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1.
This article describes an empirical investigation of the extent to which incorrect arithmetic algorithms persist over time. The use of subtraction procedures by children aged 9–11 was charted over time periods of 1–3 months. The ways in which several bugs might be related to a single misconception were considered and a set of “bug classes” was identified. The results indicated that the prevailing tendency to attribute stable procedural knowledge and systematic behavior to children of this age is misguided. They provide some insight into the development of mathematical knowledge under the influence of conventional instruction.  相似文献   

2.
Abstract

The authors examined the thinking of children who had the opportunity to construct personal knowledge about division of fractions. The authors based this study on a teaching experiment design and used relevant contexts/situations to foster students' development of knowledge. Participants were a group of mixed-ability, 5th-grade mathematics students. They used pictures, symbols, and words to resolve situations and communicate their solutions. The authors analyzed the solutions to describe the students' constructions of division-of-fractions concepts and procedures. All strategies that the students used represented some manifestation of conceptual knowledge about addition and subtraction of fractions and a definition of division. Some students developed formal symbolic procedures, and others developed pictorial procedures; none invented an invert-and-multiply procedure. Through the window of constructivism, this study allowed the authors to glimpse children's constructions of knowledge and provided alternatives to the traditional view of the expected procedure (invert and multiply) that children should learn for division of fractions.  相似文献   

3.
First- and second-grade children were successfully taught symbolic multi-digit addition and subtraction procedures by first doing the procedures with a physical embodiment of the first four places of the base-ten system. Relationships between the embodiment and the numerical symbols were supported by close linking of the physical and the symbolic procedures and by the use of base-ten, named-value (standard English), and embodiment-name words. Most children successfully extended the procedures to ten-digit symbolic problems done without the embodiment. For many children who made procedural errors on delayed tests, the mental representation of the procedure with the physical embodiment was strong enough for them to use it to selfcorrect their symbolic procedure. The physical embodiment also seems to support the learning of various other concepts related to place value.  相似文献   

4.
民事诉讼法学教学方法初探   总被引：4，自引：0，他引：4  
民事诉讼法是一门实践性很强的学科,很多学者对其教学方法进行了大量的探讨。本人根据多年的教学经验,在《民事诉讼法学》的教学实践中,进行了大胆的尝试,认为在教学中应注重讲授式、问题式、讨论式、复习式、网络式五种教学方法。  相似文献   

5.
目前,由于缺乏系统适用的教科书和严谨可靠的评价体系,使我国中度智力残疾儿童的特殊教育面临极大的困难.我们试图通过文献资料的分析和实际的教学实验研究,尝试编写出适合于弱智学校和普通学校特教班使用的中度智力残疾学生"实用语算"系统教材.并在此基础上,研究开发配套使用的教具和学具,编制适宜的教学评价体系.经过前期的研究,我们已形成一些理论上的认识和基本原则,努力处理好以下几个方面的关系.1,在教学目的上,处理好人格培养、能力发展和知识学习的关系;2,在教学内容上,处理好个体心理发展内在逻辑与知识体系内在逻辑的关系;3,在教学方法上,处理好教与学的关系;4,在教学形式上,处理好班级授课与个别教学的关系;5,在教学评价上,处理好评价与目的的关系;6,在教材选编上,突出地方特色与统一文化背景的关系.  相似文献   

6.
The use of mentoring group conversations as a tool to support pre-service teachers’ professional development has become more common. However, there is still a lack of research that shows how conversations are used to develop knowledge. The present paper is based on ethnographical observations of mentoring group conversations, and describes how pre-service teachers who participate in an obligatory mentoring model use their conversations as an arena in their search for professional knowledge. Three areas were focused upon during the conversations: the teachers’ role and teaching practice, conditions for professional development and conditions related to the profession. The pre-service teachers mainly used conversations to question, discuss, share and reflect over pedagogical and didactical dilemmas related to teaching activities in the classroom and to their own as well as other teachers’ behaviour and attitudes in different situations. The paper provides an insight into how a mentoring model can contribute to professional preparation.  相似文献   

7.
This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher’s mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and ascending a priori analysis and an a posteriori analysis. This analysis shows a development of different didactical situations and some links between mathematical knowledge and pertinence. In the conclusion, the contribution of the frameworks from both French and Anglo-American origins is briefly addressed.  相似文献   

