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1.
Eight middle school mathematics teachers’ perceptions and uses of curriculum materials and the Common Core State Standards for Mathematics (CCSSM) were investigated. Adapting a noticing framework and models of dialogic instruction and direct instruction, teachers’ noticing practices with curriculum materials and the CCSSM when planning, enacting, and reflecting on lessons were examined. Teachers who were committed to implementing the CCSSM and who were using one of two substantively different curriculum programs were purposefully selected. Data sources included multiple forms of interviews and classroom observations. The teaching evidenced three distinct noticing patterns. These patterns indicated that teachers’ curriculum materials were associated with how teachers perceived and enacted the CCSSM. Teaching with a curriculum program that was designed as a thinking device prioritized the Standards for Mathematical Practice of CCSSM evidenced noticing that was consistent with dialogic instruction. Teaching with a curriculum program that was designed as a delivery mechanism prioritized the Content Standards of CCSSM and evidenced noticing consistent with direct instruction. Findings indicated that the designated curriculum and contributed to differing interpretations of CCSSM and served as a lens for noticing. However, a dialogic curriculum program was not sufficient to support dialogic approaches in practice. One pattern showed teachers planning dialogic lessons, but the lesson enactments were not consistent with teachers’ plans, with evidence that the teachers were not aware that their practices differed from dialogic approaches. Implications for research and practice are discussed.  相似文献   

2.
The focus on professional noticing in mathematics education has recently gained increased interest as researchers work to understand how and what is noticed and how this translates into practice. Much of this work has focused on the professional noticing practices of inservice teachers and preservice teachers, with less attention focused on those educating teachers. This research explores how novice mathematics teacher educators professionally notice as they engage in teaching experiments and create models of student’s mathematical thinking. Findings indicate the novice teacher educators are including some evaluative comments in their professional noticing practices but lack in-depth interpretive analysis about student thinking and rarely make connections between student’s thinking and the broader principles of teaching and learning. These findings provide evidence for the importance of supporting teacher educators with developing their abilities to professionally notice.  相似文献   

3.
As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children’s competencies related to children’s mathematical thinking, and children’s community, cultural, and linguistic funds of knowledge or what we refer to as children’s multiple mathematical knowledge bases. Teachers’ noticing supports students’ learning in deep and meaningful ways. Researchers designed and enacted a video analysis activity with prospective teachers in their mathematics methods course. The activity served as a decomposition of practice in order to support prospective teachers in engaging in an approximation of the practice of noticing. Our findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. We also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning). Implications for teacher educators interested in designing and enacting activities to support noticing are discussed.  相似文献   

4.
Emotions are central to how students experience mathematics, yet we know little about how specific instructional practices relate to students’ emotions in mathematics learning. We examined how dialogic instruction, a socially dynamic form of instruction, was associated with four learning emotions in mathematics: enjoyment, pride, anger, and boredom. We also examined whether these associations differed by student gender and prior mathematics achievement. The sample consisted of 1307 sixth through eighth grade students (51.6% female, 59.0% White, 30.8% African American, and 10.3% other race; 42.3% receive free/reduced price lunch) from 70 mathematics classrooms. Results indicated that teachers who used more dialogic mathematics instruction had students who reported more enjoyment and pride, and less anger and boredom. Males and low-achieving students reported more positive and fewer negative emotions with greater dialogic instruction compared to their female and high-achieving counterparts.  相似文献   

5.
This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin’s concept of professional vision as a way of bringing analyses of culture and power into studies of teacher noticing. The case of a high school algebra teacher who learned to notice the mathematical strengths of students from marginalized groups is used to illustrate how this might be done. The teacher’s noticing involved not only cognitive processes like attending to, interpreting, and deciding how to respond to students’ thinking, but also managing dominant ideologies that position students—especially students from non-dominant communities—as mathematically deficient rather than as sense-makers whose ideas should form the basis for further learning. The paper advances the field’s capacity for understanding the challenges that teachers face as they attempt to notice in ways that are ambitious as well as equitable.  相似文献   

6.
Insight in the way teachers' beliefs filter their interpretation of inclusive classrooms is vital to support teachers’ competences to teach diverse learners. This study explores how three types of teacher beliefs about teaching diverse learners (i.e., professional beliefs about diversity, beliefs about differentiating the curriculum, and growth mindset) are associated with their noticing of two key aspects of effective inclusive classrooms (i.e. positive teacher-student interactions (PTSI) and differentiated instruction (DI)). Data was collected in a sample of secondary education teachers (N = 462) in Flemish schools (N = 23). Teacher beliefs were measured by survey scales, while teachers’ noticing of PTSI and DI was assessed by a standardised video-based comparative judgement instrument. Survey and video data were combined in a multivariate multilevel framework. Findings indicate that teachers’ professional beliefs about diversity and beliefs about differentiating the curriculum serve as filters for noticing PTSI and DI in videoclips. For teachers’ growth mindset no significant relationship was found. These associations did not change when taking into account teachers’ sex, age, educational background or experience. Furthermore, a small part of the differences in teachers’ noticing DI is explained by the school level, suggesting that teachers within a school can share a vision. Results are discussed in the light of teacher thinking for inclusive classrooms and implications for teacher professional development.  相似文献   

7.

