Redistricting can be mathematical

Here's an article about redistricting :
MATHEMATICAL ASPECTS OF GERRYMANDERING (p. 3) by Paul Kehle.

 ...some of the interesting questions and issues that arise, capture student attention in ways that, while thoroughly mathematical, have little to do with gerrymandering. The topic is a rich and generative one completely apart from the initial thorny issue of deciding when a district map has gone beyond what is considered fair. In the explorations below and in working with students there are no boundaries to the questions worth exploring; and you and your students will likely come up with many not considered here, some even lead to questions at the frontier of mathematics and computing research. 

...In the simplified geographically square state represented by Vote Scenario 5a, there are 25 blocks, and each block gets one vote. The constitutionally required ratio of representatives to blocks in this country is 1:5 and so the 25 blocks must be partitioned into five congressional districts of 5 blocks each. In addition to other simplifications we make in this model, we assume there are only two political parties, the Green Party and the Purple Party. In the map, green and purple indicate how each block tends to vote. Another simplification in our model is a rule that we impose on the shape of the districts. To be a legal district, each block in the district must share at least one edge border with another block belonging to the same district. Even in such a simple model, students can gain familiarity with the general principles underlying the model and with the heart of the gerrymandering issue by calculating how many districts each party wins in District Map #1 and District Map #2. To win a district, we will assume that the party needs to win at least three of its five blocks.

In Iowa, a school let students create Arcade Games for projects, which involved math in planning the blueprints, slope, and business pricing, etc.

Creating rollercoaster rides could be duplicated with software, and is a long-awaited dream of mine:
http://www.ottumwacourier.com/news/student-arcade-rewards-concept-development/article_fbbc2d3a-ce63-11e8-ae59-5f40d19c4043.html

The Value of Video Games in the Classroom - Dan Meyer

In a recent post by teacher Dan Meyer (also mentioned in my last blog), he decided to find out why his students liked video games so much, by playing a lot of them! Here are some of his conclusions:

Video Games & Making Math More Like Things Students Like

December 16th, 2014 by Dan Meyer

These are the six lessons I learned:

1. Video games get to the point.
2. The real world is overrated.
3. Video games have an open middle.
4. The middle grows more challenging and more interesting at the same time.
5. Instruction is visual, embedded in practice, and only as needed.
6. Video games lower the cost of failure.

Turn Bland Math Problems into Interactive Classrooms, with Multimedia

Math teacher Dan Meyer has an interesting TED Talk, where he begins by saying he's talking about a subject he loves to a captive audience of students who hate it, but are required to take the course (often remedial learners).

Eventually, he leads into a line problem in the familiar format,

• deletes the information, and
• instead runs a video of filling a large tank with water.
  

After several boring minutes, the curious students ask how long it will take to fill (the exact math problem), and are led into a highly interactive, enthusiastic search for the answer -- eventually solved by viewing the last frame in the film. Meanwhile, the students take guesses, which are placed on the board, and find out if they're right!

1. Dan Meyer cuts down the information presented. Students generate it and filter out what's needed and not.
2. He leads them into formulating the problem (as Einstein and Herb Simon have mentioned is one of the major parts of solving any problem).

   The real world of human decisions is not a world of ideal gases, frictionless planes, or vacuums. To bring it within the scope of human thinking powers, we must simplify our problem formulations drastically, even leaving out much or most of what is potentially relevant...problem solving and decision making is centrally concerned with how people cut problems down to size - Herb Simon

3. Dan Meyer recommends the use of multimedia -- plentiful these days!
4. He turns the problem into a story.

Here's the link to the 11-minute talk: Dan Meyer's TED Talk: Math Class Needs a Makeover

Black MIDIs

There are now MIDI files that are so big, the music can't be played.

MIDI is a standardized way that digital sources (computers, electronic keyboards, digitized musical scores, musical instruments/voice speaking through a digital controller, or other MIDIs, etc.) can create music through a synthesizer, without musicians playing any instruments, although MIDI-controlled electronic music can be mixed together with living musicians.

