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1.
Learning to pose mathematical problems: Exploring changes in preservice teachers' practices 总被引：1，自引：0，他引：1
S. Crespo 《Educational Studies in Mathematics》2003,52(3):243-270
Learning to pose mathematical tasks is one of the challenges of learning to teach mathematics. How and when preservice teachers
may learn this essential practice,however, is not at all clear. This paper reports on a study that examined the changes in
the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. It reports that
their later problem posing practices significantly differed from their earlier ones. Rather than posing traditional single
steps and computational problems, these preservice teachers ventured into posing problems that had multiple approaches and
solutions, were open-ended and exploratory, and were cognitively more complex. Their problem posing style also changed. Rather
than making adaptations that made students' work easier or narrowed the mathematical scope of the problem, their adaptations
became less leading and less focused on avoiding pupils' errors. Posing problems to an authentic audience, engaging in collaborative
posing, and having access and opportunities to explore new kinds of problems are highlighted as important factors in promoting
and supporting the reported changes.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems 总被引：1，自引：0，他引：1
School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical
problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics
education reform vision that seeks to promote mathematics as an worthy intellectual activity. In this study, the authors explored
the problem-posing behavior of elementary prospective teachers, which entailed analyzing the kinds of problems they posed
as a result of two interventions. The interventions were designed to probe the effects of (a) exploration of a mathematical
situation as a precursor to mathematical problem posing, and (b) development of aesthetic criteria to judge the mathematical
quality of the problems posed. Results show that both interventions led to improved problem posing and mathematically richer
understandings of what makes a problem ‘good.’ 相似文献
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4.
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
5.
聂娇 《淮南职业技术学院学报》2021,(2):94-99
当前,地方师范院校学前师范生教学技能存在的主要问题是:教学设计的思路不清晰、缺乏导入环节,导入效果不佳、教学语言成人化,不符合幼儿认知特点和规律、板书不够规范,书写不注重细节、忽略课堂情境的调控、缺乏主动进行教学反思的意识。为此,高校要办好教学技能大赛,做好“以赛促学、以赛促训,以赛强教”;搭建师范生教学技能训练的资源平台;大力构建“实践+监督+考核”于一体的教学技能培养完整体系;秉持共建共享、合作共赢的理念,建设高质量的校外实践基地;遴选校外优秀导师,建立高素质的双师型教师队伍;学前师范生要增强自我发展意识,主动提升教学技能。 相似文献
6.
Debra McLauchlan 《Pedagogies: An International Journal》2017,12(1):130-142
ABSTRACTPlaylinks, the project documented in this paper, contributed a theatre-based artist-in-the-classroom study to the Community Arts Zone initiative. Playlinks involved 248 elementary school classrooms in pre- and post-production workshops connected to live theatre that visited their schools. Data sources included researcher field notes, teacher evaluation forms, and interviews with both teachers and theatre personnel. Findings focus on teacher perceptions of three topics: (a) student engagement, (b) learning across cognitive and affective domains, and (c) benefits for teachers. The discussion section addresses implementation problems related to artist-in-the-classroom projects. 相似文献
7.
Shuk-kwan S. Leung 《Educational Studies in Mathematics》2013,83(1):103-116
This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems. Techniques, challenges, and strategies of implementing an MPP focus were also reported. 相似文献
8.
The present study explored whether first and second order cognitive holding power perceived by children in mathematical classrooms, fluid intelligence, and mathematical achievement predicted their performance on standard problems, and especially realistic problems. A sample of 119 Chinese 4–6th graders were administered the word problem test, the cognitive holding power questionnaire, and Raven's standard progressive matrices. Results showed that: (1) children's fluid intelligence and general mathematical achievement significantly predicted their performance on both realistic and standard problems, however, second order cognitive holding power predicted their performance on realistic problems but not standard problems; (2) the relationship between first order cognitive holding power and children's correct answers to realistic problems was mediated by second order cognitive holding power; (3) children's performance on standard problems was significantly better than that on realistic problems, and children's performance on both types of problems improved with their grades. 相似文献
9.
