Constructivism, Deep Conceptual Thinking, Balance...


. . . Critical Thinking, Problem Solving, & Mathematical Processes


Critical Thinking
Why Is It So Hard to Teach?

by Daniel T. Willingham
Daniel T. Willingham is professor of cognitive psychology at the University of Virginia and author of Cognition: The Thinking Animal. He is author of American Educator's regular feature, "Ask the Cognitive Scientist." His research focuses on the role of consciousness in learning.

How Knowledge Helps
It Speeds and Strengthens Reading Comprehension, Learning—and Thinking
by Daniel T. Willingham


The Cognitive Science of Skills and Learning
Daniel T. Willingham Common Core, Inc.

The 21st-Century Skills Movement
E. D. Hirsch, Jr. Common Core, Inc.

What is Problem Solving?
by Richard Rusczyk

Letting Go in the Classroom
Rebecca Alber 10/6/09 Edutopia

What is conceptual understanding?
Devlin's Angle The Mathematical Association of America
September 2007 Keith Devlin
Mathematician Keith Devlin is the Executive Director of the Center for the Study of Language and Information at Stanford University and The Math Guy on NPR's Weekend Edition. Devlin's most recent book, Solving Crimes with Mathematics: THE NUMBERS BEHIND NUMB3RS, is the companion book to the hit television crime series NUMB3RS, and is co-written with Professor Gary Lorden of Caltech, the lead mathematics adviser on the series.

"Not Your Parents' Math"
featuring Lee Stiff, president of the NCTM, and Merryl Tisch, member of the New York State Board of Regents.
Fox News Sunday with Tony Snow (April 22, 2001)

Don't Allow 'new Math' To Multiply, Regent Says
The New York Post April 18, 2001 Kenneth Lovett, Carl Campanile and Ikimulisa Sockwell-Mason

BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING
A Bogus Dichotomy in Mathematics Education
BY H. WU AMERICAN EDUCATOR Fall 1999


Mathematical Reasoning

Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development
Guershon Harel Department of Mathematics University of California, San Diego
Larry Sowder Department of Mathematics and Statistics San Diego State University
MATHEMATICAL THINKING AND LEARNING, 7(1),27–50
Copyright ©2005, Lawrence Erlbaum Associates, Inc.


New NCTM HS Math Doc Does A Disservice
Review of "Focus in High School Mathematics," National Council of Teachers of Mathematics, 2009
Ze'ev Wurman OCTOBER 10, 2009 Ed Policy Blog


Constructivism, Deep Conceptual Thinking, Balance... - Mathematically Sound Foundations
















Let us teach our children mathematics the honest way by teaching both skills and understanding.
--H. Wu


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