I love teaching, and I hate grading. I know I’m not the only one. This semester, my math history course posed new grading challenges to me. Grading writing assignments is much more subjective than grading traditional math homework and tests, and the wide range of prior experience (some students’ most advanced math class was calculus 1, and some have taken abstract algebra or topology) proved a challenge for the math-heavy assignments. I have never been completely satisfied with my grading systems, but this semester convinced me that I really need to rethink my approach.

As Robert Talbert wrote in a recent post about grading, “Traditional grading systems work against my goals as a teacher.” Because this was a writing course, editing and revision were important parts of the process. I felt good about the way my feedback helped students improve their work, but I felt like assigning points was petty and antithetical to the collaborative atmosphere I wanted to create.

Enter specifications grading. Last month, specifications grading started popping up in my blog feed. Specifications grading is based on a recent book by Linda Nilson, founding director of the Office of Teaching Effectiveness and Innovation at Clemson University. Talbert interviewed Nilson on his blog, Casting Out Nines. The basic idea of specifications grading is that the syllabus for a class will outline exactly what students need to do to get a desired grade, be it a D or an A, and all assignments are graded pass/fail. Students who want to get a higher grade will have to do more and possibly better work, but all students will have to do acceptable work on some assignments in order to pass the class. Nilson also advocates giving students “tokens” at the beginning of the semester that can be exchanged for an extension or a second chance on an assignment.

Talbert and T.J. Hitchman had a Google hangout on the subject of specifications grading that is now available on YouTube. One thing Talbert said that stood out to me was, “You have students basically opting in to the grade and the work load that they want to take on.” That opting in is what appeals most to me about specifications grading. Some students just want to pass a class, and some want to get an A. In practice, at least for classes I’ve taught using traditional grading schemes, this means that the students who just want to pass do a mediocre job on all the assignments. Wouldn’t it be better if students had to do acceptable or even good work on the assignments they chose to do but could choose which assignments to do? Then I wouldn’t waste my time pushing and prodding students who aren’t interested in putting forth the effort necessary to get a high grade.

I have been thinking about using standards-based grading for a while, but the endless cycles of reassessment that Hitchman mentions in the hangout have been deterring me. I’m sure this is about my struggles to think creatively about standards-based grading, but specifications grading just feels more straightforward to implement. Bret Benesh wrote an interesting post comparing specifications grading as he understands it to the system he currently uses, which he calls accumulation grading, and I think his experience will help guide me as I start to think about reassessing my assessment method. I’ve checked Nilson’s book out of the library, and I hope to incorporate specifications grading into my courses next semester. I know that it will not be a magic bullet, but I think the ideas will help me create a syllabus that better serves both me and my students.

]]>- 95% of mathematicians watch from 1 to 3 hours of TV per week
- There is a 95% probability that the average number of hours of TV watched by all mathematicians is between 1 to 3 hours
- If 100 similar polls were conducted, the average number of hours of TV watched by a mathematician will lie within the interval from 1 to 3 approximately 95 times.

Whatever your answer to the question above, think about whether it is equivalent to the following correct answer: the PROCESS used to create the confidence interval has a 95% chance of success—that is, there is a 95% probability that whatever interval is created through this process will contain the true average. While it is conceivable (but unlikely) that I could find enough mathematicians to replicate my experiment 100 times, I’m still not sure what this tells me since I may get (possibly very) different upper and lower bounds for the confidence interval each time I perform the experiment.

I probably sound kind of like a really annoying Sophomore by now, but here is my honest question: what is the most reasonable way to practically use confidence intervals? Along these lines, it seems that psychologists are strongly considering using alternative methods (to the currently accepted significance level) for reporting the results of their experiments. Under consideration is the reporting of confidence intervals, which do not rely on null hypothesis testing.

I guess one question is – is this mainly a problem with education in that people don’t know what a confidence interval is, or is it that the measurement itself is not serving the purpose that most people have come to use it for

So hopefully you have some ideas for me, and maybe now someone will be inspired to conduct a survey on TV-watching habits of mathematicians at the next JMM’s.

