{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T22:53:14Z","timestamp":1776120794398,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":57,"publisher":"ACM","license":[{"start":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T00:00:00Z","timestamp":1620259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,5,6]]},"DOI":"10.1145\/3411764.3445460","type":"proceedings-article","created":{"date-parts":[[2021,5,8]],"date-time":"2021-05-08T05:53:19Z","timestamp":1620453199000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Constructing Embodied Algebra by Sketching"],"prefix":"10.1145","author":[{"given":"Nazmus","family":"Saquib","sequence":"first","affiliation":[{"name":"MIT Media Lab, United States"}]},{"given":"Rubaiat Habib","family":"Kazi","sequence":"additional","affiliation":[{"name":"Adobe Research, Seattle, Washington, United States"}]},{"given":"Li-yi","family":"Wei","sequence":"additional","affiliation":[{"name":"Adobe Research, San Jose, California, United States"}]},{"given":"Gloria","family":"Mark","sequence":"additional","affiliation":[{"name":"Informatics Department, University of California, Irvine, California, United States"}]},{"given":"Deb","family":"Roy","sequence":"additional","affiliation":[{"name":"MIT Media Lab, United States"}]}],"member":"320","published-online":{"date-parts":[[2021,5,7]]},"reference":[{"key":"e_1_3_2_2_1_1","volume-title":"Apparatus: A hybrid graphics editor","year":"2018","unstructured":"2018. Apparatus: A hybrid graphics editor and programming environment for creating diagrams. ( 2018 ). http:\/\/aprt.us\/ 2018. Apparatus: A hybrid graphics editor and programming environment for creating diagrams. (2018). http:\/\/aprt.us\/"},{"key":"e_1_3_2_2_2_1","unstructured":"2019. MAX\/MSP Visual Programming Language. https:\/\/cycling74.com\/products\/max-features  2019. MAX\/MSP Visual Programming Language. https:\/\/cycling74.com\/products\/max-features"},{"key":"e_1_3_2_2_3_1","unstructured":"2019. Symbolism: A Computer Algebra Library for C#. https:\/\/github.com\/dharmatech\/Symbolism  2019. Symbolism: A Computer Algebra Library for C#. https:\/\/github.com\/dharmatech\/Symbolism"},{"key":"e_1_3_2_2_4_1","unstructured":"Jo Boaler. 2015. Memorizers are the lowest achievers and other Common Core math surprises. https:\/\/hechingerreport.org\/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises\/.  Jo Boaler. 2015. Memorizers are the lowest achievers and other Common Core math surprises. https:\/\/hechingerreport.org\/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises\/."},{"key":"e_1_3_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.5555\/1923363.1923381"},{"key":"e_1_3_2_2_6_1","volume-title":"A modern introduction to dynamical systems","author":"Brown Richard","unstructured":"Richard Brown . 2018. A modern introduction to dynamical systems . Oxford University Press . Richard Brown. 2018. A modern introduction to dynamical systems. Oxford University Press."},{"key":"e_1_3_2_2_7_1","unstructured":"SageMath Documentation. 2020. The Coercion Model. http:\/\/doc.sagemath.org\/html\/en\/reference\/coercion\/sage\/structure\/coerce.html  SageMath Documentation. 2020. The Coercion Model. http:\/\/doc.sagemath.org\/html\/en\/reference\/coercion\/sage\/structure\/coerce.html"},{"key":"e_1_3_2_2_8_1","unstructured":"Vinod Goel. 1993. Sketches of thought: A study of the role of sketching in design problem-solving and its implications for the computational theory of mind.(1993).  