Concreteness fading fosters children's understanding of the inversion concept in addition and subtraction

Ching, Boby Ho-Hong; Wu, Xiaohan

doi:10.1016/j.learninstruc.2018.10.006

Cited by 17 publications

(6 citation statements)

References 69 publications

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“…This shows that learning from concrete materials that "fade" to abstract symbols benefits transfer, the progression from concrete to abstract is better than the reverse, learning from concrete materials is similar to learning from abstract symbols, and the benefits of "fading" extend to children with low and high prior knowledge (Fyfe et al, 2015). Ching and Wu (2019) examined the effectiveness of various instructional strategies that aimed to enhance children's understanding of the inversion concept using 140 kindergarten pupils randomly assigned to each group of concrete-only, abstract-only, concreteness fading, abstract-to-concrete, and control. All the intervention (experimental) groups showed significantly greater progress than the control group in solving the inversion problems in the post-tests.…”

Section: Discussionmentioning

confidence: 95%

“…The superior benefits of concreteness fading appeared more prominent in the post-test scores for children with lower prior knowledge. The findings of Ching and Wu (2019) brought to light two key implications: (1) concrete representations should not be avoided in teaching mathematics, and (2) the order of the various representations is key for effective learning.…”

Section: Discussionmentioning

confidence: 99%

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Cultural Symbols Didactize Concreteness Fading in Basic Multiplication

Ali

2024

J. of Instr. Math.

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The purpose of this study is to use cultural Adinkra artifacts to present “Concreteness Fading” in the basic multiplication of one-digit and one-digit numbers. Employing a quantitative approach, the researcher adopted a one-group pretest-posttest quasi-experimental design, and randomly selected 51 participants from 300 student teachers. Data collection involved two sets of tests, analyzed in two stages through task-based transcripts and paired-sample t-tests. The first stage analyzed the tasks the student teachers solved using “Concreteness Fading”. The results revealed smooth and joyful navigations of the stages of Concreteness Fading using the Adinkra symbols. The second stage analyzed the performance of the student teachers with t-test statistics to show significant differences between the control and experimental groups. The results of one sample t-test and paired samples t-test showed that student teachers solved more problems correctly using Concreteness Fading than the conventional concrete manipulatives. Following the findings, we concluded that heavy use of only concrete objects and examples without abstracting can be detrimental to teaching mathematics. We, therefore, recommended that student teachers should always avoid rushing to symbols and symbolic manipulations of mathematics but rather align their methods, techniques, and strategies in the transition through the three stages of Concreteness Fading.

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Section: Discussionmentioning

confidence: 95%

Section: Discussionmentioning

confidence: 99%

Cultural Symbols Didactize Concreteness Fading in Basic Multiplication

Ali

2024

J. of Instr. Math.

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“…Systematically fading representations of equivalence from more concrete to more symbolic (i.e., concreteness fading) can also be used to both build children’s early nonsymbolic equivalence understanding and link it to formal, symbolic representations of equivalence. Concreteness fading has been successfully used with kindergarteners to introduce the inversion principle ( a + b − b = a ; Ching & Wu, 2019). However, it is important to note that these instructional recommendations are only tentative suggestions at this point, as the present study took an individual differences approach and was not designed to determine cause.…”

Section: Discussionmentioning

confidence: 99%

Kindergarten predictors of formal understanding of mathematical equivalence in second grade.

Devlin¹,

Hornburg²,

McNeil³

2023

Developmental Psychology

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A longitudinal study was conducted to identify unique sources of individual differences in later understanding of the equal sign as a relational symbol of equivalence (i.e., formal understanding of mathematical equivalence). The sample included 141 children from a mid-sized city in the Midwestern United States (Mage = 6 years, 2 months in kindergarten; 88 boys, 53 girls; 71% white, 8% Hispanic or Latine, 7% Black, 3% Asian, 11% multiracial or other race/ethnicity; 42% qualified for free/reduced lunch). Children were assessed on three categories of skills in kindergarten including number knowledge, relational thinking, and executive functioning. These skills were hypothesized to provide a foundation for a formal understanding of mathematical equivalence (assessed in second grade) by preventing a specific, narrow misunderstanding of the equal sign that hinders learning. Results showed that kindergarten relational thinking, particularly tasks assessing nonsymbolic equivalence understanding, uniquely and positively predicted formal understanding of mathematical equivalence and negatively predicted the specific misunderstanding of the equal sign in second grade, controlling for IQ, gender, and free/reduced lunch status. Exploratory analyses unpacking the categories of skills into individual tasks also indicated specific areas of kindergarten instructional focus that may help children construct understanding of mathematical equivalence in future years.

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“…A wide range of research rooted from the mathematics learning theory proposed by Bruner (1966) and Piaget (1952) has been conducted in the past spanning from types of manipulative used (e.g., Litster et al, 2019), teaching approaches (e.g., Flores et al, 2020aFlores et al, , 2020b, content domain (e.g., Braithwaite et al, 2016;Ching & Wu, 2019), grade level (e.g., O'Meara et al, 2020) and learning context (e.g., Sekeris et al, 2020). To synthesise findings of interventional studies related to the use of manipulatives and teaching approaches rooted from Bruner's Theory (1966) and Piaget's theory (1952) in enhancing mathematics learning of students with mathematics disabilities, meta-analysis and systematic literature review has been conducted by several researchers (i.e., Lafay et al, 2019;Park et al, 2021b;Peltier et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

Chin

Meng

SUSEELAN

2022

Participatory Educational Research

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Mathematics learning is illustrated as a developmental progression in the direction of concrete-to-abstract by educational theorists. Various studies rooted in this notion were conducted in the past. This study aimed to profile the landscape of research rooted in this notion which was published from 1968 to 2021. The bibliographic data of 425 related publications were retrieved from the Scopus database for bibliometric analysis. Descriptive analysis and regression analysis were performed to profile the publication trend. Then, author bibliographic coupling analysis was carried out to identify the domains of research related to mathematics learning from concrete to abstract. The findings show an increasing trend of publication following the exponential model. The research was clustered into five research domains: (i) 'manipulatives and arithmetic learning'; (ii) 'mathematics learning of students with learning disabilities'; (iii) 'Concrete-Representational-Abstract sequence in elementary mathematics teaching'; (iv) 'Ideal mathematics teaching'; and (v) 'mathematics problem-solving and mathematics learning of students with autism spectrum disorder'. The two emergent research domains in this research area are (i) 'mathematics learning of students with learning disabilities'; and (ii) 'mathematics problem-solving and mathematics learning of students with autism spectrum disorder', which have the highest proportion of publications since 2015. The findings of this study can help researchers to understand the current landscape of research with the notion of mathematics learning from concrete to abstract, and hence propose pathways for future research.

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Concreteness fading fosters children's understanding of the inversion concept in addition and subtraction

Cited by 17 publications

References 69 publications

Cultural Symbols Didactize Concreteness Fading in Basic Multiplication

Cultural Symbols Didactize Concreteness Fading in Basic Multiplication

Kindergarten predictors of formal understanding of mathematical equivalence in second grade.

Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

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