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Systematically Improving Lessons in Teacher Education: What's Good for Prospective Teachers is Good for Teacher Educators
Abstract
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.
... While Hiebert and his colleagues foremost recommend lesson experiments to help teachers learn from teaching, they also recommend the approach for university instructors and teacher educators. At the post-secondary level, the processes are the same but now the 'students' are the undergraduate students and/or the prospective teachers and the 'teacher' is the university instructor or teacher educator (e.g., Phelps & Spitzer, 2012). ...
... Then, begin the process individually or in collaboration with others, e.g., fellow colleagues, graduate students, researchers, etc. Try to plan for at least two cycles if possible; cycles enable testing whether changes are improvements or just changes (Jansen et al., 2009). Ultimately, the best way to learn about lesson experiments is just to complete one (Phelps & Spitzer, 2012). Even when I was not sure if I was following the lesson experiment protocol correctly, I was still amazed by the detail and depth I learned about the PSTs' thinking and associated instructional factors. ...
... Research indicates that PTs can learn to evaluate evidence through targeted intervention (see, e.g. Alsawaie and Alghazo 2010; Kazemi and Franke 2004;Phelps and Spitzer 2012;Santagata and Guarino 2011;Santagata and Yeh 2013). However, this work often finds that, even after intervention, PTs still lack some skills in analyzing evidence (Bartell et al. 2013); Spitzer et al. 2011). ...
... All three sets of codes were developed based on our conceptual framework, which specifies that claims about student thinking should be in alignment with the learning goal and evidence must be relevant to the learning goal and revealing of student thinking (Hiebert et al. 2007). Codes were based on previous work analyzing PTs' skills in analyzing teaching situations (see Phelps and Spitzer 2012) and were then modified inductively to fit the current data. Coding reliability followed the process of intercoder agreement described by Campbell et al. (2013); that is, both authors coded the data individually, compared, and discussed differences until 100% agreement was reached. ...
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.
... To improve teaching, we designed a targeted goal for PTs' learning, developed an 561 intervention with hypotheses for how the intervention would support PTs' achievement of the 562 learning goal, and analyzed PTs' thinking to determine whether and what they learned from 563 instruction (Hiebert, Morris, Berk, & Jansen, 2007;Phelps & Spitzer, 2012;Thanheiser et al., 564 2015). Although this process is frequently used by mathematics educators, it is less commonly 565 discussed in relation to promoting productive dispositions among PTs. ...
Engaging prospective elementary teachers (PTs) in participating productively by making their exploratory (rough draft) thinking public during class discussions remains a constant challenge for instructors of mathematics content courses for teachers, in part because of perspectives incoming PTs may hold about interacting in academic settings. In this article, we share the effects of an intervention designed to confront PTs' incoming perspectives. PTs were provided with opportunities to label the level of completeness and correctness of their thinking before they displayed and discussed their written work publicly during a mathematics content course for teachers. Results indicated that labeling their work increased PTs' level of comfort with sharing their thinking and awareness of the value of doing so. PTs also reported that the label served as a reflection tool. The label increased the PTs' productive disposition in terms of comfort level with taking intellectual risks when doing mathematics and reflecting on their work.
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 teaching, can be improved through interventions in teacher education (see, e.g., Spitzer, Phelps, Beyers, Johnson, & Sieminski, JMTE 14(1):67–87, 2011). In this chapter, we discuss the findings of previous interventions aimed at helping prospective teachers (PTs) learn to analyze student thinking. Then, we present a replication study using a classroom intervention to teach prospective elementary teachers (N = 23) to identify and evaluate evidence of student understanding. Results of this study and previous work show that diagnostic competence is a skill that is teachable through interventions. After the intervention described in this chapter, participants performed better on a measure of diagnostic competence. In particular, they improved their ability to distinguish evidence of student thinking from nonevidence, such as a teacher’s lecture. They were also more likely to recognize that students’ procedural work cannot be used to diagnose conceptual understanding. Results will be used to suggest key features of interventions to improve diagnostic competence.
