OpenComps: Written Exam Down, Oral Exam to Go

About two weeks ago I submitted my written responses to my comprehensive exam questions. I can't go into detail about the questions, but I'll summarize them this way:

1. Here's a dichotomy from the learning sciences. Deal with it.
2. Somebody did a quantitative study X and now wants to do Y. Before you think Y is a good idea, what do you have to know about X?
3. How would you help math teachers learn about X given conditions Y?

I hadn't quite anticipated Question 1 so there was some background work to do before I could address certain details. Thankfully, I was pretty well prepared to structure my argument, and it was on this question that I did my best writing. While I'd had dreams of finishing a couple questions before the end of the weekend, my actual pace was slower than that. A lot slower. By the end of Friday, I'd written about a paragraph, and by the end of Saturday, I'd written about a page. Fortunately, that was the foothold I needed to have the rest of the 9-page paper finished on Sunday.

Next I answered Question 2. In some ways this was the question that worried me the most, but my studying definitely helped. Still, my writing was slow and it wasn't really until late Wednesday when I had this question finished. When you have three questions to answer in seven days, taking six days to answer the first two questions is less than ideal.

That left me to answer Question 3 in a bit of a writing sprint starting in the wee hours of Thursday morning, breaking to attend and teach class Thursday afternoon and evening, and then writing until 7am Friday morning to finish. Question 3 was my advisor's question and the one for which I was most prepared; in fact, a couple pages was largely a rehash of some of some things I'd blogged about in the past. Having that for a strong start certainly helped the rest of the paper take shape rather quickly.

It was a relief to reach the end of comps week, but I couldn't get too much rest because I had put off a number of things (okay, almost everything) during comps and in the weeks leading up to comps. Professors and fellow students are very understanding about it, which is great, but I wasn't entirely comfortable using comps as an excuse to not do much else during that time. In the past two weeks (including some of every day of my fall break), I've been catching up with the class I take, the class I teach, and the research project I'm on. I haven't been blogging and my social media activity has been pretty minimal during this time, but I'm starting to feel caught up.

The last hurdle to clear is the oral examination, scheduled for this Tuesday morning. I'm not too concerned about it, and thankfully, the message from my comps committee has been not to worry. But between now and then I will be going back over my responses, double-checking the literature I cited, and reading a few new things I uncovered during the comps process. My advisor hinted at some things he wants to talk about and I'll be sure to prepare for those things, too.

OpenComps: Final Preparations

By 9 am Friday, November 2nd, my advisor will email me my three comprehensive exam questions. I have exactly a week to answer them. He says I'm prepared, and I appreciate his confidence in me. I think I'm reasonably prepared, too, and I greatly appreciate that among my numerous anxieties, test-taking isn't one of them. Far from it, in fact. See, I'm one of those mystical kids that policymakers have in mind when they come up with laws like No Child Left Behind. I'm the one who actually likes taking tests and fools himself into thinking they're just a harmless yet useful snapshot of broad academic knowledge and skill. Give me a #2 pencil and bubbles to fill in and I'll happily work for hours.

There won't be any bubbles on my comprehensive exam, but there will be hours of work. Over the past week I've been making my final preparations, most of which are designed to make next week go as smoothly as possible. A summary:

Ready My References

I think my personal library will have most of the math and learning science books I might want, but I felt like some extra perspectives and guides concerning experimental design, casual inference, and statistics might come in handy. I know I can't expect to read any of these cover-to-cover in the course of the next week, but if nothing else the examples and explanations they contain could be valuable.

Having books around is a luxury, but for this level of work, it's even more important to have a way of keeping track of the hundreds of journal articles that I might want to use in my comps responses. I've been using Mendeley as my reference manager since the spring of 2010. Regardless of what tool you use -- Zotero, RefWorks, Endnote, Papers, etc. -- it's important during any writing period to have something that allows you to focus on writing, not scrambling for citation information and digging through the APA style book.

One of the best investments I've made as a grad student has been my diligent attention to the annotation, curation, and metadata accuracy of my Mendeley library. I was somewhat lax about it during my master's year and my first year of the PhD program, but then I spent most of two weeks of a summer going back through every PDF, every book, every syllabus, and every paper I wrote to make sure I had everything neatly cataloged. And I haven't relaxed since. Right now I have 890 references in my personal library, with others in group collections, and I can find or cite any of them in just seconds.

If there's one thing I can't let myself do is turn my comps into a massive search for new literature. I admit, I love the thrill of the hunt, and I've spent many hours digging around in Google Scholar tracking down papers that I realistically have no time to read. I need to trust that most of what I need I already have and I've already read, and keep my literature hunting to a minimum.

