Thursday, December 22, 2011

Is there an App for That?

Visualizing data is very useful and can be done well, or not so well. Technology has certainly helped to produce many attractive, artistic displays of data and information. If you click here you will go to a website with many examples of visual data. Lots of interesting things to explore. Have fun. Two examples are

I particularly like the second graph as it predicts where technology is headed, no easy task. Another very interesting site that has been available for a few years now is Gapminder which presents visual data via animation. Click here for an example.

Monday, November 28, 2011

Some interesting reading...

Despite being written in 2008, this is an interesting and relevant paper, whether or not you're an "Apple person": Apple Classrooms of Tomorrow - Today, Learning in the 21st Century.

Also, it is worth the time to read about the Punahou School in Hawaii. Be sure to watch the video.


In addition to attending the conference at the Cedars School for Excellence in Greenock, Scotland which I blogged about earlier, I gave talks at two mathematics conferences. At both the Northwest Mathematics Conference in Portland, OR and at the California Mathematics Council - Southern Division Conference in Palm Springs, CA I gave a talk entitled Back to Basics - The Pythagorean Theorem. The premise was that the Pythagorean theorem is not only one of the oldest theorems in mathematics but is also one of the most basic and widely used theorems in secondary school mathematics. If one peruses the mathematics materials used at Phillips Exeter Academy (once on the Mathematics department page, click on Teaching Materials), it is astonishing at how many times the Pythagorean theorem makes an appearance...from Alex in the desert to determining the depth of a lake by yanking on a lily pad to calculating just how far it is to the horizon when standing atop Mt. Washington. Some applications are obvious, some subtle. At any rate, whether you teach mathematics or not, I thought you might enjoy these Pythagorean Fun Facts:

The Pythagorean Theorem - In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.

  • The book The Pythagorean Proposition contains 370 proofs.
  • An algebraic proof was published by U.S. President James A. Garfield
  • There is debate as to whether the theorem was discovered once, or many times in many places.
  • The earliest reference to the theorem was in the Egyptian papyrus Berlin 6619 written between 2000 and 1786 B.C.E.
  • Pythagoras lived from 569 to 475 B.C.E.
  • Pythagoras used algebraic methods to construct, um, Pythagorean triples.
  • Around 400 B.C.E. Plato gave a method for finding Pythagorean triples using algebra and geometry.
  • Around 300 B.C.E., in Euclid's Elements, the oldest known extant proof of the theorem is presented.
  • A verse of the Major-General's Song in the comic opera The Pirates of Penzance makes an oblique reference to the Pythagorean theorem.
  • The Scarecrow in the Wizard of Oz makes a more specific reference to the theorem, misstating it.
  • Greece, Japan, San Marino, Sierra Leone, and Suriname have issued postage stamps depicting Pythagoras and the theorem.
  • In 2000, Uganda released a coin with the shape of an isosceles right triangle. The coins tail has an image of Pythagoras.
  • In Neal Stephenson's book Anathem, the Pythagorean theorem is referred to as 'the Adrakhonic theorem'. A geometric proof is displayed on the side of an alien ship to display the aliens' understanding of mathematics. 
Source: Wikipedia

And, a review of two books on Pythagoras in the London Review of Books.

Focus on Calculus Newsletter article from November 1999

Issues Facing Secondary School Mathematics Teachers

It is a considerable understatement to say that mathematics education, particularly secondary school mathematics, has gone through significant change in the past fifteen years. Yet I believe that we have just glimpsed the tip of the proverbial iceberg and the biggest changes are about to happen. What follows are some of the reasons that have been at the core of the rapid and exciting change in secondary school mathematics and will continue to present secondary school teachers with even more challenging issues.


The advent of the personal computer in the early seventies and graphing calculator in 1985 forced changes in secondary mathematics. Suddenly the need for tables of logarithms and trigonometric ratios diminished rapidly and exciting topics and applications in mathematics became far more accessible to secondary school students. Computer programs like Green Globs, The Geometric Symposer, and the Kamischke Grapher led the way, giving us another strategy to use in helping kids understand mathematics. No longer did we have to use derivatives or Descartes Rule of Signs, among other methods, to get an accurate sketch of the graph of a function. Now students could use the graphing calculator to get an accurate graph with which they can better understand the behavior of functions. Also, problems that were dependent on calculus could now be done in precalculus. The continuing challenge facing secondary school teachers is to discover the correct balance of use of the technology. Just as total paper and pencil manipulations are obsolete, it is just as wrong to blindly push buttons with little thought about process and results.