Asha K. Jitendra Jon R. Star Michael Rodriguez Mary Lindell Fumio Someki 《Learning and Instruction》2011,21(6):731-745
This study investigated the effectiveness of an instructional program (schema-based instruction, SBI) designed to teach 7th graders how to comprehend and solve proportion problems involving ratios/rates, scale drawings, and percents. The SBI program emphasized the underlying mathematical structure of problems via schematic diagrams, focused on a 4-step procedure to support and monitor problem solving, and addressed the flexible use of alternative solution strategies based on the problem situation. Blocking by teacher at three middle schools, the authors randomly assigned the 21 classrooms to one of two conditions: SBI and control. Classroom teachers provided the instruction. Results of multilevel modeling used to test for treatment effects after accounting for pretests and other characteristics (gender, ethnicity) revealed the direct effects of SBI on mathematical problem solving at posttest. However, the improved problem solving skills were not maintained a month later when SBI was no longer in effect nor did the skills transfer to solving problems in new domain-level content. 相似文献
10.
Nerida F. Ellerton 《Educational Studies in Mathematics》2013,83(1):87-101
Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs are a good place to start the process of redesigning mathematics curricula so that school mathematics will pay more than lip service to problem posing. Data are presented and analyzed showing that teacher education students can recognize the need for problem posing both in their own programs and in school mathematics curricula. Examples of problems posed by teacher education students are presented and discussed. An active learning framework for interpreting the role of problem posing in mathematics classrooms is presented. 相似文献
11.
Anabela Abreu Malpique Deborah Pino-Pasternak Debora Valcan 《Reading and writing》2017,30(8):1789-1812
Accumulating evidence indicates handwriting automaticity is related to the development of effective writing skills. The present study examined the levels of handwriting automaticity of Australian children at the end of kindergarten and the amount and type of writing instruction they experienced before entering first grade. The current study involved 177 kindergarten children enrolled in 23 classrooms from seven government-funded primary schools in Western Australia. Individual child level data (e.g., handwriting automaticity and word-reading skills) were collected and teachers were asked to complete a survey assessing the amount of time and types of writing activities developed in their classrooms (e.g., teaching basic skills and teaching writing processes). Hierarchical linear models were conducted to examine total variance attributable to child and classroom levels. Results showed a total variance of approximately 20% in children’s handwriting automaticity attributable to differences among classrooms when gender and word-reading skills were controlled for. Large variability was noted in the amount and type of writing instruction reported by a subset of participating teachers. Handwriting automaticity was associated with the teaching of revising strategies but not with the teaching of handwriting. Implications for writing development and writing instruction are discussed. 相似文献
12.
《Teaching and Teacher Education》2002,18(6):739-758
Despite recent calls for teachers to promote and increase students’ communication and discussion in their classrooms, prospective teachers have limited opportunities to explore issues of classroom talk during their teacher preparation programs. In this study, prospective teachers attending a mathematics methods course were encouraged to attend to and investigate their developing teacherly talk through a letter writing exchange with school students. This paper reports on their tendency to respond to the correct answers with praise and to supply the answers when students reached an incorrect result. It explores the ways in which they began to interrogate and problematize such practices and to consider alternative forms of teacher responses to students’ right and wrong answers. Features of the course's field-related experience and the teacher educators’ interventions that promoted and supported the preservice teachers’ investigations are also discussed. 相似文献
13.
“Success stories,” i.e., cases in which mathematical problems posed in a controlled setting are perceived by the problem posers or other individuals as interesting, cognitively demanding, or surprising, are essential for understanding the nature of problem posing. This paper analyzes two success stories that occurred with individuals of different mathematical backgrounds and experience in the context of a problem-posing task known from past research as the Billiard Task. The analysis focuses on understanding the ways the participants develop their initial ideas into problems they evaluate as interesting ones. Three common traits were inferred from the participants' problem-posing actions, despite individual differences. First, the participants relied on particular sets of prototypical problems, but strived to make new problems not too similar to the prototypes. Second, exploration and problem solving were involved in posing the most interesting problems. Third, the participants' problem posing involved similar stages: warming-up, searching for an interesting mathematical phenomenon, hiding the problem-posing process in the problem's formulation, and reviewing. The paper concludes with remarks about possible implications of the findings for research and practice. 相似文献
14.
This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.
相似文献15.
16.