Vinod Goel. 1993. Sketches of thought: A study of the role of sketching in design problem-solving and its implications for the computational theory of mind.(1993)."},{"key":"e_1_3_2_2_9_1","first-page":"72","article-title":"Sage","volume":"10","author":"Gray Michael","year":"2008","unstructured":"Michael Gray . 2008 . Sage : A New Mathematics Software System. 10 , 6 (2008), 72 \u2013 75 . http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=4653208. Michael Gray. 2008. Sage: A New Mathematics Software System. 10, 6 (2008), 72\u201375. http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=4653208.","journal-title":"A New Mathematics Software System."},{"key":"e_1_3_2_2_10_1","doi-asserted-by":"crossref","unstructured":"Mark\u00a0D Gross and Ellen Do. 1996. Ambiguous intentions: a paper-like interface for creative design. (1996).  Mark\u00a0D Gross and Ellen Do. 1996. Ambiguous intentions: a paper-like interface for creative design. (1996).","DOI":"10.1145\/237091.237119"},{"key":"e_1_3_2_2_11_1","unstructured":"Christian Grossauer Florian Perteneder Michael Haller Jagoda Walny John Brosz Anthony Tang and Sheelagh Carpendale. 2012. MathSketch: Designing a dynamic whiteboard for instruction contexts. (2012).  Christian Grossauer Florian Perteneder Michael Haller Jagoda Walny John Brosz Anthony Tang and Sheelagh Carpendale. 2012. MathSketch: Designing a dynamic whiteboard for instruction contexts. (2012)."},{"key":"e_1_3_2_2_12_1","unstructured":"Md\u00a0Abdul Halim. 2006. A comparative study of mathematics curriculum at primary level in Bangladesh and India (West Bengal). Bangladesh Education Journal(2006) 41.  Md\u00a0Abdul Halim. 2006. A comparative study of mathematics curriculum at primary level in Bangladesh and India (West Bengal). Bangladesh Education Journal(2006) 41."},{"key":"e_1_3_2_2_13_1","doi-asserted-by":"crossref","unstructured":"Brian Hempel Justin Lubin and Ravi Chugh. 2019. Sketch-n-Sketch: Output-Directed Programming for SVG. ArXiv abs\/1907.10699(2019).  Brian Hempel Justin Lubin and Ravi Chugh. 2019. Sketch-n-Sketch: Output-Directed Programming for SVG. ArXiv abs\/1907.10699(2019).","DOI":"10.1145\/3332165.3347925"},{"key":"e_1_3_2_2_14_1","unstructured":"Wolfram\u00a0Research Inc.2019. Mathematica Version 12.0. Champaign IL 2019.  Wolfram\u00a0Research Inc.2019. Mathematica Version 12.0. Champaign IL 2019."},{"key":"e_1_3_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3173574.3174164"},{"key":"e_1_3_2_2_16_1","volume-title":"Mental models: Towards a cognitive science of language, inference, and consciousness. Number\u00a06","author":"Johnson-Laird Philip\u00a0Nicholas","unstructured":"Philip\u00a0Nicholas Johnson-Laird . 1983. Mental models: Towards a cognitive science of language, inference, and consciousness. Number\u00a06 . Harvard University Press . Philip\u00a0Nicholas Johnson-Laird. 1983. Mental models: Towards a cognitive science of language, inference, and consciousness. Number\u00a06. Harvard University Press."},{"key":"e_1_3_2_2_17_1","volume-title":"CHI","author":"Kang Seokbin","unstructured":"Seokbin Kang , Ekta Shokeen , Virginia Byrne , Leyla Norooz , Elizabeth Bonsignore , Caro Williams-Pierce , and Jon\u00a0 E. Froehlich . 2020. ARMath: Augmenting Everyday Life with Math Learning . In CHI \u2019 20. Seokbin Kang, Ekta Shokeen, Virginia Byrne, Leyla Norooz, Elizabeth Bonsignore, Caro Williams-Pierce, and Jon\u00a0E. Froehlich. 2020. ARMath: Augmenting Everyday Life with Math Learning. In CHI\u2019 20."