Effective mathematics interventions should be explicit and include students’ active involvement with multiple representations of the mathematical concept. The concrete‐representational‐‐integrated ...(CRA‐I) sequence includes these characteristics and has been shown as an effective practice for students who struggle in mathematics. The purpose of the current study was to use CRA‐I, to teach the partial products algorithm. Three fifth‐grade students receiving Tier 3 instruction within a multi‐tiered system of support participated in the study, using base 10 blocks, number lines, and arrays. The researchers used a multiple probe across students design and collected data regarding students’ progress, mastery, and conceptual understanding. There were functional relations between CRA‐I and each of the skills related to progress, mastery, and conceptual understanding. Implications and conclusions will be discussed.
Practitioner points
Students learned the partial products algorithm using base ten blocks, arrays, and a strategy.
Students’ understanding of place value and its application to estimating products improved after intervention.
Students maintained their performance 2 months after instruction.
As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits ...in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on students’ automaticity. Research reported observational data regarding strategy-use, but not growth in number sense and understanding of operations. This study investigated the effects of an intervention using the concrete-representational-abstract-integrated (CRA-I) sequence. The purpose of this study was to assess the effects of CRA-I on students’ number knowledge (magnitude, place value, and flexibility in strategy-use) and understanding of addition (commutative property and relation to subtraction). The researchers used a multiple probe across participants design. In addition, the researchers collected descriptive data on students’ automaticity. There was a functional relation between CRA-I and students’ number sense and understanding of addition, and students’ automaticity increased.
The current study investigated the effects of the concrete-representational-abstract integrated sequence (CRA-I) for teaching fifth grade students receiving tier two interventions within a ...multi-tiered system of support (MTSS). The research questions addressed the following: the extent to which students' rational number skills changed as a result receiving CRA-I, the extent to which students receiving CRA-I decreased their fraction estimation error, the extent to which students receiving CRA-I and their teachers perceived it to be socially valid, and the extent to which students who received CRA-I intervention maintained their performance two months after instruction. Using a quasi-experimental design with randomly assigned matched pairs, researchers taught 11 students using CRA-I and compared their performance to 11 of their peers in a comparison group who waited to receive intervention. The researchers found a significant difference in performance favoring the CRA-I group. The implications of the results will be discussed.
State standards include fluent use of standard computational algorithms. However, learning and using them require conceptual understanding of numbers and operations. Previous research using the ...concrete–representational–abstract (CRA) sequence has been effective in teaching computational algorithms to students at risk of and students with learning disabilities by emphasizing conceptual understanding. However, all the research was face-to-face and few captured the impact of the intervention on students’ conceptual understanding. The current study occurred during the COVID-19 pandemic, so researchers modified CRA for remote instruction. This study investigated the effects of modified CRA on the fluency and accuracy of three sixth-grade students with learning disabilities. They also included an assessment of conceptual understanding. The researchers used a multiple probe across participants design, demonstrating a functional relation between CRA and students’ fluency and accuracy. Researchers assessed conceptual understanding with informal measures that required application of their conceptual understanding. The results and implications are discussed.
The purpose of this study was to investigate the effects of the concrete-representational-abstract–integrated (CRA-I) sequence on students with learning disabilities’ performance when learning ...fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The intervention involved explicit use of fraction blocks, coins, base ten blocks, number lines, pictures, and abstract symbols to teach unit fractions, fraction and decimal equivalence, addition of fractions with unlike denominators, and writing fractions as decimals. The researchers demonstrated a functional relation between CRA-I and three different behaviors related to fraction concepts: decreased error in estimating fraction magnitude, addition of unlike fractions, and writing fractions as decimals. The findings show promise in the use of CRA-I for teaching fraction concepts to students with learning disabilities.
Augmentative and alternative communication (AAC) interventions have been shown to improve both communication and social skills in children and youth with autism spectrum disorders and other ...developmental disabilities. AAC applications have become available for personal devices such as cell phones, MP3 Players, and personal computer tablets. It is critical that these new forms of AAC are explored and evaluated. The purpose of this study was to investigate the utility of the Apple iPad™ as a communication device by comparing its use to a communication system using picture cards. Five elementary students with autism spectrum disorders and developmental disabilities who used a picture card system participated in the study. The results were mixed; communication behaviors either increased when using the iPad or remained the same as when using picture cards. The implications of these findings are discussed.
Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and ...procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence of instruction has been shown to be an effective means of teaching conceptual understanding of fractional numbers. The purpose of this study was to compare the effects of CRA with remedial multitiered systems of support (MTSS) Tier 2 instruction for teaching fraction concepts. Thirty-one fifth-grade students participated in two different Tier 2 interventions; one group received typical Tier 2 instruction with their general education teachers and the other received CRA instruction with the researchers. The researchers measured student performance using a pretest and posttest and found significant differences in progress favoring the CRA group. Results and implications are discussed.
Students who have difficulty with mathematics may have trouble understanding underlying concepts of numbers and operations. The concrete-representational-abstract (CRA) instructional sequence of ...instruction provides a way for teachers to help students gain meaning from numbers and the mathematical concepts those numbers represent. This study addresses evidence-based practices and applies CRA methods to instruction address concepts such as rounding, regrouping, and equivalent fractions. The purpose of this study was to investigate the effects of CRA instruction on the performance of elementary students across varied areas of need related to poor conceptual understanding and proficiency in completing tasks related to numbers and operations. The researchers implemented a multiple baseline across behaviors design for two students who were at risk for mathematics failure. A functional relation was found for CRA intervention and rounding, regrouping, and fraction concepts for the two students. Results and implications are discussed.
The concrete–representational–abstract (CRA) sequence of instruction is an explicit methodology for teaching mathematics using multiple representations of concepts. Learning concepts through multiple ...representations fosters conceptual understanding and mathematical thinking. This article describes how a special education teacher used explicit CRA instruction with two elementary students with emotional and behavioral disorders. Its aims are to describe and provide a rationale for explicit CRA instruction. We describe lesson activities, methods, materials, and procedures. Finally, we offer suggestions for effective implementation.
Recent multiplication with regrouping research shows that the combination of the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) has been effective in ...several studies. More evidence is needed to demonstrate CRA-SIM’s effectiveness across settings and students. Therefore, the purpose of this study was to replicate previous findings in which CRA-SIM led to improved performance of students receiving tertiary interventions. This study extended the research by including problem-solving application in order to align the intervention with current standards for mathematics. Three elementary students receiving tertiary interventions participated in the study. The researchers used a multiple baseline across students design to show a functional relation between CRA-SIM and student performance. In addition to mastery of multiplication with regrouping, students applied their knowledge, discriminating between different operations when solving word problems. The implications and program components that influenced these results will be discussed.
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