Concreteness Fading in Mathematics and Science Instruction: a Systematic Review

Fyfe, Emily R.; McNeil, Nicole M.; Son, Ji Y.; Goldstone, Robert L.

doi:10.1007/s10648-014-9249-3

Cited by 244 publications

(210 citation statements)

References 60 publications

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“…More specifically, students learned more about place value when they worked with concrete representations before abstract ones, but only when there was no instructional guidance provided on their structural similarities. It is possible, as Fyfe et al (2014) [8] speculated, that presenting concrete representations before abstract ones could replace the need for any direct instruction on how the representations are structurally similar (see Canobi, 2009 [43] for a study showing how problem sequencing can positively impact learning with no explicit instruction). The students may have constructed a grounded understanding of place value concepts from the manipulatives because base-ten blocks are designed to make the proportional relationships between the denominations perceptually evident.…”

Section: Discussionmentioning

confidence: 99%

“…A review by Fyfe et al (2014) [8] demonstrates that the preponderance of evidence supports a concrete-to-abstract sequence in mathematics instruction. Concrete or otherwise "grounded" representations (see Belenky & Schalk, 2014) [14] can activate prior knowledge, which in turn can support the interpretation of subsequently presented abstract symbols, which by themselves are less transparent and as such more difficult to interpret (Fyfe et al, 2014;Koedinger & Nathan, 2004) [8,24].…”

Section: Representational Sequencing In Instructionmentioning

confidence: 99%

“…The studies comparing different representational sequences have been difficult to compare, however, because of differences in outcomes measures, differences in the nature of the tasks used in the instructional interventions, and differences in the experimental conditions being compared-that is, few studies directly compared abstract first, concrete first, and iterative orders to each other. Moreover, sequencing by itself may not tell the whole story; as suggested by Fyfe et al (2014) [8], effective forms of sequencing (i.e., concreteness fading) may replace the need for explicit instructional support, but other, less beneficial, sequences may require it. As such, research on the potential moderating effects of instructional guidance may serve to shed light on the inconclusive results in the representational sequencing literature.…”

Section: Representational Sequencing In Instructionmentioning

confidence: 99%

“…Specifically, without instructional guidance, students in the manipulatives-first condition would outperform the students in the other two sequence conditions. As Fyfe et al (2014) [8] concluded from their own review, concrete instantiations likely replace explicit explanations when they are presented before abstract ones. With instructional guidance, on the other hand, we predicted that students in all sequence conditions would benefit relative to those in the no-guidance conditions, but that the symbols-first condition would benefit the most because there are few cues in the context that would scaffold the meaning they attribute to the symbols used in the standard algorithm.…”

Section: Present Studymentioning

confidence: 99%

“…There is evidence to suggest that the order in which different types of mathematical representations-concrete and otherwise-are presented to students during instruction is predictive of students' learning of mathematical concepts. Presenting concrete instantiations before abstract ones can be beneficial (e.g., Fyfe, McNeil, Son & Goldstone, 2014) [8], for example, but the question of representational sequencing has led to inconclusive results on the whole (e.g., Rittle- Johnson & Koedinger, 2009) [9]. Lending clarity to the issue of representational sequencing for elementary students' mathematics learning was a primary objective of our study.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

2017

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Concrete objects used to illustrate mathematical ideas are commonly known as manipulatives. Manipulatives are ubiquitous in North American elementary classrooms in the early years, and although they can be beneficial, they do not guarantee learning. In the present study, the authors examined two factors hypothesized to impact second-graders' learning of place value and regrouping with manipulatives: (a) the sequencing of concrete (base-ten blocks) and abstract (written symbols) representations of the standard addition algorithm; and (b) the level of instructional guidance on the structural relations between the representations. Results from a classroom experiment with second-grade students (N = 87) indicated that place value knowledge increased from pre-test to post-test when the base-ten blocks were presented before the symbols, but only when no instructional guidance was offered. When guidance was given, only students in the symbols-first condition improved their place value knowledge. Students who received instruction increased their understanding of regrouping, irrespective of representational sequence. No effects were found for iterative sequencing of concrete and abstract representations. Practical implications for teaching mathematics with manipulatives are considered.

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Section: Discussionmentioning

confidence: 99%

Section: Representational Sequencing In Instructionmentioning

confidence: 99%

Section: Representational Sequencing In Instructionmentioning

confidence: 99%

Section: Present Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

2017

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Altering element interactivity and variability in example‐practice sequences to enhance learning to write Chinese characters

Lu¹,

Kalyuga²,

Sweller³

2020

Applied Cognitive Psychology

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Summary The isolated elements and variability effects of cognitive load theory were used to alter the element interactivity of Chinese characters when instructing novice learners (72 overseas students at a Chinese university) in writing characters using worked examples‐practice procedures. A group of characters with more than eight strokes was disassembled into three individual components. Students were required to trace examples and practice writing of either similar sequences of isolated components followed by integrated components of full characters (Isolated–Integrated sequences); variable sequences of isolated followed by integrated components (Variability–Integrated sequences); or conventional Integrated–Integrated sequences of full characters. It was hypothesized that the fully integrated stroke‐movements form of example‐practice sequences would result in less learning due to a greater cognitive load. The results demonstrated that the participants in both the Isolated–Integrated and Variable–Integrated groups performed significantly better than the Integrated–Integrated group with the Variable–Integrated group outperforming the Isolated–Integrated group.

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The role of manipulation of concrete representations in early cardinal comprehension

Rodríguez

Salsa

Martí

2021

Infant and Child Development

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This study examines the impact of manipulation on the performance of 3.5-and 4-year-old children in the Give-N task with concrete representations (sets of bottle caps and pictures of dots) and spoken number words. In this task, children were asked to give a certain number of items (cookies) using the three representational formats.Children were assigned to one of two conditions: manipulation (children could physically interact with the objects and pictures) or observation (children watched as the experimenter presented the representations). Resultsshow that manipulation had different effects according to the age of the children. For 3.5-year-olds, manipulation with objects but not with pictures consisted in taskirrelevant actions, and hindered performance. For 4-yearolds, however, manipulation with both concrete representations were task related and did not disrupt performance. The mere contemplation of the objects and pictures, without physically interacting with them, facilitated performance in both age groups, in comparison with number words. Emerging cardinal comprehension seems to be influenced not only by the kind of representations used by children, but also by the type of physical exploration afforded during the task.

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Concreteness Fading in Mathematics and Science Instruction: a Systematic Review

Cited by 244 publications

References 60 publications

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

Altering element interactivity and variability in example‐practice sequences to enhance learning to write Chinese characters

The role of manipulation of concrete representations in early cardinal comprehension

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