Sandy M. Spitzer

• Towson University

In this paper, we investigate the links between prospective elementary teachers’ (PTs’) ability to notice student mathematical thinking, their mathematical knowledge for teaching (MKT) and their ability to decompose learning goals into component conceptual parts (Morris et al., 2009). Previously, researchers have proposed theoretical connections be...

This study examined elementary and secondary prospective teachers’ (PTs’) abilities to analyze a classroom lesson in order to make claims about student thinking around specific mathematical learning goals based on relevant and revealing evidence. Previous research suggests PTs have some skills in analyzing evidence but apply them inconsistently. Ou...

Previous research has found that prospective elementary teachers hold beliefs about mathematics that potentially hinder learning, sometimes called “math myths.” However, since these research studies were conducted, mathematics education and teacher education in the United States has changed, so more recent work is needed. This historical replicatio...

One goal in teacher education is to prepare prospective teachers (PTs) for a career of systematic reflection and learning from their own teaching. One important skill involved in systematic reflection, which has received little research attention, is linking teaching actions with their outcomes on student learning; such links have been termed hypot...

To engage in lifelong systematic learning, prospective teachers (PTs) must be prepared to analyze teaching on the basis of its effects on student learning. The authors present results of an intervention study aimed at developing PTs' ability to analyze a classroom video sample. The intervention used an online discussion board activity structured al...

In order for teachers to improve over time, they must be proficient at collecting and analyzing evidence of student thinking and learning (Hiebert, Morris, Berk, & Jansen, J Teacher Educ 58(1):47–60, 2007). This specific type of diagnostic competence, which focuses on diagnosing student learning with the specific goal of studying and improving teac...

We propose that an often overlooked competence for teaching is diagnosing learning goals. We propose further that this competence is an empirical process of hypothesis generation, testing, and revising. To understand our argument, diagnosis must be conceived as a process of analysis and mathematical decomposition, and learning goals must be treated...

Teacher noticing of student mathematical thinking is increasingly seen as an important construct, but challenges remain in operationalizing and assessing teachers’ analyses of their classrooms. In this chapter, we present a methodology for analyzing teachers’ professional noticing of student mathematical thinking based on its alignment to mathemati...

Although researchers and educators have suggested teaching prospective teachers (PTs) to investigate and learn from their own teaching over time, little research has investigated PTs’ beliefs about such an approach. This qualitative study examines prospective elementary teachers’ conceptions and values about systematically studying and improving th...

Students discover why certain regular polygons tessellate and how M. C. Escher translated and rotated modifications of polygons to create tessellations.

Researchers have advocated building a knowledge base for teacher education based on practitioner knowledge. In this article, the authors, two teacher educators, present knowledge gained from their systematic study of two lessons to help prospective teachers learn to study teaching. They offer a detailed look at the lessons' successes and shortcomin...

This study investigated the effects of a classroom intervention on prospective elementary teachers’ ability to evaluate evidence of student achievement of mathematical learning goals. The intervention was informed by a framework for teacher education which aims to provide prospective teachers (PTs) with the skills needed to systematically learn fro...

In this study, we examined prospective middle school mathematics teachers’ reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers’ descriptions of students’ thinking and frequency of their interpret...