Learning algebra

Eugene, OR October 17, 2009 H. Wu

A QUALITY MATH CURRICULUM IN SUPPORT OF EFFECTIVE

TEACHING FOR ELEMENTARY SCHOOLS

WILLIAM HOOK, WAYNE BISHOP AND JOHN HOOK 3 January 2007

A Close Examination of Jo Boaler’s Railside Report

by Wayne Bishop , Paul Clopton , and R. James Milgram

Microsoft Math Partnership YEAR 1 REPORT

JULY 2008 DUANE B. BAKER, Ed.D. GREGORY A. BIANCHI, Ed.D. KARI M. PETERSON, Ph.D. CANDACE A. GRATAMA, Ed.D. Prepared for the Microsoft Corporation and the Puget Sound Educational Service District

Baker Evaluation, Research, and Consulting, Inc (The BERC Group)

College-Preparatory Curriculum for All: The Consequences of Raising Mathematics Graduation Requirements on Students’ Course Taking and Outcomes in Chicago

Author(s): Elaine M. Allensworth, Ph.D. and Takako Nomi, Ph.D., Consortium on Chicago School Research University of Chicago

Minority Performance After A Remedial Mathematics Course

August 20, 1999

David Tello, University of Illinois-Chicago (UIC)

Faculty Mentor: Rodrigo Carramiñana, Ph.D., Mathematics

The Impact of Mathematics Specialists in Virginia

Dr. William Haver May 21, 2008

Committee on Education and Labor

United States House of Representatives

Good intentions are not enough

Richard Askey

The Role of Long Division in the K-12 Curriculum

David Klein R. California State University, Northridge

James Milgram Stanford University

Abstract

We discuss the role of long division in the K – 12 mathematics curriculum. We begin by reviewing the reasons that most math educators today depreciate the topic and other topics in the curriculum that derive from it, such as polynomial long division or polynomial factorization. Later we show that this view is simply wrong mathematically. The role of long division is not just to divide one rational number by another, but the algorithm itself contains the initial exposure of topics which become crucial in the core applications of mathematics in our society today. Following the introduction, we discuss methods for teaching long division in such a way that the underlying concepts can be understood by students. We then provide more details about the ways in which these concepts develop in later mathematics course, and why they are so important.

Long Division: A Touch-Stone for a Few Teaching Principles

Ron Aharoni

Algorithms

Greta Bornemann, George Bright, Boo Drury and Karrin Lewis,

Mathematics Teaching and Learning Team, OSPI

The Case For Long Division

Brian D. Rude, 2004

The Case Against Long Division

Anthony Ralston

BEYOND PEMDAS: TEACHING STUDENTS TO PERCEIVE ALGEBRAIC STRUCTURE

Ethan Michael Merlin, Master of Arts, 2008

“Order of operations” and other oddities in school mathematics

H. Wu September 13, 2007

BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING

A Bogus Dichotomy in Mathematics Education

BY H. WU AMERICAN EDUCATOR Fall 1999

The Effects of Interleaved Practice

KELLI TAYLOR and DOUG ROHRER 30 July 2009

Department of Psychology, University of South Florida, USA

The shufﬂing of mathematics problems improves learning

Doug Rohrer Kelli Taylor August 2006

What Should Be Taught in the Elementary Mathematics Curriculum

H. Wu June 2, 2007

Future High School Math Teachers and Upper Level Math Courses

Dr.Richard Hill Michigan State University

What (Future) High School Teachers Need to Know about Trigonometry

Dr.Richard Hill Michigan State University

The Mathematics K-12 Teachers Need to Know