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1.
“Accepting Emotional Complexity”: A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom 总被引：1，自引：0，他引：1
Peter Op ’t Eynde Erik De Corte Lieven Verschaffel 《Educational Studies in Mathematics》2006,63(2):193-207
A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students’ learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and motivational processes in a specific context. Understanding the role of emotions in the mathematics classroom then implies understanding the nature of these situated processes and the way they relate to students’ problem-solving behaviour. We will present data from a multiple-case study of 16 students out of 4 different junior high classes that aimed to investigate students’ emotional processes when solving a mathematical problem in their classrooms. After identifying the different emotions and analyzing their relations to motivational and cognitive processes, the relation with students’ mathematics-related beliefs will be examined. We will specifically use Frank’s case to illustrate how the use of a thoughtful combination of a variety of different research instruments enabled us to gather insightful data on the role of emotions in mathematical problem solving. 相似文献
2.
Hassan Alamolhodaei 《Asia Pacific Education Review》2009,10(2):183-192
The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence),
working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample
of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2)
Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working
memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation
among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings
could help to provide some practical implications for adapting problem solving skills and effective teaching/learning. 相似文献
3.
In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students
in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted
and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection
was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working
with two different groups of students. Case study methods were used to identify and analyze critical events that occurred
throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with
students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches
to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies;
(3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with
students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations
to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent
with the nature of their interactions and perceived role with students. The implications inform the development of an expanded
learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics
in technology-rich environments. 相似文献
4.
Despina A. Stylianou 《Educational Studies in Mathematics》2011,76(3):265-280
Representation is viewed as central to mathematical problem solving. Yet, it is becoming obvious that students are having
difficulty negotiating the various forms and functions of representations. This article examines the functions that representation
has in students’ mathematical problem solving and how that compares to its function in the problem solving of experts and
broadly in mathematics. Overall, this work highlights the close connections between the work of experts and students, showing
how students use representations in ways that are inherently similar to those of experts. Both experts and students use representations
as tools towards the understanding, exploration, recording, and monitoring of problem solving. In social contexts, experts
and students use representations for the presentation of their work but also the negotiation and co-construction of shared
understandings. However, this research also highlights where students’ work departs from experts’ representational practices,
hence, providing some directions for pedagogy and further work. 相似文献
5.
The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase
to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study
of 61 students 12–13 years old. In this study we identified different types of approaches to problems that determine the behavior
of students in the problem-solving process. The research found two aspects that explain the students’ approaches to problem
solving: (1) the presence of a dualistic belief system originating in the student’s school experience; and (2) motivation
linked to beliefs regarding the difficulty of the task. Our results indicate that there is a complex relationship between
students’ belief systems and approaches to problem solving, if we consider a wide variety of beliefs about the nature of mathematics
and problem solving and motivational beliefs, but that it is not possible to establish relationships of causality between
specific beliefs and problem-solving activity (or vice versa). 相似文献
6.
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
7.
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
8.
Marilena Pantziara Athanasios Gagatsis Iliada Elia 《Educational Studies in Mathematics》2009,72(1):39-60
The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems.
Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems’
structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first to introduce three well-defined types of diagrams, that is, network, hierarchy, and matrix,
which represent different problematic situations. In the present study, we investigated the effects of these types of diagrams
in non-routine mathematical problem solving by contrasting students’ abilities to solve problems with and without the presence
of diagrams. Structural equation modeling affirmed the existence of two first-order factors indicating the differential effects
of the problems’ representation, i.e., text with diagrams and without diagrams, and a second-order factor representing general
non-routine problem solving ability in mathematics. Implicative analysis showed the influence of the presence of diagrams
in the problems’ hierarchical ordering. Furthermore, results provided support for other studies (e.g. Diezman & English, 2001) which documented some students’ difficulties to use diagrams efficiently for the solution of problems. We discuss the findings
and provide suggestions for the efficient use of diagrams in the problem solving situation. 相似文献
9.
In this article, we describe how using prediction during instruction can create learning opportunities to enhance the understanding
and doing of mathematics. In doing so, we characterize the nature of the predictions students made and the levels of sophistication
in students’ reasoning within a middle school algebra context. In this study, when linear and exponential functions were taught,
prediction questions were posed at the launch of the lessons to reflect the mathematical ideas of each lesson. Students responded
in writing along with supportive reasoning individually and then discussed their predictions and rationale. A total of 395
prediction responses were coded using a dual system: sophistication of reasoning, and the mechanism students appeared to utilize
to formulate their prediction response. The results indicate that using prediction provoked students to connect among mathematical
ideas that they learned. It was apparent that students also visualized mathematical ideas in the problem or the possible results
of the problem. These results suggest that using prediction in fact provides learning opportunities for students to engage
in mathematical sense making and reasoning, which promotes students’ understanding of the mathematics that they learn. 相似文献
10.
