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1.
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
2.
In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a multiple perspective approach to history, Sfard’s theory of thinking as communicating, and theories from mathematics education about concept image, concept definition and concept formation. It will be explained how history and extracts of original sources by Euler from 1748 and Dirichlet from 1837 were used to (1) reveal students’ meta-discursive rules in mathematics and make them objects of students’ reflections, (2) support students’ learning of the concept of a function, and (3) develop students’ historical awareness. The results show that it is possible to diagnose (some) of students’ meta-discursive rules, that some of the students acted according to meta-discursive rules that coincide with Euler’s from the 1700s, and that reading a part of a text by Dirichlet from 1837 created obstacles for the students that can be referenced to differences in meta-discursive rules. The experiment revealed that many of the students have a concept image that was in accordance with Euler’s rather than with our modern concept definition and that they have process oriented thinking about functions. The students’ historical awareness was developed through the course with respect to actors’ influence on the formation of mathematical concepts and the notions of internal and external driving forces in the historical development of mathematics. 相似文献
3.
The attitude construct is widely used by teachers and researchers in mathematics education. Often, however, teachers’ diagnosis
of ‘negative attitude’ is a causal attribution of students’ failure, perceived as global and uncontrollable, rather than an
accurate interpretation of students’ behaviour, capable of steering future action. In order to make this diagnosis useful
for dealing with students’ difficulties in mathematics, it is necessary to clarify the construct attitude from a theoretical viewpoint, while keeping in touch with the practice that motivates its use. With this aim, we investigated
how students tell their own relationship with mathematics, proposing the essay “Me and maths” to more than 1,600 students
(1st to 13th grade). A multidimensional characterisation of a student’s attitude towards mathematics emerges from this study.
This characterisation and the study of the evolution of attitude have many important consequences for teachers’ practice and
education. For example, the study shows how the relationship with mathematics is rarely told as stable, even by older students:
this result suggests that it is never too late to change students’ attitude towards mathematics. 相似文献
4.
Reuven Babai Tali Brecher Ruth Stavy Dina Tirosh 《International Journal of Science and Mathematics Education》2006,4(4):627-639
One theoretical framework which addresses students’ conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students’ reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common external features. In this paper, we explore the cognitive processes related to the intuitive rule more A–more B and discuss issues related to overcoming its interference. We focused on the context of probability using a computerized “Probability Reasoning – Reaction Time Test.” We compared the accuracy and reaction times of responses that are in line with this intuitive rule to those that are counter-intuitive among high-school students. We also studied the effect of the level of mathematics instruction on participants’ responses. The results indicate that correct responses in line with the intuitive rule are more accurate and shorter than correct, counter-intuitive ones. Regarding the level of mathematics instruction, the only significant difference was in the percentage of correct responses to the counter-intuitive condition. Students with a high level of mathematics instruction had significantly more correct responses. These findings could contribute to designing innovative ways of assisting students in overcoming the interference of the intuitive rules. 相似文献
5.
Reuven Babai 《International Journal of Science and Mathematics Education》2010,8(2):203-221
According to the intuitive rules theory, students are affected by a small number of intuitive rules when solving a wide variety
of science and mathematics tasks. The current study considers the relationship between students’ Piagetian cognitive levels
and their tendency to answer in line with intuitive rules when solving comparison tasks. The findings indicate that the tendency
to answer according to the intuitive rules varies with cognitive level. Surprisingly, a higher rate of incorrect responses
according to the rule same A–same B was found for the higher cognitive level. Further findings and implications for science and mathematics education are discussed. 相似文献
6.
?se Hansson 《Educational Studies in Mathematics》2012,81(1):103-125
In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status. 相似文献
7.
Chris Rasmussen Oh Nam Kwon Karen Allen Karen Marrongelle Mark Burtch 《Asia Pacific Education Review》2006,7(1):85-93
This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results
of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The
IO-DE project capitalizes on advances within mathematics and mathematics education, including the instructional design theory
of Realistic Mathematics Education and the social negotiation of meaning. The main results of the comparison study found no
significant difference between project students and comparison students on an assessment of routine skills and a significant
difference in favor of project students on an assessment of conceptual understanding. Given these encouraging results, the
theoretical underpinnings of the innovative approach may be useful more broadly for undergraduate mathematics education reform. 相似文献
8.
Joshua Gisemba Bagaka��s 《International Journal of Science and Mathematics Education》2011,9(4):817-842
The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy
and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy.
Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria
Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level
of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play
a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found
to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends
that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy,
reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional
development opportunities should also be made available to in-service teachers to continually update their knowledge and skills
and develop new strategies for teacher effectiveness. 相似文献
9.
This study is part of a project concerned with the analysis of how students work with two-variable functions. This is of fundamental
importance given the role of multivariable functions in mathematics and its applications. The portion of the project we report
here concentrates on investigating the relationship between students’ notion of subsets of Cartesian three-dimensional space
and the understanding of graphs of two-variable functions. APOS theory and Duval’s theory of semiotic representations are
used as theoretical framework. Nine students, who had taken a multivariable calculus course, were interviewed. Results show
that students’ understanding can be related to the structure of their schema for R3 and to their flexibility in the use of different representations. 相似文献
10.
Matthew Inglis Juan Pablo Mejia-Ramos Adrian Simpson 《Educational Studies in Mathematics》2007,66(1):3-21
In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted
form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate
mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use
of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role
in mathematical argumentation, and that one of the goals of instruction should be to develop students’ abilities to appropriately
match up warrant-types with modal qualifiers. 相似文献
11.