Minimize Distractions and Get Comfortable

For my last week before comps, I actually spent very little time studying and more time minimizing potential distractions. I've been to the grocery store, I've washed dishes and laundry, and I reformatted and reinstalled my operating system, virtual machine, and software on my computer because a few things had gotten flaky after a year of hard use. I've never liked studying right before a test anyway, as any attempt to "cram" is nullified by thoughts that always begin, "If I don't know it by now...." I passed my 100-hour studying mark a week or so ago and that will have to be good enough.

I'll probably work mostly at my desktop. If your computer had three monitors, 16 GB of RAM, university broadband peaking at nearly 90Mbps up and down, and a pair of Sennheiser HD 595s, you'd probably work at it, too. I might try working some in my office, and my kitchen table is nice for when a lot of open books are involved. I don't want to be stuck in my office chair for 18 hours a day, so I plan to do some heavy thinking while running and in a pinch I can even prop my laptop up on my exercise bike.

Sometimes I work in silence, but not very often. I don't want to get distracted by moving pictures, but there are a few movies I can play for background noise without losing focus, mostly because I've seen them so many times. I can get distracted by podcasts, so I'll try to listen to those selectively over the next week. I'll listen to a lot of music, and my tastes for a task like this tend to be towards the incredibly gifted (Tori Amos, Curtis Mayfield, Norah Jones, Sia) and music that's downtempo/trip-hop or otherwise having a likable female vocal/bass combo (Thievery Corporation, Zero 7, Garbage). Seriously, in the midst of an important exam, who wouldn't want to perform as relaxed and confidently as LouLou?:

OpenComps Get Less Open

Obviously, yet unfortunately, once I get my questions I'm pretty limited in what I can say about them. I'm not to receive outside help, solicited or unsolicited, and even after the exam is over I'm only to talk about the process in general terms. (I'm assuming that's in the event my committee members want to reuse the same or similar questions in the future.) Assuming I'm not exhausted by the process, I'll try to summarize my approach and workflow, lessons learned, and hopefully some epiphanies that come in the process of working through my questions. I'm looking forward to the week of writing and then readying myself for the oral defense, scheduled for November 27th.

Scholarly Reading Strategies

While I welcome greater diversity in higher education, I recognize graduate studies aren't for everybody. More specifically, I'd suggest you think twice about a PhD if you're the kind of person who doesn't like to read. The written word is the stuff on which academia survives and thrives, and as such many more scholarly words are produced than any one person could possibly read. But yet our work depends on reading huge chunks of scholarly literature.

I was only a few weeks into my first semester as a PhD student when I realized that there were going to be times when I couldn't finish all of the assigned readings for class. Thankfully, the ever-kind Elizabeth Dutro addressed this problem in class and told us all that this was okay. Yes, sometimes there were things we'd need to understand in great detail, but other times it was enough to just gain familiarity with an article in case we needed to refer to it later. Some readings (for me, Foucault comes to mind) need multiple readings before they make any coherent sense.

I discussed this with my advisor at the time, Finbarr (Barry) Sloane. Knowing that he was a voracious reader with incredible retention and memory (Vicki Hand once told me she wished her internet connected directly to Barry's brain), I asked if he had any special reading strategies. This is essentially what he told me:

I read things three times. The first time I just read and get a sense for the article. The second time I read for details, take notes, and make connections. On the third reading, I read the article out-of-order. If I can read paragraphs or sections at random and understand them without having to re-read the surrounding context, then I know I understand it.

Now I was understanding why Barry's knowledge of the literature was so strong. Unfortunately, I was also understanding why he routinely only got a few hours of sleep every night -- all that reading and re-reading takes time. He wasn't shy about his love of reading; he said that while in graduate school in the mid-1980s, he read every single article in the Journal for Research in Mathematics Education since its first publication in 1970. That's intense.

Maybe I can't read every JRME article three times between now and my comprehensive exams, but I do need to make the most of my comps readings. So long as the quantity of reading doesn't overwhelm me, my three-part strategy will be (a) read, (b) read for detail and take notes, and (c) blog a summary. That's the approach I took with my last post and I felt very good about it. (It helped that the Clements & Sarama article was less than 10 pages long.) The written part of my comprehensive exam gives me a week to answer three questions with essays/reports of about 8-10 pages each. I figure the more I've written on my blog, the more prepared I'll be to write for comps. There's also the side benefit of giving my advisor a convenient way to keep up with my preparation while he's traveling during his sabbatical this semester. I'd love to blog about at least four or five readings a week, and you'll be the first to know if I can keep up that pace.

Bonnie H. Litwiller, 1937-2012

I got word tonight that my undergraduate advisor, Bonnie Litwiller, passed away a couple days ago at the age of 74.

