The role of understanding in solving word problems

Cummins, Denise D.; Kintsch, Walter; Reusser, Kurt; Weimer, Rhonda

doi:10.1016/0010-0285(88)90011-4

Cited by 334 publications

(306 citation statements)

References 14 publications

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“…Similar to other findings regarding word problems in linear equations (Clement, 1982;Cummins et al, 1988;Stacey & MacGregor, 2000), the second major observation made from this study is that the quadratic word problems are quite difficult for students. Consistent with Cummins et al (1988), we found comprehension of the problem statement to be the central reason for students' difficulties with the word problems, rather than cognitive challenges in the solution phase of the symbolic equations.…”

Section: Discussionsupporting

confidence: 89%

“…However, students' challenges depend, not only on a formal algebraic system in the solution phase, but also on the linguistic form of the word problems in the comprehension phase (Koedinger & Nathan, 2004). Various researchers have proposed that solving algebra word problems consists of a "comprehension phase and [a] solution phase" (e.g., Cummins, Kintsch, Reusser, & Weimer, 1988;Mayer, 1982;Nathan, Kintsch, & Young, 1992). In the comprehension phase, a problem-solver comprehends and then forms the text base of the problem, utilizing words as an internal representation in his or her memory.…”

Section: Student Performance In Solving Algebra Word Problemsmentioning

confidence: 99%

“…They also emphasized factors relating to the problem's features, such as the number of words in the problem, the presence of cue words and the size of the numbers. On the other hand, the text comprehension factor is the main issue for students in solving word problems (Cummins et al, 1988;Nathan et al, 1992). …”

Section: Student Performance In Solving Algebra Word Problemsmentioning

confidence: 99%

“…According to Cummins et al (1988), inadequate mapping of phrases causes student to fail at solving word problems. Similarly, Nathan et al (1992) suggested that students make errors because they fail to see how the situational aspect of the problem is related to the formal expressions, in their attempts to produce the intended internal representations.…”

Section: Student Performance In Solving Algebra Word Problemsmentioning

confidence: 99%

“…As a result of coding students' incorrect answers, we decided to categorize student performance in solving quadratic equations with respect to their use of methods (i.e., quadratic formula, factoring method, completing square method, and square root property) to solve quadratic equations. In terms of word problems, the codes and categories came from conceptual frameworks and prior research relating to solving arithmetic and algebraic word problems (Cummins et al, 1988;Koedinger & Nathan, 2004). Students' incorrect and incomplete answers were coded and categorized with respect to their comprehension of the problem statement, setting up the correct relationship and formulating quadratic equations in one unknown, and solving the formulated quadratic equation.…”

Section: Data Collection and Analysismentioning

confidence: 99%

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Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

2015

EDUC SCI-THEOR PRACT

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This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight symbolic equations and four word problems; furthermore, semi-structured interviews were conducted with sixteen of the students. In the data analysis, the percentage of the students' correct, incorrect, blank, and incomplete responses was determined to obtain an overview of student performance in solving symbolic equations and word problems. In addition, the students' written responses and interview data were qualitatively analyzed to determine the nature of the students' difficulties in formulating and solving quadratic equations. The findings revealed that although students have difficulties in solving both symbolic quadratic equations and quadratic word problems, they performed better in the context of symbolic equations compared with word problems. Student difficulties in solving symbolic problems were mainly associated with arithmetic and algebraic manipulation errors. In the word problems, however, students had difficulties comprehending the context and were therefore unable to formulate the equation to be solved. Thus, it is concluded that the differences in the structural properties of the symbolic equations and word problem representations affected student performance in formulating and solving quadratic equations with one unknown.

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Section: Discussionsupporting

confidence: 89%

Section: Student Performance In Solving Algebra Word Problemsmentioning

confidence: 99%

Section: Student Performance In Solving Algebra Word Problemsmentioning

confidence: 99%

Section: Student Performance In Solving Algebra Word Problemsmentioning

confidence: 99%

Section: Data Collection and Analysismentioning

confidence: 99%

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Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

2015

EDUC SCI-THEOR PRACT

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Inconsistent operations: A weapon of math disruption

Jarosz

Jaeger

2018

Applied Cognitive Psychology

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SummaryWord problems embed a math equation within a short narrative. Due to their structure, both numerical and linguistic factors can contribute to problem difficulty. The present studies explored the role of irrelevant information in word problems, to determine whether its negative impact is due to numerical (foregrounding hypothesis) or linguistic (inconsistent‐operations hypothesis) interference. Across three experiments, participants solved multiplication and division word problems containing irrelevant numerical information, which was either associated or disassociated with the protagonist. Results demonstrated increased solution errors on division problems when irrelevant numbers were disassociated with the protagonist. When memory for numerical information was emphasized, disassociation was specifically impacted low‐working memory individuals. The effect of disassociation on division performance persisted even when irrelevant numbers, but not words, were removed from problems. These results suggest that, even in the presence of numerically interfering information, it is the language of word problems that often drive their difficulty.

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Connections Between Reading Comprehension and Word‐Problem Solving via Oral Language Comprehension: Implications for Comorbid Learning Disabilities

Fuchs

Seethaler

Cutting

et al. 2019

New Directions for Child and Adolescent Development

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In this article, we discuss the approach adopted within the Vanderbilt University Learning Disabilities Innovation Hub, which focuses on students with higherorder comorbidity: students with concurrent difficulty with reading comprehension and word-problem solving. The aim of the Hub' s Research Project is to test what we refer to as the higher-order comorbidity hypothesis: that language comprehension plays a critical role in reading comprehension and word-problem solving. In the Hub' s study, we test the hypothesize that language comprehension offers a coordinated approach for improving both outcomes and that this approach thus provides direction for understanding higher-order comorbidity and support for the validity of reading comprehension and word-problem solving

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The role of understanding in solving word problems

Cited by 334 publications

References 14 publications

Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

Inconsistent operations: A weapon of math disruption

Connections Between Reading Comprehension and Word‐Problem Solving via Oral Language Comprehension: Implications for Comorbid Learning Disabilities

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