This is the house that Math 2.0 built

This is the event Sue VanHattum is hosting tomorrow at Math 2.0

This is Dan Meyer’s talk last week
That inspired the event that Sue is hosting tomorrow at Math 2.0

This is Joel Duffin’s eNLVM instance
That supports problem remixing from Dan’s talk last week
That inspired the event Sue is hosting tomorrow at Math 2.0

This is Linda Stojanovska’s folding box problem
That became a lesson in Joel’s eNLVM instance
That supports problem remixing from Dan’s talk last week
That inspired the event Sue is hosting tomorrow at Math 2.0

This is the opening of the GeoGebra-NA Network Series by Dani Novak,
Who gave the idea for Linda’s folding box problem
That became a lesson in Joel’s eNLVM instance
That supports problem remixing from Dan’s talk last week
That inspired the event Sue is hosting tomorrow at Math 2.0

This is the meeting with Markus Hohenwarter and Michael Borcherds
Who built the software featured in the GeoGebra-NA Network Series by Dani,
Who gave the idea for Linda’s folding box problem
That became a lesson in Joel’s eNLVM instance
That supports problem remixing from Dan’s talk last week
That inspired the event Sue is hosting tomorrow at Math 2.0

This is the Math 2.0 beginning at The Future of Education, with Maria Droujkova
Who organized the meeting with Markus and Michael
Who built the software featured in the GeoGebra-NA Network Series by Dani,
Who gave the idea for Linda’s folding box problem
That became a lesson in Joel’s eNLVM instance
That supports problem remixing from Dan’s talk last week
That inspired the event Sue is hosting tomorrow at Math 2.0

Not too soft, not too hard

How do books come alive?
The new book format by Neil Stephenson is nice, but “too big” – it assumes hundreds of people at least actively geek about it, which means hundreds of thousands of readers.
The Ning format Steve Hargadon used for Book Discussions is “too small” – Ning groups are too fragmented for the purpose, though the idea rocks.
LivingMath reviews from Julie Brennan are “just right” – if they were in a wiki, or the Yahoo group discussions were public and searchable.

Let’s mix the three and make something like MathTropes (like TvTropes) for family math books.

Link to my 1997 picture at Shodor. The materials we made back then are still up, and used.

Dimensions

Instead of “brick and mortar” for LearnSpace we plan to open, I’d like to have something like Luminarium! What learning won’t happen in a cool space like this? One can dream, right?!

15 million people in Britain are “innumerate” – hence too many could not play the lottery that required them to compare numbers like negative eight and negative six. I wonder if the humanity will grow out of lottery any time soon, by the way.

Neil Stephenson announced his “post-book” project just a couple of days after Seth Godin announced he’s not going to make traditional books anymore. Hmmm!

I really like how WIRIS graphs. I want to teach it to talk to Makerbots.

Actually, it would be nice if more of my things, real and virtual, talked to one another. Even announcing webinars to all the places isn’t automatic at all, because of format differences. I hesitate to give mundane tasks of this sort to interns, too.

Its own context?

The following is a part of the Flow Channels brainstorm in the Natural Math wiki.

Paul Lockhart, in his “Lament” (the book version) talks about the importance of math as its own context, without trying to motivate it through any applications. I think it’s not about applications – it’s about metaphors! You can use “math as its own metaphor” so to speak, or approach it non-metaphorically, as autists supposedly do, which works great – for those who are willing to, and can, follow that path. In my observation, a tiny minority of people self-initiate or choose this self-contained approach to math, given the choice among multiple contexts as metaphor sources.
Metaphor_source_and_target.jpg
Metaphor_death.jpgHere is how metaphors work. At first, there is a single entity, which only retrospectively can be named a metaphor. For example, a kid can think that division IS fair sharing. People frequently feel uneasy and even offended if you call their metaphors “metaphors” in this stage. It’s a defense mechanism, allowing the metaphor to support enough “roleplay” for the person to develop rich images that can later sustain formal structures. Forcing early formalization breaks the play, disrupts the natural learning rhythm, and leads to despondent feelings average math classes currently invoke.