},{"key":"e_1_3_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2642918.2647375"},{"key":"e_1_3_2_2_19_1","unstructured":"Rubaiat\u00a0Habib Kazi Tovi Grossman Hyunmin Cheong Ali Hashemi and George\u00a0W Fitzmaurice. 2017. DreamSketch: Early Stage 3D Design Explorations with Sketching and Generative Design.. In UIST Vol.\u00a014. 401\u2013414.  Rubaiat\u00a0Habib Kazi Tovi Grossman Hyunmin Cheong Ali Hashemi and George\u00a0W Fitzmaurice. 2017. DreamSketch: Early Stage 3D Design Explorations with Sketching and Generative Design.. In UIST Vol.\u00a014. 401\u2013414."},{"key":"e_1_3_2_2_20_1","volume-title":"Computer Graphics Forum, Vol.\u00a038","author":"Kim Younghoon","unstructured":"Younghoon Kim , Michael Correll , and Jeffrey Heer . 2019. Designing Animated Transitions to Convey Aggregate Operations . In Computer Graphics Forum, Vol.\u00a038 . Wiley Online Library , 541\u2013551. Younghoon Kim, Michael Correll, and Jeffrey Heer. 2019. Designing Animated Transitions to Convey Aggregate Operations. In Computer Graphics Forum, Vol.\u00a038. Wiley Online Library, 541\u2013551."},{"key":"e_1_3_2_2_21_1","unstructured":"Thomas Kluyver Benjamin Ragan-Kelley Fernando P\u00e9rez Brian\u00a0E Granger Matthias Bussonnier Jonathan Frederic Kyle Kelley Jessica\u00a0B Hamrick Jason Grout Sylvain Corlay 2016. Jupyter Notebooks-a publishing format for reproducible computational workflows.  Thomas Kluyver Benjamin Ragan-Kelley Fernando P\u00e9rez Brian\u00a0E Granger Matthias Bussonnier Jonathan Frederic Kyle Kelley Jessica\u00a0B Hamrick Jason Grout Sylvain Corlay 2016. Jupyter Notebooks-a publishing format for reproducible computational workflows."},{"key":"e_1_3_2_2_22_1","unstructured":"George Lakoff and Rafael N\u00fa\u00f1ez. 2000. Where mathematics comes from. Vol.\u00a06.  George Lakoff and Rafael N\u00fa\u00f1ez. 2000. Where mathematics comes from. Vol.\u00a06."},{"key":"e_1_3_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/257089.257396"},{"key":"e_1_3_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015741"},{"key":"e_1_3_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.191"},{"key":"e_1_3_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/PACIFICVIS.2015.7156378"},{"key":"e_1_3_2_2_27_1","doi-asserted-by":"crossref","unstructured":"James Lin Mark\u00a0W Newman Jason\u00a0I Hong and James\u00a0A Landay. 2001. DENIM: an informal tool for early stage web site design. In CHI\u201901 Extended Abstracts on Human Factors in Computing Systems. ACM 205\u2013206.  James Lin Mark\u00a0W Newman Jason\u00a0I Hong and James\u00a0A Landay. 2001. DENIM: an informal tool for early stage web site design. In CHI\u201901 Extended Abstracts on Human Factors in Computing Systems. ACM 205\u2013206.","DOI":"10.1145\/634067.634190"},{"key":"e_1_3_2_2_28_1","unstructured":"Richard Liska Ladislav Drska Jiri Limpouch Milan Sinor Michael Wester and Franz Winkler. 1999. Computer algebra algorithms systems and applications.  Richard Liska Ladislav Drska Jiri Limpouch Milan Sinor Michael Wester and Franz Winkler. 1999. Computer algebra algorithms systems and applications."},{"key":"e_1_3_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3173574.3173697"},{"key":"e_1_3_2_2_30_1","volume-title":"Getting Started with MuPAD","author":"Majewski Miroslaw","unstructured":"Miroslaw Majewski . 2005. Getting Started with MuPAD . Springer-Verlag , Berlin, Heidelberg . Miroslaw Majewski. 2005. Getting Started with MuPAD. Springer-Verlag, Berlin, Heidelberg."