Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving

Sanjoy Mahajan

In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.

In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest.

Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.

Source: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=12156

Street-Fighting Mathematics (PDF File): http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf

Bill Gates' School Crusade

Daniel Golden

It's been two years since Bill Gates left his day-to-day role at Microsoft (MSFT) to concentrate on supervising the Bill & Melinda Gates Foundation—and his new enterprise is booming. Headquartered in a converted check-processing center in Seattle's Eastlake neighborhood, the 10-year-old foundation plans to move into a 900,000-square-foot campus and visitors' center near the city's Space Needle next spring. The Gates Foundation opened a London office this year; it also has offices in Washington, Delhi, and Beijing, and 830 employees around the world, up from about 500 in 2008. With assets of $33.9 billion as of Dec. 31, 2009, and America's two richest people—Gates and Warren Buffett—as trustees, the foundation plans to spend $3 billion in the next five to seven years on education. If there's such a thing as a charity behemoth, the Gates Foundation is it.

While its efforts in global health are widely applauded, its record in America's schools has been more controversial. Starting in 2000, the Gates Foundation spent hundreds of millions of dollars on its first big project, trying to revitalize U.S. high schools by making them smaller, only to discover that student body size has little effect on achievement.

It has since shifted its considerable weight behind an emerging consensus—shared by U.S. Education Secretary and Gates ally Arne Duncan—that quality of teaching affects student performance and that increasing achievement is as simple as removing bad teachers, identifying good ones, and rewarding them with more money. On this theory, Gates is investing $290 million over seven years in the Tampa, Memphis, and Pittsburgh school districts as well as a charter school consortium in Los Angeles. The largest chunk of money, $100 million, will go to Tampa's Hillsborough County school district, the eighth-largest in the U.S., with 192,000 students and 15,000 teachers. These carefully selected programs, which will favor or penalize teachers depending on whether students make larger or smaller gains than their test scores in prior years would have predicted, are intended as models that, if proven successful, can be rolled out nationwide.

Read More: http://www.businessweek.com/magazine/content/10_30/b4188058281758.htm?chan=magazine+channel_top+stories

Cutting Edge Technology Coming Soon to a Classroom Near You

By: Max Schlusselberg

In what is perhaps a sign of technology's rising prominence in the classroom, Saxe Middle School is currently in the process of gutting the room formerly used for home economics and outfitting it with rows of new computers and digital keyboards. Saxe's new computer lab is just one part of the New Canaan school system's push to incorporate technology in the learning process.

"We're adapting with the time and it's the age of technology now," said Director of Visual and Performing Arts Alan Sneath. "Teachers have really risen to the challenge of bringing technology to the next level."

Computer labs are just one way educators are using advanced technology to enrich the learning process. Beginning last year, students from elementary school to high school have been cataloging their academic progress online in digital portfolios.

In partnership with Digication.com, New Canaan's public schools are giving their students a platform to upload everything from art projects to musical performances so both teachers and parents can track their students' progress.

"Students are doing work that we're capturing digitally to take it into the 21^st century," said Sneath, who has long been a supporter of ensuring students are prepared for an increasingly digitized world. Sneath sees value in digital portfolios not only for teachers and parents but also believes that beginning next year students will be able to include digital portfolios on college applications.

And as computer labs become commonplace in all of New Canaan's public schools, educators at East Elementary School are taking the concept a step further. Beginning this year, elementary students will have laptop computers at their disposal in addition to standard desktops. According to Director of Technology Rob Miller, laptop computers allow teachers to give their students a much more tailored approach to the curriculum.

"We're engaging students' interests, which allows for a more active learning environment," said Miller. "Teachers can group students together and move them around using laptops… Students can then work on specific parts of the curriculum."

But despite all the advancements in classroom technology at New Canaan's public schools, educators believe they can't get too comfortable.

"You can't stop," said Sneath, referring to the effort of keeping classroom technology modern. "The minute you stop, it changes."

Source: http://newcanaan.patch.com/articles/cutting-edge-technology-coming-soon-to-a-classroom-near-you

Turning Eyes Growing Market

By GRACE WYLER

Turning Technologies — one of the region’s hottest software companies and the first success story of downtown Youngstown’s emerging high-tech campus — is expanding its focus on educational initiatives that use its technology to improve learning.

The company’s interactive-response technologies increasingly are being used to implement teaching and learning strategies that have been scientifically proven to boost achievement in the classroom, said Tina Rooks, the recently appointed vice president in charge of overseeing the Turning Technologies educational strategy.

