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1.
CONSTRUCTING KNOWLEDGE ABOUT THE NOTION OF LIMIT IN THE DEFINITION OF THE HORIZONTAL ASYMPTOTE 总被引：1，自引：0，他引：1
Ivy Kidron 《International Journal of Science and Mathematics Education》2011,9(6):1261-1279
Processes of knowledge construction are investigated. A learner is constructing knowledge about the notion of limit in the
definition of the horizontal asymptote. The analysis is based on the dynamically nested epistemic action model for abstraction
in context. Different tasks are offered to the learner. In her effort to perform the different tasks, the learner encounters
a situation of conflict between her concept image of the horizontal asymptote and the concept definition. The model of abstraction
in context is used to analyze two new constructions of knowledge for the learner, which permit her to reconsider her concept
image and to conceptually understand the definition of the horizontal asymptote. 相似文献
2.
《学习科学杂志》2013,22(4):453-488
3.
This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation
points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically,
our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the
learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and
interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions
indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction
in context. 相似文献
4.
Helena Johansson 《International Journal of Science and Mathematics Education》2016,14(6):1133-1152
This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students’ knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to mirror the goals stated in the curricula, and these goals are similar across national borders. The framework used for characterising the mathematical reasoning required to solve the tasks in the national physics tests distinguishes between imitative and creative mathematical reasoning. The analysis process consisted of structured comparisons between representative student solutions and the students’ educational history. Of the 209 analysed tasks, 3/4 required mathematical reasoning in order to be solved. Creative mathematical reasoning, which, in particular, involves reasoning based on intrinsic properties, was required for 1/3 of the tasks. The results in this paper give strong evidence that creative mathematical reasoning is required to achieve higher grades on the tests. It is also confirmed that mathematical reasoning is an important and integral part of the physics curricula; and, it is suggested that the ability to use creative mathematical reasoning is necessary to fully master the curricula. 相似文献
5.
This paper explores constructions of the ‘new’ university student in the context of UK government policy to widen participation in higher education. New Labour discourse stresses the benefits of widening participation for both individuals and society, although increasing the levels of participation of students from groups who have not traditionally entered university has been accompanied by a discourse of ‘dumbing down’ and lowering standards. The paper draws on an ongoing longitudinal study of undergraduate students in a post–1992 inner‐city university in the UK to examine students' constructions of their experiences and identities in the context of public discourses of the ‘new’ higher education student. Many of the participants in this study would be regarded as ‘non‐traditional’ students, i.e. those students who are the focus of widening participation policy initiatives. As Reay et al. (2002) discovered, for many ‘non‐traditional’ students studying in higher education is characterized by ‘struggle’, something that also emerged as an important theme in this research. The paper examines the ways in which these new student identities both echo the New Labour dream of widening participation and yet continue to reflect and re‐construct classed and other identities and inequalities. 相似文献
6.
Amy E. Ryken 《Journal of Mathematics Teacher Education》2009,12(5):347-364
This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in
relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning
skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation
task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial
tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures
created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving
beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings
suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices
by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking
and curriculum materials. 相似文献
7.
‘Doing the Best for the Students’: dilemmas and decisions in carrying out statutory assessment tasks
This paper considers the effects on teachers, students and the curriculum of the experience, in the spring of 1993, of the first extended assessement tasks in Design in Technology in England and Wales. It examines the frustrations experienced and the dilemmas faced by teachers in working on these tasks with students, and their attempts to resolve their resulting role conflicts. It is suggested, that in this case at least, teachers' loyalties to their ideas about good teaching and learning took precedence over the requirement to follow the Government's assessment procedures. This is because teachers felt that the tasks set by the Government were inappropriate both for student learning and for assessing the curriculum which they had followed, and that the ways in which they were expected to carry them out were detrimental both to student learning and to ‘fair’ assessment. It is suggested that in some cases this led to a ‘radicalisation’ of a comparatively conservative group. The effects on the curriculum, the schools and the teachers concerned are critically examined in the light of planned changes in the Design and Technology curriculum. 相似文献
8.