If we manage to sustain rich image making in the all-important early stage, and gently help students move on to noticing some patterns in what they do, the patterns become math, and the metaphor turns into a simile. Patterns at this stage can just as easily become science, philosophy, or any other pattern-based discipline, but let’s focus on math patterns for now. In our example, once the kid starts noticing, say, that you can’t share certain quantities fairly without splitting, she is doing math, namely division, and sharing becomes LIKE division. When the context of sharing becomes unimportant (though the vocabulary may remain), and the focus fully shifts on quantities and their properties, the metaphor “dies” (Lakoff) and the new math structure, now self-sustained, is born.

To recap the life of metaphor in the context of the model of mathematical learning created by Pirie and Kieren:

  • Metaphor promotes Image Making and supports Image Having
  • Metaphor turns into a simile during Property Noticing, when its source and its target visibly separate
  • The source of the metaphor dies, and the newly born math structure stands alone, in Formalizing

If you happen to love a context other than math – dragons, marine biology, car racing, fashion design – using it as a source of your math metaphors can be as powerful as using math as its own context. However, using math as its own context allows for mathematical elegance and depth not available otherwise. It has to happen, as well.

Flow_Channel_Context.jpg

Bonus: Madison’s poem

know what i figured out?

the meaning of words isn’t a fixed thing!
any word can mean anything!
by giving words new meanings, ordinary english can become an exclusionary code!
two generations can be divided by the same language!
to end that,i’ll be inventing new definitions for common words, so we’ll be unable to communicate.
don’t you think that’s totally spam?
it’s lubricated!
well, I’m phasing.
marvy.
fab.
far out.

Abundance of choice

http://www.examiner.com/gifted-education-in-fort-collins/mathcounts-bans-homeschool-teams

The two stated reasons for banning homeschool teams from entering MathCounts:
- Some people pretend to be homeschooler groups
- Homeschooler teams are not restricted geographically like schools are, so they have larger pools to select from

What I hear: homeschooling makes a lot of administrative sense, so some other entities would pretend to do that for administrative flexibility. Also, pre-industrial, of course pre-information age ideas about how to group people have been discarded by homeschoolers some time ago, which provides them with an academic advantage (duh).

I also suspect there is the third, unstated reason: homeschooler teams winning disproportionally many awards. This has been true historically of certain places (e.g. Olympiad winners coming from particular communities or schools) and certain education methods and certain cultures (e.g. Asian-American). Banning these superior education places and methods and cultures from competition designed to select superior kids seems counter-intuitive to me. While I acknowledge the move from MathCounts as a badge of recognition for homeschooling, it also feels a hostile and otherwise problematic. It also begs for an alternative all-inclusive competition to start or to accept “MathCounts refugees,” which will split the user base of MathCounts.

After meeting with HSLDA (an organization that speaks for a minority of homeschoolers), MathCounts decided to grandfather existing teams. This is a strange solution, given that some existing teams are unfair and even cheaters. I do not doubt the general good will of MathCounts organizers, though. They should just invite homeschooler volunteers to help them with the logistics. Homeschoolers are used to operating on incredibly slim administrative overhead, and can be very efficient.

Diane Ravitch’s book reviews were interesting. These talks “for” or “against” this or that choice assume a pretty scary and, given where we are in history, unnecessary scarcity of choices.


Picture: PLN by Alec Couros.

The article in LA Times is highly problematic because it singled out several particular teachers, which made the story more palatable to those of us who are not autistic enough to have fun with pure data, but at the same time hurt these people. They could have spinned it differently, too, with the stress on helping. I like the quiet database version.

