constructivist math

Garelick includes a terrific, short history of the old New Math, which got its start when Russia launched Sputnik and then disappeared in the early 1970s. I was surprised to learn that the old-New Math had nothing to do with constructivism, discovery learning, progressive education, or John Dewey (just to round up the usual suspects).

Instead, New Math was the pure invention of Real Mathematicians:

. . . the new-math era was one of the only times that mathematicians were given an opportunity to make proper math education available to the masses. . . . And some believe that . . . the math education that would have emerged from new math—both lower grades and high school—would have been on par with the best of the math programs overseas.

Eventually, however, . . . the logic and formalism of the program in general doomed new math. The general public, the education community, and even mathematicians themselves judged the new-math programs a failure. Mathematicians were assigned the blame, and the education establishment took back the reins.

The New New Math - constructivist math - is the creation of math educators, not mathematicians.

There's a difference.
Catherine

the Master Plan



direct instruction t/k


formative assessment more t/k

• Smartest Tractor's teaching method (algebra in 8th grade)
  
• the Gambill method of teaching algebra
  
• the Gambill method for teaching algebra in a nutshell
  

fractions

Teaching Fractions: New Methods, New Resources by Michael Meagher
Meagher's article is also available at this Texas site
I'd say this article is worth reading only if you're intensely interested in the subject....includes some interesting links to online resources at the end.

handbooks, math dictionaries, math reference

I love the Math on Call series. Catherine

Math to Learn Grades 1-2
Math to Know Table of Contents Grades 2-3
Math at Hand Grades 5-6

Math on Call Grades 6-8

Algebra to Go Table of Contents
Geometry to Go Table of Contents


see also:
RoyalRoadToGeometry
BuyThisBookToo
EnglishLanguageArtsBookRecommendation

Jaime Escalante

Stand and Deliver Revisited

journals and magazines

American Educator, published by AFT
Summer 2005: I emailed American Educator asking whether a non-union member can subscribe, and received this reply:

It's possible all you need to do is send a money order or check to American
Educator for $8.00. See address below

Thanks, Mary

Mary Singleton, Temp
American Educator Department
T: 202/879-4420
F: 202/879-4534
E: msinglet@aft.org
American Federation of Teachers, AFL-CIO
555 New Jersey Avenue NW
Washington, DC 20001
www.aft.org


Education Next


Education Week

learning disabilities

We haven't read this report, but it looks useful:

Specific Learning Disabilities: Finding Common Ground. A Report Developed by the Ten Organizations Participating in the Learning Disabilities Roundtable
American Institutes for Research (Washington, DC, February 4-5, 2002)

Daniel T. Willingham describes the 'Common Ground' report in EDUCATION NEXT:
In 2002 . . . ten different national organizations, including the Department of Education and the Learning Disabilities Association of America, released a report describing points of consensus about learning disabilities.

the Master Plan

math curricula

If you have time to read just one article on mathematics curriculum in America, click on this link and scroll down to the bottom of the page for a link to the pdf file:

A Coherent Curriculum: The Case of Mathematics

Our KTM link will take you to "The Cascading Benefits of a Common, Coherent Curriculum," the editorial accompanying "A Coherent Curriculum: The Case of Mathematics" by William Schmidt, et al in AMERICAN EDUCATOR.
Catherine

math education, how to teach math, & teaching profession

Math Coach: A Parent's Guide to Helping Children Succeed in Math by Wayne Wickelgren and Ingrid Wickelgren


+ + +


Wage Distortion by Caroline Hoxby and Andrew Leigh

What happens when all teachers, good, bad, and in-between, are paid the same?

The answer surprised me, but it probably shouldn't have. Catherine

For you lucky math-literate folks who can read a peer-reviewed economics paper -- a skill I intend to acquire sooner rather than later -- here is a link to the pdf file for Pulled Away or Pushed Out? Explaining the Decline of Teacher Aptitude in the United States by Caroline M. Hoxby and Andrew Leigh

MoreOnTeachingProfession

math problems

Intriguing Mathematical Problems by Oswald Jacoby with William H. Benson (Dover book, about $8). You might have to simplify some of the problems -- or maybe not.

The Inquisitive Problem Solver by Paul Vaderlind, Richard Guy, and Loren Larson. These problems are actually for adults, but they are nifty.

math standards

Mathematics Framework for California Public Schools (352 pages, pdf)
Mathematics Content Strands for California Public Schools (73 pages, pdf)
Content Standards & Frameworks





The State of State Math Standards 2005, report issued by Thomas B. Fordham Foundation


For Christopher and me, I use the standards written by the state of California

And I use these test problems from the Los Angeles County Office of Education to tell me whether we're anywhere near meeting grade level standards for kids in CA. (Christopher did fine on all of the grade-5 problems he'd studied, but there were quite a few topics he hadn't seen before.)

