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1.
This research describes an intensive study undertaken to determine children's representational strategies for relational numbers
(e.g. proportions, ratios, fractions). Relational numbers have three quantities associated with them: a whole and two parts.
Given these three quantities, children can form a representation based on a part-whole relationship or on a part-part relationship.
Fifteen children (6th, 7th, and 8th graders) solved fifteen probability problems which varied information content and quantitative
relationships between the quantities expressed in the problems. A quantitative and qualitative analysis revealed that children
prefer a part-part representation to solve problems with relational quantities. 相似文献
2.
Mi Yeon Lee Amy J. Hackenberg 《International Journal of Science and Mathematics Education》2014,12(4):975-1000
To investigate relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems that required explicit use of unknowns to write equations. As a part of the larger study, the first author conducted a case study of a seventh grade student, Willa. Willa’s fractional knowledge—specifically her reversible iterative fraction scheme and use of fractions as multipliers—influenced how she wrote equations to represent multiplicative relationships between two unknown quantities. The finding indicates that implicit use of powerful fractional knowledge can lead to more explicit use of structures and relationships in algebraic situations. Curricular and instructional implications are explored. 相似文献
3.
Günhan Caglayan 《Journal of Mathematics Teacher Education》2013,16(5):349-378
This study is about prospective secondary mathematics teachers’ understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations—referent preserving versus referent transforming compositions—acting on these quantities. Although multiplicative structures can be modeled by additive structures, they have their own characteristics inherent in their nature. I situate my analysis within a framework of unit coordination with different levels of units supported by a theory of quantitative reasoning and theorems-in-action. Data consist of videotaped qualitative interviews during which prospective mathematics teachers were asked problems on multiplication and factorization of polynomial expressions in x and y. I generated a thematic analysis by undertaking a retrospective analysis, using constant comparison methodology. There was a pattern which showed itself in all my findings. Two student–teachers constantly relied on an additive interpretation of the context, whereas three others were able to distinguish between and when to rely on an additive or a multiplicative interpretation of the context. My results indicate that the identification and coordination of the representational quantities and their units at different categories (multiplicative, additive, pseudo-multiplicative) are critical aspects of quantitative reasoning and need to be emphasized in the teaching–learning process. Moreover, representational Cartesian products-in-action at two different levels, indicators of multiplicative thinking, were available to two research participants only. 相似文献
4.
Lisa K. Boyce Gina A. Cook Lori A. Roggman Mark S. Innocenti Vonda K. Jump James F. Akers 《Early education and development》2004,15(4):371-386
This study examined low-income, Spanish-speaking, immigrant Latina mothers' book sharing behaviors in relation to their children's vocabulary. Participants were 47 3-year-old children and their mothers. We addressed two research questions: (a) What interactive behaviors are evident when low-income immigrant Latina mothers and their 3-year-old children look at books together? (b) For these children and their mothers, which book-sharing behaviors are related to children's expressive language? Overall, our results indicated that mothers were involved in several kinds of interactions with the books. They enhanced their children's attention to the printed text, promoted interaction or conversation with their children about what was in the books, and somewhat less often, used more complex literacy strategies. Mothers who did these things most had children with the largest vocabularies even when mothers' vocabulary was taken into account. Implications for designing interventions for similar families are discussed. 相似文献
5.
7-8岁数学学习困难与正常儿童加法策略比较研究 总被引：1，自引：0，他引：1
选取二、三年级数学学习正常和学习困难的儿童各 30名 ,共 12 0名被试。采用实验法、观察法和口语报告法相结合的方式 ,考察了两类儿童在加法任务中 ,策略选择和执行的差异及特点。研究表明 :小学低年级儿童的策略选择具有多样性、适应性和简约性的特点。从策略选择上看 ,出声、竖式、分解、对位和提取策略是小学 2— 3年级两类儿童的主选策略 ;数学学习困难儿童较多使用手指、数数、放弃和猜测等策略 ;数学学习正常儿童则较多使用提取、分解、凑数、换位和乘法策略。从策略执行上看 ,小学低年级数学学习困难儿童比正常儿童策略执行的正确率低 ,反应时长 ,有效性差 相似文献
6.
Nunes T Bryant P Burman D Bell D Evans D Hallett D 《Journal of deaf studies and deaf education》2009,14(2):260-277
Multiplicative reasoning is required in different contexts in mathematics: it is necessary to understand the concept of multipart units, involved in learning place value and measurement, and also to solve multiplication and division problems. Measures of hearing children's multiplicative reasoning at school entry are reliable and specific predictors of their mathematics achievement in school. An analysis of deaf children's informal multiplicative reasoning showed that deaf children under-perform in comparison to the hearing cohorts in their first two years of school. However, a brief training study, which significantly improved their success on these problems, suggested that this may be a performance, rather than a competence difference. Thus, it is possible and desirable to promote deaf children's multiplicative reasoning when they start school so that they are provided with a more solid basis for learning mathematics. 相似文献
7.
