Geodesic Dome Building, Part II

The dome actually worked! All three fourth grade classes rolled, measured, cut, marked, counted, and assembled two geodesic domes at the Integrated Arts Academy. A quality assurance team was established in order to ensure the newspaper rolls were strong and tight. Partner work was important, so students had one person tape while another person held newspaper rolls in place. Math was happening all around. The domes initially worked great, but then started to droop and fall after a few days. Students fixed them up and brainstormed ways to make them stronger.

This project was shared during an all-school assembly. Three of the fourth graders presented the work with a slideshow created by their class. More fourth graders sat inside one of the domes (to everyone’s delight!) in order to hold it up if it started to droop during the presentation. It didn’t need any support but it was really fun to have them sitting in there. The presentation touched on the math, art, and engineering in this project. Students also explained Buckminster Fuller's humanitarian vision for the geodesic dome.

I loved collaborating with Ada Leaphart, Judy Klima, and the fourth graders at IAA. I hope to do it again soon. There are so many wonderful opportunities to connect math and art in meaningful ways.

From Lani Guinier

I am reading the New York Times on a Sunday, sitting next to the woodstove to keep warm. In an interview entitled Redefining Diversity, Re-evaluating Merit, by Tamar Lewin, Lani Guinier has some important things to say.

The score on your SATs or other exams is a better predictor of your parents’ income and the car they drive than of your performance in college. The credentials of our testocracy legitimize a new elite, and give them an inflated sense of their worth.

Diversity is not simply a matter of having people who look different sitting next to each other but learning in the same way.

Studies show that groups made up of the highest-performing individuals are not as good at solving complex multidimensional problems - like designing environmental policies, cracking codes or creating social welfare systems - as groups with a mix of skills, backgrounds and ways of thinking, even if the individuals in the group are not all high performers.

Guinier’s new book is called The Tyrrany of Meritocracy: Democratizing Higher Education in America.

How to relate, by Alan Alda

I am watching reruns of M*A*S*H right now as I reflect on seeing the one and only Alan Alda in person at UVM’s Davis Center. I love watching M*A*S*H, as I feel it has held up really well over time and is a perfect mix of funny and tragic. The character Hawkeye Pierce, played by Alda, stands out even though the other cast members are excellent.

Alan Alda was also brilliant in Woody Allen movies, like Crimes and Misdemeanors (“If it bends, it’s funny. If it breaks, it’s not funny.”) Then I began seeing him getting involved in science with Scientific American and other shows that ran on PBS channels. Although today was a snow day and the roads were pretty bad, I and the intrepid Nina Madore weren’t going to miss the opportunity to see him live at UVM. I figured nobody would be there, but the giant Silver Maple Ballroom was packed.

I expected Alan to talk about specific science concepts, but, instead, he talked about being an effective communicator. He got rid of the podium used by those who introduced him in order to be more accessible to the audience. Actively demonstrating the theme of his talk, Alan looked carefully out at the faces in the audience and spoke in a warm, conversational manner without reading any notes. He shared the alarming statistic that 95% of Americans are not considered “science literate”. Then he went on to make the case for scientists learning to be better at relating to laypeople and working to make their research accessible.

Alan shared several ideas that scientists can use to think about improving communication. He talked about using emotion to help lodge ideas in the minds of the audience and using suspense and drama as a hook. At one point, a courageous audience member took the stage to demonstrate by walking across the stage with a very full glass of water. Another audience member was enlisted to demonstrate “the curse of knowledge” by tapping out a song. The curse of knowledge is what happens when you know something so well that you forget what it is like not to know it. In order to be a good communicator/teacher, one must break the curse and use empathy to understand the audience.

Alan’s talk was excellent. I wish more colleagues had been able to attend and that we could participate in some of the workshops he was going to be leading at UVM. His foundation, The Alan Alda Center for Communicating Science has a website worth visiting. UVM is going to begin a similar program and partner with him and his colleagues. In the meantime, elementary and middle school teachers should take a look at The Flame Challenge. Teachers of fifth and sixth graders can register here to let their students be the judges of a contest to see which scientist can best explain the answer to a science question. This year’s question is “What is sleep?”.

Alan has important messages for teachers and scientists and really anyone with a heartbeat. It’s worth visiting his website, reading more, and watching videos. Alan, thank you for coming to Vermont. I look forward to seeing UVM’s efforts in this area.

