Monday, July 25, 2016

Teaching Math with Overhead Presentations

At our school, we currently have a mixture of classroom facilities. Some classrooms just have classic chalkboards (and nothing else), while other classrooms are outfit with whiteboards, computer lecterns, and overhead projectors. Well, actually: All of the classrooms on campus have the latter (for a few years now), excepting only the mathematics wing, which has been kept classical-style by consensus of the mathematics faculty.

That said, it's been one year since I've converted all of my classes over to use of the overhead projector for presentations. In our situation, I need to file room-change requests every semester to specially move my classes outside the math wing to make this happen. But I've been extremely happy with the results. While this may be very late to the party in academia as a whole, this identifies me as one of the "cutting-edge tech guys" in our department. Note that I'm using LibreOffice Impress for my presentations (not MS PowerPoint), which I need to carry on a mobile device or network drive. My general idiom is to have one slide of definitions, a theorem, or a process on the slide for about 30 minutes at a time, while I discuss and write exercises on the surrounding whiteboard by hand.

As a recent switchover, I wanted to document the reasons why I prefer this methodology while they're still fresh for me; and I say this as someone who rather vigorously defended carefully writing everything by hand on the chalkboard in the past. Here goes:

Advantages of Overhead Presentations in a Math Class

  1. Saves time writing in class. (I think I recoup at least 20 minutes time in one of my standard 2-hour classes.)
  2. Additional clarity in written notes. (I can depend on the presentation being laid out just-so, not dependent on my handwriting, emotional state, time pressures, etc.)
  3. Can continue to face forward & speak towards the students most of the time.
  4. Don't have to re-transcribe the same material every semester. (Which simply seems inefficient.)
  5. Can have additional graphics, tables, and web links that are time-constrained by hand.
  6. Easy to go back and pull up old slides to review at a later time. We may do this within one class period, after "erasure", or across prior lectures. For extremely weak community-college students who can't seem to remember any content from day to day, we frequently must pull up slides and definitions from earlier classes; and this gives confidence when students in fact disbelieve that the material was covered earlier. Actually, this is most critical in the lowest-level remedial courses (the first course I tried it on out of desperation one day, with great success and student responsiveness). 
  7. I can carry around the same slides on a tablet in class. This allows me to assist students while they work on exercises individually and I circulate. Similar to the prior point, if one student forgets, needs a reminder, or was absent in a prior class, I can show them the needed content in my hand without distracting the rest of the class. 
  8. Greatly helps reviewing for the final exam.  I can quickly pull up any topic in its entirety from across the entire semester. (Again, trying to jog students' memories by showing it again in the exact same layout.)
  9. Having the computer overhead allows demonstration of technical tools, like navigating the learning management system, using certain web tools, a programming compiler, etc.
  10. Able to distribute the lecture material to students directly and digitally. 
  11. Enormously reduces paper usage. All of my former handouts, practice tests, science articles, etc., which used to generate stacks of copied paper are now shown on the overhead instead (on made available on the learning management system if students want a copy later). 
  12. Having written expressions in the LibreOffice math editor, it makes it compatible to copy-paste into other platforms like LATEX, MathJax, Wolfram Alpha, etc.
  13. If for some reason I transition to a larger auditorium for a particular presentation (e.g., someone organized a "classroom showcase" of this type last fall), I'm ready to go with the same presentation available on a larger screen.
  14. Less to erase (saves clean-up time). There's actually a mandated policy to clean the board after one's class at my school, and people have gotten very testy in the past if one suggests not doing that. 
I only anticipated maybe the first 5 of these items above before starting to switch my classes over; once I saw all the very important side-benefits, I became a complete devotee, and transitioned all my classes. I have a hard time seeing that I'd ever want to go back now. That said, I need to be careful about a few things:

