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1.
Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University
mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of
mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the
framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging
in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents
a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance
of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.
相似文献
| Donna KotsopoulosEmail: |
2.
Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers
to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been
expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics.
One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has
started to gain attention as an important concept in the mathematics teacher education research community, there is limited
understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article,
we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in
both mathematics education and the learning sciences.
相似文献
| Jason SilvermanEmail: |
3.
In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special
Issue of Educational Studies in Mathematics on “Semiotic perspectives in mathematics education” (Sáenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1–2),
2006). Among these issues are conceptualizations of subjectivity and the notion that particular readings of Peircean and Vygotskian
semiotics may limit the ways that authors define key actors or elements in mathematics education, namely students, teachers
and the nature of mathematics. To deepen the conversation, we comment on Brown’s approach and explore the theoretical apparatus
of Jacques Lacan that informs Brown’s discourse. We show some of the intrinsic limitations of the Lacanian idea of subjectivity
that permeates Brown’s insightful analysis and conclude with a suggestion about some possible lines of research in mathematics
education.
相似文献
| Luis RadfordEmail: |
4.
Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated
through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí)
in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential
element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content
of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics
register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual
students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to
come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key
transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and
applications for mathematics teaching and learning are presented.
相似文献
| John O’DonoghueEmail: |
5.
Jeanette M. Grover Eula Ewing Monroe James S. Jacobs 《Children‘s Literature in Education》2007,38(1):71-86
The first author, a student in a graduate children’s literature class, designed a project to locate “good” mathematics-based
children’s literature selections. However, the reference tools usually consulted (e.g., Books in Print) to locate books by topic were of little help, and those she located under individual mathematics topics were mostly traditional
mathematics books rather than good read-aloud selections. Consequently, she perused the university library’s sizeable juvenile
collection to find books that would meet her selection criteria. This article describes the influence of two landmark documents
for mathematics teaching and learning—Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989) and Principles and Standards for School Mathematics (NCTM, 2000)—as she engaged in the process.
相似文献
| Eula Ewing MonroeEmail: |
6.
Tony Brown 《Educational Studies in Mathematics》2008,69(3):249-263
This paper examines a Special Issue of Educational Studies in Mathematics comprising research reports centred on Peircian semiotics in mathematics education, written by some of the major authors
in the area. The paper is targeted at inspecting how subjectivity is understood, or implied, in those reports. It seeks to
delineate how the conceptions of subjectivity suggested are defined as a result of their being a function of the domain within
which the authors reflexively situate themselves. The paper first considers how such understandings shape concepts of mathematics,
students and teachers. It then explores how the research domain is understood by the authors as suggested through their implied
positioning in relation to teachers, teacher educators, researchers and other potential readers.
相似文献
| Tony BrownEmail: |
7.
Youjun Wang 《Science & Education》2009,18(5):631-640
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving,
hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development
of ancient Chinese mathematics, we find that the history of mathematics in ancient China is an abundant resource for materials
to demonstrate mathematics by hands-on manipulation. In this article I shall present two cases that embody this idea of a
hands-on approach in ancient Chinese mathematics, at the same time offering an opportunity to show how to utilize materials
from the history of Chinese math in modern mathematical education.
相似文献
| Youjun WangEmail: |
8.
The doctoral advisor is said to be one of the most important persons—if not the single most critical person—with whom doctoral students will develop a relationship during their doctoral degree programs
(Baird 1995). However, we have limited knowledge regarding how doctoral advisors see their roles and responsibilities as advisors. Therefore,
through in-depth interviews, we explored the perceptions of 25 exemplary doctoral advisors, who have graduated a large number
of doctoral students, about their roles and responsibilities as advisors. We conclude this article with implications for doctoral
education.
相似文献
| Ann E. AustinEmail: |
9.
Jane-Jane Lo Theresa J. Grant Judith Flowers 《Journal of Mathematics Teacher Education》2008,11(1):5-22
This article reports challenges faced by prospective elementary teachers as they revisited whole number multiplication through
a sequence of tasks that required them to develop and justify reasoning strategies for multiplication. Classroom episodes
and student work are used both to illustrate these challenges, as well as to demonstrate growth over time. Implications for
the design of mathematics courses for prospective teachers’ are discussed. Although the study is situated in the context of
multiplication, it has implications for teachers reasoning and justification in other areas of mathematics.
相似文献
| Judith FlowersEmail: |
10.
Jennifer S. Beers 《Cultural Studies of Science Education》2009,4(2):443-447
This paper draws on my personal experiences with coteaching and my participation in the research described by Wassell and
LaVan (2009). It examines the role of coteaching in the development of structures that afforded opportunities for shared reflection and
shared responsibility between stakeholders in the classroom. It also describes how the schema and practices developed through
coteaching and cogenerative dialogue helped mediate the transition between my preservice and inservice teaching experiences.
相似文献
| Jennifer S. BeersEmail: |
11.
12.
Yeping Li Dongchen Zhao Rongjin Huang Yunpeng Ma 《Journal of Mathematics Teacher Education》2008,11(5):417-430
It is generally perceived that Chinese elementary teachers have a profound understanding of the school mathematics they teach.
This perception has led to further interest in understanding teacher education practices in China. As some dramatic changes
in elementary teacher preparation have taken place in China over the past decade, this article aims to outline these changes
with a focus on curriculum provided in the new 4-year bachelor preparation programs. Sample mathematics teacher educators
in China were also surveyed to gather insiders’ views about teacher preparation practices and to identify relevant issues.
We believe that elementary teacher preparation and its changes in China can provide an important case for mathematics teacher
educators around the world to reflect on teacher education practices in their own systems.
相似文献
| Yeping LiEmail: |
13.
