Math ed articles by Warren Esty
    Articles for math educators.

Emphasizing Precalculus ideas.

"What do we need to teach about algebra, now that 'Calculators can do it all'?"  When is it all right to use calculators?  Find out in this published article, imaged as a pdf.  I love this article. It says important things about teaching. (It has one typo which is not significant: On page 3, Problem 2 should have "40" replaced by "50")
 

"Understanding Mathematics Using Graphing Calculators."  What makes a graphing calculator exercise a good one?  Find out in this published article, imaged as a pdf.
 

Here is a pdf image of a published article for educators about the philosophy of the Precalculus text by Warren Esty.
"Learning Precalculus Concepts using Graphing Calculators and Emphasizing Symbolic Language."
As far as I know, no other Precalculus text comes close to acknowledging the importance of learning to read symbolism. No other text provides reading lessons, either.
 

"Teaching about Inverse Functions." From AMATYC Review. Not all texts teach this topic the same way, and most miss the point of inverse functions entirely (A strong statement!). See why in this article.

The importance of conceptual development that is specifically algebraic is discussed in
"Algebraic Thinking, Language, and Word Problems,"
an article by Dr. Esty and Dr. Anne Teppo in the 1996 Yearbook: Communication in Mathematics, published by the National Council of Teachers of Mathematics. They have also written related articles on problem-solving and algebraic thinking in several issues of Psychology in Mathematics Education, for example, the next one.

Another article along the same line of thought, that is, algebraic thinking is more sophisticated than arithmetic thinking.
"Problem-Solving using Arithmetic and Algeraic Thinking," in PME 1995.
 

"Provide Homework Answers?" A short letter to the editor of "The Mathematics Teacher" explaining how a text can include 2-significant-digit answers to problems and instructors can still tell if students actually did the work by requiring the third digit on their homework be correct too. 

Emphasizing "The Language of Mathematics" ideas.

"A General Education Course emphasizing Mathematical Language of Reasoning", by Warren Esty and Anne Teppo, which describes the course and studies its impact on students.

"Grade Assignment based on Progressive Improvement." From The Mathematics Teacher Nov. 1992 and reprinted by the NCTM. Why grading should not be based on averages of unit-exam scores.  How to grade appropriately to reward conceptual and long-term learning. These ideas apply to all math classes. 
 

Return to the page on the Precalculus text.

Return to the page on The Language of Mathematics text.