共查询到20条相似文献，搜索用时 31 毫秒
1.
In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article
is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's
own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic
framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic
reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means
for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling,
symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning
and communicating in mathematics classrooms. 相似文献
2.
Melissa Rodd 《Educational Studies in Mathematics》2006,63(2):227-234
The theoretical frameworks presented in this Special Issue are appraised with respect to how they might enhance teachers’ or researchers’ work with ‘special needs’ students learning mathematics. The notion of ‘special needs’ is used in a broad sense, encompassing specific Special Educational Needs as well as students with low attainment. The analysis indicates that the different frameworks offer some distinctive methods for research or ideas for interventions, either individually or within multi-lens approaches. It also points to other perspectives, not represented here, that could be relevant for a growing understanding of issues of affect in mathematics education. 相似文献
3.
Teaching Mathematics in Multilingual Classrooms 总被引：1，自引：0，他引：1
In this paper we present the way in which language issues have become a relevant factor in research which aims to study the
socio-cultural aspects of mathematics education in classrooms with a high percentage of immigrant students. Our research on
language issues focuses on two aspects, namely the language as a social tool within the mathematics classroom and the language
as a vehicle in the construction of mathematical knowledge. We introduce our problem within this area and provide a rationale
for our research methodology, not avoiding its drawbacks,but rather giving examples of the kinds of difficulties we encountered.
The paper highlights the integrated nature of the social, cultural and linguistic aspects of mathematics teaching and learning,
and illustrates the fact that, even if the mathematical language can be considered universal, the language of ‘doing mathematics
within the classroom’ is far from being universal.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
We ground Cultural-Historical Activity Theory (CHAT) in studies of workplace practices from a mathematical point of view.
We draw on multiple case study visits by college students and teacher-researchers to workplaces. By asking questions that
‘open boxes’, we ‘outsiders and boundary-crossers’ sought to expose contradictions between College and work, induce breakdowns
and identify salient mathematics. Typically, we find that mathematical processes have been historically crystallised in ‘black
boxes’ shaped by workplace cultures: its instruments, rules and divisions of labour tending to disguise or hide mathematics.
These black boxes are of two kinds, signalling two key processes by which mathematics is put to work. The first involves automation,
when the work of mathematics is crystallised in instruments, tools and routines: this process tends to distribute and hide
mathematical work, but also evolves a distinct workplace ‘genre’ of mathematical practice. The second process involves sub-units
of the community being protected from mathematics by a division of labour supported by communal rules, norms and expectations.
These are often regulated by boundary objects that are the object of activity on one side of the boundary but serve as instruments
of activity on the other side. We explain contradictions between workplace and College practices in analyses of the contrasting
functions of the activity systems that structure them and that consequently provide for different genres and distributions
of mathematics, and finally draw inferences for better alignment of College programmes with the needs of students. 相似文献
5.
Barbara Jaworski 《Journal of Mathematics Teacher Education》2007,9(2):187-211
In this paper I address the challenge of developing theory in relation to the practices of mathematics teaching and its development.
I do this by exploring a notion of ‘teaching as learning in practice’ through overt use of ‘inquiry’ in mathematics learning,
mathematics teaching and the development of practices of teaching in communities involving teachers and educators. The roles
and goals of mathematics teachers and educators in such communities are both distinct and deeply intertwined. I see an aim
of inquiry in teaching to be the ‘critical alignment’ (Wenger, 1998) of teaching within the communities in which teaching
takes place. Inquiry ‘as a tool’ and inquiry ‘as a way of being’ are important concepts in reflexive developmental processes
in which inquiry practice leads to better understandings and development of theory. 相似文献
6.
7.
Current reform-driven mathematics documents stress the need for teachers to provide learning environments in which students
will be challenged to engage with mathematics concepts and extend their understandings in meaningful ways (e.g., National
Council of Teachers of Mathematics, 2000, Curriculum and evaluation standards for school mathematics. Reston, VA: The Council). The type of rich learning contexts that are envisaged by such reforms are predicated on a number
of factors, not the least of which is the quality of teachers’ experience and knowledge in the domain of mathematics. Although
the study of teacher knowledge has received considerable attention, there is less information about the teachers’ content
knowledge that impacts on classroom practice. Ball (2000, Journal of Teacher Education, 51(3), 241–247) suggested that teachers’ need to ‘deconstruct’ their content knowledge into more visible forms that would
help children make connections with their previous understandings and experiences. The documenting of teachers’ content knowledge
for teaching has received little attention in debates about teacher knowledge. In particular, there is limited information
about how we might go about systematically characterising the key dimensions of quality of teachers’ mathematics knowledge
for teaching and connections among these dimensions. In this paper we describe a framework for describing and analysing the
quality of teachers’ content knowledge for teaching in one area within the domain of geometry. An example of use of this framework
is then developed for the case of two teachers’ knowledge of the concept ‘square’. 相似文献
8.
