By Way of Introduction
Lott, Johnny W., Jenkins, Mazie, Teaching Children Mathematics
Few people have encountered the daunting task that faced Evariste Galois on the night of 28 May 1832. Knowing that he was to be engaged in a duel early the next morning, young Galois desperately needed to communicate his knowledge of new mathematics so that others could read about it if he was killed. Inheld (1975, 285) described Galois's thoughts as follows:
The traces of my work can live only if I add to the work of my mind the purely mechanical effort of writing these results with durable ink upon durable paper. Then the traces will remain.
I have no time. I have no time. I must hurry.
In 1995 as national organizations press for reform in mathematics, many educators have thoughts similar to those of Galois on the night before he was killed in the duel. We must hurry; we have no time; we must communicate mathematics to all. We cannot afford to miss this opportunity.
We are not limited, as was Galois, to ink and paper. We have many materials with which to communicate, such as the eyes, ears, and minds of a great many people. We must use all resources in our communication efforts. We must address the mathematical needs of all students; search for ways to showcase and integrate mathematics in other disciplines; investigate how mathematics can be communicated with technology; not forget to communicate mathematics to families of students; emphasize the importance of communicating mathematics by assessing as we go; and we, as teachers, must seek ways to facilitate communication of mathematics both within the class with students and outside the class using any methods possible. The Editorial Panel approached this focus issue of Teaching Children Mathematics with these goals. We felt compelled to hurry; we were impatient to see articles in print; we urged revisions where necessary; we felt an obligation to the mathematics community in this effort.
These articles highlight the various ways that everyone communicates. Maureen, a second grader from Wisconsin, explains:
Some people use math tools. They show you what they did. Some people use sign language. That is neat! If you are far away you use the telephone. Sometimes you read books. They have words so you can read and that's another way of communicating. Everybody is different so we communicate different.
Because people communicate differently, controversial topics result; some are addressed in this issue. For example, "Mathematics Communication: Creating Opportunities to Learn" by Williams Tate focuses on ideas to consider when teaching mathematics in large urban schools. Many ideas in Tate's article are appropriate to teaching mathematics to any minority population in North America, Tate's questioning of the fairness to students of teachers pretending to be color-blind in the classroom may present a topic for both teacher discussion and research. One reviewer said, "If an article invokes this much discussion, it must be worthy of being printed." We sincerely hope it stimulates thinking about teaching mathematics to all students.
Students' work has become a trademark of NCTM's publications. Giving readers the opportunity to see classroom examples of a writer's intent in an article has been both enlightening and entertaining. The student materials in "I Thik the Citanre Will Hoder Lase: Journal Keeping in Mathematics" by Sonia M. Helton illustrate communicating through journals. Keeping journals is only one method of communicating mathematics but one that more and more teachers are using in reform efforts. Some ideas are new, others have a new twist, and all are timely. For those readers who have never employed journals in their classrooms, included here are simple, direct ideas on how to get started.
Assessing what we do in mathematics has become an emphasis for the NCTM. The reform movement in mathematics education in the 1990s has required considering new methods of assement. In "Classroom Vignette: An Alternative-Assessment Tool," Walen and Hirstein demonstrate how classroom scenarios in the form of written vignettes can be a vehicle for assessment. …