共查询到20条相似文献，搜索用时 31 毫秒
1.
The Development of Everyday Mathematics in Brazilian Children with Limited Formal Education 总被引：1，自引：0，他引：1
Steven R. Guberman 《Child development》1996,67(4):1609-1623
The sociocultural context in which children acquire and use everyday mathematics was studied in Brazilian shantytown communities. Children's developing mathematical abilities and use of currency in solving commercial problems were investigated. Interviews with the parents of 105 children from 4 to 14 years of age indicated that, when sent to make purchases at local stands, the problems entailed in the responsibilities parents assigned to children involved greater arithmetical complexity with increasing age. Children's accuracy and strategy use on arithmetic tasks similar to the problems encountered in commercial transactions revealed: ( a ) many children used currency to aid their problem solving; ( b ) with increasing age, currency use declined; and ( c ) children's currency use progressed from global estimates to the mental decomposition and manipulation of currency values. The mathematical complexity of children's commercial transactions correlated significantly with their mathematics performance even when age, grade in school, and years of schooling were statistically controlled The results provide evidence that by adjusting the mathematical complexity of children's commercial transactions, parents facilitate connections between children's developing competence and their everyday activities. 相似文献
2.
In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning mathematics via problem solving. Two novice MTEs worked with an experienced MTE and reflected on the process of learning to teach via problem solving and supporting PTs in developing deep understandings of foundational mathematical ideas. Taking a position of inquiry as stance, we examined our experiences teaching mathematics content courses for PTs via problem solving. We found that all of the MTEs used and developed some MKTT through (a) understanding and deciding on the mathematical goals of both the individual lessons and the two-course sequence as a whole, (b) choosing and facilitating tasks, and (c) using questions to scaffold PTs learning and engage them in mathematical processes such as making conjectures, justifying their reasoning, and proving or disproving conjectures. 相似文献
3.
Umesh Ramnarain 《The Australian Educational Researcher》2014,41(1):43-57
A major impediment to problem solving in mathematics in the great majority of South African schools is that disadvantaged students from seriously impoverished learning environments are lacking in the necessary informal mathematical knowledge to develop their own strategies for solving non-routine problems. A randomized pretest–posttest control group design was used to empirically investigate the effectiveness of a strategies-based problem solving approach on the problem solving performance of 9th grade disadvantaged students. In this approach students receive explicit instruction on a wide repertoire of problem solving strategies. The results reported in this study show a significant improvement in problem solving performance when a strategies-based approach to problem solving was being implemented. Quantitative and qualitative analyses of the responses to the items showed how the treatment group students had internalized as part of their problem solving repertoire the strategies on which they had been explicitly instructed on. The findings of this study make a case for the adoption of this approach so that the gap between the student’s existing problem solving competence, and the cognitive demands of a problem solving task can be bridged. 相似文献
4.
Mathematics problem solving provides a means for obtaining a view of young children’s understanding of mathematics as they
move through the early childhood concept development sequence. Assessment information can be obtained through observations
and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary grade children’s approaches
to problem solving are provided in the article. Prekindergarten and kindergarten age children discover problems during play.
For example, they figure out how to use informal measurement to use construction materials such as unit blocks and Lego to
build a desired building or make a desired object. Moldable materials such as clay and play dough provided shape experiences.
The daily sequence of activities builds on their concept of time. Primary grade children solve adult- and child-generated
problems. They may use manipulatives and/or drawings to generate problem solutions prior to using symbols and notation. Teacher
and/or student devised rubrics can be used to guide evaluation. 相似文献
5.
Martin Niss 《International Journal of Science and Mathematics Education》2017,15(8):1441-1462
This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called structuring for mathematization, where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four protocols from task-based interviews with university students working on physics problems in pairs who fail when solving the problems. The obstacles encountered by the students are shown to be related to how the students approach the structuring for mathematization, but they are met at different steps in this process. Four types of obstacles are identified. 相似文献
6.
关注过程的数学教学 总被引：1，自引：0，他引：1
顾继玲 《课程.教材.教法》2010,(1)
关注数学过程,有利于更好地掌握知识与技能,培养主动探究的意识,增强应用的意识,形成良好的情感态度;在数学教学中应关注数学化的过程、问题解决的过程和反思的过程。 相似文献
7.