In this paper, we argue that history might have a profound role to play for learning mathematics by providing a self-evident
(if not indispensable) strategy for revealing meta-discursive rules in mathematics and turning them into explicit objects
of reflection for students. Our argument is based on Sfard’s theory of Thinking as Communicating, combined with ideas from historiography of mathematics regarding a multiple perspective approach to the history of practices
of mathematics. We analyse two project reports from a cohort of history of mathematics projects performed by students at Roskilde
University. These project reports constitute the experiential and empirical basis for our claims. The project reports are
analysed with respect to students’ reflections about meta-discursive rules to illustrate how and in what sense history can
be used in mathematics education to facilitate the development of students’ meta-discursive rules of mathematical discourse. 相似文献
9.
Building on the papers in this special issue as well as on our own experience and research, we try to shed light on the construct
of example spaces and on how it can inform research and practice in the teaching and learning of mathematical concepts. Consistent with our
way of working, we delay definition until after appropriate reader experience has been brought to the surface and several
‘examples’ have been discussed. Of special interest is the notion of accessibility of examples: an individual’s access to example spaces depends on conditions and is a valuable window on a deep, personal,
situated structure. Through the notions of dimensions of possible variation and range of permissible change, we consider ways in which examples exemplify and how attention needs to be directed so as to emphasise examplehood (generality)
rather than particularity of mathematical objects. The paper ends with some remarks about example spaces in mathematics education
itself. 相似文献
10.
This paper explores the nature and source of mathematics homework and teachers’ and students’ perspectives about the role
of mathematics homework. The subjects of the study are three grade 8 mathematics teachers and 115 of their students. Data
from field notes, teacher interviews and student questionnaire are analysed using qualitative methods. The findings show that
all 3 teachers gave their students homework for instructional purposes to engage them in consolidating what they were taught
in class as well as prepare them for upcoming tests and examinations. The homework only involved paper and pencil, was compulsory,
homogenous for the whole class and meant for individual work. The main source of homework assignments was the textbook that
the students used for the study of mathematics at school. ‘Practice makes perfect’ appeared to be the underlying belief of
all 3 teachers when rationalising why they gave their students homework. From the perspective of the teachers, the role of
homework was mainly to hone skills and comprehend concepts, extend their ‘seatwork into out of class time’ and cultivate a
sense of responsibility. From the perspectives of the students, homework served 6 functions, namely improving/enhancing understanding
of mathematics concepts, revising/practising the topic taught, improving problem-solving skills, preparing for test/examination,
assessing understanding/learning from mistakes and extending mathematical knowledge. 相似文献
11.
Kim Beswick 《International Journal of Science and Mathematics Education》2011,9(2):367-390
The professional literature in mathematics education is replete with calls to use tasks that are ‘authentic’, ‘relevant’ and
related to ‘real life’ and the ‘real world’. Such activities are frequently advocated for their potential to motivate and
engage students, but evidence of their ability to do so is rarely presented. This paper examines evidence in relation to the
effectiveness of context problems in achieving their intended purposes and thereby contributing to enhanced student participation,
engagement and achievement in mathematics education. It is argued that context problems are not a panacea and that categorising
problems as contextualised or de-contextualised is less helpful than the consideration of more salient aspects of tasks that
impact on their effectiveness. Such aspects also relate to the purposes for and affordances and limitations of particular
tasks in relation to the purposes they are intended to serve, along with attention to the contexts in which students learn
mathematics. Examples of theoretical and empirical programs built on these considerations are reviewed in terms of their potential
to enhance participation, engagement and achievement in school mathematics. 相似文献
12.
13.
The purpose of this paper is to contribute to the debate about how to tackle the issue of ‘the teacher in the teaching/learning
process’, and to propose a methodology for analysing the teacher’s activity in the classroom, based on concepts used in the
fields of the didactics of mathematics as well as in cognitive ergonomics. This methodology studies the mathematical activity
the teacher organises for students during classroom sessions and the way he manages1 the relationship between students and mathematical tasks in two approaches: a didactical one [Robert, A., Recherches en Didactique
des Mathématiques 21(1/2), 2001, 7–56] and a psychological one [Rogalski, J., Recherches en Didactique des Mathématiques 23(3),
2003, 343–388]. Articulating the two perspectives permits a twofold analysis of the classroom session dynamics: the “cognitive
route” students are engaged in—through teacher’s decisions—and the mediation of the teacher for controlling students’ involvement
in the process of acquiring the mathematical concepts being taught. The authors present an example of this cross-analysis
of mathematics teachers’ activity, based on the observation of a lesson composed of exercises given to 10th grade students
in a French ‘ordinary’ classroom. Each author made an analysis from her viewpoint, the results are confronted and two types
of inferences are made: one on potential students’ learning and another on the freedom of action the teacher may have to modify
his activity. The paper also places this study in the context of previous contributions made by others in the same field. 相似文献
14.