Here's a link to a post about black MIDIs, where the notes grow so thick, it creates a black visual pattern or dense cloud on the screen! Sometimes it is composed of Millions of notes!  Composers may try to surpass each other in ways that don't have much to do with music!

1. Maximizing the size of the download (such as creating a terabyte file - a billion billions) or
2. Boasting about the fact that their computers are so grand that they are able to play the huge file they created!

Follow this link to try Jingle Bells and the descriptive video at the top:

Black MIDI Songs will kill your brain and your computer (Well, it's not actually that bad!)
http://m.aux.tv/news/62071-black-midi-songs-will-kill-your-brain-and-your-computer

What's the Scarcest Resource?

Surprisingly, the famous software/hardware designer and author, Dr. Fred Brooks, says that what holds up projects usually isn't money....

Brooks: The critical thing about the design process is to identify your scarcest resource. Despite what you may think, that very often is not money. For example, in a NASA moon shot, money is abundant but lightness is scarce; every ounce of weight requires tons of material below. On the design of a beach vacation home, the limitation may be your ocean-front footage. You have to make sure your whole team understands what scarce resource you’re optimizing. 

from a 2010 Wired Magazine article:    http://www.wired.com/magazine/2010/07/ff_fred_brooks/

He is called "the father of the IBM 360" (a major leap forward in computer hardware)

and author of The Mythical Man-Month:

You can’t accelerate a nine-month pregnancy by hiring nine pregnant women for a month. Likewise, says University of North Carolina computer scientist Fred Brooks, you can’t always speed up an overdue software project by adding more programmers; beyond a certain point, doing so increases delays.  

Mobile Pocket Projectors

This describes a mobile Pocket Projector, created by the head of the MIT Media Lab, Ramesh Raskar. I'm adding this here because it would be useful for a mobile Landmarks game.  Once the student/gamer finds the right location, several fake RFID tags could be posted in different directions, seen from the same spot or street intersection.

http://web.media.mit.edu/~raskar/pocket.html

This could be used to register whether the student/gamer had arrived at the right spot to see the landmark or view.  Also, they should take a picture of what they see and the software should be able to compare whether it's the same view, within a certain amount of leeway ("tolerance").  Using RFID tags posted on lampoles, etc. would pin down someone's success or failure quicker, because image recognition by computer software is still tricky.

Working together on the educational game set FunFunctions

Summary:

• Many of the following ideas also apply to the FunFunctions development project, at this stage of open source programming and preliminary discussions.
• The MIT Media Lab has impressed at every turn, such as when I viewed their products in the Evolving Technology section of SIGGRAPH, appearing year after year with something new, such as projected stories slipping off the edges of a table as you tilt it and a miniature spinning 3d house in a glass cube that morphs when confronted with a math equation (cos, sin, etc.).
• R. Keith Sawyer is in another blog entry.

The following is from Kyle Welche's blog, at http://kylewelch.wordpress.com/2013/06/15/the-mit-media-lab/

MIT Media Lab

"The MIT Media Lab is something of an anomaly in academia.  It breaks down walls that constrain nearly all institutions of higher education.  First, it is deliberately interdisciplinary.  Whereas most graduate programs tend to focus on intra-departmental synergy more than inter-departmental synergy, the MIT Media Lab draws experts from a wide variety of fields, spanning the arts, sciences, and communications.  Rather than maintaining a uni-disciplinary lab, they have developed an intellectual ecosystem that produces ideas and permutations that can only collaborative diversity can create.
...
Additionally, the Lab favors collective ownership over individualism.  Rather than adopting the traditional academic route that rewards individuals for publishing more than their peers, the Lab does focuses on projects large enough to not consolidate credit to a single person. Additionally, collective IP ownership of products includes faculty, students, and their corporate sponsors.
...

The Media Lab’s organization revolves around specific goals.  The body of faculty, students, and sponsors is divided into teams that are dedicated to specific projects.  All research, design, and development is centered on tangible outcomes.  A list of current projects (some of which are staggeringly bold) can be found here.

