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1.
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: |
2.
This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe
and compare four perspectives—mathematics, mathematics education, cognitive psychology, and evolutionary psychology—each offering
a different view on mathematical thinking and learning and, in particular, on the source of mathematical errors and on ways
of dealing with them in the classroom. The four perspectives represent four levels of explanation, and we see them not as
competing but as complementing each other. In the classroom or in research data, all four perspectives may be observed. They
may differentially account for the behavior of different students on the same task, the same student in different stages of
development, or even the same student in different stages of working on a complex task. We first introduce each of the perspectives
by reviewing its basic ideas and research base. We then show each perspective at work, by applying it to the analysis of typical
mathematical misconceptions. Our illustrations are based on two tasks: one from statistics (taken from the psychological research
literature) and one from abstract algebra (based on our own research).
相似文献
Orit HazzanEmail: |
3.
Okhee Lee Karen Adamson Jaime Maerten-Rivera Scott Lewis Constance Thornton Kathryn LeRoy 《Journal of Science Teacher Education》2008,19(1):41-67
Our 5-year professional development intervention is designed to promote elementary teachers’ knowledge, beliefs, and practices
in teaching science, along with English language and mathematics for English Language Learning (ELL) students in urban schools.
In this study, we used an end-of-year questionnaire as a primary data source to seek teachers’ perspectives on our intervention
during the first year of implementation. Teachers believed that the intervention, including curriculum materials and teacher
workshops, effectively promoted students’ science learning, along with English language development and mathematics learning.
Teachers highlighted strengths and areas needing improvement in the intervention. Teachers’ perspectives have been incorporated
into our on-going intervention efforts and offer insights into features of effective professional development initiatives
in improving science achievement for all students.
相似文献
Scott LewisEmail: |
4.
The notion of historical “parallelism” revisited: historical evolution and students’ conception of the order relation on the number line 总被引:1,自引:1,他引:0
This paper associates the findings of a historical study with those of an empirical one with 16 years-old students (1st year
of the Greek Lyceum). It aims at examining critically the much-discussed and controversial relation between the historical
evolution of mathematical concepts and the process of their teaching and learning. The paper deals with the order relation
on the number line and the algebra of inequalities, trying to elucidate the development and functioning of this knowledge
both in the world of scholarly mathematical activity and the world of teaching and learning mathematics in secondary education.
This twofold analysis reveals that the old idea of a “parallelism” between history and pedagogy of mathematics has a subtle
nature with at least two different aspects (metaphorically named “positive” and “negative”), which are worth further exploration.
相似文献
Constantinos Tzanakis (Corresponding author)Email: |
5.
This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the
years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and
behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire.
As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant
shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving
or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the
changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same
questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students
explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary
school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently,
secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning
problem-solving. This aspect partly explains the low number of students choosing to study mathematics.
相似文献
Jacob PerrenetEmail: |
6.
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: |
7.
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: |
8.
The study presented in this article investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional
discourse while observing and analysing young students mathematical interaction followed by teacher’s intervention. The teachers’
joint professional discourse is about a combined learning and talking between two students before an intervention by their
teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting
2). The joint professional teachers’ discourse constitutes setting 3. This combination of social settings 1 and 2 is taken
as an opportunity for mathematics teachers’ professionalisation process when interpreting the students’ mathematical interactions
in a more and more professional and sensible way. The epistemological analysis of mathematical sign-systems in communication
and interaction in these three settings gives evidence of different types of mathematical talk, which are explained depending
on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented
and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher
and by the expectations of the students.
相似文献
Heinz SteinbringEmail: |
9.
In this paper we tackle the issue of an eventual stability of teachers’ activity in the classroom. First we explain what kind
of stability is searched and how we look for the chosen characteristics: we analyse the mathematical activity the teacher
organises for students during classroom sessions and the way he manages the relationship between students and mathematical
tasks. We analyse three one-hour sessions for different groups of 11 year old students on the same content and with the same
teacher, and two other sessions for 14 year old and 15 year old students, on analogous contents, with the same teacher (another
one). Actually it appears in these two examples that the main stabilities are tied with the precise management of the tasks,
at a scale of some minutes, and with some subtle characteristic touches of the teacher’s discourse. We present then a discussion
and suggest some inferences of these results.
相似文献
J. RogalskiEmail: |
10.
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: |
11.
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: |
12.