Although diagnostic competence of teachers is regarded as a key component of successful teaching, there are many open questions regarding the structure, the development and the impact of diagnostic competence. This chapter presents an overview of different approaches to pinpoint diagnostic competence theoretically and to investigate it empirically: measuring judgment accuracy, assessing competences in diagnostic situations or analyzing judgment processes. These approaches are discussed with respect to their advantages, restrictions as well as some of their main findings and they are allocated within an overarching model of diagnostic competence as a continuum, comprising diagnostic dispositions, diagnostic thinking and diagnostic performance.
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 mathematical learning goals. This process entails first deconstructing a mathematical learning goal into its conceptually important pieces (known as subgoals). Then, researchers can look for references to these subgoals in teachers’ attending, interpreting, and deciding (the three skills of noticing). When teachers reference conceptual subgoals of a learning goal in their noticing, it indicates their attention to students’ reasoning about the important mathematical ideas of a lesson. This method of data analysis can be used across a variety of contexts and allows for greater precision in understanding teacher noticing by focusing on its mathematical content and attention to relevant student thinking. In this theoretical chapter, we describe this research methodology (and the process of deconstructing learning goals and using subgoals), justify its appropriateness as a measure of teacher noticing, and provide examples from our own and others’ work to illuminate its use.
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.
To improve classroom teaching in a steady, lasting way, the teaching profession needs a knowledge base that grows and improves. In spite of the continuing efforts of researchers, archived research knowledge has had little effect on the improvement of practice in the average classroom. We explore the possibility of building a useful knowledge base for teaching by beginning with practitioners’ knowledge. We outline key features of this knowledge and identify the requirements for this knowledge to be transformed into a professional knowledge base for teaching. By reviewing educational history, we offer an incomplete explanation for why the United States has no countrywide system that meets these requirements. We conclude by wondering if U.S. researchers and teachers can make different choices in the future to enable a system for building and sustaining a professional knowledge base for teaching.
In this article, we describe features of learning goals that enable indexing knowledge for teacher education. Learning goals are the key enabler for building a knowledge base for teacher education; they define what counts as essential knowledge for prospective teachers. We argue that 2 characteristics of learning goals support knowledge-building efforts. First, learning goals should be targeted; they must be sufficiently well specified to suggest interventions for supporting learners in achieving them and to indicate the types of evidence needed to determine if the goals have been achieved. Second learning goals should be shared; they must be mutually understood and committed to by all participants in the knowledge-building process. By drawing on our experience in our local efforts to develop knowledge for preparing prospective elementary mathematics teachers, we illustrate how targeted and shared learning goals support efforts to build a knowledge base for teacher education. We then propose the use of learning progressions for supportingknowledge-building endeavors across sites.
In this paper, we describe a model for systematically improving the mathematics preparation of elementary teachers, one lesson at a time. We begin by identifying a serious obstacle for teacher educators: the absence of mechanisms for developing a shareable knowledge base for teacher preparation. We propose our model as a way to address this challenge, elaborating the principles that define the model to show its relevance. We then provide an example of the model in action, detailing how the model was used to gradually but steadily improve a single mathematics lesson for prospective elementary teachers. We conclude by presenting data indicating that the model is effective in generating and vetting knowledge that helps to improve our mathematics program over time. Although our discussion is situated in the mathematical preparation of prospective elementary teachers and draws on examples from mathematics, we argue that the model could be applied to build knowledge and improve teacher preparation in any discipline.
The authors propose a framework for teacher preparation programs that aims to help prospective teachers learn how to teach from studying teaching. The framework is motivated by their interest in defining a set of competencies that provide a deliberate, systematic path to becoming an effective teacher over time. The framework is composed of four skills, rooted in the daily activity of teach- ing, that when deployed deliberately and systematically, constitute a process of creating and test- ing hypotheses about cause-effect relationships between teaching and learning during classroom lessons. In spite of the challenges of acquiring these skills, the authors argue that the framework outlines a more realistic and more promising set of beginning teacher competencies than those of traditional programs designed to produce graduates with expert teaching strategies.
