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1.
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical modeling is treated more as a venue for learning other mathematics than as an instructional goal in its own right. From this perspective, we are compelled to ask how learning of mathematics beyond modeling may occur as students generate and validate mathematical models. We consider a diagrammatic model of mathematical modeling as a process that allows us to identify how mathematical understandings may develop or surface while learners engage in modeling tasks. Through examples from prospective teachers' mathematical modeling work, we illustrate how our diagrammatic model serves as a tool to unpack the intricacies of students’ mathematical experience while engaging in modeling tasks. 相似文献
2.
In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring
example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts.
The data we then present provides evidence of the possibility of learning new concepts through a symbiosis of induction and
abduction from experience and deduction from the relationships generated in exemplification. In other words, experience can
be organised in such a way that shifts of understanding take place as a result of learners’ own actions. Actions, in this
context, include mental acts of organisational reflection.
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| Anne WatsonEmail: |
3.
As teacher-educators, we designed and implemented a small study that mapped teacher-education students' understandings of
their own identities and how they made sense of ethnicity and class differences among their secondary students while on teaching
rounds. While we didn't set out to ‘teach’ our research participants, it was during the analysis of data from the research
project, that we began to realise the potential of research to create opportunities for learning. In this paper we speculate
on the ‘conditions’ of knowledge production and suggest that the dialogic nature of interviews and focus group discussions
can offer pedagogical spaces for learning. Research designs that incorporate opportunities for participants to re-tell narratives
over periods of time, may position participants as experts in knowledge production and may reposition them and researchers
in more equitable power relations. We present an example of one participant's narrative together with our interpretations
to explore how research potentially offers ‘evidence’ of learning. While this is tentative only, we suggest there is a need
to create spaces for pedagogy in the design and execution of educational research. 相似文献
4.
Claire Margolinas Lalina Coulange Annie Bessot 《Educational Studies in Mathematics》2005,59(1-3):205-234
Our research is concerned with teacher’s knowledge, and especially with teacher’s processes of learning, in the classroom,
from observing and interacting with students’ work. In the first part of the paper, we outline the theoretical framework of
our study and distinguish it from some other perspectives. We argue for the importance of distinguishing a kind of teacher’s
knowledge, which we call didactic knowledge. In this paper, we concentrate on a subcategory of this knowledge, namely observational didactic knowledge, which grows from teacher’s observation and reflection upon students’ mathematical activity in the classroom. In modeling
the processes of evolution of this particular knowledge in teachers, we are inspired, among others, by some general aspects
of the theory of didactic situations. In the second part of the paper, the model is applied in two case studies of teachers
conducting ordinary lessons. In conclusion, we will discuss what seems to be taken into account by teachers as they observe
students’ activity, and how in-service teacher training can play a role in modifying their knowledge about students’ ways
of dealing with mathematical problems. 相似文献
5.
We discuss Konstantinos Alexakos, Jayson Jones and Victor Rodriguez’s hermeneutic study of formation and function of kinship-like
relationships among inner city male students of color in a college physics classroom. From our Critical Complexity Science
framework we first discuss the reading erlebnisse of students laughing at and with each other as something that immediately captured our attention in being transformative
of the classroom. We continue by exploring their classroom and research experience as an emergent structure modifying their
collective as well as their individual experiences. As we analyze both the classroom and the research space as a complex system,
we reflect on the instructor/students interactions characterized by an asymmetrical “power” relationship. From our analysis
we propose to consider the zone of proximal development as the constantly emerging and transforming person experience (erlebnisse and
erfahrung). 相似文献
6.
It is impossible to consider contemporary science education in isolation from globalisation as the dominant logic, rethinking
and reconfiguring social and cultural life in which it is located. Carter (J Res Sci Teach 42, 561–580, 2005) calls for a close reading of policy documents, curriculum projects, research studies and a range of other science education
texts using key concepts from globalisation theory to elucidate the ways in which globalisation shapes and is expressed within
science education. In this paper, we consider an example from our own practice of a school-based curriculum project, Sustainable Living by the Bay, as one such instance. The first section reviews neoliberalism and neoconservativism necessary to understand how globalisation
penetrates education, while the second outlines aspects of the curriculum project itself. As there were many different facets
to the development and implementation of a project like Sustainable Living by the Bay, there is space only to elaborate two examples of the globalisation discourse. The first example concerns the government policy
initiative that funded the project while the second example focuses on learner- centred pedagogies as globalisation’s pedagogies
of choice. 相似文献
7.
In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development
of teachers’ pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4–14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group
of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be
used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand
how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical
tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth
in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study
provides a new research instrument for measuring teachers’ growth in pedagogical content knowledge.
An earlier version of this paper was presented at the American Educational Research Association Annual Meeting, New Orleans,
LA, April 2002. 相似文献
8.