The first of Sawyer’s key flow-enabling conditions is the concept that a group must be focused on a specific goal.  Sawyer notes that flow is catalyzed when a group has 'a compelling vision and a shared mission' (44). "

-----------------------

Sawyer, K. (2007). Group Genius: The Creative Power of Collaboration. New York, NY: Basic Books. ISBN-13;978-0-465-07192-0.

SmalLab - Situated Multimedia Arts Interactive Learning - one way to develop kinetic learning ideas in 3D

Interactive learning - primary and middle school students - out of their seats, in kinetic learning.
Summary:
1. First video shows example.
2. For developers - free download of 3d game engine
3. Ideas of what to put in it?
4. To make it math/science, it needs numbers and measurement.
Flow brings embodied learning to any existing Interactive Whiteboard or projection surface. Using motion-capture technology - similar to the Xbox Kinect™ - students’ bodies are the interface in Flow. Students use their hands in real 3D space to manipulate images, sounds, text, and graphics. This kinesthetic engagement opens new pathways to learning.

For example, in the Color Mixer Scenario, groups of three students collaborate control the amount of red, green, and blue light that is mixed in a virtual spotlight.  By raising and lowering their arms, they can see a dynamic mix of colors, hear the impact of their actions, and feel the relationship between gesture and how a variable changes.

2. SMALLab Learning Developer Program has free downloads of the Unity 3D game engine and they are looking for ideas!

3. Comment with your ideas for apps to develop!

This is centered in Hollywood, CA, but a system was bought by a local school system (Elizabeth, PA) and McKeesport, PA, very close to me, will soon be adding the $34,000 system! http://triblive.com/neighborhoods/yourmckeesport/yourmckeesportmore/4680784-74/smallab-classroom-learning#axzz2ejtj50p6

How will you Plug In?

Today I came across two interesting posts about new interfaces between people and 3D reality (virtual reality immersion or augmented reality, which is on-top-of reality):

How will you plug in?  --Game interfaces using Augmented Reality.

1. This one's from http://www.situatedresearch.com - Augmented Reality. 

2. Apple received a new patent today for a "submarine" 3d interface patent that has been lurking about for 17 years! (also from Situated Research, http://www.situatedresearch.com/blog/2012/07/apple-granted-patent-for-high-concept-input-techniques/

Apple Granted Patent for High-Concept Input Techniques,
"submarine" patent, from 1995 to 2012.

These are useful because these new interfaces create easier ways to connect math games up to interesting but measurably accurate game playing environments.

Sara

Math into Art

Turning the binary bits (zeroes and ones) of Twitter into spatial art!

Math into Art

Lori Hepner's Data Visualization 

http://lightbox.time.com/2011/08/26/data-visualization-twitter-portraits-by-lori-hepner/#7

Donald Duck in Mathmagic Land

The beauty of the laws of mathematics in the 1959 film, Donald Duck in Mathmagic Land, suggested by a web design student:

from 1959 Disney film on YouTube

http://www.youtube.com/watch?v=nav0kVa66xk

• Pythagoras
• Math in Music
• Golden Section 

           o   by architects and painters
           o   in nature - flowers, starfish, trees
           o   has logic and patterns

• Games (chess, Lewis Carroll, baseball, football field, 3-cushion billiards)
• Sections of Cones - drums, lenses, in the mind first - "no paper large enough to hold your imagination" (such as infinity)
• "Mathematics is the alphabet with which God has written the universe," by Galileo

Shrinking and Growing - What can Alice see?

In Alice in Wonderland, she grew larger and smaller at times.  What did she see when in these different dimensions? (Watch film below)
I still own an old NASA game on a floppy disk (unplayable), which had the players going to different dimensions!  I thought this would be a great theme for a game!  Imagine hiding treasures in the same room with your players, but they can't see them!  Math game: For instance, you could hide a treasure inside the period at the end of a sentence.  Normally unnoticed, if the player would have to solve which Power of Ten the treasure is on to even look there.

