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1.
Colin Foster 《Curriculum Journal》2013,24(4):563-585
Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite-sized learning objectives and a tendency for mathematics teachers to path-smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment-dominated curriculum and partly to a systemic de-professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non-specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non-routine mathematical tasks. Some principles for achieving this are outlined and some examples are given. 相似文献
2.
32名小学数学教师与这些教师所教班级的1691名学生参与了本研究。两个测量工具评价了教师的数学学科知识与学科教学知识,对教师的55节数学课进行了录像,并按照学习任务的认知水平与课堂对话的特点进行了编码,同时测查了学生的期末数学学习成绩。多水平分析结果表明:教师的学科教学知识、课堂学习任务的认知水平、课堂对话中教师提问问题的类型与对话的权威来源对学生的数学成绩具有显著的预测作用;而教师的学科知识对学生数学成绩的影响未达到显著性水平。 相似文献
3.
Kooloos Chris Oolbekkink-Marchand Helma van Boven Saskia Kaenders Rainer Heckman Gert 《Journal of Mathematics Teacher Education》2022,25(4):453-477
Often, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.
相似文献4.
Maria L. Blanton 《Journal of Mathematics Teacher Education》2002,5(2):117-152
This investigation uses classroom discoursein an undergraduate mathematics course tochallenge pre-service secondary mathematicsteachers' notions about mathematical discourse,what it might resemble in the classroom, andhow its various forms can be cultivated byclassroom teachers. The research setting was arequired geometry course taught by the author.Eleven pre-service mathematics teachers intheir junior or senior year of an undergraduate program participated. Results indicated participants made a transition toward an image of discourse as an active process by which students use the collective knowledge of their peers to build mathematical understanding and developed in their ability to participate in such discourse.This awareness, along with participants'analyses of their own habits of discourse asclassroom teachers, prompted shifts in theirprojected image of the role of discourse intheir future practices of teaching. Resultssuggested further that the undergraduatemathematics classroom (as opposed to themethods classroom) offers a powerful and uniqueforum in which pre-service secondary teacherscan practice, articulate, and collectivelyreflect on reform-minded ways of teaching. 相似文献
5.
The study presented in this article investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional
discourse while observing and analysing young students mathematical interaction followed by teacher’s intervention. The teachers’
joint professional discourse is about a combined learning and talking between two students before an intervention by their
teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting
2). The joint professional teachers’ discourse constitutes setting 3. This combination of social settings 1 and 2 is taken
as an opportunity for mathematics teachers’ professionalisation process when interpreting the students’ mathematical interactions
in a more and more professional and sensible way. The epistemological analysis of mathematical sign-systems in communication
and interaction in these three settings gives evidence of different types of mathematical talk, which are explained depending
on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented
and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher
and by the expectations of the students.
相似文献
| Heinz SteinbringEmail: |
6.
Katherine E. Lewis 《学习科学杂志》2017,26(2):320-365
Students with disabilities present a unique instructional design challenge. These students often have qualitatively different ways of processing information, meaning that standard instructional approaches may not be effective. In this study I present a case study of a student with a mathematical learning disability for whom standard instruction on fractions had been ineffective. With regard to theory, I draw on Lev Vygotsky’s framing of disability and then use Anna Sfard’s conceptualization of mathematics as a discourse to design a fraction re-mediation that provided a bridge from the student’s discourse to the canonical mathematics discourse. This bridging discourse was used in 5 videotaped re-mediation sessions with the case study student. A fine-grained analysis of the re-mediation sessions traced the ways in which the student’s discourse shifted over time, which enabled her to solve problems she had previously been unable to solve. This study provides a proof of concept for reconceptualizing remediation and illustrates the potential utility of a bridging discourse to help students who have a history of failure gain access to the canonical mathematics discourse and content. 相似文献
7.
This study is grounded in the theoretical position that solving problems in different ways creates mathematical connections
when learning and teaching mathematics. It acknowledges the central role teachers play in providing students with learning
opportunities, and it is based on the empirical finding that mathematics teachers are reluctant to solve problems in different
ways in the classroom. In this paper we address the contradiction between theory-based recommendations and school mathematics
practice. Based on analysis of individual interviews and two group meetings with 12 Israeli secondary school mathematics teachers,
we demonstrate that in the context of multiple-solution connecting tasks this discrepancy is caused by the situated nature
of the teachers’ knowledge. We also reveal the complex relationship between different types of teacher knowledge and argue
the significance of developing a common language between members of the mathematics education community, including teacher
educators and researchers.
The names of the teachers have been changed to protect their privacy. 相似文献
8.
