deep concept. Once you recognize it you begin to see it everywhere. Some might recognize grace as a part of many of the world’s great religions. That makes sense, because at its core it’s a theological concept, making a claim about who we are as human beings, and why. In my own religious view, I see Jesus as the ultimate giver and source of grace, endowing all human beings with worth and dignity that they don’t have to earn. But whether you are religious or not, everyone can give, receive, and be drawn to grace, graceful actions and its lessons. Because grace gives people dignity they don’t have to earn.

What does this life lesson have to do with teaching? Well, if life is one gigantic learning experience, then you’d expect any life lesson we learn would shape our teaching. But the lesson of grace has remarkable implications. Here are 4 ways that I see grace can shape our teaching. These go from easiest to hardest: giving grace to students, understanding grace in our teaching, communicating grace in the struggle, and sharing grace in our weakness.

What does it mean to give grace to our students?

The first example is something we already all do. What do you when you want to be nice to your students and you want to wake them up and 8am in the morning? Yes, you give them donuts! They didn’t have to earn that. That’s grace! (Except on evaluation day---then it’s a bribe.)

Here’s another way we show grace to our students---learning their names. By naming people, you give them DIGNITY. Imagine the other possibility: suppose you only learn the names of the people who are getting A’s, or coming to office hours. That’s not grace, because it only dignifies only the people who EARN it.

Spend time with students outside class. That’s grace: it’s a good thing they didn’t have to earn. As long as it’s not just the best students you hang out with, then it’s grace.

I have often given fun exam questions: students can earn some easy points just by sharing the most interesting thing learned in the class, or a question they’d like to pursue further. Or “write a poem about a concept in this course.” Or “Imagine you are writing a column for the newspaper ‘great ideas in math’. What would you put in it?”

These are graceful questions. They really didn’t have to earn those points, and they’re having fun while doing it.

And of course, sharing the joy of mathematics is grace. And going off on tangents in class. Many of you know that I have a collection of “math fun facts”. I have often started off calculus lectures with 5-minute “math fun facts” that have nothing to do with calculus, just to get students excited about mathematics. This is a graceful action. Because going off-topic communicates something to students: that they can learn math just because it’s cool, not because they have to “get through some material” that they’ll be tested on.

There’s a website where you can find my collection (google 'Math Fun Facts' to find it), and if you prefer a mobile version, there’s an app for that!

If we fully understand the lesson of grace, then we’ll understand: since my performance doesn’t define me, I don’t have to be the center of attention in my classroom. I can do experimental things, and fail. I can get out of the way of my students... I can open up the classroom for things like inquiry-based learning. I don’t have to be in control of everything. I don’t have to worry about what people will think of me.

I’ll give a recent example of where I had to think about these things. A couple of years ago, a former student came to me with an idea. He was creating an online learning platform, and wanted to pair up videos of my Real Analysis course with scrolling notes and social learning features, and I said: that’s interesting... what would it involve? He said: we would just have to record your class and put it on YouTube! And I hesitated.

Then he said, it would cool if my class could try out the software and he could run some experiments... and what he was suggesting sounded to me like a radical overhaul of the way I would teach my class. And it made me nervous. This is getting to be a bit much, I thought.

But upon reflection, what I realized is the only reason I hesitated is because I was fearful of losing control, fearful of crazy internet comments and what others would think of me. And I could extend him a great grace by helping him pursue his passion.

So I agreed to have the class taped. What’s interesting is the unexpected grace that occurred as a result of the YouTube experiment. The students were excited about it. They loved the fact they could watch the videos later. They didn’t stop coming to class, as I had worried about. And to my surprise, I began to get grateful e-mail from people around the world. Many of them didn’t have access to a university, were facing particular economic hardships, or learned best when they could pause and rewind lectures.

For them the videos were a grace they didn’t have to earn. I had thought at the beginning of the semester, I would just take down the videos at the end, because I was so worried. But I never took them down, because I realized they are serving a needed function for the least fortunate in our global community, and for people who learn differently.

I want to demonstrate to my students that their worthiness does NOT depend on the grades they earn in my class. Of course, I want to give my C students the same attention that my A students get. But if I am really honest with myself, I have to admit I like talking to A students, because they “get it”... they already speak the same language.

But what credit is it to me as a teacher, if I only affirm the students who already “get it”? It’s easy to affirm the student who asks great questions in class, but I must be thoughtful about how can I affirm the questions from a struggling student. Or the one who comes from a different cultural background. Or the one whose educational system didn’t provide them with the tools they need. How can I affirm these students?

I like to tell them the struggle is the more interesting place to be: because a healthy confusion is where the real learning begins. Just like in life, the most meaningful lessons are learned when our afflictions and struggles are greatest.

But I want to be clear: I am not saying extending grace is a recipe for helping my students feel good about themselves. I am saying it will help them have a right understanding about themselves. So if my students know in their bones that I have given them a dignity that is independent of their performance, then I can have honest conversations with them about their performance. I can judge their work justly AND graciously. In fact, failing a student CAN be done with grace, so that the student understands their dignity has not been tarnished even though their work has been justly assessed---just as a parent can discipline her child if the child knows her love is unconditional. Grace is precisely what makes hard conversations possible, and productive, between people. But you have to extend the grace first.

I want the failing student to understand clearly that grades are just an assessment, not a sentence. I try to meet with every failing student in person, and I will explicitly articulate the distinction between their grade, and their worthiness. I will often give them this explicit word of encouragement: that while grades attempt to measure what you have learned, they do not measure your dignity as an individual.

