indy kids newspaper

This is Indy Kids, the free online newspaper for kids from the Indypendent, a progressive and independent newspaper in NYC.

OK, it does assume all kids are in school and read the newspaper in a school setting.  They could at least address the kids directly. But homeschoolers may enjoy the articles as well as the many useful links under For Teachers.  Ostensibly for grades 4-8 and English Language learners in high school. Teacher's Guides are free and downloadable.

history of algebra

I enjoyed Lewis Carroll in Numberland: His Fantastical Mathematical Life by Robin Wilson (we liked Wilson's little book on sudokus awhile back). A book review and a podcast (scroll down a bit) from +Plus magazine (more here).

Wilson presents biographical information on Carroll (really Charles Dodgson) whose upper-middle class family homeschooled with tutors. There are brief forays into mathematics. For example, Wilson gives a quick overview of the algebraic geometry of the plane and three-dimensional space along and then some of the mathematics of Dodgson's determinents and 'Method of Condensation'.

This integration of math, biography and concise explanation is a rich mix for whole learning (akin to whole foods) that preserves context, reduces the emphasis on over-processed and highly-refined literacy, and is just more fun. Wilson is witty and the book is well-illustrated. There are many mathematics puzzles and oddities. I think many learners will respond to this integrated approach, a favorite of mine.

A similar method, less complex,  is used in a straight history book on algebra by another English author, John Derbyshire, in his Unknown Quantity: A Real and Imaginary History of Algebra. Again, added to a history of algebra are math breakouts on numbers and polynomials, cubic and quartic equations, roots of unity, vector spaces and algebras, field theory, and algebraic geometry.

To the ever-vexing question, just what is algebra?, the author, in workmanlike fashion, defines it as the part of mathematics that is not calculus and moves onto a discussion of algebra as abstraction. I prefer the wikipedia definition.

wilson's new book on carroll

Excellent: Lewis Carroll in Numberland: His Fantastical Mathematical Life by Robin Wilson (we liked Wilson's little book on sudokus awhile back). A book review and a podcast (scroll down a bit) from +Plus magazine (more here).  And more Wilson free stuff here.

Biographical information with brief forays into mathematics on Carroll's life, literary and mathematical works. Carroll grew up in a homeschooling family of sorts: upper middle class with tutors and they were quite close.  It is a biography that has appeal for lots of homeschoolers.  

I like the way mathematics is integrated into the whole.  After introducing Dodgeson's (Carroll was a pen name) 1867 book on algebra, Wilson politely pauses:

"We now explain the mathematical terms that appear in the title of Dodgson's algebra book and introduce his 'method of condensation'. If you are not interested in these, you should skip to the next section, on page 120."

Wilson then gives in only 8 pages:  The Algebraic Geometry of the Plane, Determinants, The Algebraic Geometry of Three-Dimensional Space, Dodgson's 'Method of Condensation', and Dodgson's Determinants.  

This integration of math, biography and concise explanation is a rich mix for whole learning (akin to whole foods) that preserves context, reduces the emphasis on over-processed and highly-refined literacy, and is just more fun. Wilson is witty and the book is well-illustrated. There are many mathematics puzzles and oddities. I think many learners will respond to this integrated approach, a favorite of mine.

corporate textbooks and algebra

I read an NYT article about Connecticut schools taking Algebra I online and throwing out the 1000-page textbooks that dominate high school mathematics these days. This is a very good idea. Perhaps it is time to start counting the pages of math texts, or any text, in self-defense.

(Right: a page from Euclid's classic text which ran 13 books; no known page count.)

I tried tutoring high school math one of these dinosaurs and they truly get in the way of their subject. Does it really take 180 lesson days to cover algebra 1 or are we filling time because we have it? Do we even know the core content anymore? After the fun of doing good problems in Singapore's texts, the whole pedagogical enterprise of massive corporate texts seems useless.

WESTPORT, Conn. — Math students in this high-performing school district used to rush through their Algebra I textbooks only to spend the first few months of Algebra II relearning everything they forgot or failed to grasp the first time.

So the district’s frustrated math teachers decided to rewrite the algebra curriculum, limiting it to about half of the 90 concepts typically covered in a high school course in hopes of developing a deeper understanding of key topics. Last year, they began replacing 1,000-plus-page math textbooks with their own custom-designed online curriculum; the lessons are typically written in Westport and then sent to a program in India, called HeyMath!, to jazz up the algorithms and problem sets with animation and sounds.

“In America, we run through chapters like a speeding train,” said John Dodig, the principal of the 1,728-student Staples High School here. “Schools in Singapore and India spend more time on each topic, and their kids do better. We’re boiling down math to the essentials.”

