Prospective Elementary Teacher Mathematics Content Knowledge: An Introduction

This Special Issue on the mathematical content knowledge of prospective elementary teachers (PTs) provides summaries of the extant peer-­‐reviewed research literature from 1978 to 2012 on PTs’ content knowledge across several mathematical topics, specifically whole number and operations, fractions, decimals, geometry and measurement, and algebra. Each topic-­‐specific summary of the literature is presented in a self-­‐contained paper, written by a subgroup of a larger Working Group that has collaborated across several years, resulting in this Special Issue sharing the final work. The authors hope this summative look at prospective teacher content knowledge will be of interest to the mathematics education community and will be a useful resource when considering future research as well as designing mathematics content courses for prospective elementary teachers

Prospective Elementary Mathematics Teacher Content Knowledge: What Do We Know, What Do We Not Know, and Where Do We Go?

In this Special Issue, the authors reviewed 112 research studies from 1978 to 2012 on prospective elementary teachers’ content knowledge in five content areas: whole numbers and operations, fractions, decimals, geometry and measurement, and algebra. Looking across these studies, this final paper identifies the trends and common themes in terms of the counts and types of studies and commonalities among findings. Analyses of the counts show that the number of articles published each year focusing on prospective teacher (PT) content knowledge is increasing. Most articles across the content areas show that PTs tend to rely on procedures rather than concepts. However, the focus of most articles is identifying PTs’ misconceptions rather than understanding PTs’ conceptions and the development thereof. Both the limitations of the reviews and the directions for future research studies are elaborated

Prospective Elementary Mathematics Teacher Content Knowledge: What Do We Know, What Do We Not Know, and Where Do We Go?

The authors reviewed 112 research studies from 1978 to 2012 on prospective elementary teachers\u27 content knowledge in five content areas: whole numbers and operations, fractions, decimals, geometry and measurement, and algebra. Looking across these studies, this final paper identifies the trends and common themes in terms of the counts and types of studies and commonalities among findings. Analyses of the counts show that the number of articles published each year focusing on prospective teacher (PT) content knowledge is increasing. Most articles across the content areas show that PTs tend to rely on procedures rather than concepts. However, the focus of most articles is identifying PTs\u27 misconceptions rather than understanding PTs\u27 conceptions and the development thereof. Both the limitations of the reviews and the directions for future research studies are elaborated

Investigating number sense development in a mathematics content course for prospective elementary teachers

In order to support children's learning of elementary mathematics meaningfully, elementary teachers need to understand that mathematics deeply and flexibly (Ball, 1990; Ma, 1999). In other words, they need good number sense (Reys & Yang, 1998). However, researchers have found that prospective elementary teachers tend to reason inflexibly, relying heavily on standard algorithms (e.g., Ma, 1999; Newton, 2008; Yang, 2007). Previous research has provided single snapshots or comparisons of pre/post snapshots of number sense. In this study, I analyzed prospective elementary teachers' number sense development. In earlier work, Nickerson and I created a local instruction theory (Gravemeijer, 1999) for the development of number sense (Nickerson & Whitacre, 2010). In a previous classroom teaching experiment, we found that prospective elementary teachers enrolled in a mathematics content course informed by the local instruction theory developed improved number sense (Whitacre & Nickerson, 2006). They moved from being reliant on the mental analogues of the standard algorithms to reasoning more flexibly in mental computation. In the present study, I duplicated analyses from the previous study and found similar results. I also moved beyond the previous study by investigating number sense development as a microgenetic, sociogenetic, and ontogenetic process (Saxe & Esmonde, 2005). I asked the following research questions: As prospective elementary teachers participate in a mathematics content course designed to support their development of number sense, 1. How does the number sense of individuals evolve? 2. What ideas come to function as if shared? What classroom mathematical practices emerge and become established? I approached this study from a situated perspective (Cobb & Bowers, 1999). The emergent perspective informed my approach to the research in terms of taking both social and individual lenses to the analysis of number sense development (Cobb & Yackel, 1996). I made innovations in the analysis of number sense. I documented collective activity in the class in terms of progressions through classroom mathematical practices. I also analyzed two case studies of individuals' number sense development. These analyses provide insights into the phenomenon of prospective elementary teachers' number sense development, which will inform revisions and elaboration to the local instruction theor