Noticing is a skill that is not overtly observable yet is consequential to effective mathematics instruction. Researchers have found that prospective and practicing teachers can learn to notice, but little focus has been given to those who teach teachers to notice. The purpose of the study was to characterize mathematics teacher educators’ noticing and their ability to interpret students’ thinking and connect interpretations to evidence. Participants in the study included 16 mathematics teacher educators who took part in a course designed to support noticing. Results indicate the mathematics teacher educators noticed at varying degrees and improved their noticing and incidence of connections between interpretations and evidence. Findings indicated that 19% of participants had no shift in their noticing because they were at the highest level of noticing to begin with (Robust with Strong Evidence), which was considered advanced noticing. Twenty-five percent of the participants did not shift in their noticing at all and remained at Limited, which is considered an intermediate level of noticing. The remaining 56% of the participants improved their noticing. The results of the study reveal that at the end of the course a majority of the participants were able to connect interpretations with evidence. These findings are important because they describe mathematics teacher educators’ interpretations and evidence as they notice.

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8.
Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children’s multiple mathematical knowledge bases (MMKB), including children’s mathematical thinking and children’s home and community-based mathematical funds of knowledge, in instruction. A powerful means of supporting pre-service teachers in integrating children’s MMKB in instruction may be to scaffold teachers’ noticing of potential spaces in elementary mathematics curriculum materials for connecting to children’s MMKB and then developing practices for leveraging these spaces during instruction. We focus on existing and potential spaces in written curriculum materials, or curriculum spaces, so as to better support teachers in enacting curriculum that opens spaces for connecting to children’s MMKB.  相似文献   

9.
Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children’s mathematical thinking, as well as their cultural, linguistic, and community-based knowledge. This article presents a conjectured learning trajectory for prospective teachers’ (PSTs’) development related to integrating children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge), in mathematics instruction. Data were collected from 200 PSTs enrolled in mathematics methods courses at six United States universities. Data sources included beginning and end-of-semester surveys, interviews, and PSTs’ written work. Our conjectured learning trajectory can serve as a tool for mathematics teacher educators and researchers as they focus on PSTs’ development of equitable mathematics instruction.  相似文献   

10.

Learning to name and notice students’ mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students’ mathematical strengths so PTs learn to teach mathematics while emphasizing what students know and can do. This study uses two tools MTEs can use to support PTs as they learn to name and notice students’ mathematical strengths: A LessonSketch experience, a digital platform with comic-based storyboards showing children engaged in a mathematics task, and a strengths-based sentence frame. Our study presents the findings from the 111 noticing statements from 18 PTs as they engaged in the LessonSketch digital experience and practiced making noticing statements about what children know about mathematics. The study found that after a sentence-frame intervention, the PTs are more likely to use strengths-based language and more likely to identify mathematical evidence in their noticing statements. Uncommitted language (statements that do not align with a strength- or deficit-based coding scheme), suggests a fruitful, yet complex space for supporting more PTs as they learn to name and notice students’ mathematical strengths. The paper concludes with implications for future research in teacher education.

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11.
This paper presents findings from a qualitative study of a group of 12 teachers in primary special schools in Scotland for children with moderate learning difficulties. It sets out an analysis of classroom observations and interviews that explored teachers' knowledge and beliefs about teaching and learning in mathematics with children with moderate learning difficulties. The teachers were interviewed pre‐ and post‐intervention; this was a research‐based professional development programme in children's mathematical thinking (Cognitively Guided Instruction) which teachers then developed in their classrooms. The findings showed that prior to the professional development, the teachers had a limited knowledge of children's mathematical development with teaching frequently informed by intuitive beliefs and dated and sometimes discredited practices. Most teachers had low expectations of children with learning difficulties. Post‐intervention, the teachers reviewed this stance and affirmed that a deeper understanding of children's mathematical thinking provided a more secure knowledge base for instruction. They also recognised the extent to which learners were constrained by existing classroom practices. The paper argues for the commonality of this knowledge base and considers the problematic nature of viewing such knowledge as sector specific.  相似文献   

12.
Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding.  相似文献   

13.
This study investigated a highly accomplished third-grade teacher’s noticing of students’ mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom teaching as opposed to professional development environments. Noticing was conceptualized as both attending to different elements of classroom instruction and making sense of classroom events. The teacher paid most attention to student thinking and was able to offer a variety of rich interpretations of student thinking which were presented in an emergent framework. The results also indicated how the teacher’s noticing might influence her instructional decisions. Implications for both research methods in studying noticing and teacher learning and practices are discussed.  相似文献   

