Determining the Sources of Error in a Translation from Sentence to Equation

Wollman, Warren

doi:10.2307/748380

Cited by 34 publications

(38 citation statements)

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“…When asked to construct a standard-form MF equation, students' performance was consistent with previous studies that did not specify format requirements in the equation construction task instructions (Bernardo & Okagaki, 1994;Clement, 1982;Clement et al, 1981;Fisher, 1988;Graf et al, 2004;Kaput & Sims-Knight, 1983;Martin & Bassok, 2005;Rosnick, 1981;Rosnick & Clement, 1980;Wollman, 1983). Namely, just over 60% of participants in the MF condition constructed a correct algebraic model, and the vast majority of errors were reversal equations.…”

Section: Discussionsupporting

confidence: 70%

“…Many of the participants in that study (37%) failed to construct the correct algebraic equation (6P = S), and their most common error was a reversal of the two variables (6S = P). Over the years, these and other researchers have reported similar findings, with error rates ranging between 40 and 60% (Bernardo & Okagaki, 1994;Clement, 1982;Clement, Lochhead, & Monk, 1981;Fisher, 1988;Graf, Bassok, Hunt, & Minstrell, 2004;Kaput & Sims-Knight, 1983;Martin & Bassok, 2005;Rosnick, 1981;Rosnick & Clement, 1980;Wollman, 1983).…”

Section: Introductionmentioning

confidence: 58%

“…Irrespective of the specific reason that leads students to commit reversal errors, such modeling errors are much more common in algebra than in numerical problem solving (Bernardo & Okagaki, 1994, Martin & Bassok, 2005Wollman, 1983), a domain for which students have developed strong modeling skills. For example, Martin and Bassok (2005) asked middle school, high school, and college students to either construct algebraic equations that represent relational statements, such as "There are 6 times as many nails as screws," or to solve numerical word problems with the same relational statements, such as "A certain factory produces 6 times as many nails as screws.…”

Section: Introductionmentioning

confidence: 99%

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Following the standard form: Effects of equation format on algebraic modeling

2010

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When people construct algebraic equations to represent quantitative relations, they often reverse the roles of the variables (6S = P instead of 6P = S). Results from three experiments show that a major reason for such reversal errors is people's adherence to, and interpretation of, the Standard Form of algebraic models. College students constructed, selected, and interpreted algebraic models that either had the standard multiplication format (MF: ax = y), or the mathematically equivalent division format (DF: y/a = x). A large minority of participants constructed reversed MF models, whereas most participants who were instructed to use DF equations constructed correct models (Experiment 1). Most participants understood that MF and DF models of the same relation should be mathematically equivalent (Experiment 2), but they drew a conceptual distinction between these models (Experiment 3). The authors discuss the impact of notational conventions on people's interpretation and use of representational tools.

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Section: Discussionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

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Following the standard form: Effects of equation format on algebraic modeling

2010

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“…Many researchers have attributed student difficulty to a tendency for a "directtranslation" approach (Clement, 1982;Fisher et al, 2010;Hegarty et al, 1995;Wollman, 1983). This strategy is used when students attempt to make the sequence of algebraic symbols match the sequence of objects in a word problem.…”

Section: Direct Translation and Static Comparison Strategiesmentioning

confidence: 99%

“…Several studies have reported that roughly 40% of college students fail to solve these problems correctly (Clement, 1982;Fisher, 1988;Lochhead, 1980;Philipp, 1992; Sims-Knight and Kaput, 1983;Weinberg, 2009;Wollman, 1983). We have also encountered this phenomenon while investigating common errors that students make while constructing mathematical optimization models in a junior-level undergraduate engineering course (Kenney et al, 2011).…”

Section: Introductionmentioning

confidence: 96%

POETIC: Interactive solutions to alleviate the reversal error in student–professor type problems

Kim

Phang

et al. 2014

International Journal of Human-Computer Studies

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The reversal error-reversing the relationship between two variables in a mathematical word problem-is a long-standing issue in mathematics education, despite its apparent simplicity. In this paper, we describe and study POETIC, an interactive web-based environment we developed to teach users to avoid the reversal error.POETIC uses two types of novel interactive visualization, called the Test-Case and Room-Metaphor approaches. To verify the effectiveness of these approaches, we conducted crowdsourcing-based comparison studies with 200 participants and found that both approaches significantly decreased the frequency of reversal errors for certain types of word problems. Our results show that interactive visualization of equations can reduce the occurrence of the reversal error.

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Defining Mathematics Competency in the Service of Cognitively Based Assessment for Grades 6 Through 8

Graf

2009

ETS Research Report Series

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This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated with the Cognitively Based Assessment of, for, and as Learning (CBAL) project in mathematics (for which this review helped provide a theoretical foundation) should consult Graf, Harris, Marquez, Fife, and Redman (2009).The organization of the report is motivated by the evidence-centered design (ECD) approach to assessment developed by Mislevy and colleagues (e.g., see Mislevy, Steinberg, & Almond, 2003). The first section consists of a broad literature review that characterizes mathematical competency with respect to both content and process. Subsequent sections discuss: how to model mathematical competency at

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Determining the Sources of Error in a Translation from Sentence to Equation

Cited by 34 publications

References 0 publications

Following the standard form: Effects of equation format on algebraic modeling

Following the standard form: Effects of equation format on algebraic modeling

POETIC: Interactive solutions to alleviate the reversal error in student–professor type problems

Defining Mathematics Competency in the Service of Cognitively Based Assessment for Grades 6 Through 8

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