In 2014 NCTM advocated for productive struggle by expressing the need for teachers to allow their students the time necessary to grapple with their mathematical "uncertainties." We posit pre-service teachers need opportunities to productively struggle when learning and applying their mathematical understanding in order to understand how…

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…

Contributing to research on students' multifaceted meanings for angles (e.g., angles as ray pairs, as regions, and as turns), we report on three undergraduate students' meanings for central and inscribed angles in circles. Specifically, we characterize how these meanings govern their mathematical activities when engaging in a circle geometry task,…

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…

This research report explores relationships between fractions' task representations (discrete, rectangular, or circular) and elementary prospective teachers' (PTs) fractions conceptions. Studies show PTs' conceptions of fractions are centered on a part-whole understanding, which may be problematic when teaching children about improper fractions.…

The importance of practical learning environments for developing preservice teachers' (PSTs') dispositions and skills for teaching mathematics is underscored in a growing body of literature. Hence, teacher preparation programs often include methods courses embedded within K-12 schools. Utilized to a lesser extent; however, are campus-based…

This study used participant observation to explore students' thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative…

This study examined pre-service elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course. Specifically, their explanations and justifications for common algorithms for multiplication and division of fractions were coded using an existing framework (SOLO; Biggs, 1999) for the assessment of…

Preservice teachers often enter teacher education programs with naïve views about mathematics and science as well as the various domains of knowledge needed for effective teaching. A significant body of research has demonstrated that teacher knowledge is multifaceted and consists of both subject matter knowledge and pedagogical content knowledge.…

We examine preservice mathematics teachers' conceptions of writing as a tool for learning mathematics before and after participation in and reflection on writing tasks. We describe the use of two targeted activities incorporated into a secondary methods course: writing to learn mathematics (WTLM) and reflection on that writing. Prior to…

This dissertation study examines the experiences of four Latina/o pre-service teachers (PSTs) as they learn about teaching mathematics for understanding (TM4U) and integrating a child's out-of-school mathematical knowledge and experiences during instruction. Studying the knowledge and experiences of Latina/o PSTs is necessary because PSTs…

Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…

This theoretical paper proposes a way to extend the partitive and measurement interpretations of whole number division to fractional contexts focusing on the issue of units. We define the unit-changing and unit-keeping interpretations for division and suggest a stronger and earlier focus on the concept of units in courses for prospective…

The study investigated the changes in levels of mathematics anxiety among pre-service teachers in six different sections of a mathematics method courses for early childhood/elementary education pre-service teachers. The changes were a function of using Bruner's framework of developing conceptual knowledge before procedural knowledge and using…

The constructivist perspective, which holds that children's learning of subject matter is an interaction between what they are taught and what they bring to a learning situation, could be used to improve mathematics teacher education. (PK)