Educon 2015

I can see why many Educon attendees remarked that they’d spent their own money to be there. The conference, held at Science Leadership Academy in Philadelphia is that good. It was an eclectic group of out-of-the-box thinkers, innovators, and activists. I knew I wanted to go when I saw Chris Lehmann, founding principal of the SLA, speak in Killington last year.

I was a first-timer. Day one was spent at the school - a public high school that is an inquiry-driven, project school - in partnership with the Franklin Institute. I and a few of my colleagues found a student to guide us. She patiently walked us to different classes where we watched, listened, and sat with students to chat. Students in one class passionately explained a project in which they protested the closing of a huge number of Philadelphia public schools. Students in Doug Herman’s photography class told me what they’d learned about composition and layering and why they were in the photography room even though it was actually their lunchtime. In Algebra II they had designed a catapult to hit a target and were typing a reflection about their group process. I was hooked.

Then, of course, there were many great workshops, Ignite talks, and side conversations on Saturday and Sunday. Here are some of the people I met and learned from, along with some quotes and resources.

A highlight of the conference for me and many others, I’m sure, was Raghava KK, the effervescent, charming presenter and self-proclaimed TED whore. Here’s a 4 minute TED on bias and perspectives in history. He helped me remember what it means to be truly creative. You don’t matter, he said to all the educators in the room. Art should be the medium by which stem is taught... Art is how you teach everything... Incorporate visual literacy in everything you do.

Every disagreement is a chance to learn about a different perspective.

Raghava’s co-presenter, Meenoo Rami, an SLA teacher, hosted this session in her classroom. After meeting her, I was sorry I hadn’t made it to her class on Friday.

Diana Laufenberg, of SLA, led a workshop on school transformation and Joni and I sat with a Eric Dale from the Dwight School in NYC and Andrew Gallagher of the NYC Department of Education. We enjoyed hearing about Eric and Andrew's work, marveling over the vastness of the NYC school system. Diana recommended the book Immunity to Change.

Deterritorialize departments. Get away from content and move to skills.

Jamie Gravell shared a collection of articles on Inequity in Education.

The one thing I wish I'd known about was this idea of transformational resistance.

Is the student trying to transform the environment in some way instead of doing something wrong?

Math and Social Justice, was a session I didn’t attend, but wanted to. Thank you for posting these resources.

Burlington High School (Massachusetts) has a course called Help Desk. See their great website here, which was presented by female STEM enthusiasts on their way to becoming engineers.

There was a really cool panel I was late for. I liked the conversation that was happening when I arrived, which included comments from Otis Hackney, Principal of South Philadelphia High School.

When people say ‘they don't have the background knowledge’, I say, it is your job to give them the background knowledge they need! If they walked in already knowing everything, they don't need us. As an educator you have a job to do.

What if you had a school with mostly white students and all black teachers, what would that be like?

David Jakes, Imagining Digital Spaces for Learning. In groups, we designed a digital learning space, but we were not allowed to discuss any specific tools. Anyone who is working in or redesigning a school should read Toolkit for Designing a Digital Atelier.

Have you intentionally designed a space that intentionally supports your vision of learning?

How do you design a physical space for an increasingly virtual education?

Last but not least, I was in a wonderful session called Shifting the Focus: Elevating Student Voices led by students and their teachers, Josh Block and Amal Giknis. First, the students shared their projects and then we were asked to create an “education manifesto” in 30 minutes that could be posted to twitter with hashtag #focusonvoice. The students were so open and passionate in their presentations and then were so effective as they came around to help us with our assignment...this session is one that has really stuck with me. I was fortunate enough to sit with Renee Hawkins, a very thoughtful educator from a school in Baltimore.

I don’t know how I’ll stay away from Educon next year. I had my mind blown by great thinkers, got to spend time with beloved colleagues, and had my first taste of a grapefruit brulee doughnut from Federal Donuts. As Raghava said, Don’t mess with passion.

Geodesic Dome Building, Part I

Ada Leaphart, Integrated Arts Academy Art Teacher Extraordinaire, and I have embarked on an adventure. We’ve got all the fourth graders at IAA building geodesic domes out of newspaper.

I really don’t know how this is going to end up, so that is why I have named this Part I. I hope to report back with more news as the project progresses.

Ada and I decided to keep things loose. We didn’t want to figure everything out for the students by creating our own dome first, learning all the lessons, and then presenting a tidy scenario.

