So this isn't exactly live blogging any more, as it's a day late. Well, nothing's perfect. Note that there is no need to read the accounts for Day 1, for Day 2, or for Day 3 in order to read this entry! That said, this is Day 4 of Twitter Math Camp 2013.

One Drexel Plaza features this device. Fully functional? |

Ever experience something that feels wrong, and annoying, and you wish you could change it? Hold on. Consider that the event itself might not be wrong, what might be wrong is the circumstances surrounding it. For instance, a lesson which dies a horrible death in front of one class - maybe it would work with another? Or if you keep waking up before your alarm clock - maybe that's a good thing if you set your alarm wrong?

So yes, after posting up my Day3 blog after 3am, like a sleep deprived fool I set my alarm for 8pm, instead of 8am. Ergo, when I randomly woke up before I'd had 6 hours of sleep... it was 8:45. Oh, snap. So I'm NOT complaining about that today, as the mental bug has turned into a feature. Not sure I would have forgiven myself for just sleeping through what happened next.

#### ROUNDTABLE

Many people still present and conscious! |

My Favourites Sessions:

1) Terrell Stevens (@ladyt316) talks Factoring Frenzy. She presents a two by two grid, called a 'Tic-Tac' (no Toe) where the left column was made using the product and the sum of the two numbers in the right column. Students, what do you notice? What is the pattern? She then presents boards with only the left column, asking to fill in the full Tic Tac. The left column is naturally made up of 'ac' and 'b' from a standard form quadratic; this method was so successful with students, the PreCalc teacher adopted it as well.

2) Sandra Miller (@sandramiller_tx) talks My Favourite Multiple Choice. If you use MC questions for AP prep or test prep, GradeCam.com allows you to print your own scantrons. You can then use your document camera or iPhone app to scan and grade them on the spot! This allows the teacher to circle the ones a student got wrong and give it back before the end of the period so they can retry. The free version only allows 10 question tests. Sandra has paid the $10/month version, which also gives her access to recording analysis tools (see how many people answered which letter).

3) Chris Lusto (@Lustomatical) defends the Romance Cone as discussed by Mathalicious on Day 2. How can it be a cone in 2-space? Consider a circle. Take any non-coplanar point as the apex, and draw lines from there to the boundary, and you have a cone. But there is no reason for it to be finite; we use infinite double napped cones to define conics. There is also no reason we have to stick with 3 dimensions, we can see it in 4D or 5D... or 2D. To take it further, consider topology of Euclidean space. For a challenge, think of something else for which you have a good understanding, and then try to generalize it.

4) Jennifer Silverman (@jensilvermath) talks Geogebra. She points out there's 40,000 applets for Geogebra 2, and that it's entirely dynamic with sliders. She demonstrates some of her GeoGebra tube, including Quadratic-Palooza, Multiplying integers in "Cartesian Plane" (axes 1st factor, second factor) and a rolling out of a radian protractor she's designed to demonstrate central angle of 1 rad. (A physical proradian was included for all attendees, see that web link if you want one.) She also mentioned a GeoGebra conference next week (Aug 3), in Ohio, organized by Steve Phelps (@giohio). For another source of GeoGebra, follow John Golden (@mathhombre), and Bowman Dickson (@bowmanimal) has some materials from TMC12 as well.

5) Cal Armstrong (@sig225) talks PCMI (Park City Mathematics Institute), while noting his Microsoft Surface electronic has no adaptors. There's a gathering for 3 weeks in Park City, Utah, involving 4000 math people from high school students through grad students and professors. In the morning, they do math problems, and in the afternoon, they do projects. Some are available on the web, though they are hidden behind a firewall. Talk to Cal for more information; there's also an E-Table in Texas that participates.

6) Glenn Waddell (@gwaddellnvhs) talks about the linear vertex form. In particular Algebra 1 doesn't use common vocabulary with later courses, yet you can have y=a(x-h)+k for a line, in addition to the parabola, absvalue, trig, et cetera. The only difference is that the point for the line doesn't matter, whereas it does for the others. When Glenn said this at a dept leaders meeting, some said "it's forbidden to discuss it like that!" but he proved it with sliders in Geogebra. Using the "linear vertex form", even low speed kids were able to write equations for parallel and perpendicular lines. Jennifer Silverman has since put together a GeoGebra demo here.

Word of mouth has spread in her school, such that older kids encourage others to give the programming a try, and they are willing to help out. Jasmine's help is often in the form of seeing if anyone else is having similar problems, or checking websites along with the students for information. The final product also needs to have documentation, which allows her to mark it. To get a high A-level, students need to additionally explain why their method is particularly elegant and/or provide a bibliography of sites for future students given the assignment. As she concludes, Michael Pershan throws in a plug for 'Scratch' as a language.

8) Mark Dittmer (@MisterDittmer) talks about a book, "The Choice in Teaching and Education". It's only 100 pages, and is good for reflection. He came across it after reading another book by the same authors, "Leadership and Self Deception". Picture someone you know who is a problem, believing that the people around them are threats or somehow less important. Moreover, they doesn't KNOW their attitude is a problem, and may argue against it if challenged. In such cases the self-deception has become a larger problem. Now ask yourself, do you see students as threats who will misbehave? Or is there greatness there? Mark read a snippet from the book too.

9) Roxanne Mah (@justagurl24) talks division hugs and kisses. Consider that when you divide fractions, the "rule" says invert and multiply. (But we all know students get confused about where they're inverting.) Now picture 'xoxo', as representing kisses and hugs. You "Kiss and Flip" to divide fractions.