Joanna O. Masingila Samson M. Muthwii Patrick M. Kimani 《International Journal of Science and Mathematics Education》2011,9(1):89-108
This study examined standard 6 and 8 (Standards 6 and 8 are the sixth and eighth years, respectively, of primary level schooling
in Kenya.) students’ perceptions of how they use mathematics and science outside the classroom in an attempt to learn more
about students’ everyday mathematics and science practice. The knowledge of students’ everyday mathematics and science practice
may assist teachers in helping students be more powerful mathematically and scientifically both in doing mathematics and science
in school and out of school. Thirty-six students at an urban school and a rural school in Kenya were interviewed before and
after keeping a log for a week where they recorded their everyday mathematics and science usage. Through the interviews and
log sheets, we found that the mathematics that these students perceived they used outside the classroom could be classified
as 1 of the 6 activities that Bishop (Educ Stud Math 19:179–191, 1988) has called the 6 fundamental mathematical activities and was also connected to their perception of whether they learned
mathematics outside school. Five categories of students’ perceptions of their out-of-school science usage emerged from the
data, and we found that 4 of our codes coincided with 2 activities identified by Lederman & Lederman (Sci Child 43(2):53,
2005) as part of the nature of science and 2 of Bishop’s categories. We found that the science these students perceived that they
used was connected to their views of what science is. 相似文献
12.
Oliver F. Jenkins 《Journal of Mathematics Teacher Education》2010,13(2):141-154
A structured interview process is proffered as an effective means to advance prospective teachers’ understandings of students
as learners of mathematics, a key component of pedagogical content knowledge. The interview process is carried out in three
phases with the primary objective of developing listening skills for accessing students’ mathematical thinking. The interviews
adhere to clinical interview procedures for discovering cognitive activities and, accordingly, are initiated by presenting
an open-ended mathematics task. Three rounds of interviews were completed by undergraduates enrolled in a middle school mathematics
methods course. Anecdotal data generated by their interview reports suggest that the structured interview process engenders
an interpretive orientation to listening to students and furthers awareness of how students make sense of mathematics. Features
of the interview process that may limit its potential benefits are discussed; recommendations for further study are proposed. 相似文献
13.
Dacheng Zhao Michael Singh 《International Journal of Science and Mathematics Education》2011,9(1):69-87
International comparative studies and cross-cultural studies of mathematics achievement indicate that Chinese students (whether
living in or outside China) consistently outperform their Western counterparts. This study shows that the gap between Chinese-Australian
and other Australian students is best explained by differences in motivation to achieve, attributing success to effort, the
influence of parental help and the use of extra mathematics curricula. The argument explored is, in order to promote students’
mathematics achievement, we must improve the pedagogical knowledge of classroom teachers of mathematics, as well as to encourage
parents’ involvement in the mathematics education of their children and to promote students’ motivation to learn mathematics. 相似文献
14.
Uffe Thomas Jankvist 《Educational Studies in Mathematics》2010,74(1):53-74
This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented
in a Danish upper secondary class in order to study the students’ capabilities at engaging in meta-issue discussions and reflections
on mathematics and its history. Based on videos of the implementation, students’ hand-in essay assignments, questionnaires,
and follow-up interviews, the conditions, sense, and extent to which the students are able to perform such discussions and
reflections are analyzed using a described theoretical framework. 相似文献
15.
Joe Champion Frieda Parker Bernadette Mendoza-Spencer Ann Wheeler 《International Journal of Science and Mathematics Education》2011,9(5):1093-1110
The purpose of this study was to identify the degree to which college algebra students’ value mathematical skills in their
prospective careers. A survey was administered to N = 144 students in 6 college algebra classes at a mid-sized doctoral granting university. Students in half the classes completed
a data analysis project, and half of the students planned to major in a business-related degree. Logistic regression suggested
that students held mostly positive attitudes about the value of mathematics in their career, with business students expressing
more positive attitudes than those reported by non-business students. Unexpectedly, those who completed the data analysis
project expressed less positive attitudes on 6 of the 20 survey items. 相似文献
16.
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
17.
Leigh N. Wood Glyn Mather Peter Petocz Anna Reid Johann Engelbrecht Ansie Harding Ken Houston Geoff H. Smith Gillian Perrett 《International Journal of Science and Mathematics Education》2012,10(1):99-119
We report on an international study about mathematics students’ ideas of how they will use mathematics in their future study
and careers. This builds on our previous research into students’ conceptions of mathematics. In this paper, we use data from
two groups of students studying mathematics: those who participated in an in-depth interview and those who completed an open-ended
questionnaire. We found that their responses could be grouped into four categories: don’t know; procedural skills; conceptual
skills; and professional skills. Although some students held clear ideas about the role of mathematics, many were not able
to articulate how it would be used in their future. This has implications for their approach to learning and our approach
to teaching. 相似文献
18.
19.
Gabriel J. Stylianides 《International Journal of Science and Mathematics Education》2008,6(1):191-215
Despite widespread agreement that proof should be central to all students’ mathematical experiences, many students demonstrate poor ability with it. The curriculum
can play an important role in enhancing students’ proof capabilities: teachers’ decisions about what to implement in their
classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused
on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials
offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that
can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the
proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an
analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed. 相似文献