These reflections are all inspired by:

1) Alex Etz, a UT graduate student at The Etz-Files: Blogging About Science, Statistics, and Brains — Nov. 16th and Nov. 20th posts entitled *Can Confidence Intervals Save Pyschology? *http://nicebrain.wordpress.com/2014/11/16/can-confidence-intervals-save-psychology-part-1/

2) From my friend Suz Ward at AIR — July post entitled *Confident or Credible? Two Metrics of Uncertainty for Decision Making* http://www.air-worldwide.com/Blog/Confident-or-Credible–Two-Metrics-of-Uncertainty-for-Decision-Making/

3) Christian Jarrett at the BPS Research Digest– Nov. 14th post entitled *Reformers say psychologists should change how they report their results, but does anyone understand the alternative?* http://digest.bps.org.uk/2012/08/phew-made-it-how-uncanny-proportion-of.html

Don’t get too worried: it’s about astronomy, and the two disciplines have a long history together. Mathematics is certainly necessary for astronomy, and astronomy motivated the development of much mathematics. With that justification, I’d like to introduce you to tychogirl by Christine Rueter. Her poetry combines images from space with spare, arresting text.

Rueter often make scenes from the history of space exploration visceral. This one, written in honor of the 45th anniversary of the Apollo 11 mission that landed on the moon, just grabbed me.

Rueter has posted recently about Philae’s landing on a comet and the spacecraft and rovers that are exploring the solar system where we can’t.

As with all poetry, I can’t explain what I love about Rueter’s work, but it sometimes gives me goosebumps. So I hope you’ll pardon the digression from mathematics and take a look at tychogirl.

]]>A couple years ago, xkcd described the Saturn V rocket (Up Goer 5) using only the ~~thousand~~ ten hundred most common English words. Of course, xkcd readers were eager to try it themselves, and geneticist Theo Sanderson created an online text editor for it. Thus tenhundredwordsofscience and upgoeryourphd were born. Both sites feature attempts by people from all sorts of branches of science to describe their work using only those thousand words.

Last month, David Roberts posted a proof of multiple cardinalities of infinity using only one-syllable words to the n-Category Café. Like the up-goer five challenge, the one-syllable exercise is part Oulipo and part math/science communication. The requirements are strictly enforced, leading to circumlocutions that would be clearer with a little more flexibility. (“The small round thing that passes through the sky every night as it moves around us” is not clearer than “moon,” but “moon” is 1809 on the list of most common words, so it doesn’t pass the up-goer 5 test.) You can get away with a little more with the one-syllable challenge, but it’s still tough.

The comments on the post and the related Google+ post have some good examples of mathematics written in one-syllable words or with other constraints: cartoon proofs, proofs in verse, proofs without the letter ‘e,’ and so on. I am also reminded of the (sadly dormant) @ProofinaTweet and @TinyProof Twitter accounts.

The constraints are fun to play with, and they’ve helped me think about the difference between using simple or short words and actually making a concept easier to understand. The Simple English Wikipedia is designed to have articles that are more accessible to children and adults who are learning English than the regular English Wikipedia articles are. There are guidelines, not rules, that help authors make their ideas easier for English learners. Authors are encouraged to use the 850 words on the Basic English list, but they shouldn’t adhere to that limitation if doing so results in more confusion. Flexibility is important for clarity.

When writing about math and science, people with technical backgrounds are often encouraged to avoid jargon, and in general, that’s sound advice. But sometimes, it’s better to explain the word homotopy and then use it in an article than to say “deformation of one thing into another thing without cutting it” twelve times. (By the way, that’s the Simple English Wikipedia explanation of homotopy, and it’s pretty good, isn’t it?) Jargon has a place not only in communication between experts in the same field but also in popular science writing. But it is a hurdle for readers, and I think it’s a good idea to approach it with caution. The up-goer five and one-syllable challenges feel like extreme versions of a no-jargon challenge. (OK, maybe not if you study stacks, sheaves, or schemes.)

After my recent post on higher homotopy groups, a jargon diet is probably a good idea. I didn’t participate in the up-goer 5 challenge, but the ~~one-syllable~~ just short words math ~~challenge~~ task sounds more interesting to me. I haven’t decided what proof I’m going to monosyllable-ize yet, but I will be participating. I’m interested to see what other people do with it as well. Feel free to share your contributions in the comments here, at the n-category Café, or on your own blog.

I first encountered Gwen Fisher’s work at the fiber arts exhibit at the 2014 Joint Mathematics Meetings in Baltimore. Fisher has a Ph.D. in math education and is an accomplished mathematical artist who specializes in beading. I featured one of her pieces (a beaded group of order 18) in an article I wrote about the fiber arts show. Since then, I’ve been following her blog at her website gwenbeads. She posts about her mathematically inspired beadwork and often includes explanations of the underlying mathematics.

