Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division

Milton, Jessica H.; Flores, Margaret M.; Moore, Alexcia J.; Taylor, Ja'Lia J.; Burton, Megan

doi:10.1177/0731948718790089

Cited by 29 publications

(41 citation statements)

References 24 publications

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“…Students associate previously formed representations with symbols. At this stage, education builds on conceptual understanding and develops procedural knowledge and fluency (Milton et al, 2019). Once students have mastered solving problems with numbers only, the focus in mathematics education is on spontaneity and accuracy, which is the common approach in mathematics education.…”

Section: Concrete-representational-abstract (Cra)mentioning

confidence: 99%

The Effect of Using Concrete-Representational-Abstract Sequence in Teaching the Perimeter of Geometric Shapes for Students with Learning Disabilities

AL-salahat

2022

IJEMST

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Geometry is one of the basic areas of school mathematics education, and it is important for elementary students. However, students with mathematics learning disabilities (MLD) struggle with geometry learning. Research has demonstrated that concrete-representational-abstract (CRA) teaching is an effective practice for students with learning disabilities (LD) and other disabilities. The study aimed to investigate whether the CRA sequence can support students’ understanding of calculating the perimeter of geometric shapes and solving mathematical word problems of the perimeter in Najran city in the Kingdom of Saudi Arabia. The study used the quasi-experimental research design for one treatment group of a pre-posttest. First, the perimeter test of geometric shapes, whose validity and reliability was verified, was used, and then the CRA sequence was applied to eight students in the fourth and fifth grades with LD in mathematics. The results showed that the CRA sequence improved the students’ efficiency in calculating the perimeter of geometric shapes and solving mathematical word problems on the perimeter. Also, the students maintained the learned skills three weeks post the interventional period.

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Section: Concrete-representational-abstract (Cra)mentioning

confidence: 99%

The Effect of Using Concrete-Representational-Abstract Sequence in Teaching the Perimeter of Geometric Shapes for Students with Learning Disabilities

AL-salahat

2022

IJEMST

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“…So that the teaching method using the CRA (concrete-representationabstract) sequence is considered effective. The CRA (concrete-representation-abstract) sequence is adapted from the Bruner stage in Milton which describes three stages, namely enactive, iconic and symbolic [24]. The enactive step is the steps where students are directly involved with the object of manipulation.…”

Section: Somentioning

confidence: 99%

Teaching for Understanding Mathematics in Primary School

Yuliandari¹,

Anggraini²

2021

Advances in Social Science, Education and Humanities Research

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Conceptual understanding is one indicator of an expert in mathematics. Conceptual understanding is important for students in addition to procedural skills. Students who have a good conceptual understanding will be able to find solutions with new or different procedures, while students who do not have conceptual understanding will only use standard procedures. Teaching is the most important thing in the process of developing students' conceptual understanding. The teacher as a learning designer in the classroom has a role that must be able to direct and guide students to develop conceptual understanding through effective learning. This article aims to discuss the teaching of conceptual understanding in primary schools. This article uses a structured literature review method. The author uses various documents such as national and international indexed journals, quality books that have been written by mathematical figures, especially material on understanding mathematics concepts and teaching. The results showed that the teacher could teach conceptual understanding by using the teaching language carefully and easily understood, making questions that encouraged students to think, avoiding learning shortcuts, avoiding memorizing facts and procedures, helping students make connections between concepts, and develop understanding through CRA (Concrete-Representation-Abstract).

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“…The CRA model is advantageous for the development of number fluency (Jones & Tiller, 2017). CRA is an effective strategy for students that struggle with mathematical fluency, since the concrete and representational components support procedural knowledge as part of the abstract stage (Agrawal & Morin, 2016;Miller & Kaffar, 2011;Milton et al, 2019). Additionally, since the abstract stage in CRA focuses on the completion of a task, students are best supported when they are exposed to the mathematical notation along with a math problem in the concrete and representational stages (Flores, 2010).…”

Section: Concrete Manipulativesmentioning

confidence: 99%

Lessons Learned From a Rural Classroom Study: Transitioning From Concrete to Virtual Manipulatives to Teach Math Fact Fluency to Students With Learning Disabilities

Kabel

Hwang

2021

JCSR

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As the use of technology has become more prevalent within the educational environment over the past decade, the emergence of the use of virtual manipulatives to support student learning in math has made transitioning to technology-infused math instruction unavoidable. Students in rural areas, however, have tended to receive far less technology-infused instruction due to the many challenges faced by rural schools that can adversely affect academic opportunities and disrupt equity in learning and teaching. In the current paper, we report on a classroom study conducted to examine whether the previously proven effects of concrete manipulatives can carry over into those of virtual manipulatives when teaching math fact fluency in multiplication and explored the potential for virtual manipulatives in rural classrooms from the teacher’s perspective. Quantitative and qualitative results both indicated a promising potential for usage of virtual manipulatives, with meaningful implications for practitioners. The educational implications for designing and planning effective instruction incorporating virtual manipulatives are discussed.

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Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division

Cited by 29 publications

References 24 publications

The Effect of Using Concrete-Representational-Abstract Sequence in Teaching the Perimeter of Geometric Shapes for Students with Learning Disabilities

The Effect of Using Concrete-Representational-Abstract Sequence in Teaching the Perimeter of Geometric Shapes for Students with Learning Disabilities

Teaching for Understanding Mathematics in Primary School

Lessons Learned From a Rural Classroom Study: Transitioning From Concrete to Virtual Manipulatives to Teach Math Fact Fluency to Students With Learning Disabilities

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