Exploring the Episodic Structure of Algebra Story Problem Solving

Hall, Rogers; Kibler, Dennis; Wenger, Étienne; Truxaw, Chris

doi:10.1207/s1532690xci0603_2

Cited by 97 publications

(88 citation statements)

References 19 publications

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“…Alternatively, students may choose different representations depending on problem type. There is some prior research that suggests students may change strategies based on task demands (Hall et al, 1989;Huntley, Marcus, Kahan, & Miller, 2007), which supports the prediction that students may choose different representations for computation and interpretation problems.…”

Section: Discussionmentioning

confidence: 63%

“…Knuth (2000) suggested that students' reluctance to use graphical strategies stems from the difficulty of isolating specific coordinate points in graphical representations, and from a lack of understanding that if a point falls on the line in a graph then that point is a solution to the algebraic equation of the line. Similarly, Hall and colleagues have suggested that symbolic representation might allow for ease in computation of exact points, whereas graphical representation should allow for easier visualization of overall patterns (Hall, Kibler, Wenger, & Truxaw, 1989). Thus, the preference for equations that Knuth and Herman observed may be because they only administered computation problems.…”

Section: Slope Comparison Problem In Graphical Formatmentioning

confidence: 99%

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Alternative Representations in Algebraic Problem Solving: When are Graphs Better Than Equations?

Mielicki¹,

Wiley²

2016

The Journal of Problem Solving

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Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation format might affect solution success, and whether the efficiency of solution varies depending on the nature of the problem solving task. This study addressed the question of whether symbolic or graphical representation format provides different affordances with respect to two different types of problems: computation and interpretation. Graphical representation was found to facilitate problem solving among college students, and problems that required the comparison of slopes were more difficult when presented in a symbolic format than in graphical format. Correspondence:Correspondence concerning this article should be addressed to Marta K. Mielicki, via email to mmieli2@uic.edu. Keywords:multiple representations, algebra, slope Acknowledgment:Thank you to James W. Pellegrino and Mara V. Martinez for their valuable feedback on this project.

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Section: Discussionmentioning

confidence: 63%

Section: Slope Comparison Problem In Graphical Formatmentioning

confidence: 99%

Alternative Representations in Algebraic Problem Solving: When are Graphs Better Than Equations?

Mielicki¹,

Wiley²

2016

The Journal of Problem Solving

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“…For example, one "expert" high school algebra schema is for "river problems," describing movement of a boat with and against a current (VanLehn, 1989 (Mayer, 1982). In order to capture this relevant quantitative structure independent of the surface context, a number of network notations have been developed (Hall, Kibler, Wenger, & Truxaw, 1989;Reed, 1987;Reed, Dempster, & Ettinger, 1985;Shalin & Bee, 1985 For complex problems that involve more that one triad, problem structure describes the way that these triads are linked. Shalin and Bee found that many two-step word problems could be classified as an exemplar of one of three linked structures--hierarchy, shared-whole, shared-part--and that these problem structures had an effect on problem difficulty.…”

Section: Cognitive Architecture and Mathematical Problem Solvingmentioning

confidence: 99%

“…Problems can also be characterized by a situational structure (Hall, Kibler, Wenger, & Truxaw, 1989) Although planning has been shown to aid problem solving (Schoenfeld, 1979), empirical studies indicate that its use by students is very limited (Branca, Adams, & Silver, 1980;Briars, 1983). More competent problem-solvers tend to identify an appropriate schema which requires a specific solution plan, to monitor the success of their progress as they work on their solution, and to verify the result.…”

Section: Cognitive Architecture and Mathematical Problem Solvingmentioning

confidence: 99%

Toward a Cognitive Basis for Quantitative Ability Measures

Sebrechts¹,

Enright²,

Bennett³

et al. 1993

ETS Research Report Series

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The construct validity of algebra word problems for measuring quantitative reasoning was examined from two perspectives, one focusing on an analysis of problem attributes and the other on the analysis of constructedresponse solutions. Twenty problems that had appeared on the Graduate Record Examinations General Test were investigated. Constructed-response solutions to these problems were collected from 51 undergraduates. Regression analyses of problem attributes indicated that models including factors such as the need to apply algebraic concepts, problem complexity, and problem content could account for 37% to 62% of the variance in problem difficulty. With respect to constructed-response solutions, four classes of strategies were identified: equation formulation, ratio setup. simulation, and other (unsystematic) approaches. Higher achieving students used equation strategies more and unsystematic approaches less than lower achieving examinees. Examinees' errors were classified into eight principal categories. Problem conception errors were the best predictor of performance on the constructed-response problems and on SAT-M. In contrast, procedural errors contributed to the prediction of performance on the constructed-response problems but not to standing on SAT-M. Overall, these results provide support for the construct validity of GRE algebra word problems and of SAT-M as measures of quantitative reasoning. A preliminary theoretical framework for describing performance on algebra word problems is proposed and its usefulness for more systematic design of tests is discussed.

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“…Learning to solve word problems in physics and mathematics has been examined in many studies (e.g., Hall, Kibler, Wenger, & Truxaw, 1989;Paige & Simon, 1966). Theorists have recognized that general, schematic knowledge is critical to the problem-solving process (Hinsley, Hayes, & Simon, 1977;Nathan, Kintsch, & Young, 1992;Priest & Lindsay, 1992).…”

mentioning

confidence: 99%

Causal models frame interpretation of mathematical equations

Mochon

Sloman

2004

Psychonomic Bulletin & Review

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We offer evidence that people can construe mathematical relations as causal. The studies show that people can select the causal versions of equations and that their selections predict both what they consider most understandable and how they expect variables to influence one another. When asked to write down equations, people have a strong preference for the version that matches their causal model. Causal models serve to structure equations by determining the preferred order of variables: Causes should be on one side of an equality, and a single effect should appear on the other.

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Exploring the Episodic Structure of Algebra Story Problem Solving

Cited by 97 publications

References 19 publications

Alternative Representations in Algebraic Problem Solving: When are Graphs Better Than Equations?

Alternative Representations in Algebraic Problem Solving: When are Graphs Better Than Equations?

Toward a Cognitive Basis for Quantitative Ability Measures

Causal models frame interpretation of mathematical equations

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