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1.
M.C. O'Connor 《Educational Studies in Mathematics》2001,46(1-3):143-185
This case study examines two days of teacher-led large group discussion in a fifth grade about a mathematical question intended
to support student exploration of relationships among fraction and decimal representations and rational numbers. The purpose
of the analysis is to illuminate the teacher’s work in supporting student thinking through the use of a mathematical question
embedded in a position-driven discussion. The focus is an examination of the ways that the emergence of mathematical ideas
is partially shaped by complex interactions among the mathematical contents of the question, the inherent properties of the
discourse format and participant structure, and the available computational methods. The teacher’s work is conceptualized
in terms of actions and practices that coordinate these diverse tools, in constant response to students’ concurrent use of
them.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Martin Carlsen 《Educational Studies in Mathematics》2010,74(2):95-116
The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the
concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement
in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use
of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure,
four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating
of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of
five excerpts focused on the students’ social processes of knowledge objectification and the corresponding semiotic means,
i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation
of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the
classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating
the cultural tool of geometric series. From the excerpts, it is evident that the students’ participation changes throughout
their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming
and by establishing shared meanings for the concept and its theoretical components. 相似文献
3.
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
4.
There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article
reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in
an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students
from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working
on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical
ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’
mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity.
The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development
of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning. 相似文献
5.
We present a view of knowledge construction processes, focusing on partially correct constructs. Motivated by unexpected and
seemingly inconsistent quantitative data based on the written reports of students working on an elementary probability task,
we analyze in detail the knowledge construction processes of a representative student. We show how the nested epistemic actions
model for abstraction in context facilitates following the emergence of a learner’s partially correct constructs (PaCCs).
These PaCCs provide added insight into processes of knowledge construction. They are also used in order to analyze and explain
students’ thinking in situations where some of the students’ answers were unexpected in light of their earlier answers or
inconsistent with earlier answers. In particular, PaCCs are explanatory tools for correct answers based on (partially) faulty
knowledge and for wrong answers based on largely correct knowledge. 相似文献
6.
In this paper, we investigate university students’ interaction in an attempt to construct a model of elliptic geometry. In
order to study the several ways in which geometrical meaning is produced through context and practices, we introduce three
different types of use of geometrical concepts, namely as (1) elements of representation of spatial experience, (2) objects
of traditional school practice, and (3) constituents of an abstract mathematical theory. The analysis of students’ dialog
according to this framework reveals how students develop their ability to communicate mathematically and negotiate their meanings.
Students with a different use of geometrical concepts were able to interact and understand their peers. 相似文献
7.
This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation
points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically,
our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the
learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and
interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions
indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction
in context. 相似文献
8.
Eugenia Vomvoridi-Ivanovi? 《Journal of Mathematics Teacher Education》2012,15(1):53-66
This paper explores Mexican–American prospective teachers’ use of culture—defined as social practices and shared experiences—as
an instructional resource in mathematics. The setting is an after-school mathematics program for the children of Mexican heritage.
Qualitative analysis of the prospective teachers’ and children’s interactions reveals that the nature of the mathematical
activities affected how culture was used. When working on the “binder activities,” prospective teachers used culture only
in non-mathematical contexts. When working on the “recipes project,” however, culture was used as a resource in mathematical
contexts. Implications for the mathematics teacher preparation of Latinas/os are discussed. 相似文献
9.
This paper reports a part of a study on the construction of mathematical meanings in terms of development of semiotic systems
(gestures, speech in oral and written form, drawings) in a Vygotskian framework, where artefacts are used as tools of semiotic
mediation. It describes a teaching experiment on perspective drawing at primary school (fourth to fifth grade classes), starting
from a concrete experience with a Dürer’s glass to the interpretation of a new artefact. We analyse the long term process
of appropriation of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech
and drawings under the teacher’s guidance.
相似文献
| Michela MaschiettoEmail: |
10.
11.