Marjoke Bakker Marja van den Heuvel-Panhuizen Alexander Robitzsch 《Contemporary educational psychology》2014
Our study investigated children’s knowledge of multiplicative reasoning (multiplication and division) at the end of Grade 1, just before the start of formal instruction on multiplicative reasoning in Grade 2. A large sample of children (N = 1176) was assessed in a relatively formal test setting, using an online test with 28 multiplicative problems of different types. On average, the children correctly answered more than half (58%) of the problems, including several bare number problems. This indicates that before formal instruction on multiplicative reasoning, children already have a considerable amount of knowledge in this domain, which teachers can build on when teaching them formal multiplication and division. Using analysis of variance and cross-classified multilevel regression analysis, we identified several predictors of children’s pre-instructional multiplicative knowledge. With respect to the characteristics of the multiplicative problems, we found that the problems were easiest to solve when they included a picture involving countable objects, and when the multiplicative situation was of the equal groups semantic structure (e.g., 3 boxes of 4 cookies). Regarding student characteristics, pre-instructional multiplicative knowledge was higher for children with higher-educated parents. Finally, the mathematics textbook used in school appeared to have influenced children’s pre-instructional multiplicative knowledge. 相似文献
8.
Enora R. Brown 《Early education and development》1996,7(2):149-166
Contextual and interpersonal factors contribute to the nature of children's conflicts. This study examines the effect of resource availability on dyadic interaction of African American 3-5 year-olds in a painting activity that required the resource. Forty-eight, same-sex dyads were videotaped in two resource conditions: a Limited Condition with one brush and one piece of paper and a Plentiful Condition with two brushes and two pieces of paper. The Limited Condition promoted more resource and task conflict, while the Plentiful Condition promoted more nonconflictive social and task interactions. Boys engaged in more resource, while girls engaged in more social behavior. Contingent probability analyses of interactive behavior in the Limited Condition showed that cooperative offers and waits, and competitive grasps were the most successful strategies. The interdependence of children's strategies generated unilateral and mutual oppositions. Mutual goal attainment occurred by sharing the resource and engaging in alternate behavior. Reasons were ineffective. The results underscore the role of resource scarcity and of reciprocal interaction in children's conflicts. Children resolve object conflicts independently and accomplish their goals by influencing and adjusting to their partner's goals. Resource availability and children's conflict management patterns may determine the need for adult intervention. 相似文献
9.
This paper reviews recent research in the area of initial fraction concepts. The common goal of the empirical studies which are represented in this analysis was to assist children develop a meaningful understanding of the rational number construct, founded on durable fraction concepts. Two interpretations of findings were derived from the research. One group of researchers identified initial fraction concepts emerging from the application of intuitive mechanisms, in particular partitioning in either continuous or discrete contexts, and leading to unit identification and iteration of the unit. The other group of researchers identified ideas of ratio and proportion present in young children's early thoughts about fractions.By generating links between studies, integrated research is created and consensus regarding critical problems and future directions is reached. Concluding remarks pose questions for further investigation. 相似文献
10.
Young children's understanding of many-to-one correspondence problems was studied to illuminate the developmental transition from additive to multiplicative numerical knowledge. A many-to-one correspondence exists when a fixed number of target objects (greater than 1) is associated with each of a set of referents, as in putting 3 flowers in each of several vases. Two experiments examined effects of a brief training procedure that highlighted the iterative nature of many-to-one mappings. In Experiment 1, 5- and 6-year-old children did not benefit from the training, but a subset of 7-year-olds did. In Experiment 2, 7-year-olds showed training effects that extended to generalization problems. Patterns of performance across experimental and generalization problems suggested that some children had difficulty applying what they learned from training to the experimental problems. 相似文献
11.
Mi Yeon Lee 《Educational Studies in Mathematics》2017,96(3):327-348
This study investigated 111 pre-service teachers’ (PSTs’) flexibility with referent units in solving a fraction division problem using a length model. Participants’ written solutions to a measurement fraction division problem were analyzed in terms of strategies and types of errors, using an inductive content analysis approach. Findings suggest that most PSTs could calculate fraction division and make equivalent fractions procedurally but did not have the quantitative meanings of measurement division with fraction quantities or of making equivalent fractions. Implications are discussed for the improvement of PSTs’ specialized knowledge for teaching fraction division. 相似文献
12.
