Graspable math: Towards dynamic algebra notations that support learners better than paper

Weitnauer, Erik; Landy, David; Ottmar, Erin

doi:10.1109/ftc.2016.7821641

Cited by 13 publications

(8 citation statements)

References 12 publications

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“…But they can also offer long-term benefits, such as the perceptual strategy documented in the current study. We imagine a future where computer-based tools will systematically manipulate the visual and interactive features of mathematical representations so that children pick up on the perceptual regularities that help, rather than hurt (e.g., Weitnauer, Landy, & Ottmar, 2016). …”

Section: Discussionmentioning

confidence: 99%

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

2016

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Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system—in particular, object-based attention—is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions—but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

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Section: Discussionmentioning

confidence: 99%

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

2016

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“…In order to address these issues, Weitnauer, Landy, and Ottmar (2016) have designed and developed a research-based online interactive game, From Here to There! (FH2T; freely available on https://graspablemath.…”

Section: Contextmentioning

confidence: 99%

Data from the Efficacy Study of From Here to There! A Dynamic Technology for Improving Algebraic Understanding

Ottmar¹,

Lee²,

Vanacore³

et al. 2023

JOPD

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This paper provides information on datasets for the research project that examined the efficacy of three educational technologies including “From Here to There!”, a research-based game for improving algebraic understanding. The dataset contains 4,092 7th-grade students’ data collected through a randomized control trial conducted in 2020–2021 in a large school district in the U.S. The data comprises over 400 measures, including student demographics, assessments, and students’ actions. All data is anonymized and stored on Open Science Framework (OSF) and available through a data-sharing agreement. Our data might be reused by researchers interested in students’ algebraic learning in online learning environments.

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“…In several studies, GM has been shown to increase student performance and engagement compared to static methods of instruction (Landy andGoldstone, 2007, Landy andOttmar et al, 2015b;Weitnauer et al, 2016;Manzo et al, 2017;Ottmar and Landy, 2017;Sawrey et al, 2019). One study using a puzzle-based version of GM (From Here to There) found that a 2.5-h intervention in intact classrooms with no instruction led to gains on a comprehensive test of procedural fluency covering all basic algebra identities and transformations (effect size of 0.82 improvement over regular classroom instruction; Ottmar et al, 2015b).…”

Section: Perceptual-motor Training In Gm Can Have Impacts On Student mentioning

confidence: 99%

“…After a brief training, students were able to solve difficult equations using dynamic support available in GM more efficiently than on paper (Weitnauer et al, 2016). Students' increased outcomes were partially attributable to the speed and fluency with which they moved through the content itself (Ottmar et al (2015b); Hulse et al, 2019).…”

Section: Dynamic Algebra Tools Like Gm Can Vastly Increase Efficiencymentioning

confidence: 99%

The Future of Embodied Design for Mathematics Teaching and Learning

et al. 2020

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A rising epistemological paradigm in the cognitive sciences-embodied cognition-has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students' physical movements, eye-gaze paths, and verbal-gestural utterance so as to track and evaluate emerging conceptual capacity. We-a cohort of cognitive scientists and design-based researchers of embodied mathematics-survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.

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Graspable math: Towards dynamic algebra notations that support learners better than paper

Cited by 13 publications

References 12 publications

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

Data from the Efficacy Study of From Here to There! A Dynamic Technology for Improving Algebraic Understanding

The Future of Embodied Design for Mathematics Teaching and Learning

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