Algebra Initiative Article Prompts
David Jabon and Lynn Narasimhan
1. Read the article “Algebra for Everyone: Start Early” by Katheryn Fouche (Mathematics Teaching in Middle School Volume 2, Issue 4, February 1997, page 226). Come to class prepared to discuss what you think the major idea of this article is. Write a brief reaction to the article. What questions does the article leave you with?
2. Read the Article “On the Meaning of Variable” by Alan H. Schoenfeld and Abraham\ Arcavi. (Mathematics Teacher Volume 81, Issue 6, September 1988, pages 420-427). In a short paragraph, indicate a) what you think is the main point of this article and b) at least one implication of this article for the teaching of algebra
3. Read the article “Conceptions of School Algebra and Uses of Variables,” by Zalman Usiskin from the University of Chicago. In this article, he argues that the different ways we use and conceptualize variables is related to different conceptions of algebra. In a few well-written paragraphs, summarize his conceptions of algebra and the conceptions of variables that Usiskin feels correspond. Then answer the question: What implications might Usiskin’s analysis of algebra and variables have for a teacher in the classroom?
4. Read “From Words to Algebra: Mending Misconceptions” by Jack Lochhead and José P. Mestre (From The Ideas of Algebra, K-12, edited by Arthur Coxford and Albert Shulte, Reston, VA: NCTM, 1988). Then answer the following:
a. What two types of errors do the authors specifically point out? Describe them briefly in your own words.
b. Do you agree with the authors’ statement that “the most direct technique (to address the general translation difficulty) is to start simply, providing students with ample practice at the translation process itself isolated from all other aspects of problem solving.” Why?
5. Read the article “Two Different Approaches Among Algebra Learners” by Carolyn Kieran (From The Ideas of Algebra, K-12, edited by Arthur Coxford and Albert Shulte, Reston, VA: NCTM, 1988).
a. Briefly describe the two different approaches Carolyn Kieran found in her research on beginning algebra students.
b. As a algebra teacher, what might you do differently knowing about these two different approaches that students might take?