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This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education conference proceedings. Some regional sources from various parts of the world were also included. We investigated who was writing, from and in what settings, with what theoretical frameworks, and with what sorts of study designs for what core questions. We also examined the range of findings and conclusions produced in these studies. Our analysis presented here focuses on four themes that stood out from our initial investigation of almost 300 published papers, and systematically elaborated through a focused study of a 160 papers across key journals and conference proceedings in the field. From this vantage point, the paper offers a reflection on the current state of the field of mathematics teacher education research. Our aim is to stimulate discussion that can support the development of the field, not make final pronouncements about its nature. [ABSTRACT FROM AUTHOR]

The study reported here is the third in a series of research articles (Harkness, S. S., D’Ambrosio, B., & Morrone, A. S.,in Educational Studies in Mathematics 65:235–254, ; Morrone, A. S., Harkness, S. S., D’Ambrosio, B., & Caulfield, R. in Educational Studies in Mathematics 56:19–38, ) about the teaching practices of the same university professor and the mathematics course, Problem Solving, she taught for preservice elementary teachers. The preservice teachers in Problem Solving reported that they were motivated and that Sheila made learning goals salient. For the present study, additional data were collected and analyzed within a qualitative methodology and emergent conceptual framework, not within a motivation goal theory framework as in the two previous studies. This paper explores how Sheila’s “trying to believe,” rather than a focus on “doubting” (Elbow, P., Embracing contraries, Oxford University Press, New York, ), played out in her practice and the implications it had for both classroom conversations about mathematics and her own mathematical thinking. [ABSTRACT FROM AUTHOR]

In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often mistakenly identified as examples. We describe and discuss these notions and present a study regarding kindergarten children’s grasp of nonexamples of triangles. [ABSTRACT FROM AUTHOR]

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through a symbiosis of induction and abduction from experience and deduction from the relationships generated in exemplification. In other words, experience can be organised in such a way that shifts of understanding take place as a result of learners’ own actions. Actions, in this context, include mental acts of organisational reflection. [ABSTRACT FROM AUTHOR]

ABSTRACT. This study investigates how mathematics secondary schools' teachers in \hbox{Jordan} perceive critical thinking and compares teachers' perceptions before and after educational reform. Data were collected from 12 schools twice: in 1988 and in 2004 by interviewing 47 Mathematics teachers. The interview included questions related to teachers' understanding of critical thinking, its role and importance in learning Mathematics, and instructional strategies that could help improve students' critical thinking skills. Results found no improvement in secondary Mathematics teachers' perceptions of critical thinking despite 15 years of educational reform. The majority of Mathematics teachers seemed not to have a clear and adequate understanding of critical thinking. Though most of the teachers claimed they have to teach critical thinking, more than half of them could not suggest any learning situation that could help in fostering critical thinking in Mathematics classes. Also most of the teachers claimed that critical thinking would help students in learning Mathematics; yet less than half were able to give a convincing justification for that. A small percentage of the secondary Mathematics teachers believed they can help all students to foster their critical thinking. It is thus recommended that the concept of critical thinking be transferred from the realm of rhetoric to the field of practice. The paper ends with some recommendations related to the Mathematics teachers training programs in view of the results of this study. [ABSTRACT FROM AUTHOR]

How do teachers conceptualize and deal with context of mathematics word problems in their teaching? This question is discussed based on a study of 14 experienced teachers at the elementary, junior high and senior high school levels. Bruner’s notions of paradigmatic and narrative modes of knowing formed the basis of analysis of data from sources that include interviews and classroom observations. The findings highlight the teachers’ conceptions of problem context and teaching approaches for each of these modes of knowing. All of the teachers used the paradigmatic mode in their teaching but with different depth and most engaged in some form of the narrative mode to create a classroom environment that was motivational for students to learn word problems. The paper also highlights characteristics of these two modes as they relate directly to word problems and discusses implications for instruction, learning and teacher development. [ABSTRACT FROM AUTHOR]

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations -- mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By participating over time in these varied contexts, mathematics teachers refine their conceptions about their craft -- the big ideas of mathematics, mathematics-specific pedagogy, and sense of self as a mathematics teacher. This framework guides a research project that traces the learning trajectories of teachers from two reform-based teacher preparation programs into their early teaching careers. We provide two examples from this research to illustrate how this framework has helped us understand the process of learning to teach. [ABSTRACT FROM AUTHOR]