Constructing Embodied Algebra by Sketching

Abstract

Mathematical models and expressions traditionally evolved as symbolic representations, with cognitively arbitrary rules of symbol manipulation. The embodied mathematics philosophy posits that abstract math concepts are layers of metaphors grounded in our intuitive arithmetic capabilities, such as categorizing objects and part-whole analysis. We introduce a design framework that facilitates the construction and exploration of embodied representations for algebraic expressions, using interactions inspired by innate arithmetic capabilities. We instantiated our design in a sketch interface that enables construction of visually interpretable compositions that are directly mappable to algebraic expressions and explorable through a ladder of abstraction. The emphasis is on bottom-up construction, with the user sketching pictures while the system generates corresponding algebra. We present diverse examples created by our prototype system. A coverage of the US Common Core curriculum and playtesting studies with children point to the future direction and potential for a sketch-based design paradigm for mathematics.

Authors
Nazmus Saquib
MIT Media Lab, Cambridge, Massachusetts, United States
Rubaiat Habib Kazi
Adobe Research, Seattle, Washington, United States
Li-yi Wei
Adobe Research, San Jose, California, United States
Gloria Mark
University of California, Irvine, Irvine, California, United States
Deb Roy
MIT Media Lab, Cambridge, Massachusetts, United States
DOI

10.1145/3411764.3445460

Paper URL

https://doi.org/10.1145/3411764.3445460

Video

Conference: CHI 2021

The ACM CHI Conference on Human Factors in Computing Systems (https://chi2021.acm.org/)

Session: Design Tools / Machine Learning / Fabrication / Visual Artifacts in Design and Ideation

[A] Paper Room 04, 2021-05-11 17:00:00~2021-05-11 19:00:00 / [B] Paper Room 04, 2021-05-12 01:00:00~2021-05-12 03:00:00 / [C] Paper Room 04, 2021-05-12 09:00:00~2021-05-12 11:00:00
Paper Room 04
12 items in this session
2021-05-11 08:00:00
2021-05-11 10:00:00
Japanese summary
数学のモデルやアルゴリズムは記号で抽象化されるが直感的に理解が困難である。そこで、スケッチを利用して数学のモデルやアルゴリズムを視覚的に表現できる「Noyon」を開発を行なった。
2021-06-22 05:54:34
suhr Kamikami