},{"key":"e_1_3_2_2_31_1","unstructured":"Maplesoft a division of Waterloo Maple Inc..2019. Maple. Waterloo Ontario. https:\/\/hadoop.apache.org  Maplesoft a division of Waterloo Maple Inc..2019. Maple. Waterloo Ontario. https:\/\/hadoop.apache.org"},{"key":"e_1_3_2_2_32_1","volume-title":"version 7.10.0 (R2010a)","author":"MATLAB.","unstructured":"MATLAB. 2010. version 7.10.0 (R2010a) . The MathWorks Inc., Natick, Massachusetts . MATLAB. 2010. version 7.10.0 (R2010a). The MathWorks Inc., Natick, Massachusetts."},{"key":"e_1_3_2_2_33_1","unstructured":"Maxima 2020. . System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions arbitrary precision integers and arbitrary precision floating point numbers.  Maxima 2020. . System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions arbitrary precision integers and arbitrary precision floating point numbers."},{"key":"e_1_3_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/3399715.3399821"},{"key":"e_1_3_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.7717\/peerj-cs.103"},{"key":"e_1_3_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1080\/02698590802280902"},{"key":"e_1_3_2_2_37_1","unstructured":"Roy\u00a0D Pea. 1987. Logo programming and problem solving. (1987).  Roy\u00a0D Pea. 1987. Logo programming and problem solving. (1987)."},{"key":"e_1_3_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1592761.1592779"},{"key":"e_1_3_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/3290605.3300272"},{"key":"e_1_3_2_2_40_1","volume-title":"Vega-lite: A grammar of interactive graphics","author":"Satyanarayan Arvind","year":"2016","unstructured":"Arvind Satyanarayan , Dominik Moritz , Kanit Wongsuphasawat , and Jeffrey Heer . 2016 . Vega-lite: A grammar of interactive graphics . IEEE transactions on visualization and computer graphics 23, 1(2016), 341\u2013350. Arvind Satyanarayan, Dominik Moritz, Kanit Wongsuphasawat, and Jeffrey Heer. 2016. Vega-lite: A grammar of interactive graphics. IEEE transactions on visualization and computer graphics 23, 1(2016), 341\u2013350."},{"key":"e_1_3_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508468.2514930"},{"key":"e_1_3_2_2_42_1","first-page":"10","article-title":"GAP \u2013 Groups, Algorithms, and Programming","volume":"4","author":"The GAP\u00a0Group","year":"2019","unstructured":"The GAP\u00a0Group 2019 . GAP \u2013 Groups, Algorithms, and Programming , Version 4 . 10 .2. The GAP\u00a0Group. https:\/\/www.gap-system.org The GAP\u00a0Group 2019. GAP \u2013 Groups, Algorithms, and Programming, Version 4.10.2. The GAP\u00a0Group. https:\/\/www.gap-system.org","journal-title":"Version"},{"key":"e_1_3_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/3229434.3229465"},{"key":"e_1_3_2_2_44_1","unstructured":"Bret Victor. 2011. Explorable Explanations. (2011). http:\/\/worrydream.com\/ExplorableExplanations\/  Bret Victor. 2011. Explorable Explanations. (2011). http:\/\/worrydream.com\/ExplorableExplanations\/"},{"key":"e_1_3_2_2_45_1","unstructured":"Bret Victor. 2011. Kill Math. http:\/\/worrydream.com\/KillMath\/  Bret Victor. 2011. Kill Math. http:\/\/worrydream.com\/KillMath\/"},{"key":"e_1_3_2_2_46_1","unstructured":"Bret Victor. 2011. Scrubbing Calculator. (2011). http:\/\/worrydream.com\/ScrubbingCalculator\/  Bret Victor. 2011. Scrubbing Calculator. (2011). http:\/\/worrydream.com\/ScrubbingCalculator\/"},{"key":"e_1_3_2_2_47_1","unstructured":"Bret Victor. 2011. Up and Down the Ladder of Abstraction. http:\/\/worrydream.com\/LadderOfAbstraction\/  Bret Victor. 