state standards

New York state standards

student solution to proportion problem
Mathematics Core Curriculum MST Standard 3 Revised 2005 (pdf file)
Standard 3 Mathematics (pdf file)
Standard 3 student work (pdf file)
State Assessment Elementary Intermediate
NY State learning standards A - Z
Latest News on ELA, Mathematics, and Grades 3-8 Testing
Mathematics Resource Guide with Core Curriculum
Core Subjects / Learning Standards
Math Science & Technology standards

Glencoe Pre-Algebra standardized test practice New York

mental math

Arithmetricks : 50 Easy Ways to Add, Subtract, Multiply, and Divide Without a Calculator by Edward H. Julius

BestMentalMathBook

National Mathematics Advisory Panel

all links for National Math Advisory Panel
search page listing all posts on Math Panel

physics textbooks

Asimov: "Understanding Physics" Vol. I-III. The 1988 hardcover reprints all three in one volume. You'll have to pick it/them up off of Ebay or Amazon's used books market. They're non-calculus based, if I remember correctly, and originally written in 1966. I don't think that date will be much of a problem; basic physics hasn't really changed since then.

Seemed pretty good to me, but it's been a long time since I've looked at it. "Understanding Physics" was also not written as a textbook, so you'll need something else for problem sets. Maybe the current book would work for those. JeffBoulier - 27 Nov 2005



pricing on textbooks & supplements price comparisons
PriceComparisonSaxonSingapore
Best Book Buys
(book price comparison web site)
BookFinder.com
(book price comparison web site)

Saxon Math

A World Class K-7 Math Curriculum Verified by Outstanding Experimental Research by William G. Hook (pdf file)

Urban Elementary Schools in California Show Stunning Improvement in SAT-9 Test Scores over Initial Four Year Period of New Math Standards (pdf file) by Wayne Bishop, Ph D, Department of Mathematics, California State University, LA & William Hook, Biology Department, University of Victoria, British Columbia

Singapore Math

Testimony of John Hoven on Behalf of The Center for Education Reform at the National Public Forum on the Draft 2004 Mathematics Frameworks September 24, 2001

This is it.

This is the document to print out and deliver to your superintendent, principal, school board, local PTSA, and newspaper.

Just 8 pages long, and it tells the whole story.

Also see Instructivist's post here.

+ + +


Terrific article on Singapore Math's bar modeling technique, short and readable: Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4-6 Texts Used in Singapore (pdf file) by Sybilla Beckmann.

+ + +


What the United States Can Learn From Singapore's World-Class Mathematics System (and what Singapore can learn from the United States): An Exploratory Study)
prepared for U.S. Department of Education

Essential reading, but long (192 pages, in all; pdf file )
(and see: MoreSingaporeMath)

If you have trouble hailing the website, keywords to Google include:

• Singapore
• American Institutes for Research
• Steven Leinwand

+ + +


Wall Street Journal article on Singapore Math

spatial visualization ability (open to suggestions)

[under construction]

'Spatial visualization ability' appears to be central to mathematical talent. -Catherine

And it's something that can be improved on with practice! -Carolyn

Perspective without Pain by by Philip Metzger

As the title says, it's an enjoyable introduction to the principles and practice of perspective drawing. Carolyn

The New Drawing on the Right Side of the Brain by Betty Edwards.

No matter how tough you are, this book will prove to you that you really can draw. Carolyn

Carolyn's not kidding. Check out this before-and-after drawing done by a student in a 5-day Betty Edwards workshop.

I know this isn't a fake; I took one of the 5-day workshops myself, and I saw the results, even though I only lasted 3 days.

Drawing is math. That's what I learned from Betty Edwards. (That probably wasn't what I was supposed to learn.)

Effect of Instructions on Spatial Visualisation Ability in Civil Engineering Students

Chinese flash cards

Tetris

Chinese IQ


How Spelling Supports Reading by Louisa C. Moats

teaching math

• Smartest Tractor's teaching method (algebra in 8th grade)
  
• the Gambill method of teaching algebra
  
• the Gambill method for teaching algebra in a nutshell
  

testing

Tom Loveless on the ongoing decline in difficulty of NAEP tests (aka 'our nationa's report card').

'money quote':

Proficiency with fractions is critical in preparation for algebra. In 1999, only about half of thirteen and seventeen year olds could compute accurately with fractions on the NAEP. Students who leave eighth grade not knowing how to compute with fractions enter high school as remedial math students. Students who leave high school lacking proficiency with fractions are inadequately prepared for college mathematics. On the most recent trend NAEP, both age groups were less proficient at computing with fractions than in 1982, twenty years ago.

The full report is here (pdf file).

IL state tests

textbook adoption

The Language Police

The Mad, Mad World of Textbook Adoption, a report from the Thomas B. Fordham Foundation

traumatic brain injury

Where Is The Mango Princess? by Cathy Crimmins.

Crimmins' memoir of her husband's brain injury, a book that is, amazingly, not depressing and QuiteFunnyInPlaces.

workbooks

workbook series