As a freshman at UNI, I had a temporary advisor until my program became more certain. After declaring as a math education major, Bonnie Litwiller was assigned as my advisor. I knew nothing about her. I remember asking Ed Rathmell, whom I had gotten to know while applying for a scholarship, what to expect from Litwiller as an advisor. I remember his response: "If you listen to her and do what she asks, she's great. She'll have your back when you need something. But don't cross her."

That's an uneasy way to know someone before you even get a chance to meet them. It felt like a description more fitting of mafia boss than a professor. But Rathmell's advice, as usual, was solid. Litwiller proved to be tough, and she made it clear to us that being a good math teacher was hard work. She set a good example: she and her research partner, David Duncan, would set aside a day a week where they'd lock themselves away in the library and write. As UNI isn't a top-level research university, the research activities of professors aren't always visible to the students. But Litwiller's dedication to research was clear, and there was no topic too small or journal too obscure. If she thought she had knowledge that would improve the teaching and learning of mathematics somewhere -- anywhere! -- she would write and submit for publication. She continued to write and publish even after her retirement from UNI in 2000, eventually passing the almost unfathomable mark of 1000 scholarly publications.

I took two classes with Litwiller, Teaching Middle School Mathematics and Teaching High School Mathematics. The classes were tough due to Litwiller being both picky about the quality of our work and her lack of clarity in describing what she wanted us to do. Some of us thought she was just being careless with her assignments, but I always wondered if this wasn't somehow purposeful. Either way, it was clear that she didn't want to do a lot of hand-holding. Some of us, ever so quietly yet respectfully, referred to her as the bulldog. A trusty companion that might just bite if you got out of line. If you didn't have the initiative and sense of responsibility to do quality work, I think she wanted a way for you to sort yourself out of the program. It happened, too; every semester some classmate would go missing and we'd try to find out what happened. Inevitably, someone would say, "They couldn't cut it. Litwiller dropped them from the program." You hear a lot today about colleges adopting GPA or test score requirements to improve the quality of their education majors. We didn't have those -- we had Litwiller. And just like letting a GPA decide who can be a teacher, I'm sure her judgement wasn't perfect and mistakes were made. (An acquaintance of mine, who shall remain nameless but now holds a PhD in math education, told me about a narrow escape from Litwiller's axe after a dispute over access to a local school.) But I think Litwiller had a sense for the quality that people expected from a UNI-prepared teacher, and a sense for giving us some survival skills that would get us through our first few years of teaching. There must have been far more successes than failures, too -- by the time I graduated in 1999, someone had estimated that a quarter of all the math teachers in the State of Iowa had been taught by Bonnie Litwiller.

My appreciation for Litwiller and her work has grown through my years first as a teacher and now as a graduate student in mathematics education. It was she who first introduced me to the NCTM Standards, and her direction of the NCTM Addenda Series was and still is an enormous contribution to the field of math education. What I believe was originally intended to be a six-book series to support the Standards grew into 22 total books, each designed to take the research behind the Standards and turn it into something teachers could use. Litwiller might have been the director and not the author of the Addenda Series, but it carried her trademark: getting as much useful information into the hands of teachers as possible. She gave me two books from the series, the middle school and high school books about statistics and data analysis. It was the first time I really thought about statistics education, and it's since become the area of school mathematics I find most interesting.

The world will miss Bonnie Litwiller, but she didn't leave without making a mark, both on the field of mathematics education and on me. Teacher education is a challenging business, and it's probably best to judge it with a certain amount of hindsight. For all of her toughness, she did have my back when I needed it, just as Ed Rathmell said she would. I may not have learned all that she tried to teach me, but maybe her most important lessons -- a sense of dedication and rejection of "good enough" -- have been most helpful in getting me to where I am today.

Research 2.0

Having just finished a semester as a student for the first time since 2002, I can say that advancements in web-based research tools have made research more efficient and enjoyable. I use Google Scholar all the time and, being at a research university, I can find most articles I want online. In the past semester I never once had to go to the library to hunt through a dead-tree journal. Integraing Zotero (for bibliography management) and Diigo (for web highlighting) into Firefox have also made my life easier. (I wish there was a Diigo extension for my brain so I could highlight any information anywhere, regardless of the medium. I think that goes well beyond Web 2.0.)

Research tools have come a long way, but I have some ideas about how much farther they need to go. I feel like most web research tools are still stuck in "Web 1.0," and not taking advantage of current technology. I've been envisioning a system for research publishing, indexing, and connecting that I think is possible to build. If you happen to read this and can do something to make it a reality, by all means steal every idea you can. Academia will thank you.

