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1.
Keith Weber Carolyn Maher Arthur Powell Hollylynne Stohl Lee 《Educational Studies in Mathematics》2008,68(3):247-261
In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute
to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this
debate by illustrating three learning opportunities that group discussions can create. In analyzing a videotaped episode of
eight middle school students discussing a statistical problem, we observed that these students frequently challenged the arguments
that their colleagues presented. These challenges invited students to be explicit about what mathematical principles, or warrants,
they were implicitly using as a basis for their mathematical claims, in some cases recognize the modes of reasoning they were
using were invalid and reject these modes of reasoning, and in other cases, attempt to provide deductive support to justify
why their modes of reasoning were appropriate. We then describe what social and environmental conditions allowed the discussion
analyzed in this paper to occur.
相似文献
| Keith WeberEmail: |
2.
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: |
3.
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: |
4.
A research framework for creative and imitative reasoning 总被引：1，自引：0，他引：1
Johan Lithner 《Educational Studies in Mathematics》2008,67(3):255-276
This conceptual research framework addresses the problem of rote learning by characterising key aspects of the dominating
imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking
processes, student competencies, and the learning milieu it explains origins and consequences of different reasoning types.
相似文献
| Johan LithnerEmail: |
5.
Zbigniew Semadeni 《Educational Studies in Mathematics》2008,68(1):1-17
To explicate certain phenomena, e.g., the possibility of deduction without definition, we hypothesize that an individual is
able to understand and appreciate reasoning with a due feeling of its necessity when the concept image of each concept involved
in the reasoning has reached a certain level of development; we then speak of deep intuition. This conception is presented (with a variety of examples) in the framework of D. Tall’s theory of three worlds of mathematics
(‘conceptual-embodied’, ‘proceptual-symbolic’, and ‘formal-axiomatic’).
相似文献
| Zbigniew SemadeniEmail: |
6.
Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard
mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary
and secondary teachers to a student’s non-traditional strategy for dividing fractions. Six categories of reasoning were constructed,
making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching
response, and their beliefs about mathematics teaching were investigated. We found that there were not only differences but
also similarities between the prospective elementary and secondary teachers’ reasoning and responses. We also found that those
who unpacked the mathematical underpinning of the student’s non-traditional strategy tended to use what we call “teacher-focused”
responses, whereas those doing less analysis work tended to construct “student-focused” responses. These results and their
implications are discussed in relation to the influential factors the participants themselves identified to explain their
approach to the given teaching-scenario task.
相似文献
| Sandra CrespoEmail: |
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.
Richard Lesh James A. Middleton Elizabeth Caylor Shweta Gupta 《Educational Studies in Mathematics》2008,68(2):113-130
In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its
implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaput’s belief in a Science
of Need to motivate and direct the development of tasks and tools for engaging students in reasoning about data. A Science
of Need embodies the utility value of mathematics, and engages students in seeing the importance of mathematics in both their
current and their future lives. An extended example of the design of tasks that require students to generate, test, and revise
models of complex data is used to illustrate the ways in which attention to the contributions of students can aid in the development
of both useful and theoretically coherent models of mathematical understanding by researchers. Tools such as Fathom are shown
as democratizing agents in making data modeling more expressive and intimate, aiding in the development of deeper and more
applicable mathematical understanding.
相似文献
| James A. MiddletonEmail: |
9.
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With our conceptualization of Harré and van Langenhove’s (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment
of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current
mathematics education literature and the way it may be alternatively conceptualized. This leads us to claim that changing
the way mathematics is talked about and changing the stories (or myths) told about mathematics is necessary for efforts to
change the way mathematics is done and the way it is taught.
相似文献
| Beth Herbel-EisenmannEmail: |
12.
Student teaching (guided teaching by a prospective teacher under the supervision of an experienced “cooperating” teacher)
provides an important opportunity for prospective teachers to increase their understanding of mathematics in and for teaching.