There has been a move away from calculus as the pinnacle of the mathematics curriculum pyramid and this is good. While this may seem odd to state in a newsletter devoted to the focus on calculus, it is better for students and secondary mathematics programs in the long run. Discrete mathematics, statistics, and mathematical modeling now provide students with alternatives to the calculus. Students either tired of the focus or rigor of precalculus and calculus can continue to take mathematics that will help them become informed citizens.  Moreover, calculus courses need not be watered down and those that are truly ready for college-level calculus will benefit. While many students can perform the manipulations required in calculus, few really understand the underlying theory and concepts required for moving further along in mathematics. The challenge facing secondary teachers is convincing students, parents and college counselors that all students need not take calculus in high school. Further, development of meaningful, rigorous alternative courses requires time and energy from already swamped teachers.

The information highway

There has been an incredible increase in the sharing of ideas through web symposia and the availability of free software. Considering that there are some 800 million websites and that the best search engines can reach just around 16% of them, the usefulness of the World Wide Web in secondary mathematics is just being recognized. Teachers are now challenged by how to make the best use of the web in their classes. Certainly the web is a source of data sets that can enhance the teaching of statistics but secondary teachers must continue to explore this vast resource.

Text books

Teachers have many more textbooks to choose from today. In addition to standard textbook series, there are many innovative series available: the ARISE project from COMAP, Interactive Math Program (IMP), Systemic Initiative in Montana Mathematics and Science (SIMMS) to name a few. In fact there are 13 NSF funded curriculum projects, five of them devoted to secondary school mathematics. The calculus reform projects at the college level have also given secondary teachers many more options for Advanced Placement Calculus. The challenge for secondary teachers is to continue to press for better and better textbooks. While textbook adoption guidelines in school districts make it difficult, secondary teachers must convince school administrators that it is in the best interest of students to select the most up-to-date texts possible.

The TI-89

The biggest challenge facing secondary school teachers is to determine the appropriate use of Computer Algebra System capable calculators. The TI-89 will force us to think about CAS curriculum like nothing before. While Hewlett-Packard has produced calculators capable of symbolic manipulation for nearly twelve years and computer programs like Derive, Maple, and Mathematica have all been available for years, now it’s cheap, relatively, and in your hand. Secondary teachers will be the ones to decide how to best use this technology and it would be irresponsible to not do so. Secondary teachers led the way with appropriate and creative applications of graphing calculator technology and will again do so with CAS. This time, however, the mathematics curriculum as we know it will change forever. With the TI-89 it will be more important for a student to recognize form than be able to manipulate from one form to another. There are applications of CAS at all levels of the secondary curriculum and the next few years should prove to be very exciting as we decide how best to implement it.

Tom Seidenberg, Phillips Exeter Academy

Monday, October 24, 2011

Cedars School of Excellence, Greenock, Scotland

In late September I traveled to Glasgow, Scotland to attend a conference at The Cedars School for Excellence in Greenock, Scotland. The conference, attended by 25 teachers and administrators, was focused on the use of iPads. Since all Exeter teachers now have an iPad through the generosity of the trustees, and we are exploring their use in classroom settings, this seemed more than appropriate. Schools around the world are rapidly adopting the iPad as the tool for both teachers and students to achieve ubiquitous technology in the classroom. The Cedars School for Excellence is a school with 100 students, grades Primary 1 through Secondary 13. Every student and teacher has their own iPad. The teachers and IT people at Cedars have taken great care in researching and selecting appropriate Apps for each grade level and discipline. Perhaps the most impressive use of the iPad was in their art curriculum, led by teacher Jenny Oakley. Ms. Oakley will be visiting Exeter in April and presenting some of her work at an Assembly on April 10th, 2012. She will also be speaking with our art department. Some of the Apps she demonstrated were: ArtStudio, Brushes, WordFoto, OmniSketch, TypeDrawing, Flowpaper, and ArtRage. Find one you like and let your inner artist emerge!

Click here to see some of Ms. Oakley's work in addition to that of her students.
Entrance to Cedars School of Excellence

Jenny Oakley with some of her art

Jenny Oakley with student art

Student art work
Despite the fact that the Cedars School is a tenth of the size of Exeter and was established in 1999, the advances they have made in using technology are impressive. The teachers are dedicated to finding the best ways to teach their respective subjects and have made enormous strides in finding ways to improve education through the meaningful use of technology.