A video-based program on lesson analysis for pre-service mathematics teachers was implemented for two consecutive years as
part of a teacher education program at the University of Lazio, Italy. Two questions were addressed: What can preservice teachers
learn from the analysis of videotaped lessons? How can preservice teachers’ analysis ability, and its improvement, be measured?
Two groups of preservice teachers (approximately 140 in total) participated in the program. A three-step lesson analysis framework
was applied to three lesson videos: (1) goal(s) and parts of the lesson; (2) student learning; and, (3) teaching alternatives.
Preservice teachers’ ability to analyze lessons was measured through an open-ended pre- and post-assessment. In the assessment,
preservice teachers were asked to mark and comment on events (in a lesson not included in the program) that they found interesting
for: teachers’ actions/decisions; students’ behavior/learning; and, mathematical content. A coding system was developed based
on five criteria: elaboration, mathematics content, student learning, critical approach, and alternative strategies. In both
studies, the ability to analyze instruction improved significantly on all five criteria. These data suggest promising directions
for the development of both an instrument to measure lesson analysis abilities and a model for teacher learning.
The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work those problems generated. This study draws on a transformation of participation perspective to address the questions: What do teachers learn through collective examination of student work? How is teacher learning evident in shifts in participation in discussions centered on student work? The analyses account for the learning of the group by documenting key shifts in teachers' participation across the year. The first shift in participation occurred when teachers as a group learned to attend to the details of children's thinking. A second shift in participation occurred as teachers began to develop possible instructional trajectories in mathematics. We focus our discussion on the significance of the use of student work and a transformation of participation view in analyzing the learning trajectory of teachers as a group.
Moving beyond the general question of effectiveness of small group learning, this conceptual review proposes conditions under which the use of small groups in classrooms can be productive. Included in the review is recent research that manipulates various features of cooperative learning as well as studies of the relationship of interaction in small groups to outcomes. The analysis develops propositions concerning the kinds of discourse that are productive of different types of learning as well as propositions concerning how desirable kinds of interaction may be fostered. Whereas limited exchange of information and explanation are adequate for routine learning in collaborative seatwork, more open exchange and elaborated discussion are necessary for conceptual learning with group tasks and ill-structured problems. Moreover, task instructions, student preparation, and the nature of the teacher role that are eminently suitable for supporting interaction in more routine learning tasks may result in unduly constraining the discussion in less structured tasks where the objective is conceptual learning. The research reviewed also suggests that it is necessary to treat problems of status within small groups engaged in group tasks with ill-structured problems. With a focus on task and interaction, the analysis attempts to move away from the debates about intrinsic and extrinsic rewards and goal and resource interdependence that have characterized research in cooperative learning.
Consistent with the theme of this issue, we describe the details of one continuing effort to build knowledge for teacher education. We argue that building a useful knowledge base requires attention to the processes used to generate, record, and vet knowledge. By using 4 features of knowledge-building systems we identified in the introductory article for this issue- shared goals, tangible products, small tests of small changes, and multiple sources of innovation- we examine the knowledge-building processes for K-8 teacher preparation under way at the University of Delaware. We conclude that the 4 features provide a useful mirror for clarifying the strengths and weaknesses of our local system and, at the same time, reveal a number of institutional obstacles for knowledgebuilding that lie ahead.
In the introductory essay to this special issue, we argue that a knowledge base for teacher education will grow only if the field attends directly to the processes used to study and improve its practices. We identify 4 features that characterize the processes used by a diverse set of outside-of-education systems to build knowledge for improving professional practice: shared goals across the system; visible, tangible, changeable products; small tests of small changes; and multiple sources of innovation from throughout the system. Our intent in describing these features is to set the stage for examining how knowledge can be built for educating (mathematics) teachers, a challenge addressed in this article and those that follow inthis special issue.