Anderson Hassell Norton Andrea McCloskey 《Journal of Mathematics Teacher Education》2008,11(4):285-305
The challenge that we address concerns teachers’ shifts toward student-centered instruction. We report on a yearlong professional
development study in which two United States elementary school teachers engaged in a teaching experiment, as described by
Steffe and Thompson (in: Lesh and Kelly (eds) Research on design in mathematics and science education, 2000). The teaching
experiment involved close mathematical interactions with a pair of students after school, in the context of solving fractions
tasks. By conducting a teaching experiment, we anticipated that each teacher would have more opportunity to develop insight
into students’ mathematics. We also anticipated that these insights would influence the teachers’ classroom practice, even
without explicit support for such a shift. Indeed, the teachers found that they began asking more probing questions of their
students and spending more time listening to students’ explanations, but shifts to classroom practice were limited by constraining
factors such an inflexible curriculum. 相似文献
11.
In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of
university calculus students’ collaborative development of mathematical methods for finding the volume of a solid of revolution,
in response to mathematical necessity in problem solving, without prior instruction on solution methods. The second theory
emerges from microlinguistic analysis of students’ mathematical choices and use of warrants in substantial argumentation to
communicate, clarify, and convince others of the validity of their conjectures and mathematical work. Our goal was to illuminate
mathematical argumentation by collaborative groups of calculus students at a qualitative level of detail sufficient to reveal
one view of how these students satisfied the creative drive for mathematical meaning, communication, and accuracy in problem
solving as evidenced in one classroom over several days. 相似文献
12.
Torulf Palm 《Educational Studies in Mathematics》2008,67(1):37-58
The study presented in this paper seeks to investigate the impact of authenticity on the students’ disposition to make necessary
real world considerations in their word problem solving. The aim is also to gather information about the extent to which different
reasons for the students’ behaviors are responsible for not providing solutions that are consistent with the ‘real’ situations
described in the word problems. The study includes both written solutions to word problems and interview data from 161 5th
graders. The results show an impact of authenticity on both the presence of ‘real life’ considerations in the solution process
and on the proportion of written solutions that were really affected by these considerations. The students’ frequent use of
superficial solution strategies and their beliefs about mathematical word problem solving were found to be the main reasons
for providing solutions that are inconsistent with the situations described in the word problems. 相似文献
13.
The purpose of this paper is to contribute to the debate about how to tackle the issue of ‘the teacher in the teaching/learning
process’, and to propose a methodology for analysing the teacher’s activity in the classroom, based on concepts used in the
fields of the didactics of mathematics as well as in cognitive ergonomics. This methodology studies the mathematical activity
the teacher organises for students during classroom sessions and the way he manages1 the relationship between students and mathematical tasks in two approaches: a didactical one [Robert, A., Recherches en Didactique
des Mathématiques 21(1/2), 2001, 7–56] and a psychological one [Rogalski, J., Recherches en Didactique des Mathématiques 23(3),
2003, 343–388]. Articulating the two perspectives permits a twofold analysis of the classroom session dynamics: the “cognitive
route” students are engaged in—through teacher’s decisions—and the mediation of the teacher for controlling students’ involvement
in the process of acquiring the mathematical concepts being taught. The authors present an example of this cross-analysis
of mathematics teachers’ activity, based on the observation of a lesson composed of exercises given to 10th grade students
in a French ‘ordinary’ classroom. Each author made an analysis from her viewpoint, the results are confronted and two types
of inferences are made: one on potential students’ learning and another on the freedom of action the teacher may have to modify
his activity. The paper also places this study in the context of previous contributions made by others in the same field. 相似文献
14.
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
15.