2011. Up and Down the Ladder of Abstraction. http:\/\/worrydream.com\/LadderOfAbstraction\/"},{"key":"e_1_3_2_2_48_1","volume-title":"Tangle: Explorable Explanations Made Easy.","author":"Victor Bret","year":"2012","unstructured":"Bret Victor . 2012 . Tangle: Explorable Explanations Made Easy. (2012). http:\/\/worrydream.com\/Tangle\/ Bret Victor. 2012. Tangle: Explorable Explanations Made Easy. (2012). http:\/\/worrydream.com\/Tangle\/"},{"key":"e_1_3_2_2_49_1","doi-asserted-by":"crossref","unstructured":"Martin Wattenberg. 2001. Sketching a graph to query a time-series database. In CHI\u201901 Extended Abstracts on Human factors in Computing Systems. ACM 381\u2013382.  Martin Wattenberg. 2001. Sketching a graph to query a time-series database. In CHI\u201901 Extended Abstracts on Human factors in Computing Systems. ACM 381\u2013382.","DOI":"10.1145\/634067.634292"},{"key":"e_1_3_2_2_50_1","unstructured":"Heinz Werner and Bernard Kaplan. 1963. Symbol formation.(1963).  Heinz Werner and Bernard Kaplan. 1963. Symbol formation.(1963)."},{"key":"e_1_3_2_2_51_1","unstructured":"Stephen Wolfram. 2017. What is a Computational Essay. (2017). https:\/\/blog.stephenwolfram.com\/2017\/11\/what-is-a-computational-essay\/  Stephen Wolfram. 2017. What is a Computational Essay. (2017). https:\/\/blog.stephenwolfram.com\/2017\/11\/what-is-a-computational-essay\/"},{"key":"e_1_3_2_2_52_1","unstructured":"Stephen Wolfram. 2020. Finally We May Have a Path to the Fundamental Theory of Physics and It\u2019s Beautiful. https:\/\/writings.stephenwolfram.com\/2020\/04\/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its -beautiful\/  Stephen Wolfram. 2020. Finally We May Have a Path to the Fundamental Theory of Physics and It\u2019s Beautiful. https:\/\/writings.stephenwolfram.com\/2020\/04\/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its -beautiful\/"},{"key":"e_1_3_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10648-019-09467-3"},{"key":"e_1_3_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/3173574.3173797"},{"key":"e_1_3_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392375"},{"key":"e_1_3_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/1866029.1866035"},{"key":"e_1_3_2_2_57_1","doi-asserted-by":"crossref","unstructured":"Bo Zhu Michiaki Iwata Ryo Haraguchi Takashi Ashihara Nobuyuki Umetani Takeo Igarashi and Kazuo Nakazawa. 2011. Sketch-based dynamic illustration of fluid systems. In ACM Transactions on Graphics (TOG) Vol.\u00a030. ACM 134.  Bo Zhu Michiaki Iwata Ryo Haraguchi Takashi Ashihara Nobuyuki Umetani Takeo Igarashi and Kazuo Nakazawa. 2011. Sketch-based dynamic illustration of fluid systems. In ACM Transactions on Graphics (TOG) Vol.\u00a030. ACM 134.","DOI":"10.1145\/2024156.2024168"}],"event":{"name":"CHI '21: CHI Conference on Human Factors in Computing Systems","location":"Yokohama Japan","acronym":"CHI '21","sponsor":["SIGCHI ACM Special Interest Group on Computer-Human Interaction"]},"container-title":["Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3411764.3445460","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3411764.3445460","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T21:28:48Z","timestamp":1750195728000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3411764.3445460"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,6]]},"references-count":57,"alternative-id":["10.1145\/3411764.3445460","10.1145\/3411764"],"URL":"https:\/\/doi.org\/10.1145\/3411764.3445460","relation":{},"subject":[],"published":{"date-parts":[[2021,5,6]]},"assertion":[{"value":"2021-05-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}