In our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' ("Teaching Children Mathematics", 21(1), 18-25) "13 Rules That Expire" article has been a useful resource for us to…

To shed light on the value of the area model as a tool to elicit pre-service teachers' (PSTs') understanding of fractions and area, we explored their understanding of the fractional knowledge and geometric measurement knowledge incorporated in the area model by providing PSTs area models in an "atypical" way. We administered a written…

It is important to support pre-service teachers in terms of mathematical task design so as to increase the success of their future teaching. The purpose of this study was to evaluate mathematical tasks designed by pre-service primary and elementary mathematics teachers within the framework of task design principles. For this purpose, a total of 43…

This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors' beliefs associated with…

The goal of this study is to analyze undergraduate elementary school pre-service teachers' conceptions and misconceptions of physical and virtual manipulative materials using an interpretive "framework." The "framework" involved the use of the "Concrete," "Pictorial" and "Abstract cognitive levels"…

Instructors ("N"?=?204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain-specific topics,…

In this pedagogical reflection, a White mathematics teacher educator describes what she learned from three Latina pre-service teachers who were recent immigrants from Mexico while they completed an elementary mathematics methods course. Using Rochelle Gutierrez's (2012) metaphor of a window and mirror, the author interrogates her own identity and…

Teaching is an interactive process in which teachers gather information, analyze the results, and construct a response based on this diagnosis (Cooney, 1988). Considering alternatives in constructing a response, that is, making an instructional decision, is of great importance in teaching. How might mathematics teacher educators provide…

Using the structure of a metacognitive journal, this article describes the author's discovery of an unusual method for adding fractions after carefully considering a student's response. (Contains 3 figures.)

In this study, we determined the effectiveness of the inquiry-based Itakura method for mediating alternate conceptions of preservice elementary teachers (N = 38) in an integrated mathematics, science, and technology methods course. We investigated alternate conceptions in the expansion of solids due to heating. There was a significant increase in…

In this article, the authors describe their efforts to assess prospective K-8 teachers' knowledge of proportional reasoning. Based upon their analysis of prospective K-8 teachers' work on a mathematics performance task, they discuss the implications for preparing prospective teachers to teach proportional reasoning to their students. In general,…

This exploratory study, a one group pretest-posttest design, investigated the development of elementary preservice teachers' understandings of distribution as expressed in the measures and representations used to compare data distributions. During a semester-long mathematics methods course, participants worked in small groups on two statistical…

We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…

While other research has begun to contribute to our understanding of how pre-college students reason about variation, little has been published regarding pre-service teachers' statistical conceptions. This paper summarizes a framework useful in examining elementary pre-service teachers' conceptions of variation, and investigates the question of…

These proceedings contain the papers presented at the 1995 annual meeting of the Canadian Mathematics Education Study Group. Papers are organized into four sections: (1) plenary lectures; (2) working groups; (3) topic sessions; and (4) ad hoc sessions. Papers include: (1) "The Role of Epistemology in the Analysis of Teaching/Learning…