Teresa Strong-Wilson 《Children‘s Literature in Education》2008,39(1):53-74
We are made up of stories: the stories we hear, the stories we tell. Intertextual connections form through repeatedly hearing
stories, many of which stem back to childhood. This paper foregrounds a teachers-as-readers literature circle in which a group
of Indigenous teachers in Canada discussed, among other titles, Rafé Martin’s The Rough Face Girl and Gerald McDermott’s Raven. Children’s stories are contested spaces because of the persistent presence in them of “simulacra” or imaginary representations
of Indigenous peoples. The paper describes how the teachers drew on their storied formations as Indigenous readers to gloss
the stories, as well as revised their interpretations through critical discussion with one another. 相似文献
9.
Conclusions Our aim in taking the Year 7 class was to increase our understanding of the learning process. In simple terms we were trying
to apply our ideas and White's analysis of the term ‘understanding’ further clarified our purpose. Each target of our understanding
has been affected by our experience. Two examples can be used to show how this occurred.
Our understanding of the learning approach has been modified by our understanding of students at this level. The effects of
peer group interactions have been underestimated as a factor in the learning environment. As a further example we can see
that some ways in which schools are organized are not conducive to the implementation of the learning approaches being presented.
Schools are organized so that groups of age cohorts can function effectively. The result is that school classrooms are a compromise
where competing functions of schooling and the constraints that are operating are ‘balanced’. The ideal conditions for our
approach to learning could not be present and two visitors from the ‘ivory tower’ were grateful for the opportunity to better
understand a secondary school and a group of its students. 相似文献
10.
Juan Pablo Mejia-Ramos Evan Fuller Keith Weber Kathryn Rhoads Aron Samkoff 《Educational Studies in Mathematics》2012,79(1):3-18
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research
on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper,
we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics.
Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is
not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the
proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples.
We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory. 相似文献
11.
Cecile Ouvrier-Buffet 《Educational Studies in Mathematics》2006,63(3):259-282
The definition of ‘definition’ cannot be taken for granted. The problem has been treated from various angles in different
journals. Among other questions raised on the subject we find: the notions of concept definition and concept image, conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to construct definitions.
This paper will deal with ‘definition construction processes’ and aims more specifically at proposing a new approach to the
study of the formation of mathematical concepts. I shall demonstrate that the study of the defining and concept formation
processes demands the setting up of a general theoretical framework. I shall propose such a tool characterizing classical
points of view of mathematical definitions as well as analyzing the dialectic involving definition construction and concept
formation. In that perspective, a didactical exemplification will also be presented. 相似文献
12.
Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures
Caroline Yoon Michael O. J. Thomas Tommy Dreyfus 《Educational Studies in Mathematics》2011,78(3):371-393
This paper examines how a person’s gesture space can become endowed with mathematical meaning associated with mathematical
spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of
gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures to construct a graphical
anti-derivative while working on a professional development task in a calculus modelling activity. Results indicate that mathematical
gesture spaces can encourage mathematical experimentation, lighten the cognitive load for students and can be limited by a
person’s physical constraints. 相似文献
13.
In the context of the emphasis on inquiry teaching in science education, this study looks into how pre-service elementary
teachers understand and practise science inquiry teaching during field experience. By examining inquiry lesson preparation,
practice, and reflections of pre-service elementary teachers, we attempt to understand the difficulties they encounter and
what could result from those difficulties in their practice. A total of 16 seniors (fourth-year students) in an elementary
teacher education program participated in this study. In our findings, we highlight three difficulties ‘on the lesson’ that are related to teaching practices that were missing in the classrooms: (1) developing children’s own ideas and curiosity,
(2) guiding children in designing valid experiments for their hypotheses, (3) scaffolding children’s data interpretation and
discussion and another three difficulties ‘under the lesson’ that are related to problems with the pre-service teachers’ conceptualization of the task: (4) tension between guided and
open inquiry, (5) incomplete understanding of hypothesis, and (6) lack of confidence in science content knowledge. Based on
these findings, we discuss how these difficulties are complexly related in the pre-service teachers’ understandings and action.
Several suggestions for science teacher education for inquiry teaching, especially hypothesis-based inquiry teaching, are
then explored. 相似文献
14.
When critics consider young people’s practices within cyberspace, the focus is often on negative aspects, namely cyber-bullying,
obsessive behaviour, and the lack of a balanced life. Such analyses, however, may miss the agency and empowerment young people
experience not only to make decisions but to have some degree of control over their lives through their engagement with and
use of technology, which often includes sharing it with others in cyberspace. This was a finding of research conducted by
Nicola Johnson, which also informs the two novels considered in this article, Cory Doctorow’s Little Brother and Brian Falkner’s Brainjack. The article draws on Pierre Bourdieu’s theory of acts of resistance (Acts of Resistance: Against the New Myths of our Time, 1998) to demonstrate how these fictional representations of hacker heroes make a direct address to their readers to use their
technological expertise to achieve social justice. Rather than hacking primarily to “see if they can do it,” the protagonists
of these novels acknowledge the moral ambiguity of hacking and encourage its responsible use. 相似文献
15.