The current study aimed to investigate children’s difficulties in word problem solving through assessing their ability to mathematize, or to identify the semantic role of the unknown from word problems. Fifth graders (n = 213) were given an advanced word problem reasoning task in which they had to match word problems with schematic diagrams that depict different processes (multiplication versus division) and the unknown being in different semantic roles (e.g., unit size, number of units, or total in an equal group problem). They were also tested on their mathematical problem solving as well as some potential confounding variables (i.e., intelligence and working memory) and mediators. The ability to identify the semantic role of the unknown was shown to be longitudinally predictive of children’s mathematical problem solving performance even after controlling for the effects of covariates and autoregressor. Such a relation was partially mediated by children’s ability to convert word problems into the correct number sentences/equations. The findings not only highlight the importance of unknown identification in mathematical problem solving process, but also provide a practical tool to assess such an ability. 相似文献
8.
This article deals with the investigation of the psychometric quality and constructs validity of algebra word problems generated by means of a schema-based version of the automatic min–max approach. Based on review of the research literature in algebra word problem solving and automatic item generation this new approach is introduced as a theory-based top–down method of automatic item generation featuring a quality control framework aimed to minimize the construct unrelated variance in the item parameters. The first study deals with the evaluation of an initial set of items. The results are replicated in the second study using a larger item set which also allows the investigation of the construct representation of the generated item. Since construct unrelated variance components (e.g. reading comprehension) have been controlled for in the item generation phase the results revealed some interesting insights into the cognitive processes of the actual mathematization phase of algebra word problem solving. The third study investigated the nomothetic span is using hierarchical confirmatory factor analysis. The results argue for the convergent and discriminant validity of the automatically generated items. Taken together, the results indicate that the automatic generation of construct valid algebra word problems at a high psychometric level is viable. The discussion is thus concerned with the implications of this new approach to item generation for theory development and evaluation as well as practical benefits for educational assessment and the development of intelligent tutoring systems. 相似文献
9.
Taking a positive view is a fruitful way to prompt educators to reflect on and to develop their practice. Teachers, teacher educators and children bring a wide range of ideas that provide a powerful basis for developing understanding of the complexities of classroom practice. Using appreciate inquiry the authors show how they developed their understanding of professional development as they worked with groups of teachers who investigated their science teaching practice with young children and produced case studies of practice. The authors also show how the roles and ideas of themselves as university tutors were challenged and emerged to suit the range of contexts involved. Their view of Continuing Professional Development was influenced by the lived experiences of the teachers and themselves. They worked to systematise learning through identifying commonalities of experience and reflection along four dimensions: creating spaces for growth; working with emergent purposes; action research as rhizomatic growth; and collaborative and collective action. The rich variety of outcomes shows the value of creating space for growth for children and for adults. The energy and enthusiasm liberated motivated the participants to explore their worlds in ways that were difficult to predict at the start of the project. 相似文献
10.
儿童数学认知障碍不仅涉及到多项认知成分和心理过程的作用机制,还涉及到诸如前额叶皮层等认知神经机制。执行功能是对个体的意识和行为进行监督和控制的各种操作过程,与数学认知能力的发展有着密切的联系。执行功能可以从认知神经机制、工作记忆机制、抑制控制机制以及问题解决等方面对儿童数学认知障碍进行预测和解释。 相似文献
11.
A Comparison of Verbal and Written Descriptions of Students' Problem Solving Processes 总被引：1，自引：0，他引：1
David K. Pugalee 《Educational Studies in Mathematics》2004,55(1-3):27-47
12.
Lynda C. Lin Eva M. Pomerantz Lucy R. Zheng Richard W. Robins 《Child development》2021,92(4):1223-1237
Although Latinx parents’ perceptions of the climate of their children’s schools may play a role in their children’s academic adjustment, research examining this idea is sparse. Every 2 years beginning when children were in fifth grade (Mage = 10.86 years) until they were in 11th grade, Mexican-origin mothers (N = 674) reported on their perceptions of the climate of their children’s schools; information on children’s academic adjustment was collected from children and mothers. Multilevel modeling indicated that when mothers had more positive school climate perceptions, their children valued school more and performed better in school, but did not necessarily hold higher educational expectations. The findings suggest the importance of schools in creating welcoming environments for Mexican-origin parents. 相似文献
13.
Annick Fagnant 《European Journal of Psychology of Education - EJPE》2005,20(4):355-367
This article relates to an empirical study based on the use of mathematical symbolism in problem solving. Twenty-five pupils
were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems.
In their classical curriculum, these pupils have received a traditional education based on a “top-down” approach (an approach
that is still applied within the French Community of Belgium): conventional symbols are presented to the pupils immediately
with an explanation of what they represent and how they should be used. Teaching then focuses on calculation techniques (considered
as a pre-requisite for solving problems). The results presented here show the abilities (and difficulties) demonstrated by
the children in making connections between the conventional symbolism taught in class and the informal approaches they develop
when faced with the problems that are put to them. The limits of the “top-down” approach are then discussed as opposed to
the more innovative “bottom-up” type approaches, such as those developed by supporters of Realistic Mathematics Educations
in particular. 相似文献
14.