Thursday, October 20, 2011

Presentation prior to faculty workshop, September 1, 2011

When Tom Hassan named me the Bates-Russell Distinguished Faculty Professor in the spring of 2010, he also charged me with investigating classroom technology…what’s out there, how is it being used effectively, and how might Exeter benefit. My tenure in this position began with a conference at the Urban School in San Francisco in July 2010. The Urban School’s Center for Innovative Teaching hosted its annual Integrated Technology Symposium for principals, heads of schools, academic and faculty deans, directors of technology and education professionals interested in visioning the future of their schools. This workshop focused on establishing 1:1 schools. That is, schools in which all students have a laptop computer with them in all classes.

I followed this conference up in May of 2011 with a two-day visit to the Urban School to see this 1:1 program in action. Also, while in California, I visited the Branson School and Redwood High School in Marin County. Being a form Redwood Giant, I felt enough years had passed since my graduation that I could safely enter the school and not be sent immediately to the Dean of Boy’s Office. While all of the schools I visited had substantially more classroom technology for both teacher and student use than we here at Exeter currently have, it was the Urban School program that was most impressive. Here I sat in English, Spanish, and history classes where students and teachers used laptop computers seamlessly.

In English, students read a poem by John Donne which was projected on the interactive whiteboard. Then students came up and marked what they thought were important parts of the poem, then the discussion centered on why each student had made the annotations they had made. Since a SmartBoard was used, all images were saved to a folder so students could access them later. In another English class, students were working on what makes good writing. A poorly written paragraph was projected and students, again working in pairs, revised the paragraph on their laptops, then emailed them to the teacher who projected them on the board. At the conclusion of the class the teacher explained to me how the students do peer editing via groups on email. She said, ”I can’t imagine teaching English without a laptop.” In Spanish the teacher used an interactive whiteboard to work on grammar. He’d project a question in Spanish and the kids would orally respond. He then had students look at exercises on their laptops. In history, Contemporary China taught by Clarke Weatherspoon, the kids, working in pairs, used a program called Inspiration to chart what they thought were significant changes in China from 1970 to 1980. They then shared their results with the class via the projector again hooked up to an interactive white board.

So, how does all this relate to Exeter? I think we all agree that we have a great school… but great isn’t greater or greatest. A Harkness classroom is without equal but can Harkness-table discussions be improved with technology? Can we make an Exeter education better? What are the advantages of technologically rich classrooms? On a more individual level, what will we do with these iPads? I can envision a mathematics class where students all have an iPad with our materials downloaded in PDF-format. They do their homework on their iPad using one of the many note-taking applications, like Penultimate, and we project solutions, wirelessly, to an interactive whiteboard where we can annotate and make corrections, which can be saved and shared via an application such as Dropbox. All of this ultimately saves class time allowing for more Harkness table discussion, which is what we are all about.

We need to address these questions and more or we leave ourselves open to being passed by while reveling in our current success only to look up and find other schools way ahead of us. While change within Exeter may happen slowly, change in the outside world can happen all too quickly and we must be ready to adapt. A great example of adaptability is the digital camera… Imagine the look on executives’ faces at Eastman Kodak when someone one walked into the board room with a digital camera. Kodak, whose mainstay since 1935 had been Kodachrome film, adapted and refocused on digital photography and digital printing. They stopped production of film in 2009. To quote Jack Welch, former CEO of General Electric, “If the rate of change inside an institution is less than the rate of change outside, the end is in sight.”

I think we can continue to offer an outstanding education to our kids and be leaders in the use of educational technology. We owe it to our current and future students to stay abreast of changes in educational technology or risk becoming irrelevant.

You don’t have to be a techie to stay abreast of this rapidly changing area of education. I can’t program a computer to save my life. The only time I was interested in programming was when a program called C+ came out. I figured any language entitled with my grade point average I could understand. Wrong.

Our students are already adept at using computers, smart phones, and tablets. It’s clearly a different world than that in which most of us grew up. We should embrace and take advantage of the technology that our students are so comfortable with. The iPad “gift” from our trustees is a huge beginning and will allow us to explore the benefits of technology and discuss them in both department and faculty meeting venues throughout this year.

The conference I attended at the Urban School was run by our speaker this morning, Howard Levin.

Howard Levin is the Director of Educational Innovation and Information Services, leading the educational technology program at Convent and Stuart Hall Schools of the Sacred Heart after holding the same position at Urban School for the past 12 years.

In his position at Urban, Howard was responsible for implementing a 1:1 student and teacher laptop program, making Urban the first high school in the San Francisco Bay Area to distribute laptop computers to all students and teachers.

