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1.
To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with concrete representations and progress stepwise to representations that are more idealized. Various researchers have suggested that concreteness fading is a broadly applicable instructional approach. In this theoretical paper, we conceptually analyze examples of concreteness fading in the domains of mathematics, physics, chemistry, and biology and discuss its generalizability. We frame the analysis by defining and describing MERs and their use in educational settings. Then, we draw from theories of analogical and relational reasoning to scrutinize the possible cognitive processes related to learning with MERs. Our analysis suggests that concreteness fading may not be as generalizable as has been suggested. Two main reasons for this are discussed: (1) the types of representations and the relations between them differ across different domains, and (2) the instructional goals between domains and subsequent roles of the representations vary.
相似文献2.
The present study investigates the effects that concreteness fading has on learning and transfer across three grade levels (4–6) in elementary school science education in comparison to learning with constantly concrete representations. 127 9- to 12-years-old elementary school students studied electric circuits in a computer-based simulation environment, where circuits remained concrete (bulbs) throughout the learning or faded from concrete to abstract (bulbs to resistors). The most important finding was that the outcomes seemed to be influenced by a developmental factor: the study found a significant interaction between condition and grade level in relation to learning outcomes, suggesting that the outcomes generally improved as a function of grade level, but that there were notable differences between the conditions regarding the improvement of outcomes across the three grades. According the results, learning with constantly concrete representations either took less time or resulted in better learning compared to concreteness fading. Because transfer is one of the central arguments for concreteness fading, a somewhat surprising finding was that the concrete condition succeeded at least as well as the fading condition on transfer tasks. The study also discusses why the results and issues related to the conceptualisation and operationalisation of central concepts in the study call for caution towards generalization and for more research with young learners across different grades. 相似文献
3.
Experts are more proficient in manipulating and translating between multiple representations (MRs) of a given concept than novices. Studies have shown that instruction using MR can increase student understanding of MR, and one model for MR instruction in chemistry is the chemistry triplet proposed by Johnstone. Concreteness fading theory suggests that presenting concrete representations before abstract representations can increase the effectiveness of MR instruction; however, little work has been conducted on varying the order of different representations during instruction and the role of concreteness in assessment. In this study, we investigated the application of concreteness fading to MR instruction and assessment in teaching chemistry. In two experiments, undergraduate students in either introductory psychology courses or general chemistry courses were given MR instruction on phase changes using different orders of presentation and MR assessment questions based on the representations in the chemistry triplet. Our findings indicate that the order of presentation based on levels of concreteness in MR chemistry instruction is less important than implementation of comprehensive MR assessments. Even after MR instruction, students display an asymmetric understanding of the chemical phenomenon on the MR assessments. Greater emphasis on MR assessments may be an important component in MR instruction that effectively moves novices toward more expert MR understanding. 相似文献
4.
Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt perceptual support. Although most work on concreteness focuses on conceptual support through examples or analogies, here we consider notational concreteness—perceptual-motor supports that provide access into the dynamic structure of a representation itself. We hypothesize that perceptual support may be maximally beneficial as an initial scaffold to learning so that later static symbol use may be interpreted using a dynamic perspective. This hypothesis meshes with other findings using concrete analogies or examples, which often find that fading these supports over time leads to stronger learning outcomes. In an experiment exploring this hypothesis, we compared gains from the fading out of dynamic concrete physical motion of symbols during instruction with the introduction of motion over the course of instruction. In line with our theoretical perspective, concreteness fading led to significantly better achievement than concreteness introduction after Day 2 of the intervention. 相似文献
5.
