{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T10:46:58Z","timestamp":1769597218656,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MTI"],"abstract":"<jats:p>In the realm of collegiate education, calculus can be quite challenging for students. Many students struggle to visualize abstract concepts, as mathematics often moves into strict arithmetic rather than geometric understanding. Our study presents an innovative solution to this problem: an immersive, interactive VR graphing tool capable of standard 2D graphs, solids of revolution, and a series of visualizations deemed potentially useful to struggling students. This tool was developed within the Unity 3D engine, and while interaction and expression parsing rely on existing libraries, core functionalities were developed independently. As a pilot study, it includes qualitative information from a survey of students currently or previously enrolled in Calculus II\/III courses, revealing its potential effectiveness. This survey primarily aims to determine the tool\u2019s viability in future endeavors. The positive response suggests the tool\u2019s immediate usefulness and its promising future in educational settings, prompting further exploration and consideration for adaptation into an Augmented Reality (AR) environment.<\/jats:p>","DOI":"10.3390\/mti8030019","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T03:31:23Z","timestamp":1709263883000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Enhancing Calculus Learning through Interactive VR and AR Technologies: A Study on Immersive Educational Tools"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3434-5990","authenticated-orcid":false,"given":"Logan","family":"Pinter","sequence":"first","affiliation":[{"name":"Computer Science, College of Engineering, West Texas A&M University, Canyon, TX 79016, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8515-062X","authenticated-orcid":false,"given":"Mohammad Faridul Haque","family":"Siddiqui","sequence":"additional","affiliation":[{"name":"Computer Science, College of Engineering, West Texas A&M University, Canyon, TX 79016, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1016\/j.procs.2020.05.127","article-title":"Enhancing student motivation with use of augmented reality for interactive learning in engineering education","volume":"172","author":"Kaur","year":"2020","journal-title":"Procedia Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1007\/s12652-017-0547-8","article-title":"Augmented reality in education and training: Pedagogical approaches and illustrative case studies","volume":"9","author":"Wang","year":"2018","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Garz\u00f3n, J. (2021). An Overview of Twenty-Five Years of Augmented Reality in Education. Multimodal Technol. Interact., 5.","DOI":"10.3390\/mti5070037"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1007\/s10639-018-9806-3","article-title":"Determining the trends of using augmented reality in education between 2006\u20132016","volume":"24","author":"Altinpulluk","year":"2019","journal-title":"Educ. Inf. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s10055-018-0363-2","article-title":"Virtual and augmented reality effects on K-12, higher and tertiary education students\u2019 twenty-first century skills","volume":"23","author":"Papanastasiou","year":"2019","journal-title":"Virtual Real."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1089\/cyber.2018.0150","article-title":"Augmented Versus Virtual Reality in Education: An Exploratory Study Examining Science Knowledge Retention When Using Augmented Reality\/Virtual Reality Mobile Applications","volume":"22","author":"Huang","year":"2019","journal-title":"CYberpsychology, Behav. Soc. Netw."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Huang, X., Zou, D., Cheng, G., and Xie, H. (2021). A Systematic Review of AR and VR Enhanced Language Learning. 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Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6988","DOI":"10.1080\/10494820.2022.2057549","article-title":"Learning with digital technology-facilitated empathy: An augmented reality approach to enhancing students\u2019 flow experience, motivation, and achievement in a biology program","volume":"31","author":"Wang","year":"2023","journal-title":"Interact. Learn. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Petrov, P.D., and Atanasova, T.V. (2020). The Effect of Augmented Reality on Students\u2019 Learning Performance in Stem Education. Information, 11.","DOI":"10.3390\/info11040209"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Phon, D.N.E., Ali, M.B., and Halim, N.D.A. (2014, January 11\u201313). Collaborative Augmented Reality in Education: A Review. Proceedings of the 2014 International Conference on Teaching and Learning in Computing and Engineering, Kuching, Malaysia.","DOI":"10.1109\/LaTiCE.2014.23"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/BF02905780","article-title":"Development and use of the ARCS model of instructional design","volume":"10","author":"Keller","year":"1987","journal-title":"J. Instr. Dev."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.compedu.2018.03.019","article-title":"Use of the ARCS model in education: A literature review","volume":"122","author":"Li","year":"2018","journal-title":"Comput. Educ."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pinter, L., Izquierdo, M., and Siddiqui, M.F.H. (2023, January 29\u201331). Revolutionizing Learning: An Interactive VR Application for Solids of Revolution. Proceedings of the Proceedings of the 7th International Conference on Education and Multimedia Technology, Tokyo, Japan.","DOI":"10.1145\/3625704.3625742"},{"key":"ref_17","unstructured":"Kaufmann, H., and Schmalstieg, D. (2023, December 29). Construct3D\u2014An Augmented Reality System for Mathematics and Geometry Education. Available online: https:\/\/www.ims.tuwien.ac.at\/projects\/construct3d."},{"key":"ref_18","unstructured":"Kaufmann, H., and Meyer, B. (2023, December 29). Simulating Educational Physical Experiments in Augmented Reality. Available online: https:\/\/publik.tuwien.ac.at\/files\/PubDat_170658.pdf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.procs.2015.12.251","article-title":"Augmented reality app for calculus: A proposal for the development of spatial visualization","volume":"75","author":"Quintero","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1385","DOI":"10.1007\/s12008-019-00595-2","article-title":"Developing spatial mathematical skills through 3D tools: Augmented reality, virtual environments and 3D printing","volume":"13","year":"2019","journal-title":"Int. J. Interact. Des. Manuf. (IJIDeM)"},{"key":"ref_21","unstructured":"Sanderson, G. (2023, December 29). Manim. Available online: https:\/\/github.com\/3b1b\/manim."},{"key":"ref_22","unstructured":"Sanderson, G. (2023, December 29). The Essence of Calculus. Available online: https:\/\/www.youtube.com\/watch?v=WUvTyaaNkzM."},{"key":"ref_23","unstructured":"Sanderson, G. (2023, December 29). But What Is a Convolution?. Available online: https:\/\/www.youtube.com\/watch?v=KuXjwB4LzSA."},{"key":"ref_24","unstructured":"Sanderson, G. (2023, December 29). Who Cares about Topology?. Available online: https:\/\/www.youtube.com\/watch?v=AmgkSdhK4K8."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"e20210239","DOI":"10.1590\/1806-9126-rbef-2021-0239","article-title":"Anima\u00e7\u00f5es de conceitos da teoria de erros usando Manim\/Python","volume":"44","author":"Coluci","year":"2022","journal-title":"Rev. Bras. Ensino F\u00edSica"},{"key":"ref_26","unstructured":"Arag\u00f3n, X., Serrano, Z., and Jos\u00e9, F. (2022). Manim Com a Eina de Visualitzaci\u00f3 Matem\u00e0tica, RecerCAT."},{"key":"ref_27","unstructured":"(2023, December 29). GeoGebra\u2014The World\u2019s Favorite, Free Math Tools Used by over 100 Million Students and Teachers. Available online: https:\/\/www.geogebra.org\/."},{"key":"ref_28","unstructured":"(2023, December 29). About the Oculus XR Plugin. Available online: https:\/\/docs.unity3d.com\/Packages\/com.unity.xr.oculus@1.0.0\/manual\/index.html."},{"key":"ref_29","unstructured":"(2023, December 29). Unity XR Interaction Toolkit Documentation. Available online: https:\/\/docs.unity3d.com\/Packages\/com.unity.xr.interaction.toolkit@2.3\/manual\/index.html."},{"key":"ref_30","unstructured":"(2023, December 29). Using Shader Graph. Available online: https:\/\/docs.unity3d.com\/Manual\/shader-graph.html."},{"key":"ref_31","unstructured":"Vanifato, V. (2023, December 29). Expression Parser. Available online: https:\/\/github.com\/codewriter-packages\/Expression-Parser."},{"key":"ref_32","unstructured":"Blumhardt, N. (2023, December 29). Sprache. Available online: https:\/\/github.com\/sprache\/sprache."}],"container-title":["Multimodal Technologies and Interaction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2414-4088\/8\/3\/19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:07:44Z","timestamp":1760105264000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2414-4088\/8\/3\/19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,1]]},"references-count":32,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["mti8030019"],"URL":"https:\/\/doi.org\/10.3390\/mti8030019","relation":{},"ISSN":["2414-4088"],"issn-type":[{"value":"2414-4088","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,1]]}}}