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This paper is methodologically based, addressing the study of mathematics teaching by linking micro- and macro-perspectives.
Considering teaching as activity, it uses Activity Theory and, in particular, the Expanded Mediational Triangle (EMT) to consider the role of the broader social frame in which classroom teaching is situated. Theoretical and methodological
approaches are illustrated through episodes from a study of the mathematics teaching and learning in a Year-10 class in a
UK secondary school where students were considered as “lower achievers” in their year group. We show how a number of questions
about mathematics teaching and learning emerging from microanalysis were investigated by the use of the EMT. This framework
provided a way to address complexity in the activity of teaching and its development based on recognition of central social
factors in mathematics teaching–learning. 相似文献
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Students’ participation in whole-class discourse is an important feature of classroom learning. Within socio-cultural research, two explanations for this connection can be emphasised: students’ engagement and teacher-student verbal interaction. We suggest a video-based coding scheme that can be specifically connected with each theoretical strand by distinguishing between student-guided and teacher-guided participation. The aim is to explore the conditions (student characteristics) and consequences (student learning) of both types of classroom participation. The results of two video studies with standardised pre- and post-assessments – one in secondary school mathematics (932 students, 40 classes) and one in primary school science (681 students, 35 classes) – emphasise both the relevance of students’ prior knowledge for participation in whole-class discourse and the role of student-guided participation in learning. 相似文献
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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
5.
Bharath Sriraman 《Interchange》2006,37(1-2):151-178
This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use
of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly
diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the
Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich
mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual
counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse.
In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting
problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos.
The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher
education are discussed. 相似文献
6.
Elizabeth de Freitas 《Teaching Education》2013,24(1):43-55
This paper reports on an action research project designed to explore the complexities of pre‐service mathematics teacher resistance to social justice issues. Research on equity and mathematics education has indicated that such resistance seems particularly strong for mathematics teachers. Twelve pre‐service mathematics teachers participated in a course‐based research project to explore this issue. Participants completed a classroom discourse analysis and a self‐study narrative as part of their secondary mathematics methods course. The findings suggest that attention to issues of identity construction within school mathematics can be successfully embedded in methods courses in order to better prepare mathematics teachers to teach for diversity. 相似文献
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In our ongoing qualitative classroom research, we adopt a sociocultural perspective to investigate discourse, and its role in how children and teachers make meaning of mathematics in a fifth grade inquiry classroom. Our theoretical perspective draws primarily on Vygotsky (1978, 1986) and Bakhtin (1981, 1986) each of whom examines how social forms of meaning influence individual cognition. The episode described in this paper examines the process whereby individual and group developmental trajectories are constructed, and allows us to explore the relationship between discourse and knowing. We combine a longitudinal design with a case study approach to focus on the collaborative mathematical problem solving. We use video capture to help us listen to children's discussions in classroom activities and small group interactions. Our analysis of the verbal data recorded on video identifies patterns of interaction, development and change in participants' use of mathematical language and concepts, and their evolving understanding, through discussion and argument, of an algebraic expression constructed by one of the children. The findings lead us to argue for i) a more generative view of the zone of proximal development as a site of learning and of identity formation, ii) an expanded view of the role of the teacher in inquiry classrooms, and iii) an appreciation for the valuable roles difference and resistance play in knowledge building. 相似文献
8.
Melissa L. Shirley Karen E. Irving Vehbi A. Sanalan Stephen J. Pape Douglas T. Owens 《International Journal of Science and Mathematics Education》2011,9(2):459-481
Connected classroom technology (CCT) is a member of a broad class of interactive assessment devices that facilitate communication
between students and teachers and allow for the rapid aggregation and display of student learning data. Technology innovations
such as CCT have been demonstrated to positively impact student achievement when integrated into a variety of classroom contexts.
However, teachers are unlikely to implement a new instructional practice unless they perceive the practical value of the reform.
Practicality consists of three constructs: congruence with teacher’s values and practice; instrumentality—compatibility with the existing school structures; and cost/benefits—whether the reward is worth the effort. This study uses practicality as a framework for understanding CCT implementation in
secondary classrooms. The experiences of three science teachers in their first year implementing CCT are compared with matched-pair
mathematics teachers. Findings suggest that despite some differences in specific uses and purposes for CCT, the integration
of CCT into regular classroom practice is quite similar in mathematics and science classrooms. These findings highlight important
considerations for the implementation of educational technology. 相似文献
9.
Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn. 相似文献
10.
Lorraine M. Males Samuel Otten Beth A. Herbel-Eisenmann 《Journal of Mathematics Teacher Education》2010,13(6):459-471
This article examines mathematics teacher collegiality by focusing on both the ways in which teachers interacted as critical
colleagues in a long-term professional development project and the evolving role of the teacher–educator–researcher as the
facilitator of this project. The professional development collaboration comprised two phases: one focused on reading classroom
discourse literature and one focused on supporting each other through cycles of action research related to mathematics classroom
discourse. Lord’s (1994) critical colleagueship framework is used to examine how a study group of middle-grades (ages 11–16) mathematics teacher–researchers
took (or did not take) a more critical stance toward their own teaching practice and that of their colleagues. We found that
challenging interactions were related to instances in which the teachers interacted as critical colleagues and were marked
by particular features including the use of particular words and the use of personal experience as a form of evidence. We
present the ways in which we came to understand what it might look like to scrutinize one’s practice and findings related
to the development of this type of collegiality across the two different phases of this project. We end with a section in
which the teacher–educator–researcher who facilitated the professional development project reflects on the ways in which the
analysis caused her to reconsider both the nature of argumentation in mathematics study group settings and what implications
this has with respect to her own practice as a facilitator. 相似文献
11.