Bert van Oers 《Educational Studies in Mathematics》2001,46(1-3):59-85
A review of literature shows that during the history of mathematics education at school the answer of what counts as ‘real mathematics’ varies. An argument will be given here that defines as ‘real mathematics’ any activity of participating in a mathematical practice. The acknowledgement of the discursive nature of school practices requires an in-depth analysis of the notion of classroom discourse. For a further analysis of this problem Bakhtin’s notion of speech genre is used. The genre particularly functions as a means for the interlocutors for evaluating utterances as a legitimate part of an ongoing mathematical discourse. The notion of speech genre brings a cultural historical dimension in the discourse that is supposed to be acted out by the teacher who demonstrates the tools, rules, and norms that are passed on by a mathematical community. This has several consequences for the role of the teacher. His or her mathematical attitude acts out tendencies emerging from the history of the mathematical community (like systemacy, non-contradiction etc.) that subsequently can be imitated and appropriated by pupils in a discourse. Mathematical attitude is the link between the cultural historical dimension of mathematical practices and individual mathematical thinking. 相似文献
9.
Rebecca McGraw Kathleen Lynch Yusuf Koc Ayfer Budak Catherine A. Brown 《Journal of Mathematics Teacher Education》2007,10(2):95-121
In this study, we consider the potential of multimedia cases as tools for teacher professional development. Specifically,
we examined online and face-to-face discussions that occurred within groups composed of pre-service mathematics teachers,
in-service mathematics teachers, mathematicians, and mathematics teacher educators. Discussions within these heterogeneous
groups tended to focus on issues of classroom implementation of the tasks shown in the multimedia case. Secondary foci of
discussion included task characteristics and appropriateness of tasks for engaging students in thinking about mathematical
concepts and processes. Analysis of contributions to discussions across group member type revealed differences that suggest
that the variety of backgrounds and experiences of group members can blend in ways that support rich and critical discussions
of mathematics, teaching, and learning. 相似文献
10.
《Australian Journal of Learning Difficulties》2013,18(2):171-183
This article focuses on the cognitive factors that impact on students in the middle school years experiencing learning difficulties in basic mathematics. It begins with a review of selected literature providing information about the learning difficulties in mathematics. Focus then shifts to an implementation of the QuickSmart intervention. QuickSmart is a basic academic skills intervention designed for persistently low-achieving middle-years' students. In this small-scale study, 12 middle school students experiencing learning difficulties participated in the QuickSmart mathematics program. Comparisons are made between the mathematics progress of the intervention group and eight average-achieving peers. The results indicate that on measures of response speed and accuracy QuickSmart participant students were able to narrow the gap between their performance and that of their average-achieving peers. Further, on standardized tests of more general mathematical knowledge, participant students improved significantly from pre-test to post-test. Implications are drawn regarding the importance of interventions that emphasize automaticity in basic mathematics for middle years students with learning difficulties. 相似文献
11.
Gladys Sterenberg 《Journal of Mathematics Teacher Education》2008,11(2):89-105
Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance.
An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring
these images is through mathematical metaphors. As metaphors focus on similarities, they can be used to express already-held
perceptions about the nature of mathematics. In addition to providing a way of talking about current views of mathematics,
the analogous dimensions of metaphors can prompt new ways of thinking about these images. In this article, I consider the
use of metaphors as a strategy for explicating elementary teachers’ views of mathematics. I claim that the investigation of
metaphors of mathematics helped create a shared communicative space and enhanced the quality of the discussion with the teachers.
In particular, our exploration of the metaphor mathematics is a language encouraged a consideration of the humanistic dimensions of mathematics and contributed to a varied re-imaging of mathematics. 相似文献
12.
论数学教师课堂话语的本质特点 总被引：1，自引：0，他引：1
教师课堂话语是教师向学生传达信息的主要方式,也是教师调控学生课堂行为的重要手段,同时也为学生数学思维的发展起着关键的作用.数学教师课堂话语主要是指数学教师在课堂教学中,根据其知识储备和相关生活经历,结合学生在知识储备和相关生活经历等方面的特点,对数学教材话语进行双向解读的结果.包括:(1)自然性话语.具有通俗易懂、贴近生活等特点;(2)专用文字话语.具有层次性、逻辑性等特点;(3)专用符号话语.具有高度的概括性和精确性等特点. 相似文献
13.
Cecile M. Badenhorst 《Journal of Further & Higher Education》2019,43(2):263-275
Literature reviews are a genre that many graduate students do not fully understand and find difficult to write. While the genre, language and rhetorical moves of literature reviews are widely researched, less research focuses on citation use in literature reviews. Teaching students ‘how-to’ write the literature review through explicit genre awareness is not enough. What is needed, is a focus on the discursive nature of citations since citations are a core ingredient in literature reviews. The complexity of citing, referencing and using sources is difficult to teach in university classrooms, especially in courses that focus on content knowledge. When it is taught, it is often imparted to students as conventions with particular organisational features around citation styles. Or it is taught within the discourse of morality and academic dishonesty that surrounds plagiarism. What is lacking is a pedagogy that relates citing to the more complex discursive practices that are implicit and deeply embedded in particular time-bound contexts. The purpose of this research was to explore citation patterns in 23 draft and final masters’ student literature review papers to better understand the ways in which students use sources in literature reviews with the aim of informing pedagogy. Findings indicate that the concept of intertextuality, specifically, transgressive intertextuality, intertextual engagement and discursive intertextuality can help with the teaching and learning of literature reviews and citation use. 相似文献
14.
15.