The bead that caught my eye most recently is the “highly unlikely triangle,” based on the “impossible triangle,” or “Penrose triangle,” that shows up in many M.C. Escher works. Fisher’s triangles are not actually impossible, but they do seem to twist around in an unlikely way. A link from that post led me to Borromean linked beaded beads and a highly unlikely hexagon! She’s also made beaded beads named in honor of mathematicians Harold Coxeter and John Conway.

Hyperbolic geometry enthusiasts (like me!) will probably enjoy Fisher’s post about beaded tilings of the hyperbolic plane. Like crochet, it seems that beading can allow for a slight increase in area around vertices that distributes the negative curvature of the hyperbolic plane in an even—and very visually appealing—way. Fisher has beaded several different tilings of the hyperbolic plane: the {4,5} tiling (5 squares around every vertex) and the rhombitetrahexagonal and snub tetrapentagonal tilings, both of which use multiple shapes. I think the prettiest one is the snub tetrapentagonal tiling made of pink pentagons, yellow squares, and green triangles shown above.

I’ve just finished helping out with a level 2 Menger sponge build as part of MegaMenger, so I’ve also been interested in Fisher’s posts about the Genie Bottle she and her group Struggletent built at Burning Man this year. It was a giant, furnished, climbable sculpture. It was also ephemeral, spectacularly going up in flames at the end of the event. I’m tired from just a few days spent folding business cards for our Menger sponge. I’m in awe of how much effort went into the Genie Bottle!

In addition to the blog, Fisher has an etsy shop where she sells tutorials for many of her designs as well as beads, hats, jewelry, and other items she makes. She also runs a business called beAd Infinitum with fellow mathematician Florence Turnour. All of her sites are interesting if you’re into math, art, and making things!

]]>I am teaching a math history class this semester, and in addition to trying to teach my students math and history, the course satisfies an upper-level writing credit. It’s a lot to try to cram into one three-hour course! With 40 students enrolled at the beginning of the semester (enrollment has dropped a bit since then, but it’s still large), I wasn’t sure how to get my students doing a significant amount of writing, give them meaningful feedback, and let them revise their work without burying myself in a mound of paper every time an assignment was due.

In part because of that concern and in part because I like blogging, I decided to start a class blog. I have a rolling deadline system that keeps the flow of new writing somewhat manageable, and doing everything online means I can easily email comments and suggestions to my students. Now that the semester is about a third of the way through, almost all of my students have written at least one post for the blog, and I think it’s time to share it with you.

The blog is called 3010tangents because the course number for our class is math 3010, and the posts on the blog should be at least tangentially related to topics we cover in class. We started the course talking about how we write numbers, so we have some posts up there about different base systems, including an impassioned plea to switch to dozenal and an exploration of a binary monetary system in the Book of Mormon. (The religious text, not the musical.) Subsequent classes have touched on a lot of different topics, and my students’ posts reflect that. They have written about Euler, Ramanujan, Noether, al-Khwarizmi, and Zhao Shuang. They have also written about art, religion, limits, and women in math. And of course, the perennial question of whether math is invented or discovered has gotten some treatment.

One of the reasons I started the blog was to get students who are interested in math teaching and communication involved in the wider online mathematics community, so I hope some of you will stop by and give them (kind, helpful) comments on their posts or read and share them. You might even learn a little something about math history!

This is my first time running a class blog, and I am keeping track of what goes well and not so well about the experience. I’m sure I’ll write more about blogging in a math class when all is said and done.

]]>However, it is exciting to see some coverage of the “basic reproduction ratio”, R_0 , and a plethora of graphs aimed at showing the variety of scenarios that might unfold in West Africa. Amy Greer at Math.Epi.Lab is one of the researchers using the IDEA (incidence decay and exponential adjustment) model to regularly update predictions as to when this outbreak will reach its peak.

Currently, the IDEA estimate is that in December of this year, the number of cases will peak at around 13,000. Dr. Greer sees the total number of cases due to this outbreak as easily reaching 20,000. In one of her posts, she posts the evolving value of R_0, a nice reminder that this is a dynamic parameter that is estimated using Estimation Theory. In this graphic, the control parameter d “controls” the weight of the mitigating measures in reducing incidence.

Data on Ebola has been provided by the World Health Organization to the general public, and Caitlin Rivers, a computational epidemiologist at Virginia Tech, is making this data more accessible. Ms. Rivers titles her Ebola-related posts #HackEbola, and a quick twitter search shows others using the hashtag as well. World Health Organization more accessible. And her most recent post looks at the data concerning follow-ups with those who have come in contact with someone infected with Ebola.

