Translation between external representation systems in mathematics: All-or-none or skill conglomerate?

Superfine, Alison Castro; Canty, Reality S.; Marshall, Ann

doi:10.1016/j.jmathb.2009.10.002

Cited by 14 publications

(8 citation statements)

References 42 publications

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“…The Translation‐Verification Model addresses limitations of existing research (Superfine, Canty, & Marshall, 2009) by allowing researchers to systematically codify students' translation weaknesses or errors. It posits that three error types account for student weaknesses during the translation process: Interpretation Errors, Implementation Errors, and Preservation Errors.…”

Section: Discussionmentioning

confidence: 99%

Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Adu‐Gyamfi

Stiff

Bossé

2012

School Sci & Mathematics

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Translation errors and conceptual misunderstandings made by students translating among graphical, tabular, and symbolic representations of linear functions were examined. The study situated student errors in the context of the “Translation‐Verification Model” developed specifically for the purpose of explaining student behavior during the process of translating relationships from one mathematical representation to another. Three distinct error types were identified to explain student performance. An examination of the error types revealed that specific translation errors tend to occur at different stages of the translation process. Translation errors are also related to “attribute density,” the amount of information inherently encoded in a given representation. The findings of the study have implications for teaching linear relationships—student weaknesses and strengths are identified.

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Section: Discussionmentioning

confidence: 99%

Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Adu‐Gyamfi

Stiff

Bossé

2012

School Sci & Mathematics

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“…The authors agree that the representational translations have an influence on mathematical comprehension and the success of problem-solving [42]. However, studies show that students have difficulty in performing mathematical translations between and among mathematical representations [43][44][45]. Furthermore, they identify the type of student errors [46,47], techniques they use [48], and different student ability in translating process [15].…”

Section: Multiple Representationsmentioning

confidence: 99%

Efficiency of Dynamic Computer Environment in Learning Absolute Value Equation

Jokić

Takači

2020

Symmetry

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The presented study analyzes the usage of the didactic efficiency of multiple representations in a computer environment in learning absolute value functions and equations. It is known that the axis of symmetry of the graph of the absolute value function is the y-axis. The research was applied at the University of Novi Sad, Serbia. The data were collected by testing a group of 226 students: major chemistry and physics students at the beginning of their common calculus course. The students worked individually in two groups: the experimental and control group. The experimental group of students practiced using GeoGebra software, and the control group of students practiced using paper and pencil. At the end of the experiment, which lasted for two weeks (six school classes), both groups were tested with a post-test of knowledge without using a computer. It can be concluded that GeoGebra software had a positive influence on the students’ achievements in solving absolute value equations.

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“…Research on multiple representations shows that they only enhance learning when students adequately understand each individual representation (Ainsworth 2006;Eilam 2013), and when they make connections between representations (Ainsworth 2006;de Jong et al 1998;Gobert et al 2011;Gutwill et al 1999;Özgün-Koca 2008;Rathmell and Leutzinger 1991;Superfine et al 2009;Uttal 2003;van der Meij 2007). Therefore, one of the challenges curriculum designers face with regard to designing multi-representational learning environments is how best to support students in learning from multiple graphical representations.…”

Section: Multiple Graphical Representations Of Fractionsmentioning

confidence: 99%

How Should Intelligent Tutoring Systems Sequence Multiple Graphical Representations of Fractions? A Multi-Methods Study

Rau

Aleven

Rummel

et al. 2013

Int J Artif Intell Educ

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Providing learners with multiple representations of learning content has been shown to enhance learning outcomes. When multiple representations are presented across consecutive problems, we have to decide in what sequence to present them. Prior research has demonstrated that interleaving tasks types (as opposed to blocking them) can foster learning. Do the same advantages apply to interleaving representations? We addressed this question using a variety of research methods. First, we conducted a classroom experiment with an intelligent tutoring system for fractions. We compared four practice schedules of multiple graphical representations: blocked, fully interleaved, moderately interleaved, and increasingly interleaved. Based on data from 230 4th and 5th-grade students, we found that interleaved practice leads to better learning outcomes than blocked practice on a number of measures. Second, we conducted a think-aloud study to gain insights into the learning mechanisms underlying the advantage of interleaved practice. Results show that students make connections between representations only when explicitly prompted to do so (and not spontaneously). This finding suggests that reactivation, rather than abstraction, is the main mechanism to account for the advantage of interleaved practice. Third, we used methods derived from Bayesian knowledge tracing to analyze tutor log data from the classroom experiment. Modeling latent measures of students' learning rates, we find higher learning rates for interleaved practice than for blocked practice. This finding extends prior research on practice schedules, which shows that interleaved practice (compared to blocked practice) impairs students' problem-solving performance during the practice phase when using raw performance measures such as error rates. Our findings have implications for the design of multi-representational learning materials and for research on adaptive practice schedules in intelligent tutoring systems.

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Translation between external representation systems in mathematics: All-or-none or skill conglomerate?

Cited by 14 publications

References 42 publications

Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Efficiency of Dynamic Computer Environment in Learning Absolute Value Equation

How Should Intelligent Tutoring Systems Sequence Multiple Graphical Representations of Fractions? A Multi-Methods Study

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