Let's start by considering the publishers. Journals give value to academia by ensuring quality for published research and delivering research to an audience. In exchange, journals take copyright of articles and restrict access to ensure they keep a sustainable business model. As an open-source guy, I don't particularly like the system but I can understand it. A "research 2.0" model can't simply do away with publishers; journals must retain their identity and they must still coordinate peer review of articles.

So imagine a wiki-like site where each article is a page. Unlike a wiki, the responsibility of posting each article would lie with a partner journal and the content would be static. The formatting of each article would be 100% consistent. Every citation in the article would link to the corresponding entry in the article's references, and each reference entry is a link to that article.

To protect the journals, no full articles could be posted for a period of 3-5 years after they're published. The journals would make an entry for the article, including an abstract and the article's reference list (so the links to other articles would be established), but the content of the article would be protected by the publisher, much as it is now. Researchers can't afford to be 3-5 years behind the latest literature, so they would still have to pay for content and keep the journals in business. Journals can't afford to lose readers, so they'd want to be part of this "research 2.0" system.

I like how Google Scholar can figure out how often articles are cited by other articles, although I'm not sure how well it works. In "research 2.0," the consistency of the links would allow for careful and accurate analysis of the relationship between references. Now here's where the 2.0 part really comes in: users could create an account on the site that allows them to mark articles as read, and articles would be "rated" based on how often they've been cited by other highly-rated articles. The site could analyze the articles a person has read, what has been cited in those readings, and recommend other articles to read. Just like a recommendation system at Amazon or Netflix, the system would use the knowledge of what I and others have already read to recommend what I should read next. Heck, I'd even pay to subscribe to such a system, and the journals could all take a cut in exchange for their cooperation.

I can't think of a single technological barrier to making this happen, and wouldn't be surprised if engineers on the Google Scholar team have already thought of it. I'm thinking about building a personal wiki to keep track of what I've read and what those readings have linked to, but I'm not sure if entering all that information is worth all the time and trouble it's sure to take.

I'm My Own Best Teacher

I had one of those nights last night that I truly enjoy, but don't often reflect upon. It all started when I was going to write a post about something Lorrie Shepard said at the Realistic Math Education Conference about instructional and assessment tasks. But first, I thought, I should look to see what she's written about the subject so I would have a greater background.

Since I'm not currently at the university, my access to full research articles is restricted, but I know CU has a VPN through which I can look like I am at the University. I found the VPN instructions on CU's website, but because I run linux the setup was more complicated. To their credit, the university had a linux client you could download and instructions for installing it, but I wanted to use whatever client that was already in the Ubuntu repositories. It took a little while, but after downloading the university client and sorting through the source code and configuration files, I had the information I needed to get the native VPN clients running on both my netbook and workstation.

Now, back to the Shepard article. Now that I had the same access I'd have if I were at CU, I could download full copies of papers from multiple sources. I was using Google Scholar, and lately I've been trying out Zotero to manage bibliographic sources. Instead of focusing on the papers, I was focusing on how the bibliographic entries were being stored by Zotero. Zotero wasn't detecting the sources very well on its own, but I was having good luck choosing Scholar's "Import into BibTeX" option,copying the entry to the clipboard, then telling Zotero to import from the clipboard.

I'm a long-time LaTeX user, but I've never used BibTeX. For a while now I've been wanting to reformat my undergrad senior thesis I wrote in 1999, but to do so I knew I'd want to re-manage the sources I used. I found my old thesis and started searching Google Scholar for the same references and I stored them in Zotero using BibTeX imports. I had imported about half the references when I could not hold back my curiosity any longer. Could I export these from Zotero and use BibTeX and LaTeX to re-format my paper?

After a wild goose chase trying to get the Gentium font in LaTeX (I guess I'll have to make that work some other day), I spent an unknown amount of time learning how BibTeX worked with LaTeX. My thesis had been formatted in some unknown format before (something for which I had always been disappointed in myself), so this time I was determined to format the paper using an APA style. There is an APA style package for LaTeX, and after much troubleshooting I was on my way to formatting the thesis. I went to bed at 5 am with the second half of the paper left to reformat.

What's the point of telling this story? Look how much I learned through my curiosities and distractions! I learned how to configure a VPN on linux, how to import, edit, and export bibliographic entries in Zotero, how to use BibTeX, and how to get LaTeX to automatically format papers in the APA format. I had been tired throughout the day, but learning all these things drove me well into the next day, hardly tired at all.

Everybody seems to have an answer to the question, "Who was the best teacher you ever had?" My answer? Me. I'm my own best teacher. I don't mean to sound cocky; in fact, I can only make such a claim because I'm humbled by the effect that education, including my many teachers, has had on my life. It's because of them and the many great opportunities they provided that I have become the life-long learner they wanted me to be. Teachers gave me the knowledge and skills I would need to learn on my own and become my own best teacher, and for that I'm forever grateful.