Concreteness fading in learning secondary school physics concepts

Concreteness fading has been proposed as a general instructional approach to support learning of abstract mathematics and science concepts. Accordingly, organizing external knowledge representations in a three-step concrete-to-idealized sequence should be more beneficial than the reverse, concreteness introduction, sequence. So far, evidence for the benefits of concreteness fading come mainly from studies investigating learning of basic mathematics concepts. Studies on learning natural science concepts are scarce and have not implemented the full three-step-sequence. In an experimental classroom study (N = 70), we compared concreteness fading and concreteness introduction in high school science education about electromagnetic induction using a detailed assessment. Furthermore, we explored whether these sequences differentially affect the use of the different representations during instruction. Both sequences were equally effective and there were no differences in using the representations. We discuss why our results question the proposed advantages of concreteness fading and highlight conceptual differences and learning goals across domains.     

Exploring the effects of concreteness fading across grades in elementary school science education

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.     

One Instructional Sequence Fits all? A Conceptual Analysis of the Applicability of Concreteness Fading in Mathematics,Physics, Chemistry,and Biology Education

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.

     

Concreteness Fading of Algebraic Instruction: Effects on Learning

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.     

具体性对二语词汇发展类母语水平的影响研究

类母语水平是二语习得水平的上限。本文以英语本族语者词汇联想结果为参照计算联想比,考查具体性对于二语学习者词汇发展类母语水平是否有显著影响。研究问题包括：1）具体性对于二语词汇反应词的联想比有何影响？2）具体性对于二语独有概念反应词的产出有何影响？结果显示,具体词和抽象词在两个方面都表现出了显著的差异性,表明具体词发展的类母语水平更高,更加接近母语者。研究结果验证了双重编码理论和语境有效性理论。     

Asymmetric translation between multiple representations in chemistry

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.     

The effect of manipulatives on mathematics achievement across different learning styles

The current study investigates the influence of manipulatives used in combination with traditional approaches to mathematics education and how varying amounts of time spent on manipulative use influence student achievement across different learning styles. Three learning environments were created that incorporated varying proportions of traditional teaching approaches and manipulative methods. In one of the learning environments, the teacher used strictly lecture- and exercise-based teaching activities, which are more conducive to abstract learning. Abstract learners showed higher academic performance compared with concrete learners in the environment where only traditional methods were used. For the other two environments, which utilised varying combinations of manipulative tools and traditional methods, the differences in the mathematics achievement levels among students of varying learning styles were not statistically significant. The study also showed that concrete learners demonstrated higher performance in mathematics when manipulatives were used than did their counterparts in the environment where only abstract activities were used; however, in the third learning environment, increasing the amount of manipulative use did not provide an extra benefit to concrete learners.     

Cognitive process development as measured by an adapted version of Wechsler's Similarities test

This paper studies the development of taxonomic processing as measured by an adapted version of the Wechsler Similarities subtest, which distinguishes between categorization of concrete and abstract words. Two factors — age and concreteness — are also tested by a recall task. The results show an age-related increase in taxonomic categorization, especially for abstract words; this change is more pronounced for the categorization task than for the recall task. The concreteness effect is also shown to be greater for categorization. A weak correlation between the recall of concrete and abstract words suggests that different processes are linked to dual coding of concrete words. However, the strong correlation between the categorization of concrete and abstract words testifies to a general factor in this task. Finally, age- and concreteness-related effects increase as the task gains in complexity. In conclusion, we discuss the role of immediate memory in cognitive functioning.     

“Concreteness fading” promotes transfer of mathematical knowledge

Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are “faded” into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three conditions: generic, in which the concept was instantiated using abstract symbols, concrete in which it was instantiated using meaningful images, or fading, in which it was instantiated using meaningful images that were “faded” into abstract symbols. After learning, undergraduates completed a transfer test immediately, one week later, and three weeks later. Undergraduates in the fading condition exhibited the best transfer performance. Additionally, undergraduates in the generic condition exhibited somewhat better transfer than those in the concrete condition, but this advantage was not robust. Results suggest that concrete instantiations should be included in the educator's toolbox.     