Emily R. Fyfe Nicole M. McNeil Ji Y. Son Robert L. Goldstone 《Educational Psychology Review》2014,26(1):9-25
A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and combines their advantages. Specifically, we recommend beginning with concrete materials and then explicitly and gradually fading to the more abstract. Theoretical benefits of this “concreteness fading” technique for mathematics and science instruction include (1) helping learners interpret ambiguous or opaque abstract symbols in terms of well-understood concrete objects, (2) providing embodied perceptual and physical experiences that can ground abstract thinking, (3) enabling learners to build up a store of memorable images that can be used when abstract symbols lose meaning, and (4) guiding learners to strip away extraneous concrete properties and distill the generic, generalizable properties. In these ways, concreteness fading provides advantages that go beyond the sum of the benefits of concrete and abstract materials. 相似文献
6.
A large body of research in the conceptual change tradition has shown the difficulty of learning fundamental science concepts,
yet conceptual change schemes have failed to convincingly demonstrate improvements in supporting significant student learning.
Recent work in cognitive science has challenged this purely conceptual view of learning, emphasising the role of language,
and the importance of personal and contextual aspects of understanding science. The research described in this paper is designed
around the notion that learning involves the recognition and development of students’ representational resources. In particular,
we argue that conceptual difficulties with the concept of force are fundamentally representational in nature. This paper describes
a classroom sequence in force that focuses on representations and their negotiation, and reports on the effectiveness of this
perspective in guiding teaching, and in providing insight into student learning. Classroom sequences involving three teachers
were videotaped using a combined focus on the teacher and groups of students. Video analysis software was used to capture
the variety of representations used, and sequences of representational negotiation. Stimulated recall interviews were conducted
with teachers and students. The paper reports on the nature of the pedagogies developed as part of this representational focus,
its effectiveness in supporting student learning, and on the pedagogical and epistemological challenges negotiated by teachers
in implementing this approach. 相似文献
7.
Simplest Shapes First! But Let's Use Cognitive Science to Reconceive and Specify What “Simple” Means
Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and justified than the current standards. To do so, we reframed what constitutes a “simple” shape from perceptual simplicity to simplicity of properties. Our Property-Based Shape Sequence uses property-based criteria of what makes shapes “simple” and progresses in a way that affords opportunities for learners to develop hierarchical conceptions of two-dimensional and three-dimensional shapes. Our goals are threefold: (1) recommend an optimal, mathematically-correct shape learning sequence, (2) correct misconceptions that adults and children harbor about shapes, and (3) encourage cross-disciplinary collaborations between mathematics education and psychology researchers to validate the proposed learning sequence. 相似文献
8.
This study reports how an expert Chinese teacher implements mathematics textbook lessons in enacted instruction. Our video analysis indicates that both textbook and enacted teaching included only one worked example; however, the teacher engaged students in unpacking the example in great depth. Both the textbook and the enacted teaching showed “concreteness fading” in students’ use of representations. However, the Chinese teacher incorporated students’ self-generated representations and facilitated students’ active modeling of quantitative relationships. Finally, the Chinese teacher asked a greater number of deep questions than were suggested by the textbook. These deep questions often occurred as clusters of follow-up questions that were either concept-specific or promoted comparisons which facilitated connection-making between multiple representations and solutions. 相似文献
9.
In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article
is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's
own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic
framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic
reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means
for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling,
symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning
and communicating in mathematics classrooms. 相似文献
10.
As follow-up to an initial study phase, both generative learning activities and retrieval practice can substantially enhance learning, but via different functions. Generative activities are theorized to mainly serve the function of constructing coherent mental representations of the learning content that are well integrated with prior knowledge, whereas retrieval practice is theorized to mainly serve the function of consolidating learners’ mental representations in memory. In view of these complementing functions, the present study investigated whether the sequence of these activities matters. In an experiment with N = 158 university students, we varied the sequence of generative learning and retrieval practice after an initial study phase. We found that the retrieval-before-generation sequence yielded better retention and reduced cognitive load during both types of activities. We conclude that although it might seem counterintuitive, engaging learners in retrieval practice before engaging them in generative learning can be more beneficial than vice versa. 相似文献
11.