Susanne Prediger 《Journal of Mathematics Teacher Education》2010,13(1):73-93
What kind of mathematical knowledge do prospective teachers need for teaching and for understanding student thinking? And
how can its construction be enhanced? This article contributes to the ongoing discussion on mathematics-for-teaching by investigating
the case of understanding students’ perspectives on equations and equalities and on meanings of the equal sign. It is shown
that diagnostic competence comprises didactically sensitive mathematical knowledge, especially about different meanings of
mathematical objects. The theoretical claims are substantiated by a report on a teacher education course, which draws on the
analysis of student thinking as an opportunity to construct didactically sensitive mathematical knowledge for teaching for
pre-service middle-school mathematics teachers. 相似文献
12.
Salvador Llinares Ana Isabel Roig 《International Journal of Science and Mathematics Education》2008,6(3):505-532
This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving
word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15–16
years old). Four levels of the development of constructing and using mathematical models were identified using a constant-comparative
methodology to analyse the student’s problem-solving processes. Identifying the general in the particular and using the particular
to endow the general with meaning were the key elements employed by students in the processes of construction and use of models
in the different situations. In addition, attention was paid to the difficulties that students had in using their mathematical
knowledge to solve these situations. Finally, implications are provided for drawing upon student’s use of mathematical models
as conceptual tools to support the development of mathematical competence from socio-cultural perspectives of learning. 相似文献
13.
It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching practices that can facilitate students’ visualization of mathematical objects. We present one illustrative episode that shows how drawings of geometrical figures have a powerful role in structuring and modifying the mathematical activity in the classroom. It was selected from a database that we have been building to investigate the learning of mathematics in public elementary schools in Brazil. The framework of Activity Theory helped in the characterization of the episode as a system of interconnected activities. We discuss the changes and transformations perceived in those activities; and we explore the idea of miniature cycles of learning actions to focus on the mathematical learning that is taking place. We describe the dynamics and the complexity of the ongoing activity in the calculation of areas; and, how drawings form a part, and show their influence, in it. We argue that part of this influence was associated with the contradiction between abstract mathematical ideas and their empirical representations, revealed by the tensions perceived in the activities analysed; and, simultaneously, that we could see as an impelling force for the learning of the rules and norms which regulate the use of visual representations in school mathematics. 相似文献
14.
Assessment for learning in Singapore: unpacking its meanings and identifying some areas for improvement 总被引：2，自引：1，他引：1
Kelvin Tan 《Educational Research for Policy and Practice》2011,10(2):91-103
This article examines the meanings and impact of ‘Assessment for Learning’ initiatives in schools against the back drop of
assessment reform in Singapore since 1997. It is argued that Assessment for Learning’ is understood in different ways, and
these different meanings do not always benefit students’ learning. The different meanings of ‘Assessment for Learning’ in
Singapore are unpacked, and three areas for improvement for Assessment for Learning are suggested—clear standards for effective
feedback practices, assessment for sustainable learning and assessment for integrating holistic learning. 相似文献
15.
Amy E. Ryken 《Journal of Mathematics Teacher Education》2009,12(5):347-364
This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in
relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning
skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation
task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial
tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures
created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving
beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings
suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices
by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking
and curriculum materials. 相似文献
16.
Judit N. Moschkovich 《Educational Studies in Mathematics》2004,55(1-3):49-80
This case study uses a sociocultural perspective and the concept of appropriation (Newman, Griffin and Cole, 1989; Rogoff, 1990) to describe how a student learned to work with linear functions. The analysis describes in detail the impact that interaction with a tutor had on a learner, how the learner appropriated goals, actions, perspectives, and meanings that are part of mathematical practices, and how the learner was active in transforming several of the goals that she appropriated. The paper describes how a learner appropriated two aspects of mathematical practices that are crucial for working with functions (Breidenbach, Dubinsky, Nichols and Hawks, 1992; Even, 1990; Moschkovich, Schoenfeld and Arcavi, 1993; Schwarz and Yerushalmy, 1992; Sfard, 1992): a perspective treating lines as objects and the action of connecting a line to its corresponding equation in the form y = mx + b. I use examples from the analysis of two tutoring sessions to illustrate how the tutor introduced three tasks (estimating y-intercepts, evaluating slopes, and exploring parameters) that reflect these two aspects of mathematical practices in this domain and describe how the student appropriated goals, actions, meanings, and perspectives for carrying out these tasks. I describe how appropriation functioned in terms of the focus of attention, the meaning for utterances, and the goals for these three tasks. I also examine how the learner did not merely repeat the goals the tutor introduced but actively transformed some of these goals. 相似文献
17.