The interactions between a student teacher and cooperating teacher provide an obvious mechanism for such learning to occur.
We report here on data that is part of a larger study of eight student teacher/cooperating teacher pairs, and the core themes
that emerged from their conversations. We focus on two pairs for whom the core conversational themes represent disparate approaches
to mathematics in and for teaching. One pair, Blake and Mr. B., focused on controlling student behavior and rarely talked
about mathematics for teaching. The other pair, Tara and Mr. T., focused on having students actively participating in the
lesson and on mathematics from the students’ point of view. These contrasting experiences suggest that student teaching can
have a profound effect on prospective teachers’ understanding of mathematics in and for teaching.
相似文献
| Steven R. WilliamsEmail: |
13.
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: |
14.
Tim Rowland 《Educational Studies in Mathematics》2008,69(2):149-163
This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching,
and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective
elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons
was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics
teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension
of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified:
these are related to different kinds of teacher awareness.
相似文献
| Tim RowlandEmail: |
15.
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: |
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.
Socio-emotional orientations and teacher change 总被引：1，自引：0，他引：1
Raimo Kaasila Markku S. Hannula Anu Laine Erkki Pehkonen 《Educational Studies in Mathematics》2008,67(2):111-123
In this article we consider how elementary education students’ views of mathematics changed during their mathematics methods
course. We focus on four female students: two started the course with mainly positive views of mathematics and a task orientation,
two with negative views of the subject and an ego-defensive orientation. The biggest change observed was that the trainees’
views of teaching and learning mathematics became more positive. Moreover, what had been an ego-defensive orientation changed
towards a social-dependence orientation. The crucial facilitators of change seemed to be (1) handling of and reflection on
one’s experiences of learning and teaching mathematics, (2) exploring content with concrete materials, and (3) collaboration
with a partner or working as a tutor of mathematics.
相似文献
| Raimo KaasilaEmail: |
18.
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: |
19.
Since many teachers and students recognize other kinds of knowledge (faith) based on other ways of knowing, consideration
of these realities is appropriate for the science education community. Understanding the multitude of ways that clergy view
relationships between science and faith (i.e. alternative ways of knowing) would assist in understanding various ways that
people address complex issues arising from ideas about science and faith. We administered a questionnaire composed of multiple-choice
and short answer items to 63 United Methodist ministers. Findings included (1) that formal, organized faith contexts (e.g.
church services) serve as informal science education opportunities, (2) participants demonstrated considerable diversity regarding
the types of relationships developed between science and faith, and (3) participants recognized a need exists for better understandings
of science and its relationship to faith for them, their colleagues, and their congregations.
相似文献
| Daniel L. Dickerson (Corresponding author)Email: |
| Karen R. DawkinsEmail: |
| John E. PenickEmail: |
20.
Using Propensity Scores for Estimating Causal Effects: A Study in the Development of Moral Reasoning
The purpose of this study was to illustrate the use of propensity scores for creating comparison groups, partially controlling
for pretreatment course selection bias, and estimating the treatment effects of selected courses on the development of moral
reasoning in undergraduate students. Specifically, we used a sample of convenience for comparing differences in moral reasoning
development scores among students enrolled in intergroup dialogue, service learning, psychology and philosophy courses with
those of an introductory sociology course. Adopting a propensity score approach included reviewing the empirical literature
for its guidance in substantiating the reasons for including pretreatment variables (i.e., pretreatment course-taking behaviors,
race, sex, political identification, need for cognition, major, age, pretreatment moral reasoning scores) in our analysis,
measuring these variables, and reducing them into a single composite propensity score for each student in our analytic sample.
This score then served as the basis for creating a new comparison group and for allowing us to estimate unbiased (or less
biased) course-related treatment effects on moral reasoning development. Implications for higher education researchers are
discussed.
相似文献
| Matthew J. Mayhew (Corresponding author)Email: |