Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum

Cramer, Kathleen A.; Post, Thomas R.; delMas, Robert C.

doi:10.2307/749646

Cited by 176 publications

(138 citation statements)

References 14 publications

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“…Physical manipulatives do not typically contain the simultaneous linking affordance; therefore, many researchers have described the importance of transparency and linking representations when using physical manipulatives to teach concepts (Cramer, Post, & delMas, 2002). The results of this study further support these claims.…”

Section: Making Connectionssupporting

confidence: 80%

“…Research (e.g., Cramer, Post, & delMas, 2002;Sowell, 1989) and mathematics learning theories (e.g., Bruner, 1966;Cobb, 1995) emphasize the important role played by various conceptual representations in students' learning. Representations include signs, symbols, models, images, or objects that stand for a particular reality (Cai, 2005;Goldin & Shteingold, 2001) and are used to mediate and express learning.…”

Section: Representations Instructional Modalities and Fraction Learmentioning

confidence: 99%

“…Children have difficulty understanding the meaning of the denominator, keeping track of the whole, and thinking multiplicatively (Behr & Post, 1992;Kamii & Clark, 1995;Smith, 2002). To help children overcome these challenges, representations are often at the heart of teaching and learning the persistently difficult concept of fractions.Research (e.g., Cramer, Post, & delMas, 2002;Sowell, 1989) and mathematics learning theories (e.g., Bruner, 1966;Cobb, 1995) emphasize the important role played by various conceptual representations in students' learning. Representations include signs, symbols, models, images, or objects that stand for a particular reality (Cai, 2005;Goldin & Shteingold, 2001) and are used to mediate and express learning.…”

mentioning

confidence: 99%

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Using Open-Response Fraction Items to Explore the Relationship Between Instructional Modalities and Students’ Solution Strategies

Shumway

Moyer‐Packenham²,

Baker³

et al. 2016

IJEMST

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Article HistoryReceived: 17 February 2015The purpose of this study was to explore the relationship between instructional modality used for teaching fractions and third-and fourth-grade students' responses and strategies to open-response fraction items. The participants were 155 third-grade and 200 fourth-grade students from 17 public school classrooms. Students within each class were randomly assigned to two instructional treatment groups: a virtual manipulatives representations (VMR) instruction group and a physical manipulatives and textbook representations (PMTR) instruction group. A conversion mixed methods analysis was used to examine quantitative and qualitative data. The quantitative analysis showed achievement outcomes were the same for both groups. The qualitative analysis revealed shifts in learning that were otherwise hidden with solely quantitative achievement results. Specifically, the results indicated VMR group success in understanding fractions as relationships and PMTR group success in maintaining conceptualization of the whole. Overall, the results of this study corroborate previous research indicating the importance of both types of instructional modalities, showing that virtual manipulatives and physical manipulatives are effective instructional tools with positive effects on student learning. The study expands existing research by offering an opportunity to explore the nuances of students' fractions understanding and provide a window into students' shifts in fraction learning. Accepted: 29 September 2015 Keywords Virtual manipulatives Physical manipulatives Fractions Instructional modalities Open-response items IntroductionElementary teachers use a variety of instructional modalities when teaching children early fraction concepts. Their instruction often includes physical, pictorial, and symbolic representations. Some teachers use virtual manipulatives (Moyer, Bolyard, & Spikell, 2002), which combine representations (e.g., pictorial and symbolic) and representational modalities (e.g., visual and haptic). Studies indicate that using multiple representations and modalities in fraction instruction develops and expands students' understanding of fractions (Behr, Lesh, Post, & Silver, 1983;Moyer-Packenham & Westenskow, 2013;Sowell, 1989).The purpose of this study was to explore the relationship between instructional modalities used for learning fraction concepts-specifically using virtual manipulatives or physical manipulatives with textbooks-and students' solution strategies on open-response fraction items. We employed a conversion mixed methods approach (Teddlie & Tashakkori, 2006) to analyze open-response items, which we coded and quantitized for quantitative and qualitative analysis. Open-response items provide windows into students' thinking processes and strategies for solving mathematics tasks (Cai, 2000;Cai, Magone, Wang, & Lane, 1996;Lane, 1993). This study complements and extends previous studies by using open-response items to examine these phenomena in depth using qualitative...

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Section: Making Connectionssupporting

confidence: 80%

Section: Representations Instructional Modalities and Fraction Learmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Using Open-Response Fraction Items to Explore the Relationship Between Instructional Modalities and Students’ Solution Strategies

Shumway

Moyer‐Packenham²,

Baker³

et al. 2016

IJEMST

View full text Add to dashboard Cite

show abstract

“…On the other hand, brief studies often advantage experimental groups that focus on a particular set of objectives during a limited time period while control groups spread that topic over a longer period. For example, a 30-day experiment by Cramer, Post, and delMas (2002) evaluated a fractions curriculum that is part of the Rational Number Project. Control teachers using standard basals were asked to delay their fractions instruction to January to match the exclusive focus of the experimental group on fractions, but it seems unlikely that their focus would have been equally focused on fractions, the only skill assessed.…”

Section: Criteria For Inclusionmentioning

confidence: 99%

Effective Programs in Elementary Mathematics: A Best-Evidence Synthesis

Slavin

Lake

2008

Review of Educational Research

284

224

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This article reviews research on the achievement outcomes of three types of approaches to improving elementary mathematics: mathematics curricula, computer-assisted instruction (CAI), and instructional process programs. Study inclusion requirements included use of a randomized or matched control group, a study duration of at least 12 weeks, and achievement measures not inherent to the experimental treatment. Eighty-seven studies met these criteria, of which 36 used random assignment to treatments. There was limited evidence supporting differential effects of various mathematics textbooks. Effects of CAI were moderate. The strongest positive effects were found for instructional process approaches such as forms of cooperative learning, classroom management and motivation programs, and supplemental tutoring programs. The review concludes that programs designed to change daily teaching practices appear to have more promise than those that deal primarily with curriculum or technology alone.

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“…En vanlig missuppfattning av begreppet "en halv" är att det räcker med att helheten delas i två delar. Att delarna måste vara lika stora är något som inte alltid uppmärksammas (se Cramer et al, 2002). För att förstå betydelsen av begreppet en halv måste en halv separeras ut.…”

Section: Variationsmönsterunclassified

Lärares och elevers användande av laborativt material i bråkundervisningen i skolår 4-6 : Vad görs möjligt för eleverna att erfara?

Sveider¹

2015

LiU-PEK-R / Institutionen För Beteendevetenskap Och Lärande (2007-)

View full text Add to dashboard Cite

Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum

Cited by 176 publications

References 14 publications

Using Open-Response Fraction Items to Explore the Relationship Between Instructional Modalities and Students’ Solution Strategies

Using Open-Response Fraction Items to Explore the Relationship Between Instructional Modalities and Students’ Solution Strategies

Effective Programs in Elementary Mathematics: A Best-Evidence Synthesis

Lärares och elevers användande av laborativt material i bråkundervisningen i skolår 4-6 : Vad görs möjligt för eleverna att erfara?

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