| The purpose of this study is to describe prospective secondary mathematics teachers' understanding about the mathematical concept of limits in terms of the following types of knowledge: subject matter knowledge, curriculum knowledge, and pedagogical content knowledge.;To provide structure in addressing these first two questions, a five-category model describing prospective secondary mathematics teachers' understanding of the concept of limits of sequences was employed and a questionnaire was developed. The keywords characterizing these categories are basic, computational, transitional, rigorous, and abstract. The test items in the questionnaire were designed to measure prospective teachers' understanding of the limit concept in terms of these five categories of the model. For the last two research questions, open-ended questions were embedded in the questionnaire. The open-ended questions were followed up by four in-depth interviews. Because of a low response rate to the last two research questions, no conclusions were made but the data was presented and discussed.;Forty-two prospective secondary mathematics teachers participated in this study. The results indicate that this group of prospective teachers' understanding of the limit concept is more procedural oriented; there exist discrepancies between the participants' concept definitions and their concept images of limits; and the misconceptions, difficulties and errors produced by this group are similar to those found in research studies on students. Since misconceptions, difficulties, and errors prospective teachers possess might be passed to their students, implications for classroom teachers, mathematicians, mathematics educators, and teacher training institutions are presented.;The following research questions were addressed: (1) How well do prospective teachers understand the concept of limits? (2) What kinds of misconceptions, difficulties, and errors do prospective teachers have concerning the concept of limits? (3) What are prospective teachers' opinions about the involvement of the concept of limits in k-12 mathematics curriculum? (4) What are the possible misconceptions, difficulties, and errors the prospective teachers anticipate in teaching the concept of limits?... |