The entrenched attitudes of textbook companies is indicated in the article by the stated reduction of a textbook from 1000 pages to 800 pages. An 800-page text for high school algebra, first part only, is absurd.

The makers of modern mathematics learned mathematics in substantially fewer pages. Precalculus mathematics alone in most high schools means 4-5 of these 1,000 page beasts. For a truly concise book, by a university professor, look at Precalculus Mathematics in a Nutshell (from the intro):

"Contrary to popular opinion, precalculus mathematics is not a shapeless mass that no one can hope to master. This clearly written book pulls together the essentials of geometry, algebra, and trigonometry in one clearly written and accessible volume, showcasing each subject in its own chapter with readable explanations, exercises, and fully worked-out solutions. When read as a whole, the book provides a thorough analysis of all three subjects; but each subject can be mastered independently from the others. " 119 pp.

This book, which includes exercises, comes to a total of 119 pages for all of precalculus mathematics. That's algebra 1 & 2, geometry, and trigonometry which in the corporate text version would be about 4000 pages.

So add some really good problems to do for fun. Another 200 pages of problems would make 319 pages of work.

commencement addresses

Two commencement addresses making the rounds, both by writers (whose books I have enjoyed), one by Paul Hawken out in Portland and one by Barbara Ehrenreich for journalists.

the story of the jews: a 4000-year adventure

I enjoyed Stan Mack's graphic history The Story of the Jews: A 4,000-Year Adventure. An upbeat 273-page comic book/graphic non-fiction book from the gonzo cartoonist who published cartoons in the Village Voice for years.

+Plus mathematics magazine and podcasts

+Plus mathematics magazine is an Internet mathematics magazine for young people out of Cambridge. There are articles, podcasts, interviews, puzzles and loads of mathematics from all angles. Free. 

Plus provides feature articles, which describe applications of maths to real-world problems, games, and puzzles; reviews of popular maths books and events; a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers; a puzzle for you to sharpen your wits against; a lucky dip of mathematical curiosities; and opinions on various maths-related topics and news stories. We have a regular interview with someone in a maths-related career, showing the wide range of uses maths gets put to in the real world. And all past issues remain available online, which besides making for good browsing is, we hope, a useful resource for maths school students and teachers.

math books

I enjoyed Lewis Carroll in Numberland: His Fantastical Mathematical Life by Robin Wilson (we liked Wilson's little book on sudokus awhile back). A book review and a podcast (scroll down a bit) from +Plus magazine (more here).

Wilson presents biographical information on Carroll (really Charles Dodgson) whose upper-middle class family homeschooled with tutors. There are brief forays into mathematics. For example, Wilson gives a quick overview of the algebraic geometry of the plane and three-dimensional space and then some of the mathematics of Dodgson's determinents and 'Method of Condensation'.

This integration of math, biography and concise explanation is a rich mix for whole learning (akin to whole foods) that preserves context, reduces the emphasis on over-processed and highly-refined literacy, and is just more fun. Wilson is witty and the book is well-illustrated. There are many mathematics puzzles and oddities. I think many learners will respond to this integrated approach, a favorite of mine.

A similar method is used in a straight history book on algebra by another English author, John Derbyshire, in his Unknown Quantity: A Real and Imaginary History of Algebra. Again, added to a history of algebra are math breakouts on numbers and polynomials, cubic and quartic equations, roots of unity, vector spaces and algebras, field theory, and algebraic geometry.

To the ever-vexing question, just what is algebra?, the author, in workmanlike fashion, defines it as the part of mathematics that is not calculus and moves onto a discussion of algebra as abstraction. I prefer the wikipedia definition myself.

unschooling Helen Keller

From a National Geographic book, Helen's Eyes: A Photobiography of Annie Sullivan by M. Delano, about teaching Helen Keller after she was able to learn words (after the water pump incident):

"From that point on, learning became an exciting adventure, and Annie let Helen's interests lead the way to learning opportunities. No more boring, repetitious classroom lessons for them! Instead, they spent most of their days outdoors. ... Helen later recalled that 'everything that could hum, or buzz, or sing, or bloom, had a part in my education.' "

Helen Keller would go on to take classes at Perkins Institution for the Blind in Boston and eventually attend Radcliffe (and was a Socialist). Image at right is Helen Keller holding a doll with Anne Sullivan, 1888, thanks to Creative Commons.

I have read so many biographies where someone leaves school for economic or health reasons and it becomes a pivotal time in that person's life. In fact, there is a lot written about steady institutionalization and what it does to human beings. (see Illich and Holt)