Estimating Answer Strategies using Online Handwritten Data: A Study using Geometry Problems
Pages 308 - 314
Abstract
Emphasis has been placed on logical reasoning skills as a necessary ability and quality for the next generation. Developing logical reasoning skills is one of the objectives of the geometry curriculum in secondary education. Understanding an individual's strategy for finding a solution is necessary to assess his/her logical reasoning abilities. This study is the first to estimate answer strategies using online handwritten data automatically. Using geometry problems as our subject, we: 1) detect symbols written in a diagram; and 2) classify the answer strategies using XGBoost with the features combining uni-grams, bi-grams, and 1-skip-grams of symbols in their written order. Our experimental evaluation with 38 university students for a single geometry problem confirmed that answer strategies were successfully classified into three categories with an accuracy of 0.71, which shows the feasibility of the automatic detection of answer strategies.
References
[1]
Hager Gal and Liora Linchevski. 2010. To see or not to see: analyzing difficulties in geometry from the perspective of visual perception. Educ Stud Math, 74, Springer, 163–183. https://doi.org/10.1007/s10649-010-9232-y
[2]
Song Eng Goh. 2018. Guided problem solving at primary level: students’ strategies for solving challenging geometry problems. Master Thesis of Education, Nanyang Technological University, Singapore.
[3]
Michelle Cirillo and Jenifer Hummer. 2021. Competencies and behaviors observed when students solve geometry proof problems: an interview study with smartpen technology. ZDM Mathematics Education, 53, 861–875. https://doi.org/10.1007/s11858-021-01221-w
[4]
Linda Margarita Medina Herrera, Marlene Aguilar Abalo, and Saúl Juárez Ordóñez. 2019. Learning calculus with augmented reality and virtual environments. In Proceedings of the 2019 11th International Conference on Education Technology and Computers (ICETC 2019). ACM, New York, NY, USA, 18-22. https://doi.org/10.1145/3369255.3369271
[5]
Yingying Jiang, Feng Tian, Hongan Wang, Xiaolong Zhang, Xugang Wang, and Guozhong Dai. 2010. Intelligent understanding of handwritten geometry theorem proving, In Proceedings of the 15th International Conference on Intelligent User Interfaces (IUI2010). ACM, New York, NY, USA, 119-128. https://doi.org/10.1145/1719970.1719988
[6]
Jiaqi Chen, Tong Li, Jinghui Qin, Pan Lu, Liang Lin, Chongyu Chen, and Xiaodan Liang. UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression. arXiv preprint, arXiv:2212.02746, 1-11. https://doi.org/ 10.48550/arXiv.2212.02746
[7]
Pan Lu, Ran Gong, Shibiao Jiang, Liang Qiu, Siyuan Huang, Xiaodan Liang, and Song-Chun Zhu. 2021. Inter-gps: Interpretable geometry problem solving with formal language and symbolic reasoning. In Proceedings of the Joint Conference of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (ACL-IJCNLP). 6774-6786.
[8]
Ming-Liang Zhang, Fei Yin,Yi-Han Hao, and Cheng-Lin Liu., C. 2022. Plane geometry diagram parsing. In Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI). 1636–1643. https://doi.org/10.24963/ijcai.2022/228
[9]
Michael L. Winer, and Michael T. Battista. 2022. Investigating students' proof reasoning: analyzing students' oral proof explanations and their written proofs in high school geometry. International Electronic Journal of Mathematics Education, 17(2), em0677, 1-21. https://doi.org/10.29333/iejme/11713
[10]
Daichi Yoshitake, Brendan Flanagan, and Hiroaki Ogata. 2020. Supporting Group Learning Using Pen Stroke Data Analytics. In Proceedings of the 28th International Conference on Computers in Education, Asia Pacific Society for Computers in Education, 634-639.
[11]
Masato Miura, Masahiro Kudo, Kazuaki Okada, Yuki Nakayama, and Hayato Yamana. 2022. Automatic Estimation of Established Problems using Online Handwriting Data: A Case Study for Geometric Problems (in Japanese). In Proceedings of 14th Data Engineering and Information Management Forum (DEIM2022), Database Society of Japan. 1-8.
[12]
Minjoon Seo, Hannaneh Hajishirzi, Ali Farhadi, Oren Etzioni, and Cilint Malcolm. 2015. Solving geometry problems: Combining text and diagram interpretation. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing (EMNLP), 1466–1476. https://doi.org/ 10.18653/v1/D15-1171
[13]
Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. 2020. Yolov4: Optimal speed and accuracy of object detection. arXiv preprint, arXiv:2004.10934, 1-17. https://doi.org/10.48550/arXiv.2004.10934
[14]
Leland McInnes, John Healy, and James Melville. 2020. UMAP: uniform manifold approximation and projection for dimension reduction. arXiv preprint, arXiv:1802.03426, 1-63. https://doi.org/10.48550/arXiv.1802.03426
[15]
Tianqi Chen and Carlos Guestrin. 2016. XGBoost: a scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '16), ACM, New York, NY, USA, 785–794. https://doi.org/10.1145/2939672.2939785
[16]
Swati Verma, Rakesh Kumar Yadav, and Kuldeep Kholiya. 2022. Prediction of Academic Performance of Engineering Students by Using Data Mining Techniques. International Journal of Information and Education Technology, 12(11), 1164-1171. https://doi.org/10.18178/ijiet.2022.12.11.1734
[17]
Jonardo R. Asor, Gene Marck B. Catedrilla, Chester Alexis C. Buama, Monique E.Malabayabas, and Cristina E. Malabayabas. 2023. Prediction of Senior High School Students’ Performance in a State University: An Educational Data Mining Approach. International Journal of Information and Education Technology, 13(6), 925-931. https://doi.org/ 10.18178/ijiet.2023.13.6.1888
Index Terms
- Estimating Answer Strategies using Online Handwritten Data: A Study using Geometry Problems
Recommendations
Online Handwritten Gurmukhi Character Recognition Using Elastic Matching
CISP '08: Proceedings of the 2008 Congress on Image and Signal Processing, Vol. 2 - Volume 02This paper presents implementation of elastic matching technique to recognize online handwritten Gurmukhi characters. We have discussed a process that recognizes characters in two stages. First stage recognizes the strokes, in second stage, character is ...
Online Handwritten Gurmukhi Words Recognition: An Inclusive Study
Identification of offline and online handwritten words is a challenging and complex task. In comparison to Latin and Oriental scripts, the research and study of handwriting recognition at word level in Indic scripts