Children's understanding of the commutativity and complement principles: A latent profile analysis

This study examined patterns of individual differences in the acquisition of the knowledge of the commutativity and complement principles in 115 five-to six-year-old children and explored the role of concrete materials in helping children understand the prinicples. On the basis of latent profile analysis, four groups of children were identified: The first group succeeded in commutativity tasks with concrete materials but in no other tasks; the second succeeded in commutativity tasks in both concrete and abstract conditions, but not in complement tasks; the third group succeeded in all commutativity tasks and in complement tasks with concrete materials, and the final group succeeded in all the tasks. The four groups of children suggest a developmental trend – (1) Knowledge of the commutativity and of the complement principles seems to develop from thinking in the context of specific quantities to thinking about more abstract symbols; (2) There may be an order of understanding of the principles – from the commutativity to the complement principle; (3) Children may acquire the knowledge of the commutativity principle in the more abstract tasks before they start to acquire the knowledge of the complement principle. This study contributes to the literature by showing that assessing additive reasoning in different ways and identifying profiles with classification analyses may be useful for educators to understand more about the developmental stage where each child is placed. It appears that a more fine-grained assessment of additive reasoning can be achieved by incorporating both concrete materials and relatively abstract symbols in the assessment.     

Individual differences in the effect of relevant concreteness on learning and transfer of a mathematical concept

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.     

The Fallacy of Misplaced Concreteness: Its Importance for Critical and Creative Inquiry

In Science and the Modern World, Alfred North Whitehead (1925/1953) critically discusses the historical development of science and its larger impact on our civilization and culture today. The fallacy of misplaced concreteness (FMC) is a notion central to his analysis, both of the process of inquiry and to the general sustainability of quality of life. This paper is part of a panel of four presentations relevant to the theory, practice, and teaching of science. In this paper I identify the FMC as a set of variations on the central theme of misplacing concreteness, by mistaking the abstract for the concrete, and I define the component notions involved. More than half of the paper involves a representative range of concrete examples of the FMC. The realm of the aesthetic, of patient and sensitive attention, the full range of immediate bodily feeling, and the variety of real values revealed therein, turns out to be both the victim of and the remedy for the FMC. As Whitehead says: "Sensitiveness without impulse spells decadence, and impulse without sensitiveness spells brutality" (1925/1953, p. 200).     

英汉语心理词库联想反应的具体性效应对比研究

本研究探讨具体性效应对一语(汉语和英语)和二语(英语)心理词库联想反应的影响.依据Langacker (2004)的认知语法理论,本文从空间概念和感官体验两个角度首次对不同词性的具体性进行定义,并用量表验证所选词的具体性程度.研究表明,具体性效应没有改变一语心理词库语义联结的特质,但对二语心理词库有一定影响,其具体词的...     

Resolving the Effects of Concreteness on Interest, Comprehension, and Learning Important Ideas From Text

This paper reviews research suggesting that interest and importance are separate constructs mediated by concreteness and mental imagery, especially in expository text or other genres where concreteness and importance often diverge. Important expository material can be relatively more interesting or less interesting. If important expository material is concrete it tends to be interesting and well recalled. If important expository material is abstract and not well linked to concrete elaboration or examples it tends to be less interesting and less well recalled. Concrete elaboration of abstract ideas tends to improve students' recall. There appears to be no harm in adding concrete detail to well structured, coherent text to promote interest unless enough is added so that a new text with a different coherence emerges. Making already concrete text more emotionally interesting may have little effect. Using a coherent text structure that adequately implies or signals importance and supporting important information with concrete explanation are key text design implications. Dual Coding Theory provides a systematic theoretical account of the findings in this area.     

