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Time, both geologic and instantaneous, and distances, both vast and sub-atomic, are difficult to comprehend for most of us and even more difficult for teachers to help their students understand.
Visualizing Geologic Time
Multiple ways of thinking about these concepts may help to surround these difficult issues of time and space with meaning, and provide reference points that enable more of us to make sense of them.
In 1968 Ray and Charles Eames produced a groundbreaking short film, Powers of Ten, narrated by Philip Morison, that presented the distances between structures in the universe in a way that most of us can appreciate. The film also offered insights into the ideas of orders of magnitude and logarithmic scale. Since that time, many have added to the multimedia library of scale (large and small) and have helped many of us to grasp ideas too far outside of our own experience to fully comprehend. Here are some more resources for us to use in our capacities as teachers and as learners:
Scale of the Universe – a beautiful, interactive visualization of scale in the universe from the very smallest to the very largest
The Eames’s Powers of Ten video
An interactive version of Powers of Ten lets the user step through the frames of the video manually.
The Universe Solved – a 67-step, user-controlled version of Powers of Ten
Cosmic Zoom – another user-controlled look at size and scale
Exploring Earth – An animated trip from the Sun to Pluto at 300+ times the speed of light
Cosmic Zoom video by Eva Szasz – an 8:00 animated trip “from the farthest conceivable point of the universe to the tiniest particle of existence…” Math-free and word-free–from the National Film Board of Canada
Mathematics, more than most other subjects, is avoided by the general public. It is seen as incomprehensible beyond the basic level, and rarely do people outside of the field allow themselves the opportunity to engage with mathematics and enjoy its beauty. Those of us who are math educators at any level are most successful when we can help are students understand not only how to do mathematics, but to get the bigger picture of how mathematics permeates and helps to explain our daily lives.
- Steven Strogatz
Steven Strogatz, a professor of applied mathematics at Cornell University wrote a wonderful series of 15 columns about “the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.”
Whether you are a math educator or not, I know you’ll enjoy reading these columns.
The other day, during one of my many rants, a colleague delicately said to me, “I think I have to disagree with you a little about merit pay. I think it would be nice to be rewarded for doing a good job.” I had to stop for a minute…
… my colleague’s simple, honest statement sounded right. I too wouldn’t mind being rewarded for my hard work.
Then as I thought more about it and about the teachers with whom I have worked over the years, it occurred to me that merit pay is presented as some sort of incentive for teachers to be better at what they do. I asked my colleague (who is among the hardest working and dedicated educators I know), “Do you think that you’d work any harder, or do a better job because of the promise of more money?” She had to admit that she would not.
Neither would I. Although I had to consider how nice it would be to be paid more in acknowledgement of how good a teacher I am, I never questioned whether money is, in fact, an incentive to work harder or better. It makes too much sense to question. It is an idea imbued with truthiness.
Then I came upon this short, provocative video lecture. I immediately sent it to my colleague and am awaiting her response to continue this conversation. I thought it would be a good idea to open the discussion to the broader community and, perhaps, have it right here in this forum. Take a look at the video and feel free to weigh in with your own thoughts and comments.
If you can’t view the embedded video, try clicking here: Drive: The Surprising Truth About What Motivates Us.
Merit/performance pay always brings to mind (a) the divisiveness among a staff being differentially paid for the same job, (b) the placing of “difficult” or unsuccessful students between a teacher or administrator and her paycheck, (c) the many opportunities for favoritism and corruption among those who make decisions about who does a “good” job and who does a better one, and (d) the myriad logistical issues including how to measure the effectiveness of a resource room teacher, a music teacher, a phys-ed teacher or any teacher of a non-tested subject.
What is presented to the world as a way to reward “good” teachers and incentivize “good” teaching actually would more appropriately be labeled demerit pay. Paying “bad” teachers less. I can imagine merit pay becoming codified as a “good” teacher’s standard salary and “merit” hurdles being placed in the paths of teachers as they try to move up the salary scale, in effect, paying some less than the standard wage rather than rewarding some with more pay. What we really want is to be paid well (or, at least, fairly) for a very difficult and very important job.
The successes of Finnish schools have become a focus (perhaps more of an obsession) with educational reformers in the United States and elsewhere.
While the BBC video and article, Why do Finnish Schools Get the Best Results? constructs a portrait of public education that few can fail to admire, we cannot uncritically accept the they-are-great-we-stink argument and react inappropriately to the “crisis” in our own system. This film and the current educational reform movement raise a number of interesting and, perhaps, troubling questions that I believe must be addressed as we shape education policy both for the United States and in our local school systems.