Elisabetta Robotti 《Educational Studies in Mathematics》2012,80(3):433-450
In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, 1938). Thanks to “verbal thought”, language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, 1975). So, it appears language can be studied as a cognitive process (Chomsky, 1975). In this investigation, I study language as a means for making the cognitive process explicit. In particular, I analyze the role of the verbalization produced by pairs of students solving a plane geometry problem. The basic idea of my research is that, during the resolution process of a plane geometry problem, natural language can play roles beyond that of communication: Natural language can be seen as a tool for supporting students’ cognitive processes (Robotti, 2008), and, at the same time, it can also be seen as a researchers’ tool which allows us to shed light on the evolution of students’ cognitive processes. With regard to language as researchers’ tool, I show how natural language (in our case, students’ verbalization during resolution of a plane geometry problem) can be used by the researcher to make explicit, to study, and to describe the development of the students’ cognitive processes during the resolution process. To this end, I present a model I have developed that allows us to identify, in students’ verbalization, different phases of their cognitive processes. 相似文献
16.
中小学"数学情境与提出问题"教学的实验研究 总被引：1，自引：0，他引：1
Xiaogang Xia Chuanhan Lü Bingyi Wang Yunming Song 《Frontiers of Education in China》2007,2(3):366-377
This research tends to make the experimental study on the mathematics teaching model of “situated creation and problem-based
instruction” (SCPBI), namely, the teaching process of “creating situations—posing problems—solving problems—applying mathematics”.
It is aimed at changing the situation where students generally lack problem-based learning experience and problem awareness.
Result shows that this teaching model plays a vital role in arousing students’ interest in mathematics, improving their ability
to pose problems and upgrading their mathematics learning ability as well.
相似文献
17.
The general background of this study is an interest in how digital tools contribute to structuring learning activities. The
specific interest is to explore how such tools co-determine students’ reasoning when solving word problems in mathematics,
and what kind of learning that follows. Theoretically the research takes its point of departure in a sociocultural perspective
on the role of cultural tools in thinking, and in a complementary interest in the role of the communicative framing of cognitive
activities. Data have been collected through video documentation of classroom activities in secondary schools where multimedia
tools are integrated into mathematics teaching. The focus of the analysis is on cases where the students encounter some kind
of difficulty. The results show how the tool to a significant degree co-determines the meaning making practices of students.
Thus, it is not a passive element in the situation; rather it invites certain types of activities, for instance iterative
computations that do not necessarily rely on an analysis of the problems to be solved. For long periods of time the students’
activities are framed within the context of the tool, and they do not engage in discussing mathematics at all when solving
the problems. It is argued that both from a practical and theoretical point of view it is important to scrutinize what competences
students develop when using tools of this kind.
相似文献
| Annika Lantz-AnderssonEmail: |
18.
Ingeborg Krange 《Cultural Studies of Science Education》2007,2(1):171-203
Recent research has to a limited extent explored the characteristics of students’ conceptual practices as sociocultural phenomena
in general and in science education in particular. I approach this issue by studying a group of students while solving a particular
scientific problem from A to Z, and as part of this analyse how different cultural means (the knowledge domain and the tools
in use) structure the students’ interactions and how their interpersonal relations change over this period of time. The aim
is to illustrate how these cultural means intersect in productive and less productive ways during the students’ conceptual
practices. The study has its point of departure in a design experiment where a group of four students, together with their
teacher, solve different problems related to the biological phenomenon of sequencing a DNA molecule (the insulin gene). Video-recordings
of the students’ interactions constitute the basis for this analysis. The cultural means strongly structure the students’
conceptual practices during their problem solving processes. Whereas the knowledge domain structured the whole process, the
significant roles of the website and the computer-based 3D model of the insulin gene were especially apparent during the second
part of the trajectory. The intersection of these cultural means appear productive in terms of disciplinary knowledge when
the students’ became aware of how to handle this relationship. The interpersonal relations between the students and their
teacher altered slightly in the beginning and became increasingly more fixed during the students’ progression. 相似文献
19.
Nan Zhu 《International Journal of Disability, Development & Education》2015,62(6):608-627
This study investigated the impact of cognitive strategy instruction (CSI) on mathematical word problem solving of students with mathematics disabilities. A sample of fourth-grade students in a Chinese primary school was divided into a treatment group (75 students) and a comparison group (75 students). The sample consisted of students with mathematics disabilities only, students with both mathematics and reading disabilities, as well as average- and high-achieving students. Results showed that students at all ability levels (except high-achieving students) in the treatment group outperformed significantly their counterparts in the comparison group; the intervention effect was stronger for students with mathematics disabilities only than for those with both mathematics and reading disabilities. The present study indicates that CSI is a contextually and pedagogically appropriate model that has a strong potential to improve mathematical word problem solving. 相似文献
20.
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