Benefits of “concreteness fading” for children's mathematics understanding

Fyfe, Emily R.; McNeil, Nicole M.; Borjas, Stephanie

doi:10.1016/j.learninstruc.2014.10.004

Cited by 92 publications

(71 citation statements)

References 49 publications

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“…The concreteness fading version of the prototype resulted in higher post-test scores than the other versions, a difference that was statistically significant between the concrete condition and the concreteness fading condition. The ranking of the post-test means across different conditions (concrete, concreteness introduction, abstract, concreteness fading) was in line with the findings of Fyfe et al [14] who investigated the approach in mathematics learning with pupils of the same age. When examining the learning gain by gender, the benefits of concreteness fading appear to be more pronounced for females than males.…”

Section: Discussionsupporting

confidence: 88%

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Designing for concreteness fading in primary computing

Trory

Howland

Good

2018

Proceedings of the 17th ACM Conference on Interaction Design and Children

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In primary education, concepts are commonly introduced through concrete instantiations, such as physical manipulatives and kinaesthetic activities, with an expectation that learners will gradually move towards working with abstract representations. There has been considerable research in subjects such as mathematics on how children can move from working with concrete to abstract materials, but relatively little research on how this can be achieved in computing, which has recently become a more prominent subject at primary level. This paper reports on the design and evaluation of a low-fidelity prototype learning environment that aims to teach children aged 9-10 about a key computing concept (internet routing), using a concreteness fading approach commonly applied in mathematics. An empirical study with 59 children showed that those following a concreteness fading progression scored significantly higher on a post-test than those using a concrete only prototype, and had an increase in positive attitude towards computing in line with alternative approaches. We highlight the potential for an augmented reality implementation of the prototype to support investigation of further key questions raised by this research.

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Section: Discussionsupporting

confidence: 88%

“…Fyfe et al applied their model to the design of learning materials to teach children (age M = 8 years) the principles of mathematical equivalence [14]. The enactive stage implemented a combination of metaphor (balance scales as an equation) and physical manipulation (placing objects on the scales to achieve balance).…”

Section: Related Workmentioning

confidence: 99%

Designing for concreteness fading in primary computing

Trory

Howland

Good

2018

Proceedings of the 17th ACM Conference on Interaction Design and Children

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“…However, despite the ubiquity of transfer, there are some gaps in the literature, including a scarcity of applied studies. Although there are insightful sociocultural perspectives with qualitative accounts of transfer [14,15], to date research measuring transfer has been dominated by experimental approaches, controlled conditions, and customised research assessment tools [16][17][18][19]. This study, by contrast, provides a naturalistic measure of transfer, using standard university assessments (details to follow).…”

Section: Literature Reviewmentioning

confidence: 99%

“…This is especially the case in relation to transfer between mathematics and science [21], and surprising given the substantial policy and investment focus recently directed to STEM education. However, within the relatively slim literature, several different aspects of transfer have been investigated, with some studies exploring quantitative skills in university science education (see [22][23][24]), and others looking at the transfer of mathematics more generally, with both quantitative and qualitative methodological approaches (see for example, [14][15][16][17][18][19]). …”

Section: Transfer In Science/engineering Educational Researchmentioning

confidence: 99%

First-Year Mathematics and Its Application to Science: Evidence of Transfer of Learning to Physics and Engineering

Nakakoji

Wilson

2018

Education Sciences

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Abstract:Transfer of mathematical learning to science is seen as critical to the development of education and industrial societies, yet it is rarely interrogated in applied research. We present here research looking for evidence of transfer from university mathematics learning in semester one to second semester sciences/engineering courses (n = 1125). A transfer index measure was derived from extant university assessments, calculated on content-matched questions requiring mathematical concepts and skills in students' completed mathematics and science/engineering exams. We found that transfer could be measured in this way, and present path models of how transfer is associated with educational attainment and other factors. However, transfer was observed only in physics (n = 258) and engineering (n = 426); biology and molecular bioscience assessments did not provide opportunities for students to demonstrate their mathematical learning. In physics and engineering courses, mathematical attainment had a strong, direct, positive effect, with transfer of learning providing an additional direct and mediating effect upon students' performance in these subjects. In physics and engineering, transfer was also associated with higher levels of educational attainment in general. This new, applied approach to examining transfer trialed here may provide opportunities for analysing, evaluating, and improving cross-disciplinary transfer of learning within universities.

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“…However, this may not always be the case from an educational perspective (Wernet, 2017). Fyfe et al (2015) suggested that geometric concepts are the main problems behind the most important troubles when teaching mathematics. It is possible to see perspectives, such as misconceptions, conceptual errors,…”

Section: Introductionmentioning

confidence: 99%

Mathematics through the 5E Instructional Model and Mathematical Modelling: The Geometrical Objects

Tezer

Cumhur

2017

EURASIA J MATH SCI T

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The aim of this research is to investigate the effect of education on the mathematical achievement, problem-solving skills and the views of students on the 5E instructional model and the mathematical modelling method for the "Geometric Objects" unit. The students were randomly selected from the 8th grade of a secondary school in Northern Cyprus. One group was the experimental group to which the 5E instructional model applied, and mathematical modelling was applied to the other. As a data collection tool, the "Geometrical Objects Multiple Choice Achievement Test" was applied to the experimental groups. As a result of statistical analysis, it was seen that the teaching provided by the 5E Instructional Model in Experimental group 1 and the Mathematical Modelling Method in the Experimental group 2 increased the academic achievement of the students; however, the mathematical modelling method was more successful in the mathematical achievement and problem-solving skills of the students.

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Benefits of “concreteness fading” for children's mathematics understanding

Cited by 92 publications

References 49 publications

Designing for concreteness fading in primary computing

Designing for concreteness fading in primary computing

First-Year Mathematics and Its Application to Science: Evidence of Transfer of Learning to Physics and Engineering

Mathematics through the 5E Instructional Model and Mathematical Modelling: The Geometrical Objects

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