New Classroom Rules to Promote Preservice Elementary Teachers' Mathematics Learning

Do university mathematics courses required for preservice elementary teachers prepare them for the elementary classrooms envisioned by the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics (NCTM, 2000)? These mathematics courses usually fall under the jurisdiction of the mathematics department and are taught by mathematics faculty or graduate students using some form of a traditional, lecture-recitation format. Although mathematics reform has inspired active instructional revision in some university mathematics departments, there remains a strong, recalcitrant adherence to a tradition of direct instruction among mathematicians, many of whom, the brightest and most capable students in their courses, recall with nostalgic fondness and appreciation the rigor, discipline, and intensity of theorem-proof graduate courses, mirroring the deductive approach of the mathematics textbook, beginning with foundational axioms and building an edifice of powerful and elegant theory. One very successful university mathematician summarized mathematics instruction this way: the professor's role, as the master artist, is to paint a beautiful picture of mathematics for the students, who, as apprentices, copy the master's work to improve their skill; students expect and want, he continued, to see the professor exquisitely portray and carefully delineate elegant mathematics in university mathematics courses. RELATED RESEARCH Research suggests that mathematics instruction the majority of preservice elementary teachers have received is preoccupied with procedures and based upon lectures (Battista, 1999; Manouchehri, 1997; O'Brien 1999). Traditional mathematics teaching ... is still the norm in our nation's schools. For most students, school mathematics is an endless sequence of memorizing and forgetting facts and procedures that make little sense to them. (Battista 1999, p. 426) In mathematics classrooms of many colleges and universities, instructional approaches such as multiple representations, open explorations, and meaningful investigations of ideas have not replaced the lecture (Manouchehri, 1997). Ball (1990, 1996) concluded that preservice elementary teachers have a weak, fragmented knowledge of mathematics, mostly acquired facts and memorized rules; she further asserted that they have rarely seen or experienced a kind of teaching that, focusing on conceptual understanding, engages students in complex reasoning in authentic contexts. In a meta-analysis of 151 research studies Hembree (1990) discovered that preservice elementary teachers have the highest level of mathematics anxiety of any major on university campuses. Emenaker (1996) found that preservice elementary teachers, with improvement in conceptual understanding, relied less on the memorization of facts, algorithms, and formulas. There is a strong interconnectedness with regard to conceptual understanding, mathematics anxiety, and memorization. If students possess a deep conceptual understanding of mathematics, they will need to rely less on arbitrary, memorized facts and rules and will exhibit less mathematics anxiety. From 13 years of teaching mathematics courses for preservice elementary teachers, reading their mathematics autobiographies, conducting interviews, and conversing with them, the author believes most preservice elementary teachers are anxious, if not terrified, about passing courses like college algebra, which they often consider the main roadblock to their career teaching elementary school. Because of fear and anxiety, they have developed survival skills to navigate these classes. They work hard to master algorithms presented by the professor on the board, especially those that also appear throughout the homework, and concentrate on getting the correct answer because they know that correct answers will be aptly rewarded on the next test. They have learned there is one correct answer to a problem and one method to get that answer, the professor's, and a one-to-one correspondence between word problems and formulas; for every word problem there is a formula, and vice versa. …