Problem Areas of Overhead Presentations in a Math Class

  1. Boot-up time. I need to get into class about 10 minutes earlier to boot-up all the technology -- the computer itself, the network login, directories, starting LibreOffice mobile, opening the files, starting the browser if needed, etc. Our network is very slow and it's a bit unpleasant waiting for things to open up. Meanwhile, students are eager to ask questions, so overall this is a somewhat awkward/anxious moment in time. It would be better if our network were faster, and/or LibreOffice were installed on the local machines (which to date has been turned down by IT).
  2. Presenter view doesn't work on our machines. This is normally a sidebar-view visible to the presenter which shows notes and the next slide to come, etc. Unfortunately our machines weren't supplied with a separate monitor feed to make this work. During the lecture I have to keep my tablet up and manually synchronized on the side to keep track of verbal notes and so forth. 
  3. Making slides available to students is imperfect. I can just give LibreOffice files, because most students don't have it, or possibly the technical confidence to install it. I can provide it as PDFs, but then students usually print them out one-giant-slide-per-page, resulting in everyone with a huge ream of paper. I've directed people to print them (if they must) 6-slides-per-page, but most can't follow that direction. At the moment, LibreOffice cannot directly export a multi-slide-per-page PDF. (And even the normally printing facility has a bug.)
  4. Lecterns have an external power button, and unfortunately I tend to lean on the lectern, press up against the button, and shut off power to the entire system by accident. This is hugely embarrassing and triggers another 10-minute boot-up sequence.
  5. Some lecterns also have a very short power-saving time set (like a default of 20 minutes; note that's less time than I expect to spend on a single slide, as stated above). Evey day I need to remember to set the power-save mode in those rooms to 60 minutes when I start.
  6. Finally, based on my use-case, the handheld presentation clicker which I purchased is not as useful as first expected. It presents another tech item which has a several-minute discovery/boot-up sequence to get started, and I tend to press it by accident or pinch it in my pocket and advance the slide past what I'm talking about. For me I've found it better to discard that and just step to the keyboard when I need to advance the slide (again, just a few times per half-hour).

Nonetheless, all of these warning-notes are fairly minor and eminently manageable; the advantages of using the overhead in my classes pay dividends many times over. Among the top benefits are time-savings, clarity, ability to go back, opening up web access and other materials in class, digital distribution and compatibility, etc. In contrast, here is a question on MathOverflow from late 2009, where the responding mathematicians all seem very adamant about using traditional blackboards. At this point, I really don't grok any of these arguments for not using the overhead. 

Friday, July 22, 2016

Paul Halmos on Proofs

Paul Halmos on mathematical proof:
Don't just read it; fight it!

Friday, July 15, 2016

Names for Inequalities

Consider an inequality of the form a < x < b, that is, a < x and x < b. Trying to find a name for this type of inequality, I'm finding a thicket of different terminology:
  • Chained inequalities (Wikipedia). 
  • Combined inequalities (Sullivan Algebra & Trigonometry).
  • Compound Inequalities (Ratti & McWatters Precalculus, Bittinger Intermediate Algebra, OpenStax College Algebra).

Are there more? What is most common in your experience?

Monday, June 20, 2016


Purgradtory (pur' gred tor e) noun, plural purgradtories.

The several days after submitting final grades when a community college teacher must field communications from students complaining about said grades, pleading for a change of grade, asking for new extra credit assignments, and/or declaring the need for a higher grade for transfer to some outside program.

Example: I will likely be in purgradtory through the middle of this week.

Friday, June 3, 2016

Traub on Open Admissions

As recounted by Scherer and Anson in their book, Community Colleges and the Access Effect (2014, Chapter 11):
Traub famously wrote in City on a Hill: Testing the American Dream at City College, a chronicling of the 1969 lowering of admissions standards motivated by the pursuit of equity, “Open admissions was one of those fundamental questions about which, finally, you had to make an almost existential choice. Realism said: It doesn’t work. Idealism said: It must.”