PEDAGOGY THAT MAKES (NUMBER) SENSE: A CLASSROOM TEACHING EXPERIMENT AROUND MENTAL MATH

We report on a classroom teaching experiment around number sensible mental math in a semester-long content course for preservice elementary teachers. We designed, implemented, and revised an instructional sequence aimed at students ’ development of number sense with regard to mental math. The data corpus included: a number sense test administered pre and post, interviews with 13 students pre and post, students ’ written work, and the instructor’s journal. Analysis of the data suggests that students did develop greater number sense as a result of their participation in classroom activities. Particular pedagogical innovations, such as those involving the use of models for reasoning, seem to have supported students ’ development of number sense. Results can inform mathematics teaching at various levels. The development of number sense in students is a widely accepted goal of mathematics instruction (NCTM, 2000). Good number sense is especially essential for elementary teachers. Without it, they are ill-equipped to make sense and take advantage of children’s often unorthodox but very number sensible solution strategies. Mental math ability is considered a hallmark of number sense (Sowder, 1992). Much work has been done with the aim of identifying the characteristics exhibited and strategies used by individuals who are skilled at mental mat

Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Whole-Number Concepts and Operations

This report represents part of a recent effort to summarize the state of knowledge of prospective elementary teachers\u27 (PTs\u27) mathematics content knowledge and the development thereof. Extensive reviews of the research literature were conducted by a recent PME-NA Working Group across various content areas. This report focuses on whole number and operations. Research in this area is scarce. What we do know from the literature is that PTs\u27 knowledge of whole number and operations is insufficient and in need of improvement. PTs reason about whole numbers and operations in ways that are tied to the standard algorithms. At the same time, they are hard-pressed to explain why these algorithms work. PTs tend to overgeneralize about operations and to overlook important distinctions. Some of the research reviewed helps us to understand the nuances of PTs\u27 conceptions and can help to inform instruction. Further research is needed to (a) better understand PTs\u27 conceptions when they enter our programs, and (b) better understand how PTs\u27 conceptions develop

Integrating interactive simulations into the mathematics classroom: Supplementing, enhancing, or driving?

High-tech tools can be integrated to serve a number of purposes in the mathematics classroom, with different purposes being appropriate for different learning goals. We focus specifically on the various purposes for interactive simulations (sims). This study followed three experienced middle-school mathematics teachers integrating PhET sims into their classrooms for the first time. Using both our data and literature about high-tech tool integration, we offer a framework defining three categories of purpose for sims in the classroom and describe how the teacher positioned the sim to meet that purpose. We also touch on each teachers\u27 beliefs about high-tech tools in the classroom and the link between their pedagogical beliefs and sim integration practices. We believe this framework contributes to the field by defining varying categories of integration for a tool with growing utilization in the mathematics classroom

Prospective Elementary Mathematics Teacher Content Knowledge: An Introduction

This Special Issue on the mathematical content knowledge of prospective elementary teachers (PTs) provides summaries of the extant peer-­‐reviewed research literature from 1978 to 2012 on PTs’ content knowledge across several mathematical topics, specifically whole number and operations, fractions, decimals, geometry and measurement, and algebra. Each topic-­‐specific summary of the literature is presented in a self-­‐contained paper, written by a subgroup of a larger Working Group that has collaborated across several years, resulting in this Special Issue sharing the final work. The authors hope this summative look at prospective teacher content knowledge will be of interest to the mathematics education community and will be a useful resource when considering future research as well as designing mathematics content courses for prospective elementary teachers. The following sections in this issue provide background information on our overarching framework for the mathematical content knowledge of prospective elementary teachers as well as our rationale for conducting the summary of research. We briefly describe the intent and history of the Working Group that conducted the summaries, followed by the methods utilized in the summary process. Finally, we provide a description of what follows in each subsequent paper and close with our intentions of how this Special Issue might be used by our reader