Joseph B. W. Yeo 《International Journal of Science and Mathematics Education》2017,15(1):175-191
Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended, to mean the same construct, while others distinguish between these terms. It is difficult to hold a meaningful discussion or to define clearly an area of research on open tasks if the idea of what constitutes the construct of openness is vague. Moreover, what students learn depends on the types of tasks that they are given, and different kinds of tasks place differing cognitive demands on students. Thus, the objectives of this article are to clarify the types of mathematical tasks and develop a framework to characterise their openness based on five task variables: goal, method, task complexity, answer and extension; and to discuss how different types of tasks and openness may affect student learning. The openness framework can help teachers to design or select more appropriate tasks to cater to students with different abilities in order to develop in them various kinds of mathematical thinking processes, and it can also make it easier for researchers to study the interaction between different types of openness and student learning. 相似文献
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10.
Abstract In the present study the relationship between teaching and learning was examined using a conceptual framework that links dimensions of instructional tasks with gains in student learning outcomes. The greatest student gains on a performance assessment consisting of tasks that require high levels of mathematical thinking and reasoning were related to the use of instructional tasks that engaged students in the “doing of mathematics” or the use of procedures with connections to meaning. In addition, student performance gains were greater for those sites whose tasks were both set up and implemented to encourage the use of multiple solution strategies, multiple representations, and explanations. Whereas, student performance gains were relatively small for those sites whose tasks tended to be both set up and implemented in a procedural manner and that required a single solution strategy, single representations, and little or no mathematical communication. 相似文献
11.
采用追踪研究设计,以小学生数学学习为例,考察新课程改革的实施效果。研究从学生对数学的基本理解与计算能力、复杂问题解决能力、数学交流与应用意识以及对数学学习的兴趣与数学素养三个方面,实证分析参加新课程与原课程两组学生之间的差异。结果表明,使用新课程的学生对数学的基本理解与计算能力从整体上表现较好,但不如使用原课程学生在此方面的优势明显;与使用原课程学生相比,使用新课程的学生在高层次思维能力方面表现出明显优势,新课程比较明显地提高了学生的复杂问题解决能力、数学表达与交流及应用意识;新课程提高了学生学习数学的兴趣,学生也形成了良好的数学素养。 相似文献
12.
《师资教育杂志》2012,38(3):325-338
ABSTRACT This investigation examines the views of pedagogical content knowledge of 12 student teachers of mathematics drawn from three different training groups. Attitudes towards and understandings of pedagogical content knowledge were elicited using six Likert‐item statements whilst information on students' learning was obtained through open‐ended questioning. Differences between groups were apparent only in tendencies to give extreme responses and to adopt outlying positions. These differences may be attributable to differences in values or prior knowledge and to training parallels with the social construction of mathematical meaning. Indications of the acquisition of pedagogical content knowledge appeared in all training groups and seemed to be linked to a hierarchical view of mathematics; possible limitations for student learning are implied. Students' views also highlight the importance of reflection upon subject matter knowledge and awareness of learning processes when transforming mathematical ideas for teaching purposes. It is suggested that the role of prior learning is worthy of further investigation. 相似文献
13.
Dynamic computer environments can facilitate students' active participation in the construction of mathematical concepts and
techniques—a long-standing goal among educational reformers. This paper analyzes techniques developed by students in an open-ended
computer activity, examines learning styles of inventive students, and discusses use of student-generated mathematical techniques
in developing new software to (1) cultivate mathematical inventiveness in more students and (2) encourage students to relate
their own techniques to more general mathematical ideas. New software was designed to provide an informal, interactive introduction
to functions and related algebraic ideas. A fundamentally constructivist approach was supplemented with coaching available
upon student request. Each type of function was targeted with a sequence of challenges, hints to support the challenges, and
games for synthesis and application. Students combined algebraic techniques to construct functions and manipulated the functions
to cause specific behaviors in their graphs. The software succeeded in accommodating diverse student learning styles, initiating
students into use of a wider variety of techniques, and inducing students to take an interactive approach to constructing
mathematical knowledge.
The development described in this paper was supported in part by the National Science Foundation (NSF MDR 84-70608). Any views
expressed herein are those of the author and do not necessarily reflect the views of the National Science Foundation. 相似文献
14.