The present study examines private speech and strategy-use patterns for solving simple number fact problems in addition. The progressive differentiation by grade between children's levels of private speech internalization--including silence--was investigated and related to children's developmental patterns for subcategories of strategy-use internalization. Comparisons were made between 67 children with math difficulties (MD) and 67 children without MD from Grade 2 to Grade 7 in primary schools. Two separate laboratory investigations were performed for each child to examine private speech and strategy-use internalization. Analysis was based on private speech category differences, strategy-use differences, and differences in the occurrence of private speech-strategy-use combinations. Children without MD showed a grade-determined shift from less to more internalized private speech and from the use of backup strategies to retrieval strategies. In contrast, the private speech and the strategy-use internalization of children with MD, reflected in inaudible private speech and backup strategy use, seemed to converge at earlier developmental levels. The development of children with MD seemed almost to stop at the inaudible private speech-backup strategy combination level. The silence-retrieval strategy combination level was the primary alternative for typical math achievers. In all, the characteristics of the development curves of the children with MD were consistent with a developmental difference and not with a developmental delay model. Implications for intervention and future research methodology are discussed. 相似文献
13.
主体间性理论的引入,有助于我们以一个全新的视角来看待幼儿园语言教学活动中的师幼互动,它具有整体性、平等性、理解性等特点,要实现师幼互动的主体间性,则要求幼儿园教师做到:关注每一位幼儿、统整教学内容、统整教学方式方法;创设开放而平等的语言学习环境、教师合理进行角色定位;了解幼儿的语言发展水平、尊重幼儿的心理需要。 相似文献
14.
Parmjit Singh 《Educational Studies in Mathematics》2000,43(3):271-292
The purpose of this study was to construct an understanding of two grade six students' proportional reasoning schemes. The
data from the clinical interviews gives insight as to the importance of multiplicative thinking in proportional reasoning.
Two mental operations, unitizing and iterating play an important role in student's use of multiplicative thinking in proportion
tasks. Unitizing a composite unit and iterating it to its referent point enables one to preserve the invariance of a ratio.
Proportions involved the coordination of two number sequences, keeping the ratio unit invariant under the iteration. In the
iteration process, one needed to explicitly conceptualize the iteration action of the composite ratio unit to make sense of
ratio problems and to have sufficient understanding of the meaning of multiplication and division and its relevance in the
iteration process. One needed to have constructed multiplicative structures and iteration schemes in order to reason proportionally.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
研究相空间中二阶非完整力学系统的Lie对称与守恒量．首先利用系统运动微分方程在无限小变换下的不变性建立Lie对称的确定方程和限制方程，得到Lie对称的结构方程和守恒量；其次研究上述问题的逆问题；最后举例说明结果的应用． 相似文献
16.
儿童数学认知策略研究新进展 总被引：10，自引：0，他引：10
认知策略是指向认知目标的一种心理操作,主体通过使用策略,可以达到解决问题的目的,关于儿童数学认知策略的研究是探讨个体整个认知策略发展的重要途径之一。儿童数学认知策略的特性主要表现为多样性和差异性、竞争性和适应性、突变性和渐进性。儿童数学认知策略的发展主要受教育环境、工作记忆、数学焦虑的影响。微观发生学的研究方法为儿童数学认知策略的研究提供了一个新的视角。目前儿童数学认知策略研究的新趋势主要集中在有意识和无意识之间的关系、影响儿童数学认知策略发展的内在因素和外在因素之间的关系、进一步扩大儿童数学认知策略的研究范围等方面。 相似文献
17.
18.
方程是初中代数中非常重要的内容 ,新世纪版教材在处理方程的内容时 ,突出了方程是表示现实世界中一类具有相等关系问题的数学模型、方程的一般性解法、方程的近似解、方程的应用以及方程与函数的联系等方面 ,强调发展学生的符号意识 相似文献
19.
Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers,
2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The
critical components suggested were individuals’ understanding of the rational number subconstructs, unitizing, quantities
and covariance, relative thinking, measurement and “reasoning up and down”. In this study, we empirically tested a theoretical
model based on the one suggested by Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and
instructional strategies for teachers, 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005), as well as an extended model which included an additional component of solving missing value proportional problems. Data
were collected from 238 prospective kindergarten teachers. To a great extent, the data provided support for the extended model.
These findings allow us to make some first speculations regarding the knowledge that prospective kindergarten teachers possess
in regard to proportional reasoning and the types of processes that might be emphasized during their education. 相似文献
20.
于树漫 《湖南科技学院学报》2007,28(4):153-155
在今日中国,儿童阅读比以前有了巨大发展,但总体状况仍不理想。这与儿童图书馆建设不力是有重要关系的。本文分别呈现了中国儿童阅读的基本情况和儿童图书馆建设的当前局面,分析了问题的成因,提出了对应的发展建议,旨在推动中国的儿童图书馆建设与儿童的阅读发展。 相似文献