KTM User Pages
KTM index here ACT prep & review
Ask the Cognitive Scientist
arithmetic (special issue of American Educator)
assessment (& go to Math Supplements for specific tests & advice on assessing your own child)
classic and historical mathematics textbooks
Class Struggle by Jay Mathews WAPO ed columnist
math dictionaries & math reference
journals and magazines
the Master Plan
National Mathematics Advisory Panel
price comparison web sites, books
Saxon math research
standards & testing
traumatic brain injury
Crash Course for the ACT (Princeton Review Series)
Special issue of American Educator on math ed, Fall 2005:Helping Children Learn Mathematics Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide?
Mathematical Knowledge for Teaching: A Research Review Mathematics for Teaching: Then and Now What I Learned in Elementary School by Ron Aharoniexcellent: the single best article on teaching elementary mathematics I've read to date Catherine 9-2005 Harold Stevenson remembered
E.D. Hirsch articles the moder lode
Classroom Research and Cargo Cults
Reading Comprehension Requires Knowledge—of Words and the World (pdf file)
Caroline Hoxby's papers on the web Rising Tide: If every school in the nation were to face a high level of competition both from other districts and from private schools, the productivity of America’s schools, in terms of students’ level of learning at a given level of spending, would be 28 percent higher than it is now. I used to wish I was Nora Ephron. Now I wish I was Caroline Hoxby. Catherine
don't trust the tests
The Knowledge Deficit by Diane Ravitch
A brief & important essay on the political impossibility of rigorous high-stakes testing: "The New York example demonstrates that the political system will not tolerate a denial of diplomas to large numbers of students. That is why it makes little sense to set a single bar for all students. A single standard will inevitably be a low standard. What is needed is a credential system with multiple gradations, for example, a local diploma, a state diploma, and a diploma with honors, each representing different levels of academic achievement. Standards for each level should be both challenging and realistic, making it possible to set goals that inspire all students to increase their efforts without turning the tests into a snap for most students."
Education Next plans to publish periodic assessments of state standards. Here's the chart for 2003.
Elementary Mathematics for Teachers by Thomas H. Parker and Scott J. Baldridge
I am working my way through Parker and Baldridge's text, which teaches teachers (and parents) how to use Singapore's Primary Mathematics series. note: Scott Baldridge will be teaching a summer workshop August 1-5, 2005 at the Madison Country Day School in Madison, WI.
The Principal’s Guide to Raising Math Achievement by Elaine K. Mc Ewan
Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning)
by Liping Ma Life-changing.
review (pdf file; requires Adobe reader) by Roger Howe
Teaching with Original Historical Sources in Mathematics
Frontline interview: Jay Giedd
"Giedd is a neuroscientist at the National Institute of Mental Health. Recently, he spearheaded research showing for the first time that there is a wave of growth and change in the adolescent brain. He believes that what teens do during their adolescent years -- whether it's playing sports or playing video games -- can affect how their brains develop."
'Ask the Cognitive Scientist'
a series of columns by Daniel T. Willingham published in American Educator
Very important, and pure pleasure to read. Catherine
arranged in alphabetical order, but the most important are probably these:
Allocating Student Study Time: "Massed" versus "Distributed" Practice
"Brain-Based" Learning: More Fiction than Fact
Do Visual, Auditory, and Kinesthetic Learners Need Visual, Auditory, and Kinesthetic Instruction? Inflexible Knowledge: The First Step to Expertise Practice Makes Perfect--But Only If You Practice Beyond the Point of Perfection
(and see: SummaryOfPracticeMakesPerfect) The Privileged Status of Story Reframing the Mind
(a deconstruction of multiple intelligences, published in Education Next) Students Remember...What They Think About Understanding ADHD Why Students Think They Understand When They Don't
How Praise Can Motivate—or Stifle
interview with Ingrid Wickelgren, coauthor of Math Coach
Class Struggles by Jay Mathews
If you have time to read just one article on constructivist mathematics curricula in America, go to Barry Garelick's 'An A-Maze-ing Approach to Math' in Education Next. 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.
the Master Plan
direct instruction t/k
formative assessment more t/k
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.
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
Stand and Deliver Revisited
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
American Federation of Teachers, AFL-CIO
555 New Jersey Avenue NW
Washington, DC 20001
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:
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.
Math Coach: A Parent's Guide to Helping Children Succeed in Math by Wayne Wickelgren and Ingrid Wickelgren
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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
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.
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.)
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
Arithmetricks : 50 Easy Ways to Add, Subtract, Multiply, and Divide Without a Calculator by Edward H. Julius
all links for National Math Advisory Panel
search page listing all posts on Math Panel
JeffBoulier - 27 Nov 2005
pricing on textbooks & supplements price comparisons
Best Book Buys
(book price comparison web site)
(book price comparison web site)
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
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.
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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.
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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:
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Wall Street Journal article on Singapore Math
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
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
The Language Police
The Mad, Mad World of Textbook Adoption, a report from the Thomas B. Fordham Foundation
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.