- What do we consider success? Is it scores on tests in mathematics, science, and literacy? Is it the development of skills, attitudes, and social abilities that enable learners to lead productive, satisfying lives?
- What about Finnish society makes their schools effective?
- Are Finnish (or Korean, or any other) methods appropriate for American schools?
- What do we in the United States do well? How can we make sure that we don’t lose our strengths in the process of educational reform?
- What are the purposes of schooling? How do we construct learning environments that help all stakeholders achieve their goals?
- What are the purposes of testing? Do the assessments we use address those purposes? Do they support learning and teaching?
Serious, informed, good-faith discussion needs to replace polemics if we are to address the weaknesses, exploit the strengths and improve the state of education in the United States at the federal, state and local levels. An example of why this is necessary and of how it is not what is happening now is this new-found Finno-philia. If Finnish schools are characterized by shorter school hours, supportive administrators, mixed ability grouping, academic freedom, and professionalism, we have to wonder why we ignore these things and focus on high-stakes testing, deprofessionalizing educators, authoritarianism and longer hours as we try to emulate their success.
Click here to read the article and watch the short video. Then, let’s start a productive discussion here that can inform our own work in the classroom and in our discussions with family and friends, the public and the policy-makers.
One-room Schoolhouse, Fruita, Utah c. 1900 Photo © 2002, Mitch Bleier
No, I have not seen the new education “reform” film, Waiting for Superman, so I will refrain from having or expressing an opinion on any content other than what I have seen in the trailer. My familiarity with some of the players in the film does, however, push me to respond quickly with a call for those engaging in the school-reform debate to inform themselves about the facts used in the arguments and about the motives of those who are most vocal in these arguments, and to examine their own assumptions about public schools and those who attend and work in them.
At the dawn of the 19th century, a group of wealthy, charitable New Yorkers sought and received a charter from New York State for the Public School Society of New York, whose intention it was to provide education for poor children not served by charitable and religious institutions, who might otherwise fall prey to “immorality and vice,” and, presumably, begin to prey upon the decent people of New York City. These early education-reform efforts took the form of monitorial or Lancasterian methods of schooling in which one teacher, assisted by a number of monitors drawn from the most capable of students, could educate hundreds, perhaps more than a thousand children.
Much recent reform, including the pervasive standards movement has been driven by the 1983 report, A Nation at Risk. Decentralization, NCLB, re-assertion of mayoral control, RTTT, and the charter school movement have brought us to where we are today. Public schools are in trouble. Funding, public confidence, and political support, so necessary for success and improvement are eroding at an alarming rate. This is a call for educators to keep themselves informed of the issues, and the arguments on all sides of these important education debates…and to be clear about their own stance on these issues. This may require a rethinking of the purpose(s) of public education, and a reassertion of the rights of children and the benefits to society of a well-educated population well-equipped to question and challenge the status quo.
Here are links to some resources to help us all keep on top of things:
Please feel free to respond to this post and to add resources here.
- Bridging Differences – a long-running back-and-forth conversation between Deborah Meier and Diane Ravitch about education issues and education policy
- Waiting for Superman – the official website of the film
- The Inconvenient Truth About Waiting for Superman – the official website of the response to Waiting for Superman
- Not Waiting for Superman – another response to the film–this one initiated by Rethinking Schools.
- New York City Charter School Center
- Stories from School – National Board certified teacher leaders share how education policy impacts classrooms
Lancasterian Schooling for the Poor
Photographer Eric Fischer has produced maps of 40 major American cities that show the distribution of Asian, Black, Latino and White residents. The maps, in which each dot represents twenty-five people, reveal interesting , and
Racial distribution in New York City by Eric Fischer
sometimes remarkable patterns of racial distribution. Because Fischer departs from the usual practice of representing areas in solid colors to use dots, diversely populated areas are visible as multi-colored patterns…but diversely populated areas are not very common.
These maps might be presented to a group without any framing information. A discussion might be begin with participants speculating about what the dots and colors signify. Then, the conversation could turn toward interpretation and analysis. This might be especially powerful as local residents examine the area where they live.
Although Fischer has mapped forty cities, New York is one of the most striking for its patterns of population distribution.
Let us know if you have any interesting experiences with these maps.
Note: These pictures are available in several resolutions. I have found that the “large” size has the most impact on a computer screen or on an interactive white board.
If you want to read more about Eric Fischer and these maps, there is an article in New York Magazine and another on the Fast Company website.
An exercise that I do with my (mostly adult) students is The Science Toolkit. I give them an iron nail and one meter of cotton postal string in a Ziploc bag and have them go outside for twenty minutes and see what they can use these items for.