“We do not know what is the real story anymore”: Curricular contextualization principles that support indigenous students in understanding natural selection 
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下载免费PDF全文 We propose a process of contextualization based on seven empirically derived contextualization principles, aiming to provide opportunities for Indigenous Mexican adolescents to learn science in a way that supports them in fulfilling their right to an education aligned with their own culture and values. The contextualization principles we empirically derived account for Nahua students' cultural cognition, socialization, and cultural narratives, thus supporting Indigenous students in navigating the differences between their culture and the culture and language of school while learning complex science concepts such as natural selection. The process of curricular contextualization we propose is empirically driven, taking culture and socialization into account by using multiples sources (cognitive tasks to explore teleology, ethnographic observation of students' community and classroom, and interviews with students and community members) and builds on the scholarship in Culturally Relevant Pedagogy and Indigenous Education. We used these principles to redesign a middle school biology unit on natural selection to make it more culturally relevant for Nahua students. The enactment of this unit resulted in students being engaged in science learning and achieving significant learning gains. The significance of this study lies in presenting evidence that learning science in culturally relevant ways supports the learning of challenging biology concepts. We provide evidence that Western science can be learned in ways that are more aligned with Indigenous students' Traditional Indigenous Knowledge, thus informing the implementation of educational policies aiming to improve the quality of secondary education for Indigenous adolescents. Our proposed contextualization principles can benefit students of all cultural identities who feel that their religion, language, or traditional knowledge are not aligned with school science, facilitating their access to culturally relevant science education. 相似文献
12.
Remote learning during the COVID pandemic has led to short- and long-term consequences for students' learning. So far, data on learning loss in early schooling have been limited. In this paper, we evaluate the effect of remote learning on 1st graders' school readiness skills and 2nd–8th graders’ performance in mathematics, reading and science using rich data collected in Hungary before and during the pandemic (n ≈ 55,000). The results show that kindergarten children and 1st–4th-grade students were significantly negatively affected by COVID restrictions compared to their older peers. This difference was extremely large in schools with a high share of disadvantaged students. More specifically, 1st–4th-grade low-SES students made little or no progress while learning from home. 相似文献
13.
Mathematical Modelling: the Interaction of Culture and Practice 总被引：1，自引：0，他引：1
Susan Molyneux-Hodgson Teresa Rojano Rosamund Sutherland Sonia Ursini 《Educational Studies in Mathematics》1999,39(1-3):167-183
Using a sociocultural approach we analyse the results of a Mexican/British project which investigated the ways in which mathematics
is used in the practice of school science and the role of spreadsheets as a mathematical modelling tool. After discussing
the different school cultures experienced by two groups of pre-university 16–18 year old students we analyse how these different
cultures influenced their practice of mathematics, as well as their work with mathematical spreadsheet modelling activities.
There were clear differences between the two groups of students in their preference for external representations, in their
understanding of the kind of answers they were expected to produce and in the way they conceived the role of mathematics in
the practice of science. Although students preferences for a particular representation were not significantly modified by
the use of a spreadsheet as a modelling resource, at the end of the study the students recognised the value of using a more
diverse set of representations. The results obtained suggest the possibility of enhancing students' capability to shift between
a wider range of representations, including graphical, algebraic and numeric ones, using a modelling approach embedded in
a computer environment such as a spreadsheet.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
Multimedia effects in learning receive much attention in research. In contrast, effects of different picture types in testing materials are hardly studied. The present computer-based experiment with n = 404 students investigates the effects of adding a representational picture (RP) or a decorative picture (DP) to text-based educational test items on students' performance, metacognition, test-taking motivation and item processing in the domains of science and mathematics. The data show that RPs enhanced students' performance, perception of ease and test-taking pleasure in both scientific and mathematics items. Furthermore, RPs increased time on task (TOT) in mathematics, but not in scientific items. DPs had no significant effect on students’ performance, test-taking pleasure or perceived ease, while DPs reduced TOT in mathematics items. Explanations for the process-related differences are discussed. The pattern of results indicates that the multimedia principle and the coherence principle from instructional psychology can be transferred to educational testing material. 相似文献
15.
