TIAN Bundle 4

Articles and References (For Teachers)
About Algebraic Thinking

Driscoll, Mark and John Moyer. “Using Students’ Work as a Lens on Algebraic Thinking” in Mathematics Teaching in the Middle School, 6:5 (January 2001): 282–287. http://my.nctm.org/eresources/mtms/focus_mtms04.asp. This article focuses on the use of student work to help teachers focus on teaching and learning algebra.

Kalchman, Mindy S.  “Walking through Space: A New Approach for Teaching Functions” in Mathematics Teaching in the Middle School, 11:1 (August 2005): 12–17. Kalchman shares a real-life scenario for introducing several key aspects of linear functions.

Kriegler, Shelley. “Just What is Algebraic Thinking?” Submitted for Algebraic Concepts in the Middle School. http://www.math.ucla.edu/~kriegler/pub/algebrat.html. Kriegler discusses three lenses for looking at algebra: algebra as abstract arithmetic, algebra as language, and algebra as a tool for the study of functions and mathematical modeling.

Mooney, Edward S. “Cookies” in Mathematics Teaching in the Middle School, 12:7 (March 2007): 374–377. This brief article gives you insight into students’ mathematical thinking about this problem: Tim ate 100 cookies in 5 days. Each day he ate 6 ore than the day before. How many cookies did he eat on the first day?

Mooney, Edward S. “Elizabeth’s Long Walk” in Mathematics Teaching in the Middle School, 12:5 (December 2006): 263–265. This brief article gives you insight into students’ mathematical thinking about this problem: Elizabeth visits her friend Andrew and then returns home by the same route. She always walks 2 km/h when going uphill, 6 km/h when going downhill, and 3 km/h when on level ground. If her total walking time is 6 hours, then what is the total distance she walks?

Peterson, Blake E. “Counting Dots and Measuring Area: Rich Problems from Japan” in Mathematics Teaching in the Middle School, 12:4 (November 2006): 214–219. Students look at a set of dots and create a variety of generalizable patterns.

Smith, Margaret S., Amy F. Hillen, and Christy L. Catania.  “Using Pattern Tasks to Develop Mathematical Understandings and Set Classroom Norms” in Mathematics Teaching in the Middle School, 13:1 (August 2007): 38–44. This article discusses the use of pattern blocks to help students develop algebraic reasoning and to establish classroom norms and practices.

Thomas, David A. and Rex A. Thomas. “Discovery Algebra: Graphing Linear Equations” in The Mathematics Teacher, 92:7 (October 1999): 569 – 572. http://my.nctm.org/eresources/article_summary.asp?from=B&uri=MT1999-10-569a. In this article, Thomas shares his personal classroom experience moving toward a new approach to teaching algebra.

Additional Resources

Driscoll, Mark. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6–10. Portsmouth NH: Heinemann.