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1.
Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning provides the foundation for advanced mathematics and algebraic reasoning. For students who struggle in mathematics, instruction in multiplication algorithms should ensure conceptual understanding so that students have a foundation for success in advanced mathematics. The concrete representational abstract (CRA) sequence addresses conceptual understanding and the strategic instruction model (SIM) supports procedural knowledge. The current pilot study combined these methods to teach elementary students the partial products algorithm. Twelve students in grades four and five participated in the study, receiving instruction from teachers in their school during an intervention period. Within a pre-experimental design, using pre- and postintervention data, students showed a significant change in performance. The article will describe and show how teachers implemented the CRA-SIM interventions and discuss implications for practice. 相似文献
2.
杨玉东 《天津师范大学学报(基础教育版)》2010,11(3):18-21
现代认知心理学将知识分为陈述性知识和程序性知识。这两类知识获得的心理过程及其在头脑中的表征、保持与激活等特点都有显著的差异。陈述性知识的教学策略主要有：促进陈述性知识习得的策略;促进陈述性知识保持的策略;促进陈述性知识有效提取的策略。程序性知识的教学策略主要有：掌握程序性知识的陈述形式;明晰程序性知识应用的条件;从陈述性知识到程序性知识的转化;从程序性知识到陈述性知识的转化等。 相似文献
3.
Bas Kolloffel Tessa H. S. Eysink Ton de Jong Pascal Wilhelm 《Instructional Science》2009,37(6):503-517
The current study investigated the effects of different external representational formats on learning combinatorics and probability
theory in an inquiry based learning environment. Five conditions were compared in a pre-test post-test design: three conditions
each using a single external representational format (Diagram, Arithmetic, or Text), and two conditions using multiple representations
(Text + Arithmetic or Diagram + Arithmetic). The major finding of the study is that a format that combines text and arithmetics
was most beneficial for learning, in particular with regard to procedural knowledge, that is the ability to execute action
sequences to solve problems. Diagrams were found to negatively affect learning and to increase cognitive load. Combining diagrams
with arithmetical representations reduced cognitive load, but did not improve learning outcomes. 相似文献
4.
Junin Quechua Children's Understanding of Mind 总被引：2，自引：0，他引：2
Penelope G. Vinden 《Child development》1996,67(4):1707-1716
2 tasks that examine the child's understanding of false belief, representational change, and the appearance-reality distinction were conducted among 34 4- to 8-year-old Junin Quechua children in Peru. A majority of children demonstrated an understanding of the appearance-reality distinction, though there was a clear improvement with age. Both younger and older children, however, performed poorly on questions that tested their understanding of representational change and false belief. These results raise questions as to whether or not thinking about thought and its relation to action develops in a similar manner in all cultures. If the Junin Quechua children's understanding of the appearance-reality distinction is grounded in the same representational ability that is necessary to understand one's own and another's misrepresentation of reality, then we must look for other factors that prevent them from performing correctly on tasks that test their understanding of false belief and representational change. 相似文献
5.
A tale of two representations: the misinformation effect and children's developing theory of mind 总被引：1，自引：0，他引：1
The present research investigates representational ability as a cognitive factor underlying the suggestibility of children's eyewitness memory. The misinformation effect is used as an index of children's suggestibility, and performance on the false belief task is used as an assessment of children's representational abilities (N = 117). Analyses that considered the effect of representational ability and general memory ability on children's susceptibility to misleading information showed that differences in representational ability and general memory ability predicted participants' susceptibility to misleading information. These results demonstrate that the eyewitness memory of children who lack either multirepresentational abilities, sufficient general memory abilities, or both (i.e., most 3- and 4-year-olds) is less accurate than the eyewitness memory of children with both multirepresentational abilities and sufficient memory abilities (i.e., most 6-year-olds and adults). Thus, it appears that the earliest age at which children's eyewitness memory can be considered to be similar to that of adults is 6 years of age, when children's mental representational abilities are similar to those of adults. These results suggest that one factor underlying children's vulnerability to misleading information is the number of representations of an event that they can simultaneously hold and compare. 相似文献
6.
Pasi Nieminen Antti Savinainen Jouni Viiri 《International Journal of Science and Mathematics Education》2013,11(5):1137-1156
This quantitative case study used a pre- and posttest design for exploring the gender differences in secondary school students’ (n?=?131, 45 males and 86 females) learning of the force concept when an interactive engagement type of teaching was used. In addition, students’ ability to interpret multiple representations (i.e., representational consistency) was documented by a pre- and posttest and scientific reasoning ability by a pretest only. Males significantly outperformed females in learning of the force concept, pre- and posttest representational consistency, and pretest scientific reasoning. However, the gender difference in learning of the force concept was not significant when ANCOVA was conducted using pretest results of representational consistency and scientific reasoning as covariates. This appeared to indicate that the gender difference in learning gain was related to students’ abilities before the instruction. Thus, the teaching method used was equally effective for both genders. Further, our quantitative finding about the relation between representational consistency and learning of the force concept supports the assumption that multiple representations are important in science learning. 相似文献
7.