My favorite math and epidemiology blog so far has been Musings on Infection, in which computational epidemiologist David Hartley ponders various infectious diseases, but especially focuses, in his last half a dozen posts and on his twitter feed, on Ebola. In his post “Epidemiology and behavior in the time of Ebola”, Hartley points us at some great articles, and gives some food for thought, including the possibility that Ebola could become endemic due to the distrust between healthcare workers and the local population. It is interesting to see how different estimates are holding up. Looking back, one of the earlier studies that Hartley references on a September 02 post entitled “Why Model Infectious Disease”, the graphic from physicist Alessandro Vespignani’s paper predicted the number of cases today to be between about four and eleven thousand. Indeed, the current number of cases is 6,500 according to the CDC, which is well within Vespignani’s range.

The ability to isolate currently infected individuals and follow up with those who have been exposed will play a huge role in determining the evolution of the “effective reproductive number” – the number of individuals that are actually infected by each currently infected person. So I leave you with a tool that you might consider using with your students or just play with for your own edification. The game VAX, developed by Phd candidate Ellsworth Campbell, is a great way to get a feel for how disease can spread through a network depending on the connectivity of the network and the ability to vaccinate those who are healthy (not yet a possibility for Ebola) and quarantine those who are infected.

Hope all of this helps to better inform you as to some of the mathematics involved in helping to analyze the current situation in West Africa. Please let me know if you have a favorite blog that discusses mathematics and epidemiology.

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The Heidelberg Laureate Forum is a chance for stodgy old Turing, Abel, Nevalinna, and Fields laureates to get an infusion of fresh ideas from the 200 young math and computer science researchers who graciously agreed to attend. Or maybe it’s a chance for 200 fresh-faced, eager young mathematicians and computer scientists to take in some of the wisdom of the laureates who graciously agreed to attend. Either way, it will be a chance for mathematicians and computer scientists to network not only within their respective groups but across the aisle, as it were.

The opening ceremony for the meeting was Sunday night. I don’t know whether the highlight was the reappearance of the odds-defying saxophone quartet that John Cook wrote about last year or International Mathematical Union president Ingrid Daubechies’ joke that mathematics is a very old profession, but of course not *the* oldest profession. Two themes of the opening comments by organizers were about speaking slowly to communicate well and about using our powers for good, especially in the case of computer science, where as we have seen recently (hi NSA, what’s up? Nothing to see here…), computer security can have very serious consequences. As Alexander Wolf, president of the Association of Computing Machinery, which awards the Turing Prize, pointed out, these cautions about computer science represent something of a victory: the benefits of computing are so widespread and obvious that they are just taken for granted. It is hard to imagine a world without them.

From the look of the program, we are in for a lot of outstanding talks this week. Personally, I hope to get a better feel for some of the big ideas in computer science from some of the speakers. But we all know that a lot of the real benefit of a meeting is what happens between talks and on excursions. I’m looking forward to making connections during those in-between times!

This year, the meeting has both a German and an Engligh blog. I’ll be blogging (in English) while I’m at the meeting, so you can find me over there. I might even livetweet a few of the talks, so you can also follow me on Twitter if you’re not already. The hashtag for the meeting is #hlf14. Tschüss!

*This blog post originates from the official blog of the 2nd Heidelberg Laureate Forum (HLF) which takes place in Heidelberg, Germany, September 21 – 26, 2013. 24 Abel, Fields, and Turing Laureates will gather to meet a select group of 200 young researchers.*

In August, Matilde Lalin wrote a guest post on Terry Tao’s blog about attending conferences with young children focused on the options for nursing mothers. The three main options she identifies are: travel with a caretaker, hire a caretaker at the conference location, or leave the child at home and pump. (The fourth option, not going to the conference at all, is one many families end up choosing, as Kate Owens mentions in the comments, but can come at a cost of opportunities for collaboration and networking.)

In addition to the financial considerations for each option, Lalin writes about scheduling and other logistical concerns, including the choices parents have to make about what to skip when they attend a conference with a child. She includes practical suggestions for conference organizers about how to make conferences easier for nursing mothers and links to several organizations that are helping support academic parents. Of course, many of her suggestions also apply to parents who are traveling with kids but not breastfeeding.

