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1.
This study examines how various teacher characteristics and contextual factors are related to early primary teachers’ beliefs about mathematical teaching and learning and teachers’ attitudes toward their own learning of mathematics. A total of 396 early primary teachers across Nebraska participated in the study. Teacher characteristics and contextual factors were grouped into four sets: teacher professional background, teacher mathematical knowledge for teaching, teaching contexts, and students’ experiences. Multiple regression analyses were conducted with each set of predictors separately, as well as with all four sets together. The results showed significant relationships between teachers’ mathematical knowledge for teaching and teacher-centered beliefs, motivation in learning mathematics, and anxiety toward learning mathematics. Teacher certification level, the number of college math courses taken, and perceived support from colleagues and administrators were also related to some aspects of teachers’ mathematical beliefs and attitudes. The findings suggest the potential role of teachers’ mathematical knowledge for teaching in improving teachers’ mathematical beliefs and attitudes. 相似文献
2.
《International Journal of Educational Research》2002,37(2):195-210
Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics. 相似文献
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The goal of the study presented in this article was to examine how variations in task design may affect mathematics teachers’ learning experiences. The study focuses on sorting tasks, i.e., learning tasks that require grouping a given set of mathematical items, in as many ways as possible, according to different criteria suggested by the learners. We present an example of a sorting task for which the items to be grouped are related to basic concepts of analytical geometry that are connected to the notion of loci of points. Based on a design experiment of three iterations with practicing secondary school mathematics teachers, we report on intended and enacted objects of learning inherent in three versions of the task. Empirically based suggestions are drawn about design of sorting tasks that potentially evoke desirable learning experiences. 相似文献
5.
Melissa D. Boston 《Journal of Mathematics Teacher Education》2013,16(1):7-31
This investigation describes secondary mathematics teachers’ learning and instructional change following their participation in a professional development workshop, the Enhancing Secondary Mathematics Teacher Preparation Project (ESP) (2004–2005), specifically focused on the selection and implementation of cognitively challenging mathematical tasks. Data consist of a pre/post-assessment of teachers’ knowledge of the cognitive demands of mathematical tasks and videotaped discussions and written artifacts from the professional development sessions. A mixed methods approach was used to identify connections between teachers’ learning and their experiences in the ESP workshop. Results indicate that ESP teachers developed new ideas about the influence of mathematical tasks on students’ learning. Increases in teachers’ knowledge of the cognitive demands of mathematical tasks were closely linked to ideas represented in frameworks and discussions from the ESP workshop and to teachers’ experiences in solving challenging mathematical tasks as learners. 相似文献
6.
In this study, 12 pre-service mathematics teachers worked in teams to develop their knowledge and skills in using teacher-led spreadsheet demonstrations to help students explore mathematics concepts, stimulate discussions and perform authentic tasks through activity-based lessons. Pre-service teachers’ lesson plans, their instruction of the lessons designed, experiences and lesson enactment outcomes were examined. The pre-service teachers in the study were able to develop and demonstrate their knowledge and skill adequately in designing and enacting activity-based mathematical lessons supported with spreadsheets. The results also showed that the pre-service teachers’ use of the spreadsheet as an instructional tool promoted student in-depth mathematical concept formation and an activity-based learning approach to make lessons less teacher centred and more interactive. 相似文献
7.
Ilhan Karatas 《欧洲师范教育杂志》2014,37(3):390-405
This study examines the effect of three different computer integration models on pre-service mathematics teachers’ beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM) group and 33 fifth-year students in the Exploring Mathematical Relationships with Mathematical Software (EMReMaS) group. The results indicated a remarkable change in beliefs within the EMReMaS and IM groups concerning computer use in teaching and learning mathematics. The present study offers empirical evidence that the pre-service mathematics teachers’ experiences in computer-based mathematics courses played a significant role in this change. Teacher education programmes should consider this learning method for pre-service teachers. 相似文献
8.