Instead, we have never attempted to create a geodesic dome out of newspaper or anything else, for that matter. Sometimes STEM+Art (I, unlike others, am not wanting to call that STEAM) should be messy and students should have the fun of making mistakes and doing all the figuring.

Before the students got started building, Ada showed a photo of a geodesic dome and asked students what they noticed. We got some math+art conversation going from that, as students noticed many geometric shapes, like triangles, pentagons, hexagons, and trapezoids. Then we talked about old Bucky Fuller (every class asked if he was still living) and how he really wanted to make the world a better place for everyone by using an efficient structure like a dome for shelter.

Kids couldn’t wait to get started. Here are the instructions we are using from PBS.

It turns out, you can roll newspaper in a loose, floppy, weak way or you can roll it in a very tight, very strong roll. Students shared successful and unsuccessful techniques. Among the successful techniques invented by students are 1) Asking someone else to help you tape the roll, 2) asking someone else for help, period, 3) twisting the roll when it is finished to make it even tighter, and 4) using a pencil to act as the center of the roll, then shaking it loose once the roll is finished.

We ended up with enough rolls to make one or two domes. 65 usable rolls are needed. Next time we will need to establish a Quality Control group to assess, select, and count the rolls we’ve got. Ada and I aren’t sure how the whole thing is going to go. At the end of it all I would like to set the dome on fire in the playground. I am not sure we will get permission for that. Oh well, we’re going to roll with it.

Sugata Mitra: School in the Cloud

Sugata Mitra recently won the TED Prize for 2013. His wish is to build a virtual school where children learn from each other.

Well, I bumped into this whole thing completely by accident. I used to teach people how to write computer programs in New Delhi, 14 years ago. And right next to where I used to work, there was a slum. And I used to think, how on Earth are those kids ever going to learn to write computer programs? Or should they not? At the same time, we also had lots of parents, rich people, who had computers, and who used to tell me, "You know, my son, I think he's gifted, because he does wonderful things with computers. And my daughter -- oh, surely she is extra-intelligent." And so on. So I suddenly figured that, how come all the rich people are having these extraordinarily gifted children? (Laughter) What did the poor do wrong? I made a hole in the boundary wall of the slum next to my office, and stuck a computer inside it just to see what would happen if I gave a computer to children who never would have one, didn't know any English, didn't know what the Internet was. - Sugata Mitra

Salt + Fat

The Extraordinary Science of Addictive Junk Food by Michael Moss, Published Feb. 20, 2013 in the New York Times Sunday Magazine.

I enjoyed this article in last weekend’s New York Times. In it, you will find important information about the workings of the food industry and will have a better understanding of the obesity epidemic. Also, I couldn’t help but notice how mathematics is such an important part of the story. When you get to the part about the food guru Howard Moskowitz, (“I’ve optimized soups, I’ve optimized pizzas. I’ve optimized salad dressings and pickles. In this field, I’m a game changer.”) notice his ability to use statistical analysis to take bucketfuls of taste test data and turn it into usable information. This is why he has become a legend in his field.

Learning to code

http://www.code.org/

Watch this video. I completely agree that learning to code is learning to think. I think it is getting easier to teach, too, because there are lots of resources like Scratch and the Lego Mindstorms, plus tons of other links on the code.org. We are running out of time and excuses when it comes to our kids.

How much time do you have?

Teachers: Do you ever find yourself with a little time on your hands and nothing planned? There are zillions of videos out there these days - many are awful and many are wonderful. If you have a short space in the day, you can treat your students to something fun and thought-provoking. Here are some videos I like, with running times, to keep up your sleeve for just the right moment.

Eratosthenes (2:16)
This guy figured out the size of the earth a very long time ago in an elegant way using his knowledge of geometry.

Richard Tapia (2:21)
The kid loved race cars and became a mathematician.

Frostie Dancing to Shake a Tail Feather (2:43)
What can I say? It’s a surefire mood improver.

OK Go, This Too Shall Pass (3:54)
A band makes a music video ala Rube Goldberg. A TV smashes, people are shot with paint.

Doodling in Math Class: Infinity Elephants (4:36)
Makes you want to grab a pencil and start drawing fractals.

Artist of the Floating World (4:47)
An artist creates a giant pair of floating dice and sets them adrift in the ocean.

Brooklyn’s Rube Goldberg (5:34)
A real page turner.

