Fall 2003 Readings


9/29:Algebra: Language of Process and Generalizations

"Promoting Algebraic Reasoning Using Students' Thinking" by J. Bishop, A. Otto & C. Lubinski


10/1:Algebra: Language of Process and Generalizations 

"Tunja Sequences as Examples of Employing Students' Powers to Generalize" by John Mason 

"The Volume of a Pyramid: Low-Tech and High-Tech Approaches" by Masha Albrecht 

"Geometric Meaning in the Geometric Mean Means More Meaningful Mathematics" by Matt Fluster




10/8:  Variables and Algebraic Symbols


Text: Chapter 6




10/15:  Variables and Algebraic Symbols


"Learning Mathematical Symbolism: Challenges and Instructional Strategies" by R. Rubenstein & D. Thompson


"The Many Uses of Algebraic Variables" by R. Philipp


"Teaching Algebraic Expressions in a Meaningful Way" by L. Chalouh & N. Herscovics


"From Words to Algebra: Mending Misconceptions" by J. Lochhead & J. Mestre



10/22:  Technology in the Teaching of Algebra


Text: Chapter 7




10/29:  Expanding the Notion of Function


Text: Chapter 5


"A Function is a Mail Carrier" by M. Sand



11/3:  Expanding the Notion of Function


"Thinking and Writing Mathematically: Achilles and the Tortoise as an Algebraic Word Problem" by J. Martinez


"Making Sense of Slope" by A. Crawford & W. Scott


"Understanding Connections between Equations and Graphs" by E. Knuth


"Blake's Slope-Intercept Surprise" by J. Misener




11/12:  Linking Multiple Representations


"Why Representations?" by J. Schultz & M. Waters


"Algemetic" by L. McMullin


"Multiple Representations and Connections Using Technology" by C. Embse and V. Yoder


"Kinematics and Graphs: Students' Difficulties and CBLs" by P. Hale



11/17:  Role of Proof


"Types of Students' Justifications" by L. Sowder & G. Harel


"Ideas for Developing Students' Reasoning: A Hungarian Perspective" by A. Szombathelyi & T. Szarvas


"A Unified Framework for Proof and Disproof" by S. Epp


"Prove It!" by Amy Prince


"I Would Consider the Following to be a Proof …" by W. Dodge, K. Goto & P. Mallinson



11/24:  Expanding Students' Understanding of Algebraic Equivalence or Identity


"Listening to Middle School Students' Algebraic Thinking" by J. Smith III & E. Phillips


"Enhancing Discourse on Equations" by M.Lee


"Equivalent Representations in the Learning of Algebra" by F. van Dyke and T. Craine