“We have always known that students learn better when they engage,” Rooks said. “What we have discovered is that TurningPoint systems can engage students in a way that allows immediate feedback and progress monitoring.”

By allowing assessment and instruction to occur simultaneously, the company’s response technologies have helped prove the effectiveness of teaching methods that previously were too time-consuming to test in a classroom setting, such as pre- and post-testing and differentiated instruction based on students’ varying levels of understanding, Rooks said.

“The technology facilitates these practices that have been known to be valid,” Rooks said. “These theories often have not been put into play.”

Rooks, who has a doctorate in instructional technology, has been working with the U.S. Department of Education to help come up with ideas for implementing assessment strategies.

Turning Technologies initially focused its educational initiatives on customers in the company’s K-12 market. It is now expanding to apply its learning strategies to international clients and other customers using the technology in corporate or nontraditional classroom settings, Rooks said.

“We are finding that quite a bit of our practices are universal,” she said.

Turning Technologies has been expanding its Educational Consulting Team to capitalize on the success of these learning-assessment solutions, said chief executive Mike Broderick.

“We have really gotten to the point where there is a real body of data saying that, when [the software] is implemented in the classroom, it works,” Broderick said. “It is almost beginning to snowball.”

In the past two years, the team has grown from one — Rooks — to seven members. This group, made up of educators and educational experts, work with Turning Technologies’ sales representatives to help customers learn how to use the technology to improve achievement, Broderick said.

Turning Technologies’ educational initiatives represent a major growth opportunity for the company and likely will continue to expand, he said.

“We probably have our products in less than 2 percent of classrooms,” Broderick said. “We think the opportunity for growth is exponential.”

Source: http://www.vindy.com/news/2010/jul/07/turning-eyes-growing-market/

Generic Education

Generic education is the part of education which is of general value, the education a resident on planet earth in the 21st century should have in order to be reasonably knowledgeable and universally understood by others. Generic Education provides the common language for the definition and interpretation of facts, a step-up on the ladder to greater understanding and potential enlightenment. Generic Education is globalization at the grassroots level, a prime requirement for economic and industrial globalization to work.

What is Generic Education
The concept of generic education was proposed by Win Straube in his book, "QGE=A, Quality Generic Education is the Answer". Generic Education means the identification and practice of objective, unarguable values. Generic Education can be taught and learned anywhere because it is free from cultural or political baggage, yet it is understood on all sides as a shared, generally accepted version. Generic Education is universally measurable, which means that learners’ proficiency in the studied subjects can be tested. It also means that the tests used are either identical or at least comparable in different locations and as administered at different times. In other words: The level of proficiency to pass a specific test needs to be as close to identical to every other such test as possible.

Generic Education means "proficiency in" a certain science, art, or other subject which is agreed on by all or almost all. For example, 2 plus 2 equals 4, "love" in French is "amour", the moon is a satellite of planet earth, and the water we drink is H2O. These examples from mathematics, languages, astronomy, and chemistry demonstrate their generic educational nature. Of course there are fields of study which may have a generic base but are everything but generic when studied in-depth, such as psychology. In these circumstances, there may be different "schools" teaching particular views that are hotly contested by others. The contested parts need to be excluded from Generic Education, although a particular view may eventually become the commonly held belief or "truth". That is when it would become suitable for Generic Education.

Quality Generic Education
Quality generic education is the best generic education available at the lowest possible cost, and universally acceptable and interchangeable. Thus the classroom can come to anybody at any place where he/she can be in front of a computer or TV screen, such as in his home or in a location set up for the learning experience, like a satellite campus of a community college. Likewise, anybody being exposed to such educational presentations will be able to interact with them, asking questions, receiving additional and deeper background information, taking tests, and communicating with a teacher, regardless whether that teacher is physically nearby or continents away. In addition, learning support would be supplied by "education facilitators" who could be the parents or one parent, fellow students, or others.

How Does Quality Generic Education Work
Here are a few random examples of how Generic Education via Distance Learning actually works, though many more modes of operation are in use worldwide, always suited to a particular audience. Basically they all consist of three or four components:
1. The production and preparation of learning materials.
2. The presentation of either live or recorded lectures.
3. Transmission via electronic media such as television or computer networks, internet and email hookups; at times interactive for teacher/student exchanges and also for student-to-student exchanges.
4. Some of the programs include personal meetings or classroom attendance, particularly in preparation of and for examinations. However, many programs work entirely long distance where teacher and student never meet in person.

Source: http://wikibin.org/articles/generic-education.html