Wednesday, December 26, 2012

GeoGebra Animation

There was a challenge to make a GeoGebra Christmas card this year, through Instagram with a #ggbxmas tag, and there were a few really sterling entries. Like this one from Wengler, a lovely Pentomino puzzle from Renata, or milanoff's slick animation. I'm not an Instagrammer (yet)...

... but I tried to make a card too, and just wanted to share two bits that helped me make my mediocre effort. Making the card made me think that this would be an excellent class challenge, which could really help contextualize some algebraic topics.

The above image was made using GeoGebra's nice export to animated gif feature. The original sketch is at GeoGebraTube.

The first was to make a function that would be 0 for a while, then increase to 1, then stay at 1. There's smooth (mathematically speaking) ways to do that, but a piecewise linear function is good enough for most uses:
f(x) = If[x < 0, 0, If[x < 1, x, 1]]
Then it's a really nice use of graph transformations to adapt it. Want it to start increasing at x = 5? f(x-5). Want it to scale between 0 and 4? 4*f(x). Want it to take  6 units, starting at x=3, to increase from -1 to 8? That's a good problem! (Would 9*f((1/6)(x-3))-1 work?)

My first couple of pieces were animated by using the function directly on a point definition. Like Joseph's left foot,
A=(12f(1 / 3 d), 0)
and then I defined the rest of Joseph relative to that point. In GeoGebra you can do arithmetic with points like vectors and use the coordinate commands to reference part of a point.
A+1 = A+(1,1)
B=A + (0.5, 0)
C=0.5 (A + B) + (0, 1)
(x(A), y(A)+1)
W=(0, 1) + f(1 / 8 (d - 4)) ((12, 1) - (0, 1))
But then I realized that instead of animating each vertex, I could make the shape I wanted, and then use geometric transformations to move an image of it, controlled by a vector. So for the second time moving the Holy Family into the stable, I made vectors like:
Joe = 2.5(f(d - 7), 0)
Vector[(5f(d - 7), 0)]
And then moved shapes by translating by that vector.
poly7'=Translate[poly7, Mary]
I used the translate tool to do that, clicking on the names in the algebra view, but this is how it looks as an input bar command or in the algebra view. (Took me a while using GeoGebra before it occurred to me that using tools you can select from the algebra view, and that I didn't have to be able to click on it in the sometimes complicated graphing view.)  This technique is much more powerful, and lets you fine tune by changing the vectors instead of having to go change multiple vertices. Which is the kind of thing I have told students in linear algebra before, but never really had to do!

So Merry Christmas and Happy Holidays to all, and a GeoGebrafied New Year!

Wednesday, December 12, 2012


Michigan is just having a darling political month. First, becoming a Right to Work state, bitterly betraying our proud history of organized labor in as sleazy a manner possible. (Even if you supported Right to Work, hopefully you would be ashamed of how it was passed.) But now we're busy wrecking public education also.

Here's the gist of a letter I drafted about it:
To whom it may concern:

Please do not allow House Bill 6004 nor Senate Bill 1358 to become law.

These two bills will establish an Education Achievement Authority (EAA) operating outside the authority of the State Superintendent of Schools and the State Board of Education. Funding for the EAA would be without any oversight from the legislature. Any school in the state into the new EAA district could be taken in by this new government-run statewide district, and then these schools could then specify which students they would serve. The EAA can seize unused school buildings built and financed by local taxpayers and force sale or lease to charter, non-public or EAA schools. This completely bypasses our State Board of Education as well as local government, leaving the Education Achievement Authority with no elected oversight.

Furthermore, there are hugely negative impacts on the funding of existing local public school districts. Local districts are already financially compromised. And with this legislation moving so quickly, most citizens are not aware of it. They would not approve when they do find out. I urge representatives to be representative in this matter.  You can gather the necessary information to see the impending disaster. Vote no on these bills!

Doing all this for an experimental school model that has yet to be verified is nothing short of gambling with our children’s educational future. I am in favor of creating room for innovation and personalization, but this takes us farther and farther away from research verified successful educational models.

Another bill that seems disastorous, especially in combination, is House Bill 5923. It creates several new forms of charter and online schools with no limit on the number. Selective enrollment policies could lead to greater segregation and the bill creates new schools without changing the overall funding available, further diminishing and compromising resources for local public schools. This also creates unequal access to quality programming.

My spouse persisted in getting it through to the  Governor's office, and got this reply.

Thank you for recently contacting the Executive Office of Governor Rick Snyder regarding education in the state of Michigan. Governor Snyder appreciates your valuable input and has asked that I respond directly on his behalf.

If you're interested, we've just released a series of videos, where parents and educators speak out about the impact of the Education Achievement Authority in their school.  Take a moment to review the videos by clicking here:

To address the link between Michigan’s economy and the quality of Michigan’s public schools, Governor Snyder sought to address the state’s Persistently Lowest Achieving schools in his education agenda – currently designated as Priority Schools by Michigan Department of Education.  These are schools that are persistently low achieving and regularly in the bottom 5% of student achievement. Michigan started ranking schools under the School Improvement Grant three years ago, and then refined it for the state Persistently Lowest Achieving legislation and federal Elementary Secondary Education Act flexibility. For years, the lowest achieving schools have been identified without the tools to do anything about it.  The Education Achievement Authority is that tool.

The goal of the Education Achievement Authority of Michigan (EAA) is that all students should have access to a quality education and successfully complete their K-12 educational experience career and be college ready.  One of the principal objectives of the EAA is to transform public education from a one-size fits all model.

The EAA’s approach to teaching is to institute a system known as student centered learning.  In student centered learning, they test each student individually to determine their achievement level in each subject.  They then develop a unique education plan for each individual student, working with that student at their individual level.  In student centered learning, no longer are students moved on just because they have spent nine months sitting in a chair.  They move on when they master a particular subject.  Students no longer identify themselves in grades based on their age, but by their achievement level in various subjects.

All EAA direct-run schools use a cutting edge, digital learning platform that allows teachers to provide a personalized learning experience to each student. Each student is empowered to own and navigate her own learning path.  The EAA is dedicating both public and private resources to building a new learning platform to give kids who simply have not had a chance an opportunity for a bright future.

Again, thank you for contacting the Governor’s office. Should you have further questions or comments regarding this or any other state-related matter, please do not hesitate to contact this office if there is anything we can be doing for you.


Melanie Ellison
Constituent Services Division
Executive Office of the Governor, Rick Snyder
O: 517-335-7858
 How are we ever going to make progress in education if we are losing ground to this sort of unsubstantiated posturing for profit?