Mobius metaphor

Jos Leys makes great math movies, including this gem of a metaphor:

I can’t wait to use his Mobius Bloom’s footage to strengthen the point I’ve been trying to make – that the Creating tasks are not for advanced students, gifted people, or graduate school only! Actually, struggling students, young kids and noobs need Creating tasks much more.

There are always jobs for kid, teen and grown-up interns at Natural Math. You help the world, develop valuable skills, and enhance your portfolio. What’s not to love?

Yesterday Karen Mellendorf of MonarchBooks alerted me to a math t-shirt from Woot, with this design:

I was too slow to buy the limited edition, but I really admired the thoughtfulness and deep knowledge of “who’s who in math entities” that went into designing it. It’s a list of topics for two-three years of a good math club meetings, right there! Including the Mobius strip, of course.

Birthday Cactus

Katherine is twelve today. Wild! Her main “homeschool” activities now is this math encyclopedia research for my project, a Pecha Kucha presentation (“Maria! More than two hundred people already registered!”), “42 communities” rite of passage, and finding apprenticeships for the fall. Looks like it will be art and cooking. You are awesome, Katherine! I love you!

Here is the full video from that Physics+Modeling field trip. Skate rink works nothing like our physics models!

Never underestimate the power of dailies and weeklies. I am happy to see where Math 2.0 is going. It is turning into a hub I wanted to use and did not have two years ago. I blame weekly events. “We are what we repeatedly do.”

I hope Katherine’s costume party will catch “Through the looking glass” exhibit in ArtSpace. Several girls she invited were in our Art+Math Renaissance Wonderland unClass (long name, I know).

We will test the settings a bit more and then invite people who participated in math game discussions in with Colleen King, Dmitri Droujkov and me to join Colleen’s new forum.

Speaking of support

Ironically, some of the more developed, well-supported and widely used community meta-currencies happen in massively multiplayer online games. Also, the name for these currencies has the word “dragon” in it, of which I highly approve. Everything is better with dragons!

I hope we can learn from Carrboro Creative Coworking. They helped a lot of lovable local projects.

I would dearly love for my webinar software to do what my laptop+projector does so well: stream whatever is on my screen and sync it with the sound. As it is, you can tell people to view a video in their browser, but you can’t view in-sync and thus point out a frame to everybody. Nibipedia-like software may provide a solution, if this “bookmarking of a moment in the video” can be done in real time. Right now any “live” media does not do well at all with “live” event software I know! Yet people like Steve Hargadon can do amazing things with tools we do have, and help others.

Off I go to the Cary Homeschoolers party. The local family educator networks have been incredibly kind and supportive toward our family.

Raider time

Raiders in MMO games are people who play beyond casual. Geeks go deep, and spend their “raider time” focusing on something, playing with it, perfecting skills, paying incredible attention to detail. Dan Meyer, who presented yesterday at Math 2.0 series, spends raider time with video. But it does not have to be this subjects. Combine your incredible love for X (any X) and raider time you spend on it, your love for subject Y (any Y) and your desire to teach it, work hard on teaching techniques, and something wonderful will happen no matter what X and Y are.

Lockhart says math has to be its own context: X=Y, straight up, no metaphors, but possibly rule-based (abstract) games. He is also successful in his teaching, because he loves his math-as-its-own-context. It is sufficient and it works for him. It’s not necessary. Instead of Math+Math+Teaching it could have been Origami+Math+Teaching or Infographics+Math+Teaching.


One of contexts I love is Mars. I just learned we will be working on four high school level STEM modules for NASA, about Mars exploration. I am super-excited.

Learnspace

Career Exploration homeschool coop met yesterday. So many opportunities, and a great commons support for teens. Yay us! We may go to Rare Earth Farms (grass-fed, organic beef) soon. Modern organic farmers are Renaissance people.

“Learnspace” planning is going ahead. We are looking at models like coworking and hackerspaces. I hope to learn from places like Kid’s Museum on what to do about “the nasties” like insurance. On the brighter note, there are nine group leaders now who said they will contribute ideas and time to making this happen.