Kristen D. Ritchey 《Reading and writing》2008,21(1-2):27-47
This study examined the development of beginning writing skills in kindergarten and the relationship between early writing
skills and early reading skills. Sixty children were assessed on beginning writing skills (including letter writing, individual
sound spelling, and real and nonsense word spelling) and beginning reading skills (including letter name and letter sound
knowledge, global early reading ability, phonological awareness, and word reading). Children’s beginning writing abilities
are described, and they exhibited a range of proficiency in their ability to write letters, spell sounds, and spell real and
nonsense words. Global early reading proficiency, phonological awareness, and/or letter sound fluency predicted letter writing,
sound spelling, and spelling of real and nonsense words.
Appreciation is expressed to the participating students and teachers at Dwight D. Eisenhower School and to Margaret Boudreau
and Joan Foley for assistance in scoring students’ responses. 相似文献
17.
数学问题提出的实证研究述评 总被引：2，自引：0，他引：2
问题提出是指从一个数学情境中创造新问题或在解决问题过程中对问题的再阐述.在当今数学教育的课程改革中,问题提出成为许多数学家和数学教育家关注的焦点,许多国家都把培养学生的问题提出能力作为一项重要的课程目标.国内外众多学者对数学问题提出进行了大量的实证研究,主要集中在以下几个方面:问题提出与数学理解、问题提出与问题解决、问题提出的认知策略、问题提出的教学实验.这些研究的不足之处在于:研究内容较窄;缺乏认知方面的研究;研究方法比较单一;对学生差异性教学关注不够,等等. 相似文献
18.
Anthony Adams 《Technology, Pedagogy and Education》2013,22(2):179-188
Abstract This article considers how teachers working across three countries can create a collaborative writing environment in their classrooms. It reports on the first phase of a research programme conducted by university lecturers in the United Kingdom, Australia and Canada, investigating ways of developing teachers' expertise in the linking of information technology (IT) and pedagogy. It examines writing practices in the secondary classroom, in particular focusing on collaborative writing, and explores how this can be extended and developed through the use of IT. The research operates at three levels of collaboration: first, between the researchers involved; secondly, between teachers sharing their pedagogical expertise; and thirdly, between school students engaging in writing across the limits usually imposed by time and space. A fundamental hypothesis is that experienced and capable teachers of writing in different countries can extend their pedagogical skills through working together. Such collaboration between both teachers and school students has only recently become a possibility as a result of wider access to the Internet and the World Wide Web, on which it is eventually intended to publish results of the research, including examples of student work. 相似文献
19.
Irene Bloom 《Journal of Mathematics Teacher Education》2007,10(4-6):399-403
This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying mathematical structure of the problem. The results of this study revealed that with careful implementation, these tasks were effective for generating powerful mathematical thinking in preservice mathematics teachers, improving their problem solving, and generally enhancing the habits-of-mind exhibited by successful mathematicians (Carlson & Bloom, 2005). 相似文献
20.
Limin Chen Wim Van Dooren Qi Chen Lieven Verschaffel 《International Journal of Science and Mathematics Education》2011,9(4):919-948
In the present study, which is a part of a research project about realistic word problem solving and problem posing in Chinese
elementary schools, a problem solving and a problem posing test were administered to 128 pre-service and in-service elementary
school teachers from Tianjin City in China, wherein the teachers were asked to solve 3 contextually challenging division-with-remainder
(DWR) word problems and pose word problems according to 3 symbolic expressions. Afterwards, they were also given 2 questionnaires
wherein they had to evaluate 3 different pupil reactions to, respectively, 1 problem solving item and 1 problem posing item
about DWR. First, our results revealed that teachers behaved quite ‘realistically’ not only when solving and posing DWR problems
themselves but also when evaluating elementary school pupils’ DWR problem solving and problem posing performance. Second,
we found a correspondence between teachers’ own performance on the tests and their evaluations of pupils’ reactions. Third,
the present study provides some further insight into the role of one of the instructional factors that is generally considered
responsible for the strong and worldwide tendency among elementary school children to neglect real-world knowledge and realistic
considerations in their endeavours to solve and pose mathematical word problems, namely the teachers’ conceptions and beliefs
about this topic. 相似文献