8.
This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach, clinical interviews were conducted with ten 5–6-year-old children. The aim was to document how children combine knowledge of addition facts, calculation procedures and arithmetic concepts when solving a multiple-step task and how children’s application of different types of knowledge and overall solving approach changes and develops when children engage with solving the task in a series of problem solving sessions. The study documents children’s pathways towards developing a more effective and systematic approach to multiple-step tasks through different phases of their problem solving behaviour. The analysis of changes in children’s overt behaviour reveals a dynamic interplay between children’s developing representation of the task, their improved procedures and gradually their more explicit grasp of the conceptual aspects of their strategy. The findings provide new evidence that supports aspects of the “iterative model” hypothesis of the interaction between procedural and conceptual knowledge and highlight the need for educational approaches and tasks that encourage and trigger the interplay of different types of knowledge in young children’s arithmetic problem solving.  相似文献   

9.
This study investigated the effect of initial instruction on the processes children use to solve addition and subtraction word problems. Prior to instruction and following a two-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different addition and subtraction situations. Prior to instruction, the children's solution processes directly modeled the action or relationships described in the problem. Following instruction, they generally used a separating strategy for all subtraction problems. Although they could solve the problems, few children could coordinate their solutions with the arithmetic sentence they wrote to represent the problem.  相似文献   

10.
This paper presents an epistemological analysis of typical didactical activities noted in early‐years science lessons, which was carried out in an attempt to diagnose the extent to which the teaching practices adopted by early‐years educators are successful in supporting young children’s understanding in science. The analysis of didactical activities used a framework that allowed us to discover whether they promoted desired connections between theoretical ideas, evidence and the material world. Theoretical ideas, evidence and the material world are entities internal to scientific inquiry and, in educational contexts, connections between them are considered essential in assisting the development of young children’s scientific thinking. The results indicated that in the early‐years science classroom scientific activity was mainly confined to the representational level. Intervention practices into the material world were limited, and were based on collected evidence. No interventions based on ideas were identified in the science lessons. Missing links between evidence and theory and between ideas and the material world suggest that the didactical activities analysed did not promote scientific understanding.  相似文献   

11.
This paper describes a teaching method that enables students to design efficient and effective algorithms for reporting information systems applications. Adopting the general principles of transformative learning, students are immersed in a series of activities and interventions to enable learning. The activities provided opportunities for students to design algorithms, also using knowledge gained during the interventions. The interventions allowed students to gain knowledge about the output data structures such as list, table, and cube; the sequence control structures that may take different execution times; and the assumptions such as source data tables and mapping rules—all of which can contribute to the design of efficient and effective algorithms. 88 undergraduate business students in an advanced information systems course learn the principles of designing algorithms through critical reflection and reinterpretation consistent with the principles of transformative learning. The algorithms designed by students reveal that attention to the output data structures, sequence control structures, and assumptions enables the design of efficient and effective algorithms.  相似文献   

12.
ABSTRACT— This article gives an overview of developmental trends in research on metacognition in children and adolescents. Whereas a first wave of studies focused on the assessment of declarative and procedural metacognitive knowledge in schoolchildren and adolescents, a second wave focused on very young children's "theory of mind" (ToM). Findings from a recent longitudinal study are presented that demonstrate developmental links between early ToM and subsequent declarative metacognitive knowledge, mainly mediated by language competencies. The relevant literature further indicates that developmental trends in declarative and procedural metacognitive knowledge clearly differ. Whereas the findings for declarative metacognitive knowledge show steady improvement through childhood and adolescence, mainly due to increases in knowledge about strategies, the results are not similarly clear-cut for procedural metacognition. Age trends observed for this component of metacognition are significant for self-control activities but not pronounced for monitoring abilities. These findings have important implications for education, emphasizing the role of strategy training procedures in different instructional domains and illustrating teachers' potential impact on the improvement of monitoring and control processes.  相似文献   

13.
An important task for the preschool teacher is to create meaningful learning situations where children have opportunities to experience science. However, many teachers have both weak subject knowledge and a lack of confidence to teach science. The aim of the project presented in this article was to capture how nine preschool teachers developed their learning of and self-confidence in teaching science during a two-year professional development (PD) project while coplanning, coteaching, and coreflecting on their teaching activities. During the project, the preschool teachers’ self-confidence and attitudes played an important role for the their approach to science activities. Their collaborative learning and reflection became important for their PD and for the way science phenomena were included in the preschool context. As such, the project is based on opportunities for preschool teachers to develop their ideas about science and to reframe their work with the aim to stimulate children’s curiosity for science.  相似文献   