Eleni Deliyianni Athanasios Gagatsis Iliada Elia Areti Panaoura 《International Journal of Science and Mathematics Education》2016,14(2):397-417
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1701 primary and secondary school students. Eight components, which all involve representational transformations, were encompassed under the construct of representational flexibility in fraction and decimal number addition. This structure reveals that, for both concepts, the representational transformation competences of recognition and conversion, and therefore representational flexibility as well, were affected by the complexity of the concepts involved and the direction of the conversion, respectively. Results also showed that two first-order factors were needed to explain the problem-solving ability in fraction and decimal number addition, indicating the differential effect of the modes of representation that is diagrammatic and verbal form on problem-solving ability irrespective of the concepts involved, as in the case of the conversions. Representational flexibility and problem-solving ability were found to be major components of students’ representational thinking of fraction and decimal number addition. The proposed framework was invariant across the primary and secondary school students. Theoretical and practical implications are discussed. 相似文献
8.
9.
Deliyianni Eleni Gagatsis Athanasios Elia Iliada Panaoura Areti 《International Journal of Science and Mathematics Education》2015,14(2):397-417
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1701 primary and secondary school students. Eight components, which all involve representational transformations, were encompassed under the construct of representational flexibility in fraction and decimal number addition. This structure reveals that, for both concepts, the representational transformation competences of recognition and conversion, and therefore representational flexibility as well, were affected by the complexity of the concepts involved and the direction of the conversion, respectively. Results also showed that two first-order factors were needed to explain the problem-solving ability in fraction and decimal number addition, indicating the differential effect of the modes of representation that is diagrammatic and verbal form on problem-solving ability irrespective of the concepts involved, as in the case of the conversions. Representational flexibility and problem-solving ability were found to be major components of students’ representational thinking of fraction and decimal number addition. The proposed framework was invariant across the primary and secondary school students. Theoretical and practical implications are discussed.
相似文献10.
The aim of this study was to explore whether a representational approach could impact on the scores that measure students’ understanding of mechanics and their ability to reason. The sample consisted of 24 students who were undergraduate, preservice physics teachers in the State University of Malang, Indonesia. The students were asked to represent a claim, provide evidence for it, and then, after further representational manipulations, refinement, discussion, and critical thought, to reflect on and confirm or modify their original case. Data analysis was based on the pretest–posttest scores and students’ responses to relevant phenomena during the course. The results showed that students’ reasoning ability significantly improved with a d-effect size of 2.58 for the technical aspects and 2.51 for the conceptual validity aspects, with the average normalized gain being 0.62 (upper–medium) for the two aspects. Students’ conceptual understanding of mechanics significantly improved with a d-effect size of about 2.50 and an average normalized gain of 0.63. Students’ competence in mechanics shifted significantly from an under competent level to mastery level. This paper addresses statistically previously untested issues in learning mechanics through a representational approach and does this in a culture that is quite different from what has been researched so far using student-generated representational learning as a reasoning tool for understanding and reasoning. 相似文献
11.
Two studies addressed the role of representation ability and control of attention on solutions to an appearance-reality task based on two types of objects, real and representational. In Study 1, 67 preschool children (3-, 4-, and 5-year-olds) solved appearance-reality problems and executive processing tasks. There was an interaction between object type (real vs. representational) and question type (appearance vs. reality) on problem difficulty. In addition, representational ability predicted performance on appearance questions and inhibitory control predicted performance on reality questions. In Study 2, 95 children (4- and 5-year-olds) who were monolingual or bilingual solved similar problems. On appearance questions, groups performed equivalently but on reality questions, bilinguals performed better (once language proficiency had been controlled). The difference is attributed to the advanced inhibitory control that comes with bilingualism. 相似文献
12.
Students with mathematics disabilities (MD) experience difficulties with both conceptual and procedural knowledge of different math concepts across grade levels. Research shows that concrete representational abstract framework of instruction helps to bridge this gap for students with MD. In this article, we provide an overview of this strategy embedded within the explicit instruction framework. We highlight effective practices for each component of the framework across different mathematical strands. Implications for practice are also discussed and a detailed case study is provided. 相似文献
13.
The purpose of this study was to explore the relationship between teachers’ (N = 69) participation in constructivist chemistry professional development (PD) and enhancement of content (CK) and pedagogical
content knowledge (PCK) (representational thinking and conceptual change strategies) and self-efficacy (PSTE). Quantitative
measures assessed CK, PCK, and PSTE. Document analysis focused on PCK. Elementary teachers gained CK, PCK, PSTE, and designed
lessons to advance thinking from macroscopic to abstract models. Middle/secondary teachers gained PSTE, PCK, and introduced
macroscopic models to develop understanding of previously taught abstract models. All implemented representational thinking
and conceptual change strategies. Results suggest that: (1) constructivist PD meets the needs of teachers of varying CK, and
(2) instruction should connect representational models with alternative conceptions, integrating radical and social constructivism. 相似文献
14.