徐彦辉 《宁波大学学报(教育科学版)》2022,(5):66-072
数学理解包括三种基本形态,即:记忆性理解、解释性理解和探究性理解,这三种数学理解分别对应着“记得、晓得和明得”三种不同的状态。三种数学理解对数学学习都是有价值的,但仅有记忆性和解释性理解是不够的,探究性理解才是数学教学的最终目标。实践中,不少水平不高的教师常常只能让学生达到记忆性理解,有一定水平的教师能让学生达到解释性理解,真正让学生达到探究性理解的教师并不是很多。教师要不失时机地促进学生数学理解层级的迭代升级,促使学生最终达到探究性理解,吴文俊院士数学学习的经验对把握数学理解的三种基本形态有借鉴和启迪意义。在课堂教学中引导学生从事生动活泼的数学探索性活动常常是一个相当艰难的过程,对教师的数学探究素质提出了较高的要求,教师应努力引导学生去探求数学知识的意义和发现的过程,促使学生数学探究性理解方式的养成。 相似文献
9.
ULLA RUNESSON 《欧洲师范教育杂志》1997,20(2):161-169
In order to adapt teacher education to new demands in mathematics classrooms, it is necessary to change the courses in mathematics at the university. Teachers’ beliefs about mathematics, learning and teaching has great impact on their teaching. At the University of Göteborg, a co‐operative project has been conducted in order to design a programme based on problem solving in courses taken by prospective Comprehensive School teachers (grade 4‐‐9). The main purpose of the project has been to make student teachers more reflective about mathematics as such, about learning and teaching. Another purpose of the project has been to use a teaching method in a university course‐‐a method which could be applied in a school classroom. The student teachers have worked co‐operatively in small groups of 3‐4 students and the educators role has been that of a facilitator. A preliminary evaluation indicates that student teachers have developed an insight into the complexity of learning and teaching, even though there are variations in this respect. However they still have difficulties in applying the method to teaching mathematics at school. 相似文献
10.
This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, Human Development 52:109–128, 2009) to understand students’ mathematical thinking. This study challenged teachers’ pedagogical assumptions about what it means to teach for student understanding. Clinical task-based interviews opened a window into students’ knowledge, problem-solving and reasoning, and helped teachers reflect on their teaching and assessment of student learning. Teachers also learnt about what it means to establish a culture of thoughtful questioning in the classroom and developed an emerging awareness that this requires a readiness to hear students’ ideas and connect informal or invented strategies with classroom mathematics. 相似文献
11.
Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms. 相似文献
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This article investigates why students reported liking a student-driven learning design better than a highly guided design despite equivalent gains in knowledge assessments in both conditions. We created two learning designs based on the distinction in the literature between student-driven and teacher-led approaches. One teacher assigned each of her two 5th-grade classes to one design (n = 52); both designs addressed the mathematical concepts for the same amount of time. Data were collected using written assessments, surveys, and video. Students in both classes improved equivalently on assessments. On surveys, students in the student-driven condition were significantly more positive about learning. Video was coded to examine why students were more positive in the student-driven design. This analysis showed students engaging more frequently with data in discussing strategies, questioning peers, and aligning outcomes with prior experiences. We trace the association between students’ positive responses to learning and richer engagement in mathematical practices to specific features of the student-driven design. Furthermore, we reject competing explanations (e.g., amount of off-task behavior or adult intervention). We conclude that designing learning opportunities that promote mathematical practices affords opportunities to cultivate students’ disciplinary interest. We discuss implications for teachers and curriculum designers who are responding to new mathematics standards. 相似文献
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CÅNDIDA QUEIROZ MOREIRA 《欧洲师范教育杂志》1997,20(2):171-189
Change is always difficult, and there is no great doubt that teachers need time to come to terms with it. This fact is, however, too often forgotten. In the spirit of my earlier work, this paper is shaped by an action research perspective. It provides some insights into the learning experiences of a group of eleven experienced secondary mathematics teacher, who were enrolled in a Perspectives on Mathematics Education two semesters course, within the context of a Masters on Mathematics Teaching programme, held at a Department of Mathematics, in a Portuguese University. The first part of the paper highlights the conflicting pressures and stresses suffered, during the first semester course, by the participating teachers. Confrontation with new ideas about both mathematics and mathematics education, as well as work overload, had a damaging impact on the teachers’ self‐confidence and morale. The second part of the paper covers the second semester course by addressing three fundamental questions for teachers, which aimed at helping the students bridge the academic mathematics and the mathematics education worlds. Finally, brief scenarios of three participating teachers’ professional development throughout the course are discussed in order to illustrate the challenges they had to face and the possibilities the course (and the Masters programme) offered to promote individual change. 相似文献
14.