14.
The purpose of this study was to understand what preservice teachers and knowledgeable others professionally notice as they engaged in repeated cycles of a modified version of lesson study, as a component of a field experience in a teacher education program. The study also centered on comparing the professional noticing practices of preservice teachers with other lesson study participants, including classroom teachers and university facilitators. Data analyzed included videos of weekly lesson study analysis meetings for seven weeks for each of four teams. Each team included six preservice teachers, a classroom teacher, and a university facilitator. Findings indicate that preservice teachers primarily noticed elements about the classroom environment and teacher pedagogy, but included instances of noticing centered on students' mathematical thinking. In contrast, classroom teachers and university facilitators, as knowledgeable others, typically noticed general events and were less focused on students' mathematical thinking. Analysis of noticing trends over the seven weeks indicated that noticing levels remained steady initially, dropped in the fourth and fifth week, and resumed original status in the final weeks. Results that the preservice teachers' noticing comments were at higher levels than the knowledgeable others are contrary to other research studies and indicate that incorporating lesson study with appropriate scaffolds into a field experience for preservice teachers may be a viable option for encouraging noticing of students' mathematical thinking.  相似文献   

15.
The purpose of the study was to investigate how Lesson Study influences pre-service teachers’ learning to professionally notice students’ mathematical thinking. The initial and last video-recorded discussions were analysed using a qualitative method. Findings suggest that Lesson Study can be useful means to improve pre-service teachers’ noticing expertise in reviewing and planning lessons. However, to maximise the effect of Lesson Study on developing pre-service teachers’ noticing expertise, several modifications need to be made to the Lesson Study protocol, which are discussed.  相似文献   

16.
This study explores how 4th and 5th grade teachers’ reflective practice developed as they participated in a remote video-based coaching intervention to implement dialogic classroom text discussions. Drawing on a professional vision framework, we analyzed teachers’ verbal and written reflections to examine how teachers’ noticing and reasoning about their videoed classroom interactions developed over time. Findings suggest teachers became more focused on the connection between their discussion moves and students’ thinking in video, and their reasoning about these interactions became more interpretive and in-depth over time. Implications for research on how teachers learn dialogic pedagogies are discussed.  相似文献   

17.
Abstract

In this article, we share a model of flipped instruction that allowed us to gain a window into our students’ mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be used to design experiences that help students make sense of mathematics during class sessions.  相似文献   

18.
Considering the rising proportion of English learners (ELs) in general education, little is known about how this change in classroom composition relates to the frequency of instructional activities and skills. This study uses a multimodal perspective on learning mathematics in a multilingual context, which recognizes the diverse modes of communication that students draw on in mathematics classrooms. We examined national data using quantitative analyses and investigated the mathematics practices that were more likely to occur in kindergarten classrooms that did and did not have ELs. We found teachers reported greater frequency of manipulatives and count/calendar activities in mathematics instruction when there were EL students in the classroom. Teachers in classrooms with ELs also reported a greater frequency of mathematics content that involved teaching shapes and practical skills. The findings indicate that teachers tended towards a supportive multimodal approach to instruction when ELs were present.  相似文献   

19.
This article responds to calls that have been made for research into how teachers incorporate new assessment ideas into their practice. We draw on a large‐scale study that examined the implementation of reform in mathematics in grades 7–10 in Ontario, Canada. We present teacher questionnaire data, and focus on data gathered from case studies for details of what new assessment practices look like in classrooms. We show teachers using a variety of forms of assessment and using assessment to improve student learning. Observed assessment practices went beyond tests to include the use of journals, observation, questioning, self‐assessment and unique forms of ‘quizzes’. These practices allowed teachers to examine students’ mathematical thinking and provided feedback to students and teachers to improve student learning. We also observed the important role of collaboration, coherence, and the teachers’ beliefs in supporting new assessment practices.  相似文献   

20.
ABSTRACT

Digital video technology has been increasingly employed to investigate teacher professional noticing. While extensive research has been undertaken to explore the specialised knowledge base underlying teacher professional noticing, there is a need to more closely examine the methodological consequences of video-based approaches for understanding the nature of professional noticing. This paper draws upon a recent study that investigated primary school teachers’ professional noticing of mathematics and science classrooms to discuss issues, challenges, and opportunities that emerge with a video-based research approach. In this study, the latest video technology was employed to allow primary school teachers to take active roles in capturing, selecting and reflecting on significant classroom events on their own and with colleagues. Drawing upon examples from this study, this paper highlights the methodological potential and challenges of video-based approaches to investigating teacher noticing in classrooms, and discusses how this noticing relates to reflection stimulated by classroom videos. It further reveals the tension between the dual priorities of empowering the teacher participants in research and enabling valid interpretations by the researchers in an attempt to gain insight into the complexity of teachers’ professional noticing.  相似文献   

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