As a result, technology at Urban is integrated throughout the curriculum to achieve natural and seamless use to support student learning, communication and organization - all without computer skills training classes.

Wednesday, October 19, 2011

Report to the faculty, December 26, 2010

As you may or may not remember (if you were here), last spring Tom Hassan named me the Bates-Russell Professor. The deed of gift for this position stipulates that the Bates-Russel Professor will keep the faculty apprised of what he is doing. So, here goes…

For my entire 35-year teaching career, the first 15 years in public schools in Washington State, I have been interested in, and have promoted, the use of technology in teaching mathematics. Early on, this consisted of Apple II software programs like Green Globs (You can Google it. Little did I know that it is still being produced, most likely a software lifetime-award winner.), and various other function-graphing programs that gave teachers new strategies for presenting and students new strategies for understanding functions. Then, in the middle to late 80’s, the graphing calculator appeared on the scene. Gradually these technologies – computers, software, graphing calculators – have merged more and more so that they are almost indistinguishable…smart phones capable of running Wolfram Alpha (an incredibly powerful mathematics program), the iPod Touch, tablet PCs, and the iPad.

Obviously my interest is focused on mathematics teaching but I am a proponent of using technology in all academic areas. Thus, I have chosen to spend the five years of my term as the BRP seeking out school programs that show effective use of technology in all academic areas. Moreover, I will continue to travel to mathematics conferences to give talks on how computers and calculators can be used to teach and enhance the learning of mathematics and promoting our own, unique mathematics curriculum. To that end, this fall I spoke at the Northwest Mathematics Conference in Spokane, WA in October, and the California Mathematics Council Southern Division Meeting in Palm Springs, CA in November.

In terms of the general use of technology in education, in July I attended a conference on laptop programs (sometime referred to as 1:1 programs) at The Urban School in San Francisco. The Urban School has been a 1:1 school since 2002. This means that everyone, teachers, administrators, and students, have a laptop computer. Computers are available to all, whenever and wherever they are needed. In fact, the Urban School has 425 computers for 400 users – students use the MacBook and faculty use the MacBook Pro. The remaining 25 computers are spares; no computer labs are necessary. The guiding principles of The Urban School program are mission-based in an effort to ignite a passion for learning. They believe that a 1:1 program allows them to extend the learning process beyond the classroom. Ever had one of those Harkness discussions that you wish would never end just as the end of the period arrives? A 1:1 program would allow for that discussion to continue – The Urban School uses a program called First Class. The folks at The Urban School fully believe that computers add value to the learning process.

Various members of The Urban School’s academic departments spoke about how 1:1 computing has impacted their classrooms: a French teacher talked about digital tools in French and how they use United Nations Radio; a science teacher talked about visualizing the abstract; an English teacher talked about thinking and learning in a 1:1 environment, how the computer helps students with organization; a music teacher spoke about applications to music and drama; and a history teacher spoke about how computers allowed students to be productive contributors to a world-wide community. Students at the Urban School are participating in two different Oral History Projects, one in which they interview Holocaust survivors in the San Francisco area and another where they interview people who experienced the struggle for civil rights in the south in the 1950’s and 1960’s, via Skype.

I plan on visiting The Urban School again, this spring, when students are in class so that I can see the 1:1 program in action. If any of you have any specific things you would like me observe or ask about, please contact me. If you would like to read about The Urban School technology program and specifically the 1:1 program, click here.

As I mentioned earlier, I also plan on visiting other schools using technology in, hopefully, successful and meaningful ways. In addition to being interested in 1:1 computing, I am very interested in how tablet PCs and iPads (I personally have become addicted to this technology and think it will have a huge impact on education) are being used in teaching. Please feel free to contact me with any questions, comments, or suggestions.
If you’ve made it this far, thank you for your interest,

Tom Seidenberg
Mathematics Department

The Bates-Russell Faculty Professorship

The Bates-Russell Faculty Professorship is a five-year appointment, the professorship was established in 1999 in honor of the late Emeritus Instructor of English Robert Bates ’29; ’44, ’50 (Hon.) by his former student and lifelong friend George Russell Jr. ’50; P’75. The endowed position provides time away from the classroom for an Academy instructor to undertake special projects and independent research related to teaching at Exeter, and to participate in educational initiatives at other schools and colleges.

The endowed position provides time away from the classroom for an Academy instructor to undertake special projects and independent research related to teaching at Exeter, and to participate in educational initiatives at other schools and colleges.