Transfer of strategies between problems sharing the same formal structure is facilitated by a semantic recoding that makes evident the structural similarities between the problems. Two experiments were carried out among 4th and 5th grade pupils, with an experimental group trained to compare strategies in order to reinterpret an arithmetic word problem so that the calculations are consistent with the interpretation, and a control group. The experimental group in Experiment 1 improved significantly by choosing the alternative strategy in problems different from those used in training but no significant progress was observed in the control group. Experiment 2 showed that the improvement observed in the experimental group could not be attributed to the fact that children only learned to use a superficial rule. These results support the idea that the activity of problem re-representation may be a crucial step in mathematization. 相似文献
15.
Affect and Meta-Affect in Mathematical Problem Solving: a Representational Perspective 总被引：1，自引：0，他引：1
We discuss a research-based theoretical framework based on affect as an internal representational system. Key ideas include the concepts of meta-affect and affective structures, and the constructs of mathematical intimacy and mathematical integrity. We understand these as fundamental to powerful mathematical problem solving, and deserving of closer attention by educators. In a study of elementary school children we characterize some features of emotional states inferred from individual problem solving behavior, including interactions between affect and cognition. We describe our methodology, illustrating theoretical ideas with brief qualitative examples from a longitudinal series of task-based interviews. 相似文献
16.
“数学化”的数学教学及其策略探讨 总被引：1，自引：0，他引：1
刘兰英 《上海师范大学学报(哲学社会科学版)》2010,(6):104-107
“数学化”教学就是以“数学化”为核心的数学教学,其实质就是激发学生数学地组织现实世界的过程。它是有效数学教学的核心和数学课程改革的关键。文章提出了实施“数学化”教学的三条主要策略,即教学要源于数学现实又要升华数学现实,要注重培养学生的数学建模能力,以及要尊重学生差异并促其个性化地实现数学知识的“再创造”。 相似文献
17.
In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated
as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified
for solving mathematical word problems. Second, it is argued that so called hybrid animations would be most effective for
acquiring these prerequisites, because they show the continuous transition from a concrete, but superficial problem representation
to a more abstract, mathematical problem model that forms a basis for solving a problem. An experiment was conducted, where
N = 32 pupils from a German high school studied either only text-based worked examples explaining different problem categories
from the domain of algebra or worked examples augmented with hybrid animations. Learners with hybrid animations showed superior
problem-solving performance for problems of different transfer distance relative to those in the text-only condition. 相似文献
18.
数学问题解决中的模式识别的研究视角,可以分为基于数学解题认知过程与解题策略角度、基于"归类"的视角、基于数学问题解决中模式识别与其他因素的关系的视角等,具体研究领域涉及几何解题中的视觉模式识别、几何问题解决中的模式识别、解代数应用题的认知模式、数学建模中的模式识别等.由于在知觉领域与问题解决领域"模式识别"的表述存在一定的混乱性,将基于数学问题解决的模式识别界定为:当主体接触到数学问题后,与自己认知结构中的某数学问题图式相匹配的思维与认知过程.并进一步通过其与"归类"的区别与联系、与"化归"的区别与联系使"基于数学问题解决的模式识别"的概念得以澄清.在范围上,把问题解决中的模式识别界定为一种思维过程的阶段或者思维策略,认为它是解题的重要组成部分,但并不是解题的全部.对于未来的展望,期望系统的理论研究、期望对学生问题解决中模式识别的认知过程与机理的实质性的研究以及对学生问题解决中模式识别的教学实验研究. 相似文献
19.
20.
This paper reports on a qualitative study in which three third grade students were presented with a mathematical challenge related to the volume of a cuboid. The task required the construction of containers and the enumeration of the multi-link cubes1 held by each of the containers. The study videotaped and investigated the students working as a group through potentially seven different problem solving categories, and how they dealt with the student-generated mathematical dilemmas that surfaced during their exploration of the original problem. The tapes were examined for the problem solving actions that the students demonstrated, and an analysis of the students' counting strategies and solutions explored the connection between the children's spatial structuring and their use of numerical operations in enumerating 3-D rectangular arrays of cubes. The notions of perseverance and control are considered as they emerge during autonomous problem solving and the mathematical residue that results from the developing understanding of volume is discussed.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献