Based on the book Powers of Ten  ... 5-star Amazon.com reviews say, "In forty-two consecutive scenes, each at a different 'power of ten' level of magnification, readers are taken from the dimension of one billion light years to the realm of the atom. The text and other illustrations depict what we can perceive at each progressively smaller level of magnitude. " [Book by Morrison, Morisson, Eames and Eames]
"Back in 1968, designers Charles and Ray Eames made a 10-minute documentary film, titled Powers of Ten, showing what the universe looks like at different scales. Philip and Phylis Morrison were scientific advisors on the movie, which Philip narrated, and it was chosen in 1998 for preservation in the National Film Registry, which selects 'culturally, historically or aesthetically significant motion pictures' for preservation. The Morrisons' book translates the film onto paper.

Starting with a view of a billion light-years, the book (like the film) moves inward, with each page being at one-tenth the scale of the previous one. In 25 steps, you're looking at a picnic by the shores of Lake Michigan, then plunging into a human hand, down through the cells inside it, the DNA inside the cells, the atoms inside the DNA, and the subatomic particles inside the atom. By the time you've gone a total of 40 steps, you're in a world of quantum uncertainty.

There is no better guide to the relative sizes of things in the universe, and no better teacher about what exponential, scientific notation really means. --Mary Ellen Curtin

_______________

Wikipedia link: http://en.wikipedia.org/wiki/Powers_of_Ten

Great Film!

Watch Powers of Ten (cached copy)

http://webcache.googleusercontent.com/search?q=cache:http://www.powersof10.com/film

___________________

Watch Cosmic Zoom, 8-min. film by Eva Szasz, 1968 http://www.nfb.ca/film/cosmic_zoom

at National Film Board of Canada.

Hiding inside the "Scale of Universe" by Cary Huang

My son, Daniel, just sent me a link to this cartoonlink Travel through dimensions of the Universe. Travel at your own speed at http://scaleofuniverse.com/ or just watch this video:

Developed by Cary Huang at htwins

Create a math game: hide objects in different layers, based on real dimensions, as this video is.

Create a Gigapan Game

Here's a place to create Gigapan games.  

Create your own game for free, http://gigapan.org/cms/create-games 

Gigapans can zoom in to incredible levels while preserving fine resolution, by combining multiple photos taken with their small Gigapan robot and stitching them together!

For me, I would like to hide objects on different levels that can't be seen in the overall picture.  They call this an Easter Egg hunt.  Here's one example by Gordon Atwell: It should actually work if you click on it!!
To see it full page, go to http://gigapan.org/gigapans/3768. This would be the 3d simulation the student goes through after drawing a pathway on a 2-1/2 d map, like Google Earth.

Moving through space and beginning math

Zander watching a squirrel. A clear wall or plane - the glass window - divides the short distance between the cat  and the squirrel.

This visual-spatial game interface can be used to teach many things, but it was first of all designed to teach math. 

For instance, a beginning math student could be told to go ten feet straight ahead, then turn right and go 3 feet, in an L shape.  At the beginning, they are just learning shapes, lengths, and angles.  The answer to the problem is an L-shape or a final spot they land on.

If they solve the problem while on land or an online game, they will begin to think of math as related to everyday space, which it is!) and begin to associate math with navigating through space.   Spatial abilities and visualization skills and abilities are related to math and science success, so the more you can get people to think that way, the better. There's been a good bit of research about this.

Travel through an equation: RFID visually tracks where people go

Here's some OpenSource (freely developed and available)  RFID software  that shows where people go in a conference.
It seems like it could be used to create math solutions (dots or lines). As players solve the math puzzles, or follow street maps, their pathway should show up as a math solution.  For instance, you could have someone travel the beltway around a city to create a circle.

Here's the software used, OpenBeacon: http://www.openpcd.org/OpenBeacon_Active_RFID_Project

Jobs for Autism

Here's an interesting letter from the Chairman of Jobs for Autism, which has similar aims to those of Mary Hart's Computing Workshop (see earlier blog on this subject).
A letter from the Founder and Chairman of Jobs For Autism, Mr. Jeffrey Stein

In 1988, the film "Rainman," in which Dustin Hoffman played a socially impeded person who could memorize certain facts and numbers that enabled him to break the bank in Las Vegas, gave many people their first glimpse of a form of autism. That was the year that I learned of autism as we discovered that my son, then three years old, was exhibiting certain traits that are characteristic of autism.