14.
This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered.  相似文献   

15.
远程教育媒体选择的程序教学过程中,一个完整的、巧妙的、高效的程序教学过程,必须使得学习者从头至尾,在每个阶段或环节、步骤当中,处于一种积极地观察、学习的状态。本文认为,远程教育的教学媒体选择程序操作可分为直线式、复线式、支线式、交线式、曲线式、虚线式六种操作模式,较之传统的课堂教学,远程教育更加有赖于程序教学法,只有不断运用程序教学原则,鼓励教师和学习者在远程教育的媒体教学活动中,程序"步步选",任务"步步清",知识"步步得",大脑"步步通",才能真正降低远程教育的教学难度,提高远程教育的媒体教学效益。  相似文献   

16.
Recent advances in the way that adults perform computation in our society require reconsideration of the assumptions underlying current elementary mathematics instruction. The widespread use of calculators and computers for situations requiring precise calculation removes much of the motivation for teaching the current addition, subtraction, multiplication, and division algorithms. Yet precisely this use of computing technology now puts a premium on the exercise of estimation techniques for verifying the reasonableness of computations. These techniques, especially those that can be used mentally (without the use of any external tools), have been used informally for years, but never formalized for instruction. This paper discusses a range of estimation techniques, and presents in detail a series of mental estimation procedures based on the concepts of measurement and real numbers rather than on counting and integers. A set of techniques for teaching these procedures is described. These estimation techniques are evaluated against the multiple functions that elementary mathematics instruction needs to serve.NoteThis research has been supported by The Spencer Foundation. Thanks to Randy Souviney, Margaret Riel, Marilyn Quinsaat, Andrea Petitto, Bud Mehan, and Karen Johnson for comments on earlier drafts.  相似文献   

17.
Deaf children's use of cognitive strategies in simple arithmetic problems   总被引：3，自引：0，他引：3  
Research shows that deaf children have inferior achievement in simple arithmetic compared to their hearing agemates. The reported study investigates whether the reasons for deaf children's poor achievement can be sought in their strategy development. As this is a central issue, the strategies used by deaf children when solving symbolic addition and subtraction problems are identified, classified and compared to findings from earlier research, involving both deaf and hearing children. The effect of Sign Language in strategy invention and use is the main concern in this study. One result from the present study is that structural aspects of Sign Language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but instead to refined procedural competence. This is a development in simple arithmetic that is compatible with that of less able hearing children. The counting procedures used by the deaf children involve both oral counting and Sign Language counting. Due to the small sample size, and the shortcomings of the research design, the results are more suggestive than conclusive. Thus, further studies are needed in this area.This revised version was published online in September 2005 with corrections to the Cover Date.  相似文献   

18.
The aim of this study was to scrutinize the assessment of teacher knowledge in a school‐based course at one Swedish pre‐service teacher education program. In a general education school‐based course, teacher educators visited the student teachers at their school placements and met them and their school mentors in student‐teaching conferences to assess their teacher knowledge. The findings primarily show that the assessment procedures are influenced by teacher educators’ organization of the school visits and conferences. Secondly, the organization of the school visits and conferences influences who the potential and actual assessors at the conferences can be and are. Thirdly, the assessed student teacher knowledge at the conferences is described as procedural knowledge in a knowledge‐in‐practice perspective, almost exclusively in the area of relational, emotional, and caring learning objectives and aspects of teaching activities. Fourthly, the findings show that propositional knowledge in a knowledge‐for‐practice perspective is hardly mentioned or assessed.  相似文献   

19.
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20.
This is a commentary paper in the volume on “Teachings situations as object of research: empirical studies within theoretical perspectives”. An essential object of mathematics education research is the analysis of interactive teaching and learning processes in which mathematical knowledge is mediated and communicated. Such a research perspective on processes of mathematical interaction has to take care of the difficult relationship between mathematics education theory and everyday mathematics teaching practice. In this regard, the paper tries to relate the development in mathematics education research within the theory of didactical situations to developments in interaction theory and in the epistemological analysis of mathematical communication.  相似文献   

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