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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. Our goal was to describe in more detail the strengths and weaknesses in PTs' ability to analyze evidence of student thinking. Results indicate that PTs can make some appropriate claims about student learning in a lesson transcript, but more often make overly broad and general claims. PTs were able to support their claims with specific student work but often used poorly aligned evidence. PTs also often explicitly recognized the shortcomings of evidence from the lesson transcript, but then relied on that evidence to make claims about student thinking. Finally, PTs' background, such as number of teacher education courses completed, does not appear to strongly influence their ability to make claims and support them with evidence, though secondary PTs were more likely to recognize the limitations of evidence than elementary PTs. These results have implications for teacher educators, pointing to the importance of designing interventions to help PTs look beyond the most visible and salient features of a lesson when analyzing student thinking.

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 replication examined current prospective teachers' (PTs') beliefs, using a mixed-methods approach, with the goals of investigating the nature of those beliefs and comparing them to historical trends. Our quantitative and qualitative results help us understand PTs' perceptions of these myths, and our historical comparison reveals many myths appear to be stable and resistant to change. Our work adds nuance to the field's understanding of PTs' beliefs about mathematics and how they have changed (or not) over time. By examining the myths that PTs' perceive as true or false, we can help teacher educators interested in changing these beliefs.

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 their own teaching. Participants (N?=?6) were students at a university in the USA enrolled in a semester-long mathematics methods course designed around one model for systematically improving teaching ("learning-from-teaching" [LFT], also known as "lesson experiments"). Interview results show that the PTs had a high level of procedural knowledge about the LFT skills and reported liking and intending to use all or part of the LFT model. However, results also reveal that four of the six PTs held multiple misconceptions and all six PTs placed less value on improving teaching than on other teaching goals. PTs' conceptions and values about improving teaching may limit their ability to successfully learn from their own teaching, which has implications for how teacher educators teach PTs about lesson experiment skills such as writing learning goals or examining student learning.

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 shortcomings as well as potential revisions. They also reflect on their use of a model for systematically studying lessons, sharing details about their learning during this process. This article attempts to provide a visible, tangible product for other teacher educators interested in helping prospective teachers examine evidence of student learning.

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 from their own teaching practice. Prospective teachers (N = 160) participated in an intervention aimed at addressing their misconceptions about evidence of student learning. Results revealed that after the intervention, PTs were less likely to consider teacher behaviors to be evidence of student learning and more likely to discount student responses that were irrelevant to a specified learning goal. However, PTs were still likely to take procedural fluency as evidence of conceptual understanding and may have become overly skeptical of student understanding. Implications of the study suggest new ways of developing prospective teachers' ability to systematically study and improve their teaching.

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one's teaching. Thirty K-8 preservice teachers completed 4 written tasks. Each task specified a learning goal and then asked the preservice teachers to complete a teaching activity with this goal in mind. For example, preservice teachers were asked to evaluate whether a student's responses to a series of mathematics problems showed understanding of decimal number addition. The results indicate that preservice teachers can identify mathematical subconcepts of learning goals in supportive contexts but do not spontaneously apply a strategy of unpacking learning goals to plan for, or evaluate, teaching and learning. Implications for preservice education are discussed. (Contains 9 tables and 1 footnote.)

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 interpretations about how teaching affected their students' learning. Thirty-three participants responded to open-ended questionnaires or interviews that elicited reflections on their own teaching practice. Prospective teachers used two forms of nuance when describing their students' thinking: (1) identifying students' specific mathematical understandings rather than general claims and (2) differentiating between individual students' thinking rather than characterizing students as a collective group. Participants who described their students' thinking with nuance were more likely to interpret their teaching by posing multiple hypotheses with regard to how their instruction affected their students' learning. Implications for supporting continued growth in reflective thinking skills are discussed in relation to these results.

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 replication examined current prospective teachers' (PTs') beliefs, using a mixed-methods approach, with the goals of investigating the nature of those beliefs and comparing them to historical trends. Our quantitative and qualitative results help us understand PTs' perceptions of these myths, and our historical comparison reveals many myths appear to be stable and resistant to change. Our work adds nuance to the field's understanding of PTs' beliefs about mathematics and how they have changed (or not) over time. By examining the myths that PTs' perceive as true or false, we can help teacher educators interested in changing these beliefs. [ABSTRACT FROM AUTHOR]

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 their own teaching. Participants (N = 6) were students at a university in the USA enrolled in a semester-long mathematics methods course designed around one model for systematically improving teaching (learning-from-teaching[LFT], also known aslesson experiments). Interview results show that the PTs had a high level of procedural knowledge about the LFT skills and reported liking and intending to use all or part of the LFT model. However, results also reveal that four of the six PTs held multiple misconceptions and all six PTs placed less value on improving teaching than on other teaching goals. PTs’ conceptions and values about improving teaching may limit their ability to successfully learn from their own teaching, which has implications for how teacher educators teach PTs about lesson experiment skills such as writing learning goals or examining student learning. [ABSTRACT FROM PUBLISHER]