Using a Journal Article as a Professional Development Experience
Title: Using Communication to Develop Students’ Mathematical Literacy
Author: David K. Pugalee
Journal: Mathematics Teaching in the Middle School
Issue: January 2001, Volume 6, Issue 5, pp. 296 - 299
Rationale for Use
The article considers a classroom episode where two common problems are presented and students use a rubric to rate the response of peers and discuss their rationale for the score.
The PSSM Overview states: “As students are asked to communicate about the mathematics they are studying--to justify their reasoning to a classmate or to formulate a question about something that is puzzling--they gain insights into their thinking. In order to communicate their thinking to others, students naturally reflect on their learning and organize and consolidate their thinking about mathematics.” (p. 12)
- Present the following task: Describe the process of finding dimensions of a pool having a perimeter of 18 meters and an area of 18 square meters (p. 297 of the article).
The Communication Standards for grades PreK-12 stress that mathematics instructional programs should enable students to:
- Share several solutions to the above problem.
- Introduce the rubric in figure 1 and discuss how it could be used by students to communicate about solutions.
- Alternately, have teachers present the above problem to students in class before the PD meeting. Working in small groups have teachers share a sample of students’ work with other participants. Then teachers use the rubric to assess the mathematics communication of the students.
- Discuss the need to communicate the units required when describing perimeter and area. Although the answers may be numerically equal the units are distinct: linear versus square units.
Extension: Are there any other whole number dimensions of rectangles that have a perimeter and area that are numerically equal? Note: There is one other possibility a 4 by 4 square.
With respect to the Communication Standard:
- Organize and consolidate their mathematical thinking through communication;
- Communicate their mathematics thinking coherently and clearly to peers, teachers, and others;
- Analyze and evaluate the mathematical thinking and strategies of others; and
- Use the language of mathematics to express mathematical ideas precisely
- What part of the standard do you find particularly interesting? Why?
- What idea from the Standard has implications for your approach to instruction?
- What idea in this Standard would you like to explore further or know more about?
- If time allows read the article and discuss how as it addresses the Communication Standard.
- How can teachers encourage young adolescents, who are often self-conscious, to share their thinking with others?
- Below appear comments written by the teacher on students’ papers that were intended to extend the students’ abilities to communicate effectively.
- Where could you strengthen your description?
- Could you elaborate on what you were thinking?
- Could you incorporate a diagram in your paper?
Add to this list of sample comments with others generated by the group.
- Classroom communication can be enhanced by selecting engaging real world tasks that contain more than one method of solution. Discuss possible sources of such tasks.
- From 1993 to 2003, the Balanced Assessment in Mathematics Program existed at the Harvard Graduate School of Education. This project developed a large collection of innovative mathematics tasks for grades K to 12. The project has over 300 mathematics tasks which remain freely available through their web site at: http://balancedassessment.concord.org
- Visit the site, examine, and download a sample task.
- Bring the task to your next session to share with colleagues and identify how it connects to the Communication Standard.
- Often parents are confused when they see classrooms where students and teacher are engaged in rich discourse. This discourse may be falsely interpreted as important mathematics not being taught. How do you respond to a parent about such concerns with respect to communication in the mathematics classroom?
Have teachers explore the importance of adaptive reasoning as described in Adding it Up: Helping Children Learn Mathematics (2001, by Kilpatrick and Findell; National Academy Press).
Connections to other NCTM Publications
- Rubenstein, R. N. (2000, April). Word origins: Building communication connections. Mathematics Teaching in the Middle School, 5, 493-498.
- Bay, J. M., & Ragan, G. A. (2000, April). Improving students’ mathematical communication and connections using the classic game of “telephone”. Mathematics Teaching in the Middle School, 5, 486-489.
- Preston, R. V., & Garner, A. S. (2003, September). Representation as a vehicle for solving and communication. Mathematics Teaching in the Middle School, 9, 38-43.
- Richardson, K., & Stein, C. (2008, September). Developing spatial sense and communication skills reflect and discuss. Mathematics Teaching in the Middle School, 14, 101-107.
- Robichaux, R. R., & Rodrigue, P. R. (2003, December). Using origami to promote geometric communication. Mathematics Teaching in the Middle School, 9, 222-229.
- Whitin, D. J., & Whitin, P. (2000). Math is language too: Talking and writing in the mathematics classroom. Reston, VA: National Council of Teachers of Mathematics.