They always are surprised at how useful this simple toolkit can be. They use the nail to dig, and the string to mark off a study area; tie the string to the nail and use their newly made device to scratch circles on pavement or in soil; collect samples in the Ziploc bag; and lots more.
The exercise concludes with participants suggesting additional items to include in their kits. A magnifier, a permanent marker to mark their strings to be used for linear measurements, and other items are proposed and participants customize the kits for their own purposes.
These toolkits become part of our equipment and we carry them everywhere. I once gave a class the task of exploring the flora and fauna around a brand new school building in the Mojave Desert. The building had not even been around long enough to be populated by spiders, lizards and the other common life forms that make the human habitat their own. One particularly resourceful group of students searched and searched until they heard water flowing in a storm drain below their feet. They took the thimble-like cap off of a water bottle, untwined the strands of the cotton string and made a basket that they lowered down into the drain to collect a sample of water. Once inside, they examined the water with a microscope and discovered a rich array of microorganisms to study.
When to introduce the toolkit is a critical decision. It may be a great introduction to the creative and accessible activities of the scientist that we all can do, but it may require some rapport to be established between teacher and students to ensure buy-in and willingness to try something that may seem a little silly when you hand them a bag with a nail and a string. We often finish by constructing a list of additional items that participants would include in their own kits for their own needs (e.g., a mirror, a magnet, a hand lens, waterproof paper and pencil).
[Note: The toolkit was suggested by a hydrologist from the Clark County (Nevada) Water District–it is similar to one he carries with him at all times. The activity was developed by Bradley Iverson, of the Clark County School District, and me.]
Thinkfinity.org contains 55,000 standards-based K-12 lesson plans, student materials, interactive tools and reference materials from its eleven consortium partners that are reviewed by the nation’s leading education organizations to ensure that content is accurate, up-to-date, unbiased and appropriate for students.
Thinkfinity’s consortium partners are:
- American Association for the Advancement of Science
- Council for Economic Education
- International Reading Association
- National Center for Family Literacy
- National Council of Teachers of English
- National Council of Teachers of Mathematics
- National Endowment for the Humanities
- National Geographic Society
- ProLiteracy
- Smithsonian National Museum of American History
- The John F. Kennedy Center for the Performing Arts
Discomedusae by Ernst Haeckel
As the 20th century began, the influential and often controversial biologist and philosopher, Ernst Haekel was documenting the living organisms he was studying by creating beautiful, detailed plates like the one to the left. Take a look at his Kunstformen der natur (1904).
Artist and scientist often reside in the same person, each aspect illuminating the other. Albrecht Dürer, John James Audubon and countless others have simultaneously observed, documented and marveled at the natural world.
Explore the work of Edward Weston, Ansel Adams, Eadweard Muybridge, Ron Mueck, Joseph Albers, and think about the intersections between arts and sciences. This is not even taking into account artists not strictly in the visual camp (e.g., Pilobolus Dance Theater, John Ford, etc., etc.). Also, virtually every composer of music explores the biology, physics, mathematics and psychology of sound whether consciously or unconsciously.
Science and mathematics often are selected for integration in curricula because they are seen as an obvious pair. The arts, even when taken seriously–not as an add-on or an extra–too rarely articulate with the sciences in schools. A little effort, a little planning time, opportunities for arts and science teachers to experience each other’s work and talk about it may lead to synergy that will ignite the pedagogical lives of educators and artists to generate exciting and meaningful learning experiences for students.
For example, an artist/art teacher and a scientist/science teacher can develop a series of field trips to museums, and local forests or natural areas. Pre-trip, trip, and post-trip experiences can be planned, conducted, analyzed, reflected upon and shared with colleagues. Such a first step could be of any scope and may even start here among the readers of and contributers to this blog.
Anyone out there up for a little adventure? Summer is coming and offers us time for leisurely planning and this project may provide us with an excuse for a few trips to the museum and a few hikes in the woods. Anyone?
In The Botany of Desire, Michael Pollan examines the mutually beneficial relationship between humans and plants from the plant’s point of view. While we normally think of plants in terms of their usefulness to us–building materials, medicines, food,etc.–Pollan explores how apple trees, tulips, marijuana, and the unassuming potato masterfully manipulate humans into taking care of their most fundamental needs–reproduction and seed dispersal. Our desires for sweetness, beauty, intoxication and control, in Pollan’s narrative are the tools the plants use to achieve their purposes.
Along the way we get lessons in philosophy, history, politics, science and more.
Click here for a Teachers Guide to the PBS film based on the book that is appropriate for high school or college undergraduate students.
Pollan, M. (2001). The botany of desire. New York: Random House
BxNS PEN 
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