While the Rainman stereotype exists, it's rare. Unfortunately most of those afflicted with autism will not be able to earn substantial sums of money by beating the casinos. Rather, most face a more mundane existence that often culminates in the odd part-time job or years spent hanging around perhaps having an interest in something so strong that it borders on an obsession.


If a non-autistic person was as singularly focused on something as many autistic people are, they could be successful economically in that pursuit. But because of the perceptions of society, this usually does not occur for those within the autistic spectrum.  Therefore, a large proportion of people with autism spend their time helping around the house or doing nothing. This is a huge waste to society as well a waste for the individual. Those with autism who do work, usually go into a job that involves a routine and little contact with the public. Jobs such as warehouse work, data entry, mailroom and gardening are typical.


According to Steve Broach, a policy manager with the National Autistic Society (NASA) only 12 per cent of those with Asperger’s  syndrome [a common form of autism where the afflicted person is high functioning] are in full-time employment, despite the vast majority wanting to work.


Having a son with autism, I know that many if not all autistic people have potential greater than that recognized by schools or health care providers. When my son was first diagnosed, we were told that he might never speak well enough to communicate, that reading was highly unlikely and that he might never be self-sufficient. Even at the age of three and one half years, he had a fanatical devotion to basketball. Although he could barely speak and most people except for me thought he did not comprehend much, he taught himself how to read the TV Guide at four and one half just so he would know when the Lakers were on television. Even today, if you ask him how much is 120-40, he will be stumped. However if you tell him the Lakers lead the Pistons 120-80, he will immediately tell you that the Lakers are up by 40.


Although some people born with autism go on to achieve great things, the majority of them are not given the opportunity to fulfill their potential. The purpose of this website is to assist those with autism in realizing their true potential and to provide employment opportunities in areas that have not usually been open to the disabled or handicapped. These areas include the entertainment industry, professional and amateur sports, and even the legal profession.


The goal of our organization, is to raise awareness of the talents and capabilities of those within the spectrum, as well as serving as a forum for the spread of ideas, from education to health and nutrition, including new insight, discoveries and positive information, all designed to help those within the autism spectrum and their families, to improve their quality of life.  We welcome your involvement and input.

-Jeffrey Stein

Description of Game - Architecture Layers

There are 4 layers to the set of educational games I've been trying to create, called FunFunctions:

1. 2d-3d visual/spatial math games

2. authoring interface that connects games to 3d landscapes.  The solutions only have to have (x, y, z) points or lines.  Then they can be shown in any landscape. Teachers can control it more.

3. the landscapes are shapes, "billboards" and buildings placed on a terrain. Architectual students could build them, such as by using Auto CAD.

4. cognitive tutor: All the games would be displayed on a pallette that only shows games that are

a.  appropriate to the player's math level, 

b. favorites: the player's choice of conquered modules , or 

c. teachers' guidance could add more.

To begin with,  I want to get a full game running. I've had little ones running about 1993 and 2002, but I need to do this again and am thinking of using the a mobile handheld, combined with Google Earth and GigaPan. (The handdrawn sketch from the last blog applies to this).

Volunteer Artists and Programmers are needed

1. Artists are needed to create:

• 2d - landscapes, signs, quiz pictures in 2d and 3d
• 3d - architecture, plants, objects
• video - of 3d walkthroughs
• interfaces - what the players use to control what's going on
• find landmarks and treasures, as goals; search gigapans for useful ones
• think of optical illusions or ways to hide objects to make it difficult for the player 

2. a project manager to integrate these all

3. programmers would fit this together in an automatic way, running an invisible "cognitive tutor" or "intelligent tutoring system" in the background that knows what to present to the player next  but allows teacher guidance and player preferences.

4. Problems need to be written out and organized ( by level and type) and matched up with math textbooks.

5. Other: scan photos, organize existing videos and problems, list them

6. Put lists into databases for programmer to use.

There are other things.