The Effects of Concreteness on Mathematical Manipulative Choice

There is mixed evidence as to whether concrete manipulatives (e.g., toy animals) are better than abstract manipulatives (e.g., counters) for teaching mathematical concepts to children. Concreteness is defined as the amount of extraneous information a manipulative provides, and in this study we aimed to unpick which dimensions of concreteness influence manipulative choice. Researchers, teachers, and parents completed a comparative judgment task comparing images of manipulatives varying in different dimensions of concreteness, selecting which they would choose to teach arithmetic to children. The findings indicated homogeneous, 3-dimensional manipulatives were the most preferred across all groups to teach arithmetic to children, regardless of more extraneous features. This contradicts research recommendations to minimize the use of concrete manipulatives due to their distractive qualities. Instead, it suggests that some concrete features may be preferred in more naturalistic contexts. More research is required to investigate how different dimensions of concreteness influence learning outcomes for children both in artificial research contexts and in practice.     

Influence of word meaning on the acquisition of a reading vocabulary in second-grade children

The acquisition of a reading vocabulary for abstract and concrete words was examined in 62 second-grade children. Words had been learned as part of a basal reader program or as part of outside reading. Word recognition speed and reading accuracy were examined for abstract and concrete words using lexical decision and word naming tasks. The size of the concreteness effect was similar for both processing tasks. In neither task did concreteness influence reaction times, but abstract words were read with less accuracy than concrete words in both tasks. Further, these concreteness effects in reading accuracy were larger for words that were part of a basal reading program than for words acquired during free reading. We conclude that word meaning influences the entry of words at a time when children are developing a sizeable reading vocabulary.     

The Concept of Intelligence in Psychology as a Fallacy of Misplaced Concreteness

During the 20th century, mainstream psychologists exhibited a dogmatic belief in the reality of the abstraction of human intelligence as a cluster of functional behaviours. In confusing this abstraction for the concrete totality of the human intellectual experience, psychologists have committed what Alfred North Whitehead calls a "fallacy of misplaced concreteness" (1925/1967, p. 58). That is, they have mistaken a narrowly abstract conception of intelligence for concrete reality. This mistake has contributed to a dogmatic and naive ignorance of other possible explanations for intelligent human experience. If psychology truly desires to be a legitimate science in endeavouring to understand human intelligence, it must take into account concrete aesthetic experiences that are fundamental to the growth of creative consciousness and human knowledge.     

浅谈数学中的美

数学本身具有许多美的特性,它们是形象、生动而具体的,数学中的符号美、统一美、和谐美和奇异美均展现着数学自身的美。     

论施喻者不同映射方式下的交际目的

传统的观点认为人们总是用具体的源域映射抽象的目标域。实际上,具体或抽象并不是某一个域的必然属性。王文斌提出,两个域之间的映射通过具体与抽象两两组合而成,即以具体隐喻具体、以具体隐喻抽象、以抽象隐喻具体、以抽象隐喻抽象。隐喻研究多集中在隐喻产物上,而对施喻者使用隐喻的目的研究较少。基于此,本文探讨施喻者在运用这四种不同映射方式时不同的交际目的。     

Teaching the Conceptual Revolutions in Geometry

Mathematics begins in human experience thousands of years ago as empirical and intuitive experiences. It takes the deliberate naming of concepts to help crystallize and secure those observations and intuitions as abstract concepts, and to begin separating the concept of number from specific instances of objects. It takes the creation of compact symbols to enable efficient calculation and to begin raising a consciousness of this activity we call mathematics. And it takes the sustained development and discussion of mathematical conventions and practices to create entire domains of mathematical thought, such as we find in geometry. The major innovations and conceptual reformulations are few in number, but these represent perhaps the greatest challenges to learners. Historically significant transformative events have their counterpart in the cognitive growth of the individual. This article examines the interplay between these big ideas in cultural history and the deliberate processes of cognitive change that are their counterpart in the educational process.