Patricia S. Moyer 《Educational Studies in Mathematics》2001,47(2):175-197
Teachers often comment that using manipulatives to teach mathematics is ‘fun!’ Embedded in the word ‘fun’ are important notions
about how and why teachers use manipulatives in the teaching of mathematics. Over the course of one academic year, this study
examined 10 middle grades teachers’ uses of manipulatives for teaching mathematics using interviews and observations to explore
how and why the teachers used the manipulatives as they did. An examination of the participants’ statements and behaviors
indicated that using manipulatives was little more than a diversion in classrooms where teachers were not able to represent
mathematics concepts themselves. The teachers communicated that the manipulatives were fun, but not necessary, for teaching
and learning mathematics.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
Colleen Vale Alasdair McAndrew Siva Krishnan 《Journal of Mathematics Teacher Education》2011,14(3):193-212
A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior
secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’
reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical
structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing
teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support
their students’ present and future learning of mathematics. Further research is needed about professional learning approaches
and tasks that may enable teachers to imbed and develop awareness of structure in their practice. 相似文献
16.
Despina A. Stylianou 《Journal of Mathematics Teacher Education》2010,13(4):325-343
Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics.
The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives
on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle
school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have
developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation
as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral
role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than
as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications
for mathematics teacher education, prospective and practicing, are discussed. 相似文献
17.
Creativity is viewed in different ways in different disciplines: in education it is called ‘innovation’, in business it is
‘entrepreneurship’, in mathematics it is often equated with ‘problem solving’, and in music it is ‘performance’ or ‘composition’.
A creative product in different domains is measured against the norms of that domain, with its own rules, approaches and conceptions
of creativity. 相似文献
18.
Sigmund Ongstad 《Educational Studies in Mathematics》2006,61(1-2):247-277
The article investigates in the first part critically dyadic and essentialist understanding of signs and utterances in mathematics
and mathematics education as opposed to a triadic view. However even Peircean semiotics, giving priority to triadic, dynamic
sign may face challenges, such as explaining the sign as a pragmatic act and how signs are related to context. To meet these
and other hurdles an explicit communicational, pragmatic and triadic view, found in parts of the works of Bühler, Bakhtin,
Habermas, and Halliday, is developed. Two basic principles are combined and established in a theoretical framework. Firstly,
whenever uttering, there will exist in any semiotic sign system, dynamic reciprocity and simultaneity between expressing through
form, referring to content, and addressing as an act. Secondly, meaning will be created by the dynamics between given and
new in utterances and between utterances and contextual genres. The latter principle explains how meaning merge in communication
dynamically and create the basis for a discursive understanding of semiosis and hence even learning at large. The second part
exemplifies each of the three main aspects and the dynamics of utterance and genre and given and new by excerpts from a textbook
in mathematics education. The concept ‘positioning’, in use for operationalisation, is explained in relation to main principles
of the framework. The article ends focusing crucial implications for validation when moving from a dyadic to a triadic understanding
of mathematics and mathematics education. 相似文献
19.
Cynthia Nicol 《Educational Studies in Mathematics》2002,50(3):289-309
The integration of academic and vocational subject matter is offered in response to efforts to make the study of mathematics
meaningful and engaging for all students,as well as aid in the preparation of a mathematically literate workforce. Yet,teachers
often come to mathematics education with more ‘pure’ than ‘applied’ backgrounds making it difficult for them to draw upon
their own experiences to make subject matter meaningful. This paper analyses prospective teachers' opportunities to connect
subject matter with workplace contexts. It examines the degree of importance prospective teachers place on workplace connections
and the ways in which they incorporate these connections in classroom lesson plans. Results suggest that given opportunities
to visit workplace sites, it is not a trivial task for prospective teachers to: 1) make the mathematics in work explicit,
and 2) keep the mathematics contextualized when designing activities and problems for students. These results have implications
for teacher education and the support prospective teachers require in building networks connecting mathematics, pedagogy,and
work.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
The Practices of Mathematicians: What do They Tell us About Coming to Know Mathematics? 总被引：1，自引：0，他引：1
Leone Burton 《Educational Studies in Mathematics》1998,37(2):121-143
In 1997, an interview-based study of 70 research mathematicians was undertaken with a focus on how they ‘come to know’ mathematics,
i.e. their epistemologies. In this paper, I discuss how these mathematicians understand their practices, locating them in
the communities of which they claim membership, identifying the style which dominates their organisation of research and looking
at their lived contradictions. I examine how they talk about ‘knowing’ mathematics, the metaphors on which they draw, the
empiricist connections central to the work of the applied mathematicians and statisticians, and the importance of connectivities
to the construction of their mathematical Big Picture. I compare the stories of these research mathematicians with practices
in mathematics classrooms and conclude with an appeal for teachers to pay attention to the practices of research mathematicians
and their implications for coming to know mathematics.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献