10) Edmund Harriss (@Gelada) talks Mathematical Play. How can we make it easier for students to play with mathematics, such that they can find something cool... even if they may not understand it until they see it again in a later course. (Or at his level; he's a university professor.) He illustrated this by hacking Desmos to produce the following graph; it's a function in two variables, cos(x-r)/[x^2+1]. Sliders produce interesting results. Edmund actually makes physical cards with designs like this on them, which he will put on the wiki. Note also that the answer to a student question is allowed to be "That is a reason to take Calc3 in college."

That concluded the scheduled favourites, at which point Lisa Henry opened the floor for anyone else to toss something up.

#### GROWTH

11) James Cleveland (@jacehan) talks Blogging Motivation. For those who are motivated by deadlines (or who constantly revise), schedule your post to go out sometime within the next week. Better finish your writing before it posts!

12) Anthony (@aanthonya) talks Google Voice. It's a free account, and gives him a phone number for school related help. It can be set to ring on all his phones at the same time (home, cell, etc) and if he doesn't answer, service will transcribe the message left and send as a text (sometimes humourously).

13) Max Ray (@maxmathforum) talks MathPickle.com, run by Gordon Hamilton, a Canadian Mathematician. He's currently compiling 13 gaming analogies to unsolved problems in mathematics, and raising 13 million dollars so there is money available to those who solve them; half a million to whoever discovers it, other half to a teacher who inspired them. Max illustrated one of these games with the group.

Red team picks a composite number. Blue team picks a prime number. Red team picks a prime number and multiplies by their first. Blue team picks a composite number such that their own product is EQUAL to Reds' - if they can, they win, if they can't, red wins. Who has the harder job here? The unsolved question: Is there a strategy such that blue can ALWAYS win? The connection: Factoring products of very large prime numbers; solve this and you can hack secure transactions.

At this point there were a few rapid announcements that I couldn't shorthand fast enough. I do recall Justin Lanier (@j_lanier) talking about "Exploring the MathTwitterBlogosphere", a new Blogging Initiative for October 2013. Watch for info in September.

Paper? Sheet music? What's that? |

At this point, Lisa Henry (@lmhenry9) came back up. There were acknowledgements of the rest of the committee (Shelli, Anthony, James, Jessica, Max). Lisa then mentioned how it was a freshman English teacher who inspired her, and she left us with two thoughts. "Can miles truly separate you from friends?" (If you love someone, aren't you already there?) & "Don't be dismayed at goodbyes. Farewells are necessary so you can meet again." (Be that in a few minutes or a few years.)

She got a standing ovation. And at 10:45am, that was it.

Feedback forms were filled out, the origami dragon logo was torn down, and people said their individual goodbyes. I was thinking of acknowledging a few people here, but on second thought, no - don't want to miss a mention, and everyone was great anyway.

Michael Pershan's got 99... origami birds? Wait. |

#### NOW WHAT

After 11:15, I went back to the hotel to check out by noon. Think the last person I talked to was Glenn in the elevator, which I remember because he told me that the digits of Pi actually produce a scannable bar code (which he had on his shirt). Incidentally, I'm hyper organized, so the fact that I didn't check out until 11:55am is a testament to how much this conference threw me for a loop. Feel free to skip the next italicized paragraphs, as I wander Philadelphia.

This has a familiar ring |

*In brief: Sheraton people were very good about making change for me. First stop, Institute for Contemporary Art, literally a block from hotel. Whoever made the green and pink guide sheets, I read those. Then thank goodness for maps in subway system, made me less worried; remember I'm flying blind, no net access to online maps. Liberty Bell Center. Washington Square. Penn's Landing. My only food of the day about 3pm (aside from a muffin at TMC). Then rain as I head to Town Hall. Hide out there.*

Dominos game: Rained out |

*Rain mostly clears, I go to "Your Move" game artwork (1997) that Max told me about. Monopoly pieces near Pennsylvania railroad, funny! Next JFK Plaza and love statue; I miss my wife. Walk down Benjamin Franklin Parkway. Pours rain again, so I'm pulling a Rocky, running up stairs to Philadelphia Museum of Art to find shelter. Carrying all my stuff. Trying to protect my laptop. Wait there, but soon it's 5pm, no choice, must get to train station. Fifteen minute walk to 30th St. is wet. Train down to Airport, arriving just before 6pm.*

It was a Rocky Road |

MANY math teachers had troubles at the airport, as the rain apparently knocked out power in some terminals. It was the most rain Philadelphia has seen in a day for over 140 years. I had to wait a half hour as US Airways computers were down. When I did go through security, they had to pat me down because I was so wet the machine gave them odd readings. Shuttlebus to Terminal F involved 3 second dash through pouring rain (did see a rainbow too). Couldn't get WiFi signal. Then flight systems went down again.

At 9:15pm, was announced that they would be doing a "manual boarding" of my 8:45pm flight. (I'm picturing manual dialing of a Stargate, because that's what I do.) They actually tore that perforated part of my ticket off. Left gate about 9:45pm, but taxied around for a good half hour. Out window, amazing visual of a plane taking off with lightning strikes in the background made me think "take your time". Back to Ottawa for 11:30pm, my wife is there. Local busses not running to my house anymore, took a taxi home.

And that's day 4. In all I've apparently earned 19.5 professional development hours (according to my certificate). So I guess that's all my work hours for July; don't expect an analysis as I did for June! Do expect some further reflections after this experience though.

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