Wednesday, May 25, 2016

Jose Bowen's Tales from Cyberspace

A few weeks ago I went to a CUNY pedagogy conference at Hostos Community College. It featured a keynote speech by Jose Antonio Bowen, author of the book Teaching Naked, which is nominally a manifesto for flipped classrooms, in which more "pure" interactions can occur between students and instructors during class time. Weirdly, however, he spends the majority of his time waxing prosaically about how incredible, saturated, future-shocky technology is today, and how we must work mostly to provide everything to students outside of class time using this technology.

Here's how he started his TED-Talky address that Friday: He contrasted the once-a-week pay phone call home that college students would make a few decades ago ("Do dimes even exist anymore?") with the habits of college students today, supposedly contacting their parents a half-dozen times daily. In fact, he claimed, his 21-year-old daughter will actually call him for permission to date a young man when she first meets/starts chatting with him online. She supposedly argues in favor of the given caller by using three websites (shown floridly by Bowen on the projector behind the stage):
  • She has started chatting with the man on Tinder.
  • She has looked up his dating-review score on Lulu.
  • She has examined his current STD test status on Healthvana.
Now, that's heady stuff, and of course the audience of faculty and administrators "ooh"'ed and "ahh"'ed and "oh, my stars!"'ed in appropriate pearl-clutching fashion. Review dates and look up STD status before a date online? Kids these days -- we're so out of touch, we must change everything in the academy!

But this presentation doesn't pass the smell test. First of all, we should be suspicious of an adult daughter supposedly interrupting her real-time chat to "get permission" from her father. That's just sort of ridiculous. Admittedly at least Tinder really is a thing and you can chat on it; that much is true. (Although Bowen presented this as the daughter and a friend communally chatting to two guys together, which is not a group event that can actually happen.) But worse:

The dating-review site Lulu doesn't actually exist anymore. In February of this year (3 months ago), the site was acquired by Badoo and the dating-reviews shut down. If you go to the link above you'll realize that the whole site is offline as of this writing. (Link.) And:

You can't access anyone else's STD result on Healthvana. Yes, Healthvana is a site that allows you to quickly access and view your own STD results without returning to a doctor's office to pick them up. But it's only for your own results, and it requires an account and password to view them after a test. Obviously there are all kinds of federal regulations about keeping medical records private, so it's not even conceivable that those could be made available to the general public on a website. One might theoretically imagine a culture in which one pulls up your own STD records on a phone and shows it to someone you're meeting -- but there's no evidence that actually occurs, and of course it's strictly impossible in Bowen's account, in which his daughter had not yet physically met with her supposed suitor. (Link.)

That "Reefer Madness"-like scare-mongering accounted for the first 30 minutes of Bowen's hour-long presentation, at which point I couldn't take anymore bullshit and I got up and left the auditorium. In summary: The half of Bowen's presentation that I saw was entirely fabricated and fictitious, frankly designed to frighten older faculty and staff for some reason that is opaque to me. Keep that in mind if you pick up his book or see an article or presentation by Mr. Bowen.

How did I get clued in to the real situation with these websites, after my BS-warning radar first went off? I asked some 20-year-old friends of mine, who immediately told me that Lulu was shut down months ago, and Healthvana was nothing they'd ever heard of. Crazy idea, I know, actually talking to people without instantly fetishizing new technology.

Friday, May 13, 2016

Schmidt on Primary Teachers

Dooren et. al. ("The Impact of Preservice Teachers' Content Knowledge on Their Evaluation of Students' Strategies for Solving Arithmetic and Algebra Word Problems", 2002) summarize findings by S. Schmidt:
Nearly all students who wanted to become remedial teachers for primary and secondary education and about half of the future primary school teachers were unable to apply algebraic strategies properly or were reluctant to use them. Consequently, they experienced serious difficulties when they were confronted with more complex mathematical problems. Many of these preservice teachers perceived algebra as a difficult and obscure system based on arbitrary rules (Schmidt, 1994, 1996; Schmidt & Bednarz, 1997).