by Cynthia Ballheim, for the Editorial Panel
October 2000
In the October 1999 issue of Mathematics Education Dialogues, we asked our readers three questions regarding teacher preparation.
 Other than the mathematics that you teach, what mathematics do you need to know to be an effective teacher?
 What changes in your teacherpreparation program would have made you a better mathematics teacher as you began your career?
 What should mathematics teachers do to stay current?
Responses to question 1 favored a strong mathematical background, as well as an understanding of specific skills. All respondents agreed that a teacher should know much more about mathematics than that small piece of mathematics that they teach their students. Undergraduate degrees in mathematics were considered a necessity so that teachers could understand why various processes work and not just how to get the answers. Pedagogical techniques were also mentioned frequently.
For question 2, the overwhelming response was for more work on critical mathematics courses, onthejob mentoring, real applications, handson materials, technology, and inclass time working with students, not just observing them. Without a doubt, our readers felt that reading articles, joining list serves, attending professional conferences, taking further mathematics courses, and sharing with colleagues were the ways to stay current.
Here is what our readers had to say.
You need to know where the students have come from and what their next immediate steps in mathematics will be. Also, you need to have a working knowledge of, and appreciation for, some of the uniquely interesting topics not covered by traditional textbooks or curriculum guides.
Kathleen Heffernan
Grades 5–6 Teacher, Connecticut
Probability, statistics, business mathematics, geometry, algebra, trigonometry, and analytic geometry.
Vivian G. Dunn
High School Teacher, Georgia
I think that realworld applications, such as what job or career uses a particular type of mathematics, are important. I also think that mathematics teachers should understand various proofs; they need to know why a theorem is true or the history behind the mathematics.
Kristen Roxell
Grades 9–10 Teacher, New York
Interpreting data (test scores and grades); estimation (scheduling and pacing); spatial relationships (room arrangement).
Carol L. Boofter
Elementary Specialist, Kentucky
I believe that a basic understanding of geometry, algebra, and even such concepts as fractals and the chaos theory of mathematics can help me be a more effective teacher. A curiosity about mathematics and an application of concepts in all areas makes the teaching more effective.
Adeline Olivo
Math Coordinator, New Jersey
Take mathematics in all high school years, major in mathematics in college, and get a master's degree in mathematics, with a few education courses.
Florence N. Greville
Substitute Teacher, Virginia
After 29 years of teaching, I think that I finally have enough background information and mathematical knowledge.
David Kapolka
High School Department Chair, Michigan
Variety of other subject areas (business, science, economics, ecology, engineering, and so on), recreational mathematics, sports mathematics, money, and financial and investment mathematics.
David Blankenship
Grades 8–12 Teacher, Arkansas
How to ask the right kind of questions that will probe for students' misconceptions and also reveal when they understand a mathematical question and how to teach children to work effectively in cooperative pairs and groups.
Karen Bargabus
Grade 4 Teacher, Kansas
You need to know more about the subject than you will have to teach to your students. You have to know more about why something works or was done that way and how topics are connected.
Sylvia Lazarnick
Grades 9–12 Teacher, Vermont
As a curriculum specialist, I need to know K–12 mathematics, but more important, I need to know how children learn mathematics at different stages in their development. I believe that any classroom teacher should know at least four grades beyond the mathematics that he or she teaches.
Phil White
K–8 Curriculum Specialist, California
It is not what mathematics I need to know (of course, I need to know the mathematics that I'm teaching); it's how people learn mathematics. Knowledge about teaching and learning must be paired with the mathematics that I know.
Kelley Hessina
Grades K–12 Teacher, California
A mathematics professor that I had in college used to say you "teach from the overflow." I believe that you need to know much more than simply the mathematics that you teach. Overflow happens when you know what students will need because you "see the future." You know what courses they will have next and are intimately familiar with what is important for them to know before they get there.
Kathleen A. Collier
Grades 6–8 Teacher, Florida
Unfortunately, a great majority of teachers (mathematics and otherwise) were so woefully inadequate that, although they had good intentions, they did more harm than good. Change will not be easy. It is not totally the fault of teachers that they are inadequate; after all, were they not also educated by the very same inadequate system?
Martin Rudolph
High School Teacher, New York
Correction: In the October 1999 issue of Mathematics Education Dialogues, we erroneously identified Andrea Rothbart's state of residence. She is actually a university teacher in Missouri. We regret the error. 
