Using the Concrete-Representational-Abstract Sequence to Teach Subtraction With Regrouping to Students at Risk for Failure

Abstract

This study investigated the effects of the concrete—representational—abstract (CRA) instructional sequence on the subtraction performance of students identified as at-risk for mathematics failure. Although the CRA sequence has been demonstrated as effective for teaching a variety of mathematical skills and processes its effects when used to teach subtraction with regrouping have not been studied. This study examined the effects of CRA instruction on elementary students’ fluency in computing subtraction problems with regrouping in the tens place as well as regrouping in both the tens and hundreds places. The study also investigated the effects of CRA instruction on students’ maintenance of regrouping skills. A multiple probe across students with embedded changing behaviors design was employed. A functional relation between CRA instruction and subtraction with regrouping was demonstrated across all students. The results and their implications are discussed further.

The Relationship Between Mathematics and Language: Academic Implications for Children With Specific Language Impairment and English Language Learners

“…In order to have a baseline measure of children's mathematics skills on a traditional, language-heavy, symbolheavy task, participants completed the KeyMath3 (Connolly, 2007), a developmental assessment of mathematical concepts that has been used frequently in research, including studies with exceptional populations (Baylor, 1998;Eaves, 1992;Flores, 2009;Kratochwill & Demuth, 1976;Tinney, 1975). 4 2 The parent questionnaire was available in both English and Spanish.…”

Building Mathematical Fluency for Students with Disabilities or Students At-Risk for Mathematics Failure

“…Research has shown that CRA-SI is effective in building mathematical fluency with place value, addition and subtraction of numbers, multiplication, regrouping, fractions, integers and algebra (Bulter et al, 2003, Flores, 2010Peterson et al, 1988;Maccini & Hughes, 2000;Mercer & Miller, 1992;Morin & Miller, 1998;Strozier et al, 2012;Witzel et al, 2003). A summary of the research studies chronicled by date is provided in Table 1.…”

“…Results indicated significant improvement in students' computation of addition or subtraction facts and in students' growth rates which were compared to growth rates established by Fuchs and Fuchs (1993). Flores (2009Flores ( , 2010 extended the CRA-SI line of research to include subtraction with regrouping. This study investigated the effectiveness of the CRA sequence on the computation performance of students with specific learning disabilities and students identified as at risk for failure in mathematics.…”

“…In CRA-SI, the strategy usually involves a mnemonic that helps students remember the steps or procedures in solving the mathematical problems (Flores, 2009;Kaffer & Miller, 2011;Miller, 2009). Mnemonics used as a strategy in CRA-SI are DRAW, RENAME, FASTDRAW, STAR, and SUMLOW (Flores, 2010;Harris, Miller, & Mercer, 1995;Kaffar & Miller, 2011;Maccini & Hughes, 2000;Mercer & Miller, 1992;Strozier, Flores, Shippen, & Hinton, 2012;Witzel, Mercer, & Miller, 2003). These strategies will be discussed in more depth later in the manuscript.…”

Investigating Indonesian Teachers' ZAD in the Representation of Fractions

“…This theory became the framework of the opinion that students' original mathematics knowledge should be taught using concrete representations as manipulation objects. Manipulatives are used to promote conceptual understanding [21] and are frequently used to solve mathematics problems related to the concrete world. The results of research performed by [22] showed that students with high ability could generate various ideas in mathematics problem-solving.…”