This study examines ways of approaching deductive reasoning of people involved in mathematics education and/or logic. The
data source includes 21 individual semi-structured interviews. The data analysis reveals two different approaches. One approach
refers to deductive reasoning as a systematic step-by-step manner for solving problems, both in mathematics and in other domains.
The other approach emphasizes formal logic as the essence of the deductive inference, distinguishing between mathematics and
other domains in the usability of deductive reasoning. The findings are interpreted in light of theory and practice.
相似文献
| Michal AyalonEmail: |
14.
This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree
to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding
and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and semantic reasoning strategies
relative to a representation system of proof. We then use this conceptualisation as a basis for contrasting the behaviour
of two successful mathematics research students whilst they evaluated and proved number theory conjectures. We observe that
the students exhibited strikingly different degrees of example use, and argue that previously observed individual differences
in reasoning strategies may exist at the expert level. We conclude by discussing implications for pedagogy and for future
research.
相似文献
| Matthew InglisEmail: |
15.
We report an eye-movement study that demonstrates differences in regularity effects between adult developmental dyslexic and
control non-impaired readers, in contrast to findings from a large number of word recognition studies (see G. Brown, 1997). For low frequency words, controls showed an advantage for Regular items, in which grapheme-to-phoneme strategies could
be employed, compared with Irregular Consistent and Inconsistent items, in which rime comparisons or whole word recognition
strategies would be advantageous. We propose that in sentential contexts, dyslexic readers do not generate sufficient phonological
cues in the parafovea in order to demonstrate the regularity effects typical of unimpaired readers (e.g., S. Sereno & K. Rayner,
2000). These findings suggest that phonological strategies are sensitive to task demands, and underline the impact of methodology
on the conclusions that are drawn about dyslexic reading ability.
相似文献
| Manon Wyn JonesEmail: |
16.
Julie Gainsburg 《Journal of Mathematics Teacher Education》2008,11(3):199-219
The mathematics-education community stresses the importance of real-world connections in teaching. The extant literature suggests
that in actual classrooms this practice is infrequent and cursory, but few studies have specifically examined whether, how,
and why teachers connect mathematics to the real world. In this study, I surveyed 62 secondary mathematics teachers about
their understanding and use of real-world connections, their purposes for making connections in teaching, and factors that
support and constrain this practice. I also observed 5 teachers making real-world connections in their classrooms and I conducted
follow-up interviews; these qualitative data are used to illuminate findings from the survey data. The results offer an initial
portrayal of the use of real-world connections in secondary mathematics classes and raise critical issues for more targeted
research, particularly in the area of teacher beliefs about how to help different kinds of students learn mathematics.
相似文献
| Julie GainsburgEmail: |
17.
Adopting a self-conscious form of co-generative writing and employing a bricolage of visual images and literary genres we
draw on a recent critical auto/ethnographic inquiry to engage our readers in pedagogical thoughtfulness about the problem
of culturally decontextualised mathematics education in Nepal, a country rich in cultural and linguistic diversity. Combining
transformative, critical mathematics and ethnomathematical perspectives we develop a critical cultural perspective on the need for a culturally contextualized mathematics education that enables Nepalese students to develop (rather than
abandon) their cultural capital. We illustrate this perspective by means of an ethnodrama which portrays a pre-service teacher’s
point of view of the universalist pedagogy of Dr. Euclid, a semi-fictive professor of undergraduate mathematics. We deconstruct
the naivety of this conventional Western mathematics pedagogy arguing that it fails to incorporate salient aspects of Nepali
culture. Subsequently we employ metaphorical imagining to envision a culturally inclusive mathematics education for enabling
Nepalese teachers to (i) excavate multiple mathematical knowledge systems embedded in the daily practices of rural and remote
villages across the country, and (ii) develop contextualized pedagogical perspectives to serve the diverse interests and aspirations
of Nepali school children.
相似文献
| Peter Charles TaylorEmail: |
18.
David Tall 《Educational Studies in Mathematics》2008,68(2):185-193
Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision
of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his ‘big
ideas’ as he lived through the most amazing innovations in technology that have changed our lives more in a generation than
in many centuries before. His vision continues as is exemplified by the collected papers in this tribute to his life and work.
相似文献
| David TallEmail: |
19.
Physics teachers’ approaches to teaching physics are generally considered to be linked to their views about physics. In this
qualitative study, the views about physics held by a group of physics teachers whose teaching practice was traditional were
explored and compared with the views held by physics teachers who used conceptual change approaches. A particular focus of
the study was teachers’ views about the role of mathematics in physics. The findings suggest the traditional teachers saw
physics as discovered, close approximations of reality while the conceptual change teachers’ views about physics ranged from
a social constructivist perspective to more realist views. However, most teachers did not appear to have given much thought
to the nature of physics or physics knowledge, nor to the role of mathematics in physics.
相似文献
| Pamela MulhallEmail: |
20.
Uffe Thomas Jankvist 《Educational Studies in Mathematics》2009,71(3):235-261
This is a theoretical article proposing a way of organizing and structuring the discussion of why and how to use the history
of mathematics in the teaching and learning of mathematics, as well as the interrelations between the arguments for using
history and the approaches to doing so. The way of going about this is to propose two sets of categories in which to place
the arguments for using history (the “whys”) and the different approaches to doing this (the “hows”). The arguments for using
history are divided into two categories; history as a tool and history as a goal. The ways of using history are placed into
three categories of approaches: the illumination, the modules, and the history-based approaches. This categorization, along
with a discussion of the motivation for using history being one concerned with either the inner issues (in-issues) or the
metaperspective issues (meta-issues) of mathematics, provides a means of ordering the discussion of “whys” and “hows.”
相似文献
| Uffe Thomas JankvistEmail: |