Children show individual differences in their tendency to focus on the numerical aspects of their environment. These individual differences in ‘Spontaneous Focusing on Numerosity’ (SFON) have been shown to predict both current numerical skills and later mathematics success. Here we investigated possible factors which may explain the positive relationship between SFON and symbolic number development. Children aged 4–5 years (N = 130) completed a battery of tasks designed to assess SFON and a range of mathematical skills. Results showed that SFON was positively associated with children's symbolic numerical processing skills and their performance on a standardised test of arithmetic. Hierarchical regression analyses demonstrated that the relationship between SFON and symbolic mathematics achievement can be explained, in part, by individual differences in children's nonsymbolic numerical processing skills and their ability to map between nonsymbolic and symbolic representations of number. 相似文献
16.
We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different interpretations of the equal sign) previously reported in the literature. Moreover, the teacher and her students had trouble understanding one another's proposed algebraic models of problem situations due to differences in the criteria that each applied, and this impeded learning. These findings (a) extend an accumulating body of evidence for the role meta-representation plays in mathematics and science learning and (b) add a new dimension to researchers' growing understanding of what teachers must know in order to teach algebra and other complex mathematics and science topics effectively. 相似文献
17.
Correlational studies link spatial-test scores and science, technology, engineering, and mathematics achievement. Here we asked whether children’s understanding of astronomical phenomena would benefit from a prior intervention targeting a core component of children’s projective spatial concepts—understanding that viewers’ visual experiences are affected by vantage point. Children (8–9 years; N = 66) received outdoor and indoor experiences that did (Experimental) or did not (Control) focus on how scene appearance is affected by viewers' positions and movements. All then received an astronomy lesson about celestial motions (e.g., Sun apparent motion). Experimental-group children scored higher on immediate and 1-week perspective-taking tests and explained celestial phenomena more accurately than did control-group children. Data demonstrate that general spatial training—divorced from specific science content—can aid children’s subsequent learning of scientific phenomena. 相似文献
18.
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
19.
Kristiina Kumpulainen Anu Kajamaa 《British journal of educational technology : journal of the Council for Educational Technology》2020,51(4):1292-1307
This study investigates the sociomaterial movements of student engagement in a school's makerspace. Here, we understand sociomaterial movements as emergent and relational, comprising complex dynamics of agency across students, teachers and materials in situated, culturally framed activities. Our study draws on data comprising 85 hours of video recordings of 9–12-year-old students' (N = 94) engagement in a technology-rich makerspace in a Finnish elementary school. The video data were transcribed and analyzed qualitatively using a multimodal interaction analysis. The sociomaterial movements were found to be displayed across a tension-laden continuum between (1) procedural activity—analysis and reflection; (2) individual activity—collaboration; (3) “doing school”—empowerment; and d) alienation—identification. Together, the study offers a potential approach for investigating and understanding the often overlooked workings of sociomateriality that constitutes students' emergent engagement and learning opportunities in science, technology, engineering and mathematics (STEAM) learning contexts. 相似文献
20.
The concreteness of training materials influences learning and—perhaps more importantly—transfer. Building on prior research finding abstract representations best facilitated transfer to a game task, we conducted a similar study using training figures varying in concreteness but directly assessed transfer to modular arithmetic problems. Training figures: (a) were purely abstract, (b) were abstract but with features relevant to the transfer task, or (c) included additional concrete-relevant features. We hypothesized that concreteness—or number of relevant features—would be positively correlated with learning and transfer—especially among younger and/or lower-ability students. Although there was no overall difference in initial learning, the concrete-relevant and abstract-relevant features independently facilitated near-transfer, where concrete-relevant features supported lower-reasoning students. For far-transfer, eighth-graders benefited from the abstract-relevant features, whereas sixth-graders required additional concrete-relevant features. These findings suggest that concreteness interacts with learner and task characteristics to produce learning and transfer outcomes. 相似文献