In research oriented universities, research and teaching are often viewed as separate. Aydeniz and Hodge present one professor’s
struggles to synthesize an identity from three different spaces, each with competing values and core beliefs. As Mr. G’s story
unfolds, and he reflects upon his negotiation between teaching and research responsibilities, we seek to expand the discussion
by presenting a caution to identity researchers. The caution pertains to construction of understanding on how identities are
created, and the role that individual stories take in how identities are created and enacted. In this forum contribution,
we present several questions in the hopes of furthering the discussion on identity research, and our understanding of the
conceptualization of institutional boundaries and objectivity, as well as questions on participant involvement in the process
of research. 相似文献
16.
In this article, we examine a set of 26 children’s books on HIV/AIDS published between 1989–1999 to identify the ways in which
these texts construct HIV/AIDS and people living with HIV/AIDS. We explore how this marginalized group is depicted in these
books, and how well-meaning teachers may in fact be reproducing dominant discourses about HIV/AIDS in their curricula. In
this article we focus, in particular, on how the discourses connected to public health, medicine, and secrecy (as a discourse
across many institutions) are filtered to children and take part in constructing their beliefs and assumptions about HIV/AIDS.
We illustrate our argument with examples from the books and show why teachers need to know how to analyze texts they select
for their curricula so as to read books about HIV/AIDS critically in the classroom.
Megan Blumenreich is Assistant Professor of Childhood Education at The City College of New York, City University of New York.
Her research interests focus on urban schooling, poststructuralist approaches to qualitative research, and teacher education.
She is the coauthor of The Power of Questions: A Guide to Teacher and Student Research (Heineman, 2005).
Marjorie Siegel is Associate Professor and Chair of the Department of Curriculum and Teaching at Teachers College, Columbia
University. Her research interests include transmediation and multimodality in literacy education, content area literacies,
and literacies and technologies. She is the coauthor of Reading Counts: Expanding the role of reading in mathematics classrooms (Teachers College, 2000).
M. Himley, “Teaching the rhetoric of AIDS: Blurring the boundaries.” 相似文献
17.
Mary Ainley 《Educational Psychology Review》2006,18(4):391-405
In this paper we draw on our research on interest to explore the questions posed for this special issue. Interest is conceptualized as an affective state that represents students’ subjective experience of learning; the state that arises from either situational triggers or a well-developed individual interest. Drawing on the broad research literature on interest, and using our own findings in relation to the state of interest, we consider how interest represents an integration of affect, motivation and cognition. In particular, how the state of interest brings together motivation in the form of prior goals and interests and focuses them into on-task behavior. We illustrate ways that our research monitoring on-task sequences of affect and behavior, is confronting some of the methodological concerns posed in relation to measurement of affective states. Finally, we examine some of the paths by which triggered states of interest can contribute to productive student engagement with learning. 相似文献
18.
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
19.
This study examines young children’s ideas about natural science phenomena and explores possibilities in starting investigations
in kindergarten from their ideas. Given the possibilities inherent in how young children make sense of their experiences,
we believe it is critical to take children’s perspectives into consideration when designing any activities, and ideally, to
design activities from their perspectives and understandings. Specifically, this research focuses on 5- and 6-year old children’s explanations of
rainbows, and there are three main findings. First, our analysis demonstrates that opportunities to discuss their ideas revealed
children’s different perceptions of the phenomena of rainbows. Secondly, this research emphasizes that peer-to-peer interaction
in the co-construction of science concepts provided support to the children to learn from, and with, each other. Third, children’s initial explanations provided the teacher-researcher (second author) with a starting point
to scaffold her teaching from. Although rainbows are quite an abstract topic to try to reproduce in the classroom, the children
demonstrated their often sophisticated understandings of natural science phenomena, as well as their creative ideas as related
to rainbows. In order to foster an appreciation of themes in natural science, it is crucial to build from what children already
know and can do, and to use these emergent theories and considerations in designing curriculum. Thus, we draw implications
for the importance of teaching science at the early childhood level and for using children’s ideas as starting points in planning
instruction. 相似文献
20.
Pessia Tsamir 《Educational Studies in Mathematics》2007,65(3):255-279
This paper indicates that prospective teachers’ familiarity with theoretical models of students’ ways of thinking may contribute
to their mathematical subject matter knowledge. This study introduces the intuitive rules theory to address the intuitive,
same sides-same angles solutions that prospective teachers of secondary school mathematics come up with, and the proficiency they acquired during
the course “Psychological aspects of mathematics education”. The paper illustrates how drawing participants’ attention to
their own erroneous applications of same sides-same angles ideas to hexagons, challenged and developed their mathematical knowledge. 相似文献