Nesrin Cengiz Kate Kline Theresa J. Grant 《Journal of Mathematics Teacher Education》2011,14(5):355-374
Studies show that extending students’ mathematical thinking during whole-group discussions is a challenging undertaking. To
better understand what extending student thinking looks like and how teachers’ mathematical knowledge for teaching (MKT) supports
teachers in their efforts to extend student thinking, the teaching of six experienced elementary school teachers was explored.
During group discussions, all six teachers created opportunities for extending student thinking about important mathematical
ideas and solution methods. Findings on the nature of these episodes include identification of individual instructional actions
and the ways in which teachers’ MKT was connected to these actions. 相似文献
18.
Fredrik Sandberg 《Vocations and Learning》2010,3(2):99-115
This article critically appraises a process of recognising prior learning (RPL) using analytical tools from Habermas’ theory
of communicative action. The RPL process is part of an in-service training program for health care assistants where the goal
is to become a licensed practical nurse. Data about the RPL process were collected using interviews and observations. Through
appraising RPL as a social practice, it is held that the process progresses through a ‘caring ideology’. The caring ideology
is the foundation that makes it possible to build up health care assistants’ trust in teachers’ authority. In this process,
the teachers, by means of strategic actions, become the possessors of (the validity claim) truth. From this starting point,
the assistants’ prior experiences are strategically acknowledged in two ways: by affective comments ‘recognising’ their identity/personality
and by generating a grade in the courses for which their prior learning is being accredited. The findings show that the lifeworld
of these workers is assimilated and colonised through the RPL process and important issues such as power, gender and class
are not accounted for. These matters should not be left out in research on caring practices performed by women from low socio-economic
groups. These issues must be included if RPL processes are not merely assumed to systematically and uncritically reproduce
an existing normative discourse. Based on the RPL practice analysed here, it is proposed that a more reflexive, emancipatory
and communicative RPL process could play a central role in the development and enlightenment of health care assistants. 相似文献
19.
Gjalt T. Prins Astrid M. W. Bulte Jan H. Van Driel Albert Pilot 《Research in Science Education》2009,39(5):681-700
In science education students should come to understand the nature and significance of models. A promising strategy to achieve
this goal is using authentic modelling practices as contexts for meaningful learning of models and modelling. An authentic
practice is defined as professionals working with common motives and purposes, pertaining to a similar type of procedure and
applying relevant knowledge on the modelling issue they work on. In this study we evaluate whether the use of authentic practices
initiates adequate students’ involvement. This was done by investigating students’ interests, ownership, familiarity and complexity.
In addition, we evaluated students’ expressed modelling procedures in response to the modelling issues. We designed learning
tasks which were enacted by a focus group of students. Three primary data sources were used to collect data. Firstly, a group
discussion was organised in which students’ reflected on both authentic practices. Secondly, students filled in written questionnaires
containing items on affective and cognitive aspects. Thirdly, the realised modelling procedures by students were analysed.
The results show that students’ involvement was successfully initiated, evidenced by motivated students, willingness to continue
and the completeness and quality of the realised modelling procedures. The design of the learning tasks proved to be successful
in realising this involvement. The results obtained in this study support the strategy of using authentic modelling practices
as contexts for meaningful learning of models and modelling. 相似文献
20.
Mariana Montiel Miguel R. Wilhelmi Draga Vidakovic Iwan Elstak 《Educational Studies in Mathematics》2009,72(2):139-160
The main objective of this paper is to apply the onto-semiotic approach to analyze the mathematical concept of different coordinate
systems, as well as some situations and university students’ actions related to these coordinate systems. The identification
of objects that emerge from the mathematical activity and a first intent to describe an epistemic network that relates to
this activity were carried out. Multivariate calculus students’ responses to questions involving single and multivariate functions
in polar, cylindrical, and spherical coordinates were used to classify semiotic functions that relate the different mathematical
objects. 相似文献