There is a free iPad app from IBM called Minds of Modern Mathematics. It is a beautiful timeline of the history of mathematics and world events, and there are 9 vintage videos to watch as well. Charles and Ray Eames, a famous, husband-and-wife design team created the original interactive mathematics exhibit back in 1961, which provided the content for this app. The Eameses films are wonderful, simple, short. I enjoyed Something About Functions, and the non-verbal Exponents.

I also happened upon a great blog called MathMunch. MathMunch calls itself “a weekly digest of the mathematical internet”. They posted something about Minds of Modern Mathematics, and have a fabulous page of math videos. If you miss the old Schoolhouse Rock videos and you know a young person who could use some work on counting by 5s, MathMunch has the link. Their video collection is exhaustive, and includes videos about solving a Rubik’s Cube, paperfolding, Pi, M.C. Escher, and more.

A Pickle

There are some interesting new websites out there. One is called Math Pickle. Shannon Walters, C.P. Smith Library Guru, alerted me to this one. So far, I like most of what I’ve seen on this site, although the layout is a bit clunky. Dr. Gordon Hamilton presents activities for students based on math problems dating back several decades to mathematicians like Issai Schur and Lothar Collatz. His decision to put young Vi Hart on the same page as some of the older mathematics greats is a good sign. Math activities are presented via video, and include footage of real students. I’m less impressed with Dr. Hamilton’s philosophizing about the way math should be taught in a video entitled “Let’s Abolish Elementary Mathematics”, even though I agree with most of what he is saying.

I like the Graceful Tree Conjecture as a means of practicing subtraction with third graders and the Collatz Conjecture for fourth graders. These are captivating problem-solving activities which are an excellent way to encourage students to work together, discuss different strategies, practice skills, check their work, and have fun. I would also try the magic cauldrons addition game for second graders. Teachers will find Math Pickle a useful site for finding new activities for math class and getting a thorough explanation of how to use them.

Brahmagupta and Fibonacci

I am reading a book called The Man of Numbers: Fibonacci’s Arithmetic Revolution, by Keith Devlin.

So far, it is fascinating. I didn’t know anything about the history of mathematics, so it is all new and exciting to me. I liked Chapter 1 so much, I cajoled my kids into letting me read it aloud to them. There was some concealed eye-rolling, but they were interested once I began reading.

First, we learned about how the earliest known tally marks date back to Swaziland, circa 35,000 BC. Twenty-nine notches were carved into a baboon’s fibula. It hadn’t occurred to me that Roman numerals are really a more sophisticated version of tally marks. Devlin points out that, while it is easy to add Roman numerals, multiplication becomes problematic. Multiplying is best done with repeated addition when using Roman numerals, so anything involving two large numbers is impractical. Calculations were done using complicated finger arithmetic systems and abacus. It sounds like only a few people could do that sort of thing, and you just had to trust that the answer was correct (ahem).

The Hindu-Arabic system we use today dates back to 700 A.D. in India. My kids were surprised to hear that the symbols chosen to represent numerals may have been designed so that the number of angles match the quantity represented. You have to write the numerals in a certain, Flintstonian way for this to work.

The best part of our reading was learning about the invention of zero. The other nine numerals were well-established when an Indian named Brahmagupta entered the scene. Brahmagupta (fun to pronounce) created the number zero in the year 628. Before Brahmagupta and his gigantic book entitled Brahmasphutasiddhanta (which means “the opening of the universe”), folks were simply circling the blank spots in numbers. Brahmagupta wrote about zeroes in elliptic verse, which appeals to my sense of rhythm and brevity:

A debt minus zero is a debt.

A fortune minus zero is a fortune.

Zero minus zero is a zero.

A debt subtracted from zero is a fortune.

A fortune subtracted from zero is a debt.

The zero revolutionized the Hindu-Arabic system, making it possible to perform calculations much easier than before. I was definitely taking zero for granted before reading this book.

Now, on to Fibonacci. There was no one really named Fibonacci, but there was a guy named Leonardo de Pisa who lived in Italy in the 12th century. He brought math to the masses. I haven’t gotten to the part of the book yet that tells the history of the famed Fibonacci sequence, so I’ll have to keep reading. In the meantime, Vi Hart has released a new video entitled Doodling in Math: Spirals, Fibonacci, and Being a Plant which does an excellent job of explaining Fibonacci numbers and simultaneously making math seem young, cool, and beautiful even for those who didn't previously think so. It is worth finding 6 minutes to watch it with your students!