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Preparing Students to Enter the Gates
Michaelle F. Chappell
The author expresses the opinion that algebraic thinking, not traditional algebraic manipulations, in elementary grades contributes to minimizing the differences in mathematics-course participation and achievement that exist between males and females and different racial and ethnic groups.

Probing the Foundations of Algebra: Grade-4 Pattern Items in NAEP
Patricia Ann Kenney and Edward A. Silver
A presentation of some of the NAEP items that have been released to the public, discussion of some of the aspects of patterns and relationships they assess, and information regarding how a nationally representative sample of fourth-grade students performed on those items.

A Foundation for Algebraic Reasoning in the Early Grades
Erna Yackel
This article explores children's thinking that might be foundational to algebraic thinking and describes some instructional activities that can potentially engender such reasoning and thinking.

Experiences with Patterning
Joan Ferrini-Mundy, Glenda Lappan and Elizabeth Phillips
An example of how algebraic thinking and reasoning might be extended over grades K–6.

Literature and Algebraic Reasoning
Cheryl A. Lubinski and Albert D. Otto
Using literature to provide opportunities for students to develop algebraic thinking.

What Does Algebraic Thinking Look Like and Sound Like with Preprimary Children?
Frances R. Curcio and Sydney L. Schwartz
Two activities that provoke the emergence of algebraic thinking in preschoolers.

Liz's Pattern
Jill E. Land and Paul G. Becher
One student's unexpected discovery of a numerical pattern.

Becoming Very-Able with Variables
William R. Speer, David T. Hayes and Daniel J. Brahier
An activity for investigating algebraic symbolism and the use of variables to represent quantities.

Functions from Kindergarten through Sixth Grade
Stephen S. Willoughby
This article describes one strand of activities that develop the concept of function from Kindergarten through Sixth Grade.

Computers Support Algebraic Thinking
Douglas H. Clements and Julie Sarama
Using a computer-programming environment and logo to teach variables.

Algebraic Thinking: A Professional Development Theme
Faye Nisonoff Ruopp, Al Cuoco, Sue M. Rasala and M. Grace Kelemanik
A K-12 professional development project, Teachers Time and Transformations, created with algebraic thinking as its content focus.

Spreadsheets, Patterns, and Algebraic Thinking
Don Ploger, Lee Klinger and Michael Rooney
The results of a fifth-grade class using spreadsheets to investigate challenging mathematical topics and outlines an intuitive approach for introducing the concepts of functions and sequences.

Mathematics of Change: Ins and Outs or Ups and Downs
Cornelia C. Tierney and Ricardo Nemirovsky
An activity with variations that are useful throughout the elementary grades that involve children using small numbers to do a sequence of additions and subtractions the authors call "changes".

Patterns as Tools for Algebraic Reasoning
Kristen Herbert and Rebecca H. Brown
This article explores a lesson from the NSF-funded project MathScape: Seeing and Thinking Mathematically in which students encounter the "Crossing the River" problem.

Doing Algebra in Grades K–4
Zalman Usiskin
This article introduces terms and shows that algebra is often taught unknowingly. It then describes the algebra of grades 2-4 from the curriculum used in the Soviet Union in the late 1970s.


Math by the Month
Math by the Month: Patterns and Functions