过程性知识是基于学习者亲身体验的个体知识。在数学解题中,过程性知识制约着解题过程和结果。过程性知识的本质特性决定了其习得过程不同于陈述性知识或程序性知识。 相似文献
15.
George E. Glasson 《科学教学研究杂志》1989,26(2):121-131
The present study compared the relative effects of hands-on and teacher demonstration laboratory methods on declarative knowledge (factual and conceptual) and procedural knowledge (problem-solving) achievement. Of particular interest were (a) whether these relationships vary as a function of reasoning ability and (b) whether prior knowledge and reasoning ability predict student achievement. Ninth-grade physical science students were randomly assigned to classes taught by either a hands-on or a teacher demonstration laboratory method. Students' reasoning ability and prior knowledge of science were assessed prior to the instruction. The two instructional methods resulted in equal declarative knowledge achievement. However, students in the hands-on laboratory class performed significantly better on the procedural knowledge test than did students in the teacher demonstration class. These results were unrelated to reasoning ability. Prior knowledge significantly predicted performance on the declarative knowledge test. Both reasoning ability and prior knowledge significantly predicted performance on the procedural knowledge test, with reasoning ability being the stronger predictor. 相似文献
16.
Anne Watson O'Reilly 《Child development》1995,66(4):999-1010
Previous research suggests that young children have difficulty producing actions with imagined objects (pantomimes): They frequently substitute a body part to represent the object involved in the action. This response has also been observed in neurologically impaired adults. Study 1 examined the comprehension and production of pantomimes in 3- and 5-year-old children and normal adults to explore further this aspect of representational ability. Results indicate that young children not only have difficulty producing imaginary object representations in contrast to normal adults, they also have difficulty comprehending imaginary object representations and are better at comprehending pantomimes with a body part representation. The results from the pantomime comprehension task were replicated in Study 2 with 3- and 4-year-olds. These findings are discussed in the context of the development of representational ability as children demonstrate increasing independence from concrete environmental support in their knowledge about actions. 相似文献
17.
Mathematics and Virtual Culture: an Evolutionary Perspective on Technology and Mathematics Education
This paper suggests that from a cognitive-evolutionary perspective, computational media are qualitatively different from many
of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive
evolution suggest that human cognition has evolved through four distinct stages: episodic, mimetic, mythic, and theoretical.
This progression was driven by three cognitive advances: the ability to ‘represent’ events, the development of symbolic reference,
and the creation of external symbolic representations. In this paper, we suggest that we are developing a new cognitive culture:
a ‘virtual’ culture dependent on the externalization of symbolic processing. We suggest here that the ability to externalize
the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences
for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should
strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create
and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as
a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need
those specialized skills.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
Gordon R. Eastwood 《Journal of Experimental Education》2013,81(1):52-58
Sixty kindergarten, sixty second grade, and sixty fourth grade students performed several memory tasks under one of six conditions. The conditions differed as to the method of presentation of information. The study focused on developmental changes in children’s use of verbal, nonverbal, and spatial-positional cues for memory. The results, in general, showed consistent trends suggestive of a developmental change in representational ability, such that younger children tended to rely on visual cues and older children tended to rely on verbal cues to retain information. Children in all grades performed better when both visual and verbal cues were available and demonstrated an ability to utilize spatial-positional cues for retention. 相似文献
19.
Children's understanding of representational change and its relation to the understanding of false belief and the appearance-reality distinction 总被引：16，自引：4，他引：16
This research concerns the development of children's understanding of representational change and its relation to other cognitive developments. Children were shown deceptive objects, and the true nature of the objects was then revealed. Children were then asked what they thought the object was when they first saw it, testing their understanding of representational change; what another child would think the object was, testing their understanding of false belief; and what the object looked like and really was, testing their understanding of the appearance-reality distinction. Most 3-year-olds answered the representational change question incorrectly. Most 5-year-olds did not make this error. Children's performance on the representational change question was poorer than their performance on the false-belief question. There were correlations between performance on all 3 tasks. Apparently children begin to be able to consider alternative representations of the same object at about age 4. 相似文献
20.
Vaughan Prain Russell Tytler Suzanne Peterson 《International Journal of Science Education》2013,35(6):787-808
There has been extensive research on children’s understanding of evaporation, but representational issues entailed in this understanding have not been investigated in depth. This study explored three students’ engagement with science concepts relating to evaporation through various representational modes, such as diagrams, verbal accounts, gestures, and captioned drawings. This engagement entailed students (a) clarifying their thinking through exploring representational resources; (b) developing understanding of what these representations signify; and (c) learning how to construct representational aspects of scientific explanation. The study involved a sequence of classroom lessons on evaporation and structured interviews with nine children, and found that a focus on representational challenges provided fresh insights into the conceptual task involved in learning science. The findings suggest that teacher‐mediated negotiation of representational issues as students construct different modal accounts can support enriched learning by enabling both (a) richer conceptual understanding by students; and (b) enhanced teacher insights into students’ thinking. 相似文献