by Diane Resek
October 2000
Although newer secondary school mathematics programs are showing increased learning and more positive attitudes on the part of students, their implementation requires teachers to have broadened subjectarea knowledge and new pedagogical skills. We need to change secondary teacherpreparation programs if we want graduates who are prepared to teach these new curricula.
Change some content
We must first change the mathematics courses required. Courses in probability, statistics and discrete mathematics must be added to traditional teacherpreparation programs. This change is rather easy to make, and it seems to be happening already in many mathematics departments.
Change some pedagogy
A harder change to make in the undergraduate mathematics program for teachers, but one that is even more essential, is changing how mathematics courses in the programs are taught. In newer secondary programs, high school students construct their own understanding through active engagement with mathematics. They discover many mathematical principles on their own instead of being told everything.
Teachers in these programs must give students guidance when needed but must have enough faith in the process that they do not provide too much guidance. Giving too much guidance is akin to "telling," and students may not end up constructing their own meaning. If high school teachers have learned mathematics only through direct instruction, they have difficulty believing that people—their students in particular—can learn through guided discovery. Without a belief in guided discovery, teachers—often with the best of intentions—will sabotage new programs by teaching them the way that they have always learned.
Pedagogical changes both in undergraduate content and in methods courses will happen only if the culture of the collegiate faculty changes. Realistically, we will not see largescale changes in this direction until professors who have themselves learned mathematics in newer ways arrive in the system. However, useful measures for beginning the change process include implementing teaching and learning courses in graduate mathematics programs; seminars and extended sessions on teaching and learning styles at the Mathematical Association of America and American Mathematical Society joint meetings; and frank, open discussions examining the teaching quality in the postsecondary system.
Seeing is believing
For future teachers to believe that the newer system "works" with students, experiencing learning in a constructivist classroom is not enough. These teacherstobe must also witness students, similar to those that they will be teaching, learning under these same conditions. When future teachers take mathematics classes using the newer constructivist methods, they often do their student teaching in classes that do not use these methods. The reaction of these new teachers, like their collegiate teachers, is to believe that they themselves are able to construct their own meaning but that younger students or students who are different from themselves cannot learn in this way. New teachers may believe that high school students can learn only through direct instruction.
There may not be enough conveniently located classes that use the newer programs for all future teachers to do some of their practice teaching in such classrooms. But if all teacherstobe and collegiate teachers can at least visit such classrooms, their beliefs can be challenged.
Reflecting on it all
Finally, in addition to learning mathematics themselves under newer methods and seeing younger students learn in this way, future teachers need time with their peers to reflect on how they learn and on how they see others learning. To use newer programs, teachers must change a deeply ingrained paradigm about how mathematics is taught and learned. Such a change will happen only through honest questioning and thorough discussions.
Diane Resek, resek@math.sfsu.edu, is a professor of mathematics at San Francisco State University. She is a coauthor of the Interactive Mathematics Program, one of the newer programs for secondary school mathematics funded by the National Science Foundation. 