I don’t mind telling students that I almost didn’t make it in graduate school. Because I understand that my worthiness is not in my accomplishments, I don’t fear that people will think less of me. I know what it means to enter a program with a weaker background than my peers, to feel woefully underprepared, to feel misunderstood, to have family pressures that somehow became paramount. To wonder if I was really cut out for this profession. So I know that weakness can be powerful when a former student shares:

"He gave me the single most important piece of advice I got before heading to graduate school, which greatly shaped how my mathematical career developed. It occurred when I asked him about his graduate school days, which surprising as it may be, did not go very smoothly for him! He confessed to me that at one point he considered dropping out of Harvard! The lesson he learned was to pick an advisor you can ... thrive with, even to the sacrifice of a particular subject or project. I took this advice to heart... and as a result I thrived in graduate school which has directly resulted in my early career success as well."

This is from a student who was not the top of his class at Harvey Mudd, but he chose a graduate school where he could thrive, and it led to an NSF postdoc and he’s just finishing that now.

I don’t mind talking with students who are having serious family issues about losing both of my parents to terminal illnesses and telling them it’s okay to let academic work suffer. Because as human beings, they aren’t defined by their academic work.

I don’t mind telling students with emotional issues that it’s OK to see a counselor, because I’ve seen a counselor.

So with a struggling student, showing my weakness is extending and sharing grace. I am validating their worthiness in our shared struggles. *They don’t have to perform well to earn my favor.*

And... sometimes, showing weakness enables us to RECEIVE grace from our students. One of the nicest things a student ever said to me came when my father was dying of cancer, and I was flying back and forth to Texas multiple times to tend to his care. There was a point in the semester when my class had had more lectures from other people than from me, and it was surely disruptive for them to see a different professor every day. So I confessed to my class that I had two roles---as a son and as a teacher---and I felt I was doing neither of those roles well. One of my students said to me, so gently: “Should I be terminally ill later in life, I would want my son to act as you have.”

Ah, grace! From my student, who reminded me: I didn’t need to be so hard on myself. *I didn’t need to perform well to earn his favor.*

**So this is the Lesson of GRACE:**
** Your accomplishments are NOT what make you a worthy human being. You learn this lesson by receiving GRACE: good things you didn't earn or deserve, but you're getting them anyway.**

And this is my HOPE: that you could receive and give GRACE.

We are so trained by our accomplishment-driven culture to believe that our deeds are what make us worthy of honor or respect. To fight this, you have to surround yourself with grace-givers, people who are good at it.

All the best teachers in my life have been grace-givers. Think of that teacher whom you knew was busy, but still made you feel like you were the most important person in the world. Think of those people whom you can be authentic with---those who, even if they know all the rotten things about you, would love you anyway.

The ones around whom you feel you have no shame.

Sure, good instructional techniques are necessary for good teaching. But they are not sufficient. They are NOT the foundation. Grace-filled relationships with your students are the foundation for good teaching, because it gives you freedom to explore, freedom to fail. Freedom to let students take control of their own learning, freedom to affirm the struggling student by your own weakness. Grace amplifies the teacher-student relationship to one of greater trust in which a student can thrive.

“To teach is to create a space in which the community of truth is practiced.” ---Parker Palmer

That community and space that Parker Palmer talks about does not form without grace.

I’d like to think that I’m a good teacher because I communicate well and I choose the best examples, and that when my former students think of my teaching, they think of these things. But that is accomplishment-driven thinking isn’t it? Instead what students remember most often are those moments of grace.

Last year, at Harvey Mudd graduation event, a math major Simeon was invited to give a speech to parents about his college experience. I'd like to close my talk by sharing part of it, with his permission:

“The one class that best embodies the essence of Harvey Mudd College was a class called Real Analysis. In Real Analysis I learned to question the very definition of real numbers and everything I knew about mathematics. What do you mean I have to prove how to add two real numbers? Proof by common sense and elementary education were strictly prohibited. Real Analysis was perhaps the hardest class I’ve taken, and my first experience of struggling in math. I wasn’t getting the concepts as quickly as some of my peers, and I couldn’t help feeling incompetent in math, a subject I had always felt confident in... the “gateway” to mathematics never felt so narrow and without space for an incompetent student like me... Fortunately, there’s more to the story. During that semester I was doing a book study with Professor Su outside of class, and I was uncomfortable. Sitting before me was a super smart incredible professor, and I felt really unworthy to be hanging out with him because I wasn’t doing so well in his class, and I thought I might disappoint him once he got to know me personally. But at our last meeting, we were talking and he said, 'I want students to understand that professors don’t value students based on their academic performance'... to hear from my own professor, whom I really love and admire, at a time when I felt ashamed of my intelligence and thus unworthy of his friendship, that I wasn’t just a student in a seat, not just a letter grade or a number on my transcript, but a valuable person who he wants to know on a personal level, was perhaps the most incredible moment of my college career. And that’s the kind of place that Harvey Mudd was.”

Yes, Simeon, you get it! You understand the transformative power of grace! My hope for all of us is that we would understand grace in all its forms and how it can transform our teaching.

And not only will grace inspire our students, it will inspire us. Just like my students, the moments I remember best from my own teaching are the grace-filled moments I have shared with my students and colleagues and former teachers, many of whom are here today. I want to thank them, because I didn’t deserve those blessed moments. But they gave them to me anyway.

“We know truth, not only by reason, but also by the heart.” --- Blaise Pascal]]>