小学数学双语教学是以外语为语言背景进行的教与学的交流,其重点在于解决数学问题的同时解决语言问题。因此,教师在处理教学交流时应注意不同交流方式中教学语言的选择,其中,常规性交流适宜用纯英语进行,相关性交流尽量要使用外语,程序性交流应该最大程度地使用外语,构思性交流适宜从使用母语向使用外语逐步过渡,同时,小学双语数学教学要注重学生对语言与数学结合的思维习惯的培养。 相似文献
16.
Andrea Raiker 《Cambridge Journal of Education》2002,32(1):45-60
Teachers and learners use spoken language in the three part mathematics lesson advocated by the National Numeracy Strategy (NNS). This document recognises the importance of language by emphasising 'the correct use of mathematical vocabulary' in the raising of standards. Research into the use of vocabulary in science suggests that the use of scientific words does not necessarily demonstrate conceptual understanding. Pupils and teachers appear to ascribe different meanings to scientific words because of their relative positions on the novice/expert continuum. To explore whether mathematical words could cause similar problems, data collected from six groups of teachers and learners was subjected to discourse analysis to provide evidence of how spoken language was used and how meaning and understanding were achieved. The implications of the findings on the use of language by both teachers and learners in the NNS mathematics lesson, including vital areas for reflection by teachers, are fully considered. 相似文献
17.
Mary Macken-Horarik 《Changing English: An International Journal of English Teaching》2012,19(2):179-194
At the dawn of a national curriculum for English in Australia, grammar has appeared without any serious interrogation of the terms of its re-entry and against ambiguous evidence about its value for teaching writing. What kinds of knowledge about language do teachers need in rhetorically productive teaching? This article investigates the potential of Halliday’s notion of grammatics for understanding students’ writing as acts of meaning in context. Drawing on systemic-functional linguistics, I show how teachers can assess writing achievement using ‘big picture’ tools like genre, register and ‘small picture’ tools like Expansion. I apply these tools to two student texts that call for attention to creative uses of language and to excursions and to difficulties with logic and coherence. The paper concludes that a ‘good enough’ grammatics will enable teachers to recognize playful developments in students’ texts and also to foster their control of literate discourse. 相似文献
18.
A discipline apart: the challenges of ‘Fostering a Community of Learners’ in a mathematics classroom
This is the fifth in a series that examines the challenges that teachers in different domains face as they attempt to implement the pedagogical reform ‘Fostering a Community of Learners’ (FCL). Here we focus on the relationship between FCL and the teaching of mathematics. We argue that it is possible to teach mathematics through the FCL pedagogy, but that doing so requires some rethinking of both mathematics instruction and FCL. In particular, we describe three shifts that aided a teacher's implementation of FCL pedagogy with mathematics: the teacher developed a new perspective on mathematics that emphasized the importance of having students learn both mathematical concepts and processes; the teacher developed a new understanding of the role of the teacher in mathematics‐education reform; and the teacher modified his understanding of FCL, coming to believe that a discourse community could be the basis for FCL pedagogy in a mathematics classroom. 相似文献
19.
Núria Planas 《Educational Studies in Mathematics》2014,87(1):51-66
The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages—Spanish and Catalan—to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics classrooms in three public secondary schools were video-recorded and transcribed. In the presentation of findings, I discuss three language practices that emerged from the analyses of several classroom instances as follows: (1) caution with mathematical vocabulary, (2) invention of terms, and (3) word-for-word translation. One example is chosen to represent each practice and some of its situated effects. The first two examples support the view that the experience of language difficulties, either real or presumed, contributes to generating opportunities that may be beneficial to mathematics learning. The third example, where the focus on the mathematics is hindered, points to a contrasting finding. Unlike other studies in the field, which have reported the difficulties and obstacles that arise in learning and teaching due to bilingualism in the classroom, I propose a change of focus through the conceptualization of language as a potential for thinking and doing, and particularly for learning and teaching mathematics. 相似文献
20.
Russell Cross 《Teachers and Teaching》2013,19(4):467-478
The current educational context in many English speaking countries is one where literacy is understood to be essentially monolingual in orientation; that is, an understanding of literacy around a single common language, with the emphasis on identifying universal, normative ‘standards’ and ‘benchmarks’, such as the National Assessment Program-Literacy and Numeracy in Australia, the Primary National Strategy in the United Kingdom, and No Child Left Behind in the United States. This paper aims to problematise such assumptions by examining how teachers, themselves, understand “teaching literacy” when their students come to the teaching/learning relationship with a first language other than English. With a focus on teachers working with bilingual and multilingual students in their early stages of acquiring English as a second language (ESL), the study thus acknowledges the increasingly diverse sociolinguistic profile of students in Australia and elsewhere in the varying degrees of communicative competence they bring to the mainstream in their use of ESL. Moreover, it draws on ESL teacher knowledge and expertise which has been identified as increasingly marginalised within mainstream educational discourse. Through case studies of three ESL teachers in the middle years, salient themes around the interrelated notions of literacy as learning, language for literacy and language as literacy were identified with respect to the literacy needs of second language learners. 相似文献