Konstantinos A. Sdrolias Triandafillos A. Triandafillidis 《Educational Studies in Mathematics》2008,67(2):159-169
Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often
proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children’s transition to secondary
school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary
school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict
school mathematics as a “chain” of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies
about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts
taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean
view of semiotics in an attempt to conceptualize students’ rushed introduction to rigor in justifying mathematical statements
in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities
and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether
a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels. 相似文献
12.
Anita A. Wager 《Journal of Mathematics Teacher Education》2012,15(1):9-23
Connecting students’ cultural and community mathematical practices to school mathematics is a critical issue in mathematics
education. The goal of the study was to identify how teachers incorporate children’s cultural and out-of-school mathematics
in instruction. Four related practices were identified, and three drew on children’s cultural or out-of-school experiences:
(a) using these experiences as contexts for problems, (b) linking these experiences to school mathematics, and (c) identifying
embedded mathematical practices prominent in these experiences. A fourth category, teacher initiated situated settings, focused
on shared experiences using the classroom as a site of culture. Findings suggest that these practices represent varying levels
of complexity and that use of this framework might support teachers in better relating students’ cultural and out-of-school
experiences to mathematics. 相似文献
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Anderson Hassell Norton Andrea McCloskey 《Journal of Mathematics Teacher Education》2008,11(4):285-305
The challenge that we address concerns teachers’ shifts toward student-centered instruction. We report on a yearlong professional
development study in which two United States elementary school teachers engaged in a teaching experiment, as described by
Steffe and Thompson (in: Lesh and Kelly (eds) Research on design in mathematics and science education, 2000). The teaching
experiment involved close mathematical interactions with a pair of students after school, in the context of solving fractions
tasks. By conducting a teaching experiment, we anticipated that each teacher would have more opportunity to develop insight
into students’ mathematics. We also anticipated that these insights would influence the teachers’ classroom practice, even
without explicit support for such a shift. Indeed, the teachers found that they began asking more probing questions of their
students and spending more time listening to students’ explanations, but shifts to classroom practice were limited by constraining
factors such an inflexible curriculum. 相似文献
15.
Maxwell Peprah Opoku Richard Tawiah Elvis Agyei-Okyere Shaibu Osman Sally Adwoa Afriyie 《International Journal of Disability, Development & Education》2019,66(2):218-232
ABSTRACTThe recent development of making secondary school education free in Ghana has raised concerns about the level of preparedness of teachers to teach students with diverse needs in one classroom. Significantly, mathematics is one of the core areas that the Ghanaian government has prioritised, and it has institutionalised mechanisms to encourage participation by many students. Accordingly, this qualitative study aimed to document the level of preparedness of mathematics teachers to support the teaching of students with Down syndrome in secondary school classrooms. Twenty-seven mathematics teachers from 14 schools, made up of 18 males and nine females, took part in the study. We found that participants were in favour of implementation of inclusive education. However, regarding the prospect of teaching students with Down syndrome, most of the participants thought that the regular secondary school classroom is not a suitable environment for these students to access education, especially due to a number of challenges. The need for the government to support schools with appropriate teaching materials and facilities is discussed extensively. 相似文献
16.
Characterization of an Ordinary Teaching Practice with the Help of the Theory of Didactic Situations
In this paper, we use the theory of didactic situations to characterize a mathematics teaching practice, currently used in
secondary schools in France, which we have called interactive synthesis discussion. We have studied this practice in ordinary classes, i.e. classes where the researcher intervenes neither in the preparation
nor in the management of the lessons. We have looked at the didactic situations the teacher chooses, and how he manages his
teaching project, the students’ work in the classroom and at home, and classroom interactions. We present two case studies
of experienced teachers, one in grade 8, and the other in grade 10. 相似文献
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The purpose of this study was to explore the potential value of online video case discussions among preservice and inservice teachers, and the video case teacher as a tool for the professional development of teachers. Participants included a total of 26 preservice and inservice mathematics teachers and a veteran teacher who appeared on the video case. Using content analysis techniques, we provided a thematic analysis of the teacher discourse and demonstrated the exchanges between the participating teachers and video case teacher. We also assessed the overall effectiveness of our online forum set up for the professional development of teachers. Results indicated that participant teachers were able to make theory–practice connections by articulating specific frameworks that guided our study. The inclusion of the video case teacher was beneficial for the other teachers in several ways. We contend that online forum discussions of video cases in which collective engagement of preservice and inservice teachers, and the case teacher have a great potential to support teacher professional development. 相似文献
18.
This paper addresses the accumulating knowledge of prospective teachers of secondary school mathematics and their acquired
proficiency during the course “Psychological aspects of mathematics education,” in which we discussed theoretical models including
the intuitive rules theory. Participants’ performances are examined by means of an extensive report of two episodes, one during
the course and one afterwards. These episodes marked different stages in the prospective teachers’ analysis of their own and
of students’ solutions, which led me to conclude that exposing prospective teachers to the intuitive rules theory is important,
since their familiarity with the theory provided them with a tool to reflect on their own mathematical solutions (subject
matter knowledge; SMK), on others’ solutions, and on the tasks (pedagogical content knowledge; PCK). 相似文献
19.
We investigate experienced high school geometry teachers’ perspectives on “authentic mathematics” and the much-criticized
two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher
allows a student doing a proof to assume a statement is true without immediately justifying it, provided he return to complete
the argument later. Prompted by this episode, the teachers in our focus groups revealed two apparently contradictory dispositions
regarding the use of the two-column proof form in the classroom. For some, the two-column form is understood to prohibit a move like that shown in the video. But for others, the form is seen as a resource enabling such a move. These contradictory responses are warranted in competing but complementary notions, grounded on the corpus of
teacher responses, that teachers hold about the nature of authentic mathematical activity when proving.
相似文献
| Patricio HerbstEmail: |
20.
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