Teaching the Partial Products Algorithm Using the Concrete-representational-abstract Sequence

Flores, Margaret M.; Milton, Jessica H.

doi:10.1080/09362835.2020.1772070

Cited by 8 publications

(14 citation statements)

References 24 publications

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“…important in mastering. For example, this is the teaching strategy recommended by Ketterlin-Geller, Chard and Fien In a new study using the CPA sequence for some elementary students with low math achievement, Flores [4] found that students improved fluency and increased confidence in performing arithmetic calculations. emphasizes what they have demonstrated.…”

Section: Literature Analysis and Methodsmentioning

confidence: 99%

Pedagogical Possibilities of Implementing the Cpa (Concrete-Pictorial-Abstract) Approach

Shuxratovna

2024

ijp

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The increase in the flow of information in the field of sciences requires the improvement of technologies that serve to master it, and the introduction of new technologies. Learning materials consist of variables, characters, etc. However, mastering educational materials is not just learning symbols, but most importantly, being able to apply knowledgein everyday life. And abstract educational materials are very important in mastering science. This article explores the pedagogical possibilities of introducing the CPA (Concrete-Pictorial-Abstract) approach to primary education. Based on the analysis, itbecame clear that the CPA (Concrete-Pictorial-Abstract) approach has not been thoroughly studied by local scientists and its possibilities have not been analyzed.

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Section: Literature Analysis and Methodsmentioning

confidence: 99%

Pedagogical Possibilities of Implementing the Cpa (Concrete-Pictorial-Abstract) Approach

Shuxratovna

2024

ijp

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“…A case study using CRA to teach students with disabilities to count using flexible numbers: applying skip counting to multiplication (Gibbs et al, 2018) 13. Teaching the partial products algorithm using the concreterepresentational-abstract sequence (Flores & Milton, 2020) Cluster 4…”

Section: Research Domainsmentioning

confidence: 99%

“…The studies conducted by Flores M.M. were mainly related to the effectiveness of teaching elementary mathematics to students with special needs using a concrete-representational-abstract sequence (i.e., Flores, 2010;, Flores & Milton, 2020Flores et al, 2014bFlores et al, , 2014cFlores et al, , 2016Flores et al, , 2020aFlores et al, , 2020bMilton et al, 2019;Stroizer et al, 2015). Thereupon, the studies are highly relevant in the related research domain with 'concrete-representational-abstract sequence' and 'elementary education' as the top keywords.…”

Section: What Are the Contributions Of The Most Relevant Author In Ea...mentioning

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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“…Despite students’ ability to label place value, this type of error was consistent. While the error changed over the course of CRA instruction, it had previously interfered with students’ performance (Flores & Hinton, 2022; Flores & Milton, 2020).…”

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confidence: 99%

“…McDonald et al (2018) studied place value understanding of students who were failing mathematics and found that third– and sixth–grade students treated the first digit in the numeral 32 as three ones. Similarly, Flores and Hinton (2022) and Milton and Flores (2020) described examples of this error with fifth– and sixth–grade students with LD as they attempted to multiply two 2–digit multipliers using the standard and partial products algorithms. In both studies, students verbalized the equation 20×30 as three times two with a product of 6.…”

mentioning

confidence: 99%

Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Place Value, Rounding, and Expanded Notation

Milton

Flores

Hinton

et al. 2023

Learning Disabilities Research & Practice

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This study investigated the effects of a place value intervention with third-grade students with learning disabilities. The intervention added content to a research-based intervention using the concrete-representational-abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students' place value understanding was measured using probes in which students had to identify the value of each digit within a three-digit number, round three-digit numbers to the nearest 10 or 100, and write three equations showing an expanded form of a three-digit number. A single-case, multiple-probe-across-students design showed a functional relation between CRA and completion of items requiring place value understanding. Students completed a generalization task by estimating the sum of a given equation.

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Teaching the Partial Products Algorithm Using the Concrete-representational-abstract Sequence

Cited by 8 publications

References 24 publications

Pedagogical Possibilities of Implementing the Cpa (Concrete-Pictorial-Abstract) Approach

Pedagogical Possibilities of Implementing the Cpa (Concrete-Pictorial-Abstract) Approach

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

Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Place Value, Rounding, and Expanded Notation

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