Nondeterminism is a fundamental concept in computer science that appears in various contexts such as automata theory, algorithms
and concurrent computation. We present a taxonomy of the different ways that nondeterminism can be defined and used; the categories
of the taxonomy are domain, nature, implementation, consistency, execution and semantics. An historical survey shows how the
concept was developed from its inception by Rabin & Scott, Floyd and Dijkstra, as well as the interplay between nondeterminism
and concurrency. Computer science textbooks and pedagogical software are surveyed to determine how they present the concept;
the results show that the treatment of nondeterminism is generally fragmentary and unsystematic. We conclude that the teaching
of nondeterminism must be integrated through the computer science curriculum so that students learn to see nondeterminism
both in terms of abstract mathematical entities and in terms of machines whose execution is unpredictable.
Michal Armoni is a postdoctoral fellow at the Department of Science Teaching of the Weizmann Institute of Science. She received her PhD in science teaching from the Tel Aviv University, and her BA and MSc in computer science from the Technion. Her research interests are in the teaching and learning processes in computer science, in particular of fundamental concepts such as reduction and nondeterminism. She is currently on leave from the computer science department of the Open University of Israel. She has extensive experience in developing learning materials in computer science and in teaching the subjects at all levels from high school through graduate students. Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He holds a PhD in mathematics and computer science from the Tel Aviv University. In 2004, he received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. He is the author of numerous computer science textbooks and of Just a Theory: Exploring the Nature of Science (Prometheus 2005). His research interests include the use of visualization in teaching computer science, the pedagogy of concurrent and distributed computation, the application of theories of education to computer science education and the nature of science. 相似文献
Michal Armoni (Corresponding author)Email: |
Mordechai Ben-AriEmail: |
Michal Armoni is a postdoctoral fellow at the Department of Science Teaching of the Weizmann Institute of Science. She received her PhD in science teaching from the Tel Aviv University, and her BA and MSc in computer science from the Technion. Her research interests are in the teaching and learning processes in computer science, in particular of fundamental concepts such as reduction and nondeterminism. She is currently on leave from the computer science department of the Open University of Israel. She has extensive experience in developing learning materials in computer science and in teaching the subjects at all levels from high school through graduate students. Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He holds a PhD in mathematics and computer science from the Tel Aviv University. In 2004, he received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. He is the author of numerous computer science textbooks and of Just a Theory: Exploring the Nature of Science (Prometheus 2005). His research interests include the use of visualization in teaching computer science, the pedagogy of concurrent and distributed computation, the application of theories of education to computer science education and the nature of science. 相似文献
13.
We study in this article mathematics teachers’ documentation work: looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts,
etc. We consider that this documentation work is at the core of teachers’ professional activity and professional development.
We introduce a distinction between available resources and documents developed by teachers through a documentational genesis process, in a perspective inspired by the instrumental approach. Throughout their documentation work, teachers develop documentation systems, and the digitizing of resources entails evolutions of these systems. The approach we propose aims at seizing these evolutions,
and more generally at studying teachers’ professional change.
相似文献
Luc TroucheEmail: |
14.
An international comparison using a diagnostic testing model: Turkish students’ profile of mathematical skills on TIMSS-R 总被引:2,自引:0,他引:2
This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations
participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed
with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive skills (‘attributes’) measured
by the test were determined. One hundred sixty-two items were coded in terms of their attribute involvement, creating an incidence
matrix—the Q-matrix. Using the Q-matrix and the student response data, each student’s attribute mastery profile was determined.
Mean attribute mastery levels of Turkish students were computed and compared to those of their American peers. It was shown
that Turkish students were weak in algebra and probability/statistics. They also demonstrated poor profiles in skills such
as applying rules in algebra, approximation/estimation, solving open-ended problems, recognizing patterns and relationships,
and quantitative reading.
相似文献
Enis DoganEmail: |
15.
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: |
16.
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: |
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.
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: |
19.
It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors,
such as the affective ones, play a crucial role. In light of this observation, we present a reflection on the presence of
affective and cognitive factors in the process of proving. Proof is considered as a special case of problem solving and the
proving process is studied adopting a perspective according to which both affective and cognitive factors influence it. To
carry out our study, we set up a framework where theoretical tools coming from research on problem solving, proof and affect
are present. The study is performed within a university course in mathematics education, where students were given a statement
in elementary number theory to be proved and were asked to write down their proving process and the thoughts that accompanied
this process. We scrutinize the written protocols of two unsuccessful students, with the aim of disentangling the intertwining
between affect and cognition. In particular, we seize the moments in which beliefs about self and beliefs about mathematical
activity shape the performance of our students.
相似文献
Francesca MorselliEmail: |
20.
Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving 总被引:1,自引:0,他引:1
This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in,
mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about
proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing
research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms.
We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving
tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely
many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote
understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks
and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework
using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.
相似文献
Andreas J. StylianidesEmail: |