本文阐述了高校基层党支部是高校党员组织起来的基本形式和日常管理的基本单位,是高校基层组织的政治核心。高校基层党支部的作用和任务主要是积极宣传和正确贯彻执行党高等教育的路线、方针、政策,做好师生员工的思想政治工作。本文还提出了加强高校基层党支部建设的五条措施。 相似文献
15.
连金发 《暨南大学华文学院学报》2009,(1)
本文首先讨论实词和虚词的主要分野,再以构式和词汇属性的互动为本探索华语三种构式:两类不及物动词的构式,感受构式,数量分配构式.每个构式都做简要论述,点出其特征和用法上的限制.从本文的探索可以看出华语虽然词形没有屈折变化,但是构式和词汇固有属性之间蕴藏丰富而引人入胜的信息. 相似文献
16.
Many teachers struggle to provide equitable opportunities for students with special educational needs (SEN) to learn science concepts in the inclusive classroom. This study examines the experience of teaching in an inclusive classroom using a conceptual change approach, the Thinking Frames Approach (TFA), incorporating the use of discrepant events, social construction of scientific conceptions followed by the production of multiple student‐generated representations of their understanding. An in‐depth case study is presented of the experience of Wayne, a student with complex SEN and the effect on his behaviour and science learning based on video/audio recordings of lessons, teacher journal entries, student artefacts, questionnaire results and interviews. It was found that there were positive effects for Wayne's learning using this approach including improved behaviour, greater feelings of self‐efficacy, increased participation in small group and class discussions and improved outcomes on the same assessment tasks as peers. It is suggested that the structured approach of the TFA, the communication of understanding in different modalities, particularly drawing, and the support of peers enabled Wayne to more deeply engage in construction of understanding and may provide teachers with an easy and effective approach to authentic inclusion where real conceptual gains are made by all students. 相似文献
17.
This paper examines one mode of mathematical communication: that of student journal writing in mathematics. The focus of the discussion is a study of four years' use of journal writing in mathematics involving approximately 500 students in Grades 7 through 11 in a particular Victorian secondary school. The evaluation of the experimental use in one school of journal writing in mathematics provides a powerful demonstration of the link between language and mathematics and suggests a relationship between students' mathematical writings and their perceptions of mathematics and mathematical activity.The research reported in this paper was funded in part by a grant from the National Center for Research in Mathematical Sciences Education, University of Wisconsin-Madison. 相似文献
18.
曹荣荣 《贵州教育学院学报》2011,(9):8-10
建构主义学习观认为知识是由主体内部建构的,它强调学习是一种知识建构、知识的社会协商和社会实践参与过程,而情境认知理论的核心观点则认为“知识来源于活动”,基于情境认知的教学更强调学习环境以及学习活动设计的提供。以“无穷集合的比较”为例来观察学生的知识建构过程,研究表明只有巩固了的知识才是完备的抽象过程,也只有这样才能更好地创建新的数学建构。 相似文献
19.
Tracy Goodson-Espy 《Educational Studies in Mathematics》1998,36(3):219-245
This study utilized a psychological constructivist perspective to examine the transitions that students make from arithmetic to algebra in the context of problems, that from the expert's perspective, involve the concept of linear inequality. Unstructured interviews were used to gather data that were used to develop an explanation concerning student understanding. Thirteen college students were interviewed individually and asked to solve nine related tasks. The interviews were videotaped and the protocols were analyzed to document student conceptions. Five case studies were used to develop and substantiate an explanation regarding students' transitions from arithmetic to algebra. Cifarelli's (1988) levels of reflective abstraction and Sfard and Linchevski's (1994) theory of reification provided a framework for this explanation. This paper discusses an integration of Cifarelli and Sfard's constructs. Students who completed a transition to algebra operated at higher levels of reflective abstraction than students who were unable to complete such a transition. Operating at higher levels of reflective abstraction enabled these students to consider concepts as both processes and abstract objects. Developing this ability was found to be critical in achieving a transition to using algebraic methods. 相似文献
20.
网络课程是现代远程教育的重要载体,其建设质量与学习者的成长发展休戚相关。本文基于学习生态观理论,综合采用文献调研、深度访谈和抽样调查等方法,梳理出了网络课程学习中存在的主要生态失衡问题,并提出了相关的解决对策,希望能为网络课程建设提供有益的启示与参考。 相似文献