![\"Look,](\"https:\/\/i0.wp.com\/blogs.ams.org\/phdplus\/files\/2016\/06\/addersubtractor.png\")
<\/a>Look, this adder-subtractor is totally working, not blocked at all (unlike my writing life right now)! \u00a0Image 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)<\/p><\/div>Sometimes I love writing. Sometimes I hate everything I write: mathematical, recreational, shopping lists\u2014sometimes all the words I produce just seem icky. Writer\u2019s block is not something that should matter in math life, right? It\u2019s 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.<\/p>\n
However, thinking about how much writing I do (and how I still struggle with it) strengthens my belief that it\u2019s 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 \u201creal-life\u201d settings. I believe that writing is also a tool to build understanding\u2014by 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!<\/p>\n
Actually, making the assignments can be easy: \u201cWrite 500 words about the origin of calculus.\u201d Done, right? Sure. Until you start reading the papers that you get, and later reading the comments that students will make on the end of semester evaluations about an assignment like this. This is a terrible assignment. I know because I gave this assignment to a class when I was in graduate school. The best submitted assignments were paraphrased from Wikipedia articles. Grading was a nightmare, as you can imagine\u2014I felt guilty taking any points off, since I had given so few directions and had so little confidence in grading writing. So read a lot of awful papers, agonized, finally gave everyone most of the points, then felt creepy letting these essays pass for college-level writing.<\/p>\n
If I didn\u2019t 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\u2014a Google search on \u201cwriting assignments for college math\u201d turns up many excellent resources. As a general resource here is a collection from the MAA<\/a>, and here are a bunch of wonderful ideas from Annalisa Crannell<\/a>. 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.<\/p>\n 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. \u00a0Mostly I asked students to respond to something or explain something. \u00a0This may not be what you are looking for, but it has been a useful tool for my courses. \u00a0I should also mention (again) that whole idea of doing blogs in my math courses was inspired by reading this blog<\/a>, 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\u00a0sources. You can certainly blame me for the ones you don\u2019t like, though. And of course, please share your good writing ideas and thoughts on these assignments\u00a0in the comments!<\/p>\n For both classes, these first two prompts were always allowed:<\/p>\n 1) Explain some idea from the class up to this point in language that a non-mathematician could understand. \u00a0You could pretend that you are talking to your grandmother or your art-major roommate. \u00a0Make your explanation as intuitive and non-technical as possible, while bringing across something actually cool about the idea.<\/p>\n 2) Write about anything you found especially interesting or puzzling about the material or course so far. \u00a0Your classmates are your audience here–you can assume that your audience has a similar mathematical\u00a0background to yours.<\/p>\n 3) This was a popular and useful first week assignment:<\/p>\n Imagine that you are a famous mathematician and have written an autobiography. \u00a0Write a 200-500 word excerpt from this book, focusing on some aspect of your mathematical life up to this point. \u00a0Your audience is a general reader, at least somewhat interested in math but who may not have taken calculus.<\/p>\n 4A) I used the following for Intro to Proof:<\/p>\n There are a ton of math\u00a0blogs\u00a0out there, with a huge range of goals and aimed at very different audiences. \u00a0Steven\u00a0Strogatz\u00a0is a professor and math writer who\u00a0blogged\u00a0for the New York Times. \u00a0He\u00a0aims for a broad audience with the goal of entertaining while explaining real higher mathematics. \u00a0Here is a link where you can access several of his blog entries:<\/p>\n http:\/\/topics.nytimes.com\/top\/opinion\/series\/steven_strogatz_on_the_elements_of_math\/index.html<\/a><\/p>\n Read a couple of\u00a0Strogatz’s\u00a0blog\u00a0entries and write 200-500 words on one of the following:<\/p>\n a) Critique a piece–what does he do well? \u00a0What techniques does he employ to make the mathematical idea clear to a general audience? \u00a0Are there any things that you think he could do better?<\/p>\n b) Write a continuation of his piece, using a similar style and expanding on what he wrote.<\/p>\n 4B) For Algebra, I gave a very similar prompt but focused on this group theory post:<\/p>\n http:\/\/opinionator.blogs.nytimes.com\/2010\/05\/02\/group-think\/<\/a><\/p>\n 5) In Foundations, we were studying logic and sets, so it seemed worthwhile to bring up this guy\u2026<\/p>\n Bertrand Russell (1872-1970)<\/a> is one of the greatest figures of modern logic. \u00a0With Whitehead, Russell wrote Principia Mathematica, a nearly 2000-page tome that\u00a0rebuilt the foundations of mathematics in terms of set theory. \u00a0He was also an important figure in philosophy, and generally a public intellectual in many arenas. \u00a0His personal philosophy led him to a highly controversial lifestyle.<\/p>\n Russell wrestled with some of the same issues of language and logic that we are working with in class. \u00a0For example, in the following piece, he replies to a reader’s letter regarding his use of the word “implies”. \u00a0He 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. \u00a0His reply is enlightening:\u00a0http:\/\/www.users.drew.edu\/~jlenz\/br-on-if-and-imply.html<\/a><\/p>\n
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