Filiberto Barajas-López 《Journal of Latinos & Education》2014,13(1):14-32
Through an ethnographic and narrative inquiry approach, this study draws attention to the plight of 4 Mexican immigrant high school students and their pursuit of education and mathematics learning. Their elementary school stories and experiences show a deep relationship between the learning contexts in which these students largely do school (i.e., an English learner context) and the nature of students' relationships (or lack thereof) with teachers and their process of disengagement from mathematics learning and school. Doing school is used to convey a key distinction from simply attending school. Attending school assumes uniformity/neutrality in how students might experience schooling and is a passive way of describing student participation in school. Doing school implies that students make sense of and respond to their schooling experiences in different ways and accounts for how these experiences are shaped and/or influenced by other forces (e.g., structural forces, social forces) in and out of school. 相似文献
15.
In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development
of teachers’ pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4–14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group
of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be
used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand
how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical
tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth
in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study
provides a new research instrument for measuring teachers’ growth in pedagogical content knowledge.
An earlier version of this paper was presented at the American Educational Research Association Annual Meeting, New Orleans,
LA, April 2002. 相似文献
16.
Jelena Radišić Aleksandar Baucal 《European Journal of Psychology of Education - EJPE》2018,33(3):445-466
The study explores how teachers perceive and go about students’ thinking in connection to particular mathematical content and how they frame the notion of applied mathematics in their own classrooms. Teachers’ narratives are built around two released PISA 2012 mathematics items, the ‘Drip rate’ and ‘Climbing Mount Fuji’ (will be referred to as the Fuji item). Teachers show concordance as to the reasons that could make either of the items difficult for students and are able to provide more examples justifying their reasoning for the ‘Fuji’ item. Suggestions linked to making the items more familiar to the students mostly relate to de-contextualization of the items’ content towards a more formal mathematical record. The teachers agree that students need only basic mathematical knowledge, at a level learned during elementary school, in order to solve these problems. Yet, at the same time, many teachers have difficulty clearly verbalising which procedures students are expected to follow to be able to solve the tasks. Disagreement among the teachers is noticeable when labelling the most difficult part(s) of each of the selected items. Mathematics teachers show openness for learning on how to create math problems we examined in this study, but question the purpose and meaning in incorporating more such problems in their own teaching. 相似文献
17.
Alberto Esquinca 《International journal of qualitative studies in education》2013,26(3):279-300
This article reports on a case study of a college class for pre-service teachers on the US–Mexico border in which students participated in in-depth discussion around mathematical problems every day. This pedagogical approach promotes the socialization of students into and through the specialized discourse of mathematics. The focus of this paper is on the experience of transfronterizo students in that course. Transfronterizos are Mexican residents who periodically cross the border to attend school. For these students, whose educational background in Mexico allowed them to develop proficiency in elementary mathematical discourse in Spanish, their socialization experience includes ways in which they draw on language, and other social and learning experiences in Mexico. The focus of this paper is an assignment called Thinking Logs, a genre that required the use of mathematical discourse for teaching. Drawing on data gathered from participant observation of the course, interviews, analysis of study session discourse, and genre analysis, I highlight agentive ways that each participant used in their own socialization process. I show how participants improvised writing of models, asked for clarification in the first language, and even resisted the discourse. Students who resisted the demands might incur negative effects. Furthermore, I argue that the role of the guidance from an expert (such as a professor) is imperative in a socialization process, and I offer implications for ways that teachers can guide second language writers to develop mathematics discourse. 相似文献
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Rossella Santagata Claudia Zannoni James W. Stigler 《Journal of Mathematics Teacher Education》2007,10(2):123-140
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. 相似文献
19.
Kalinec-Craig Crystal A. Bannister Nicole Bowen Diana Jacques Lorraine A. Crespo Sandra 《Journal of Mathematics Teacher Education》2021,24(4):375-398
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.
相似文献20.
《Teaching and Teacher Education》2001,17(2):213-226
Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners. 相似文献