As a non-parent, I must admit that I hadn’t really thought about the burden of child care at conferences until Jordan Ellenberg wrote about it a couple years ago. He argues that the NSF should fund conference daycare. There are quite a few interesting comments to the post about whether or not childcare should be considered a business expense. I think the one that sums it up the best for me is by jenfns, who writes, “I guess the question is whether it should be a cost of the employer to pay for travelling employees’ childcare. Since our society does in fact have a vested interest in successful professional women bearing and raising children, I think that the answer should be yes.” Unfortunately, for federal tax purposes, child care costs are not considered “necessary” expenses, and I assume until that changes, the NSF will not be able to reimburse conference child care costs.

Last month, Laura McLay wrote on her blog Punk Rock Operations Research that the Forum for Women in OR/MS (delightfully acronym’d WORMS) is sponsoring grants to reimburse child care costs for parents traveling to the INFORMS Annual Meeting. And I just saw that the AMS and MAA are also rising to the occasion, with about 40 child care grants available for mathematicians attending the Joint Mathematics Meetings in January. Applications for those grants are open until November 18. The JMM has had subsidized (but still expensive) child care available for several years, but as far as I know, this is the first year they will also have reimbursement grants available.

Better support of child care costs will help women most directly, but it should be noted that all the grants I have seen are available to both men and women, as they should be. Women sometimes shoulder the lion’s share of the child-rearing duties, but the idea that raising children is only “women’s work” is antiquated and devalues the active role many men play in their children’s day-to-day care. Paying for child care at conferences is a way to make life easier for both men and women who are trying to balance their careers and families.

]]>Like many people, I have been following news about the events in Ferguson, Missouri with shock and sorrow for almost two weeks. I have been following these events as a human, not as a mathematician. But there’s a mathematical side to this story, too. I’m not just talking about the statistics on how many people are killed by the police each year (which we don’t even know for sure) and the racial composition of the Ferguson police force versus the people they stop and arrest, although those are both important. I’m talking about Twitter. It’s been a crucial part of how the Ferguson story has become international news, but it’s also a useful source of data about how people are responding to the tragedy.

Emma Pierson is a computational biologist currently working for 23andMe, and her blog, Obsession with Regression, focuses on data analysis, often with Twitter’s data. She writes,

“I am very excited about Twitter because it combines two qualities.

“1. People actually use it. Famous people — it’s become standard for celebrities to say “Follow me on Twitter!” — and more importantly, lots of people.

“2. It makes massive amounts of data available in a way you can process with a computer. 500,000,000 tweets are sent every day and Twitter will give you up to 1% of those. And if I know

what1% I want — for example, only Tweets containing the word “Spock” — it will give meallof them, which means I can actually heareverythingthat’s being said on a topic by millions of people worldwide. And not just what’s being said, but who’s saying it — how they describe themselves, where they live, who their friends are, and the last few thousand things they said.”

She has been blogging about Twitter data since December 2013, when 23andMe was ordered to stop providing disease risk information to their customers. She wrote a post about who was reacting to the news on Twitter and how they felt about it. Of course, being an employee of the company represents an obvious potential source of bias, so she also included a link to the tweets she analyzed so others could study them. She’s done several other interesting data analyses as well. Earlier this summer, she wrote an interesting analysis of tweets about LeBron James’ most recent career move, and of personal interest to me is her post about gender in the symphony. (Her analysis seems to match my experience. In my four years in the orchestra in college, I think we only had two men in the viola section.)

On Tuesday, Pierson wrote a post about using Twitter to study people’s reactions to current events, focusing on Ferguson. She mined a few hundred thousand tweets about Ferguson and analyzed the diferent hashtags that appeared in tweets with #Ferguson. (Part of the visualization she made is at the top of this post.) She also put her mineTweets program up on Github so others can use it to collect tweets about any topic in real time. She has some ideas for further analysis, particularly about whether the day/night-peace/violence pattern is apparent in tweets, and she’s invited others to contribute either ideas or analyses of their own.

The events in Ferguson have also highlighted the difference between the way Twitter and Facebook work. I’m not the only one whose Twitter feed has been saturated with #Ferguson, while Facebook has been nearly silent on the topic. In a Medium article, Zeynep Tufekci explains how Facebook’s algorithm for deciding what to show us caused this discrepancy and wonders what would have happened to Ferguson without Twitter. “It’s a clear example why net neutrality is a human rights issue; a free speech issue; and an issue of the voiceless being heard, on their own terms,” she writes. “Algorithms have consequences.”

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