Investigating high-school students’ reasoning strategies when they solve linear equations

Huntley, Mary Ann; Marcus, Robin L.; Kahan, Jeremy A.; Miller, Jane

doi:10.1016/j.jmathb.2007.05.005

Cited by 31 publications

(24 citation statements)

References 11 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: 62%

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: 62%

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

Mielicki¹,

Wiley²

2016

The Journal of Problem Solving

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“…The first finding is that the majority of student pairs used symbol manipulation when solving the three problems, and for the majority of student pairs symbol manipulation was their initial strategy toward solving the problems. Symbol manipulation was also the dominant strategy students used when solving other problems on the interview protocol, including a set of three linear equations of the form ax b = cx d (Huntley et al, 2007). In both this paper and the earlier one (Huntley et al, 2007), the data reported was from analysis of students' work on items posed in symbolic form.…”

Section: Discussionmentioning

confidence: 99%

“…In the sections that follow we provide a brief overview of the study participants, instrumentation and data collection, and data analysis methods. For more details, including complete explanations for our methodological choices, please refer to Huntley, Marcus, Kahan, and Miller (2007).…”

Section: Methodsmentioning

confidence: 99%

High‐School Students' Approaches to Solving Algebra Problems that are Posed Symbolically: Results from an Interview Study

Huntley

Davis

2008

School Sci & Mathematics

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A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are TIMSS items (a linear inequality and an equation involving square roots). The other problem involves square roots. We found that the majority of student pairs used symbol manipulation when solving the problems, and while many students seemed to prefer symbolic over graphical and tabular representations in their first attempt at solving the problems, we found that it was common for student pairs to use more than one strategy throughout the course of their solving. Students' use of graphing calculators to solve the problems is discussed. 380 Volume 108 (8) School Science and Mathematics 381

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“…Two additional concepts are introduced in Table . Concept 2 is based on the notion that in solving equations from a functions approach, students needed to understand connections among representations to coordinate the meaning of a solution across representation types (Huntley & Davis, ; Huntley, Marcus, Kahan, & Miller, ). Tasks were designed to support students' techniques of connecting multiple representations, especially in justifying a solution across symbols, graphs, numeric tables, and CAS feedback of “true.” For example, a task was to solve an equation in multiple representations then articulate how the solutions were related.…”

Section: Methodsmentioning

confidence: 99%

“…Students solved a series of problems involving linear equations with various solution types (i.e., one, none, or infinite solutions). Solving a symbolic equation with infinite solutions is a task type previously identified to pose great challenges for students (e.g., Huntley et al, ). The initial and final interview tasks of focus are given in Figures and .…”

Section: Methodsmentioning

confidence: 99%

Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper‐and‐Pencil

Fonger

Davis

Rohwer

2018

School Sci & Mathematics

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This research addresses the issue of how to support students' representational fluency-the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth-grade algebra students, and link to results of semi-structured interviews with students before and after the experiment. Results of analyzing the five-week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool-based representations.

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Investigating high-school students’ reasoning strategies when they solve linear equations

Cited by 31 publications

References 11 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?

High‐School Students' Approaches to Solving Algebra Problems that are Posed Symbolically: Results from an Interview Study

Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper‐and‐Pencil

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