In this study I investigated how collaborative interactions influence problem-solving outcomes. Conversations of twelve 6th-grade triads were analyzed utilizing quantitative and qualitative methods. Neither prior achievement of group members nor the generation of correct ideas for solution could account for between-triad differences in problem-solving outcomes. Instead, both characteristics of proposals and partner responsiveness were important correlates of the uptake and documentation of correct ideas by the group. Less successful groups ignored or rejected correct proposals, whereas more successful groups discussed or accepted them. Conversations in less successful groups were relatively incoherent as measured by the extent that proposals for solutions in these groups were connected with preceding discussions. Performance differences observed in triads extended to subsequent problem-solving sessions during which all students solved the same kinds of problems independently. These findings suggest that the quality of interaction had implications for teaming. Case study descriptions illustrate the interweaving of social and cognitive factors involved in establishing a joint problem-solving space. A dual-space model of what collaboration requires of participants is described to clarify how the content of the problem and the relational context are interdependent aspects of the collaborative situation. How participants manage these interacting spaces is critical to the outcome of their work and helps account for variability in collaborative outcomes. Directions for future research that may help teachers, students, and designers of educational environments learn to see and foster productive interactional practices are proposed. The properties of groups of minds in interaction with each other, or the properties of the interaction between individual minds and artifacts in the world, are frequently at the heart of intelligent human performance (Hutchins, 1993, p. 62).
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 spon- taneously apply a strategy of unpacking learning goals to plan for, or evaluate, teaching and learning. Implications for preservice education are discussed.
This paper offers a synthesis of research on cooperative learning in small groups. The main challenge for teachers who utilize cooperative learning is to stimulate the type of interaction desired according to their teaching objective. A generalization regarding student interactions is that if students are not taught differently, they will tend to operate at the most concrete level. Student participation in a task group that is structured to foster resource- or goal-interdependence appears to increase student motivation and performance. The effectiveness of the group structure depends on the task's complexity and uncertainty and on the extent to which the instructions attempt to micromanage the interaction process. Information is also offered on ensuring equity in interaction, managing the interaction, and unsettled issues, such as special curricula and assessment. Successful implementation of cooperative learning also requires staff development and principals who demonstrate effective managerial skills and instructional leadership. (LMI)
Based on rapid advances in what is known about how people learn and how to teach effectively, this important book examines the core concepts and central pedagogies that should be at the heart of any teacher education program. This book was edited in collaboration with Pamela LePage, Karen Hammerness, and Helen Duffy. It is the result of the National Academy of Education's Committee's work on teacher education. It was written for teacher educators in both traditional and alternative programs, university and school system leaders, teachers, staff development professionals, researchers, and educational policymakers, the book addresses the key foundational knowledge for teaching and discusses how to implement that knowledge within the classroom. This book recommends that, in addition to strong subject matter knowledge, all new teachers have a basic understanding of how people learn and develop, as well as how children acquire and use language, which is the currency of education. In addition, the book suggests that teaching professionals must be able to apply that knowledge in developing curriculum that attends to students' needs, the demands of the content, and the social purposes of education: in teaching specific subject matter to diverse students, in managing the classroom, assessing student performance, and using technology in the classroom. The ideas and suggestions outlined in this book have far-reaching implications for educational policy, classroom practice, and staff development and will go a long way toward informing the next generation of teachers. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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.
KeywordsProspective teachers–Evaluating teaching–Analyzing teaching–Analyzing student work–Learning to teach–Teacher preparation
This study investigated the learning-from-practice skills that pre-service teachers possess when they enter teacher preparation programs in the United States. Two subskills were hypothesized to represent, at least in part, what is required to learn from practice: (1) the ability to collect evidence about students’ learning in order to analyze the effects of instruction, and (2) the ability to use the analysis to revise the instruction. Because it seems likely that different teaching situations and contexts reveal these learning-from-practice skills in different ways and to different degrees, this study examined the skills that pre-service teachers exhibited under two experimental conditions. Thirty pre-service teachers were asked to analyze the effects of a videotaped mathematics lesson on student learning, to support their analysis with evidence, and to use their analysis to revise the lesson. Based on the results, it appears that many entry level pre-service teachers can carry out a cause-effect type of analysis of the relationships between specific instructional strategies and students’ learning, and can use this analysis to make productive revisions to the instruction. However, prospective teachers’ ability to collect evidence that supports their analysis appears to be less developed. In addition, the type of analysis that prospective teachers carried out about the effects of instruction on students’ learning differed dramatically across the two experimental task conditions.