Developmental Analysis of Understanding Language About Quantities and of Solving Problems

Riley, Mary S.; Greeno, James G.

doi:10.1207/s1532690xci0501_2

Cited by 255 publications

(230 citation statements)

References 23 publications

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“…In the arithmetic problems, the problem unknown is the result of the process or sequence of operators described. These result-unknown problems are more complex than those used in prior research on elementary arithmetic problem solving (Briars & Larkin, 1984;Carpenter & Moser, 1984;Hiebert, 1982;Riley & Greeno, 1988). These problems involve two arithmetic operators (e.g., multiplication and addition) rather than one, decimals rather than only whole numbers, and more advanced symbolic notation such as parentheses and equations with a variable on the right side (e.g., [81.90 -66]/6 = x).…”

Section: Hypotheses and Experimental Designmentioning

confidence: 99%

The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning

Koedinger

Nathan

2004

Journal of the Learning Sciences

324

255

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This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than solving mathematically equivalent equations. Contrary to some views of situated cognition, this result is not simply a consequence of situated world knowledge facilitating problem-solving performance, but rather a consequence of student difficulties with comprehending the formal symbolic representation of quantitative relations. We draw on analyses of students' strategies and errors as the basis for a cognitive process explanation of when, why, and how differences in problem representation affect problem solving. We conclude that differences in external representations can affect performance and learning when one representation is easier to comprehend than another or when one representation elicits more reliable and meaningful solution strategies than another.A commonly held belief about story problems at both the arithmetic and algebra levels is that they are notoriously difficult for students. Support for this belief can be seen among a variety of populations including the general public, textbook au-

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Section: Hypotheses and Experimental Designmentioning

confidence: 99%

The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning

Koedinger

Nathan

2004

Journal of the Learning Sciences

324

255

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“…Following Hanich (2000, adapted from Carpenter &Moser, 1984;Riley & Greeno, 1988;Riley, Greeno, & Heller, 1983), Single-Digit Story Problems comprises 14 story problems involving sums or minuends of 9 or less, reflecting change, combine, compare, and equalize relationships. The tester reads each item aloud; students have 30 sec to respond and can ask for rereading(s) as needed before the tester reads the next item.…”

Section: Outcome Measures Aligned With Procedural/estimation Skill Tumentioning

confidence: 99%

Remediating Computational Deficits at Third Grade: A Randomized Field Trial

Fuchs

Powell

Hamlett

et al. 2008

Journal of Research on Educational Effectiveness

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The major purposes of this study were to assess the efficacy of tutoring to remediate 3rd-grade computational deficits and to explore whether remediation is differentially efficacious depending on whether students experience mathematics difficulty alone or concomitantly with reading difficulty. At 2 sites, 127 students were stratified on mathematics difficulty status and randomly assigned to 4 conditions: word recognition (control) tutoring or 1 of 3 computation tutoring conditions: fact retrieval, procedural computation and computational estimation, and combined (fact retrieval + procedural computation and computational estimation). Results revealed that fact retrieval tutoring enhanced fact retrieval skill, and procedural computation and computational estimation tutoring (whether in isolation or combined with fact retrieval tutoring) enhanced computational estimation skill. Remediation was not differentially efficacious as a function of students' mathematics difficulty status. Keywords Mathematics difficulty; remediation; computationApproximately 4 to 1% of the school-age population suffers from mathematics disability (e.g., Badian, 1983;Shalev, Auerbach, Manor, & Gross-Tsur, 2000). Although the prevalence of mathematics disability is similar to that of reading disability, less systematic study has been directed at mathematics disability (Rasanen & Ahonen, 1995) despite evidence that poor mathematics skills are associated with lifelong difficulties in school and in the workplace. Mathematics competence, for example, accounts for variance in employment, income, and work productivity even after intelligence and reading have been explained (Rivera-Batiz, 1992).Some research illustrates how prevention activities at preschool (e.g., Clements & Sarama, 2007), kindergarten (e.g., Griffin, Case, & Siegler, 1994), or first grade (e.g., Fuchs, Fuchs, Yazdian, & Powell, 2002) can substantially improve math performance. For example, at the beginning of first grade, Fuchs et al. (2005) identified 169 students in 41 classrooms as at risk for math difficulties based on their low initial performance. These children were randomly assigned to a control group or to receive small-group tutoring that occurred three times per week for 20 weeks. Results showed that math development across first grade was significantly and substantially superior for the tutored group than for the control group on NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript computation, concepts, applications, and story problems. (We note that the math literature relies on the terms story problems and word problems interchangeably; in this article, we use the term story problems.) In addition, the incidence of students with mathematics disability was substantially reduced at the end of first grade, and this reduction in mathematics disability remained in the spring of second grade, 1 year after tutoring ended . Nevertheless, despite the efficacy of tutoring, students were not universally responsive. A subset of the tutored stude...

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“…There were four practice trials, one of each type of story problem: Change 1, Change 2, Change 5 and Change 6 (Riley & Greeno, 1988) using very small addends and minuends, i.e.…”

Section: Materials and Procedures For Number Tasksmentioning

confidence: 99%

Number Skills and Knowledge in Children With Specific Language Impairment.

Cowan¹,

Donlan²,

Newton³

et al. 2005

Journal of Educational Psychology

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The number skills of groups of 7 to 9 year old children with specific language impairment (SLI) attending mainstream or special schools are compared with an age and nonverbal reasoning matched group (AC), and a younger group matched on oral language comprehension. The SLI groups performed below the AC group on every skill. They also showed lower working memory functioning and had received lower levels of instruction.Nonverbal reasoning, working memory functioning, language comprehension, and instruction accounted for individual variation in number skills to differing extents depending on the skill.These factors did not explain the differences between SLI and AC groups on most skills.

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Developmental Analysis of Understanding Language About Quantities and of Solving Problems

Cited by 255 publications

References 23 publications

The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning

The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning

Remediating Computational Deficits at Third Grade: A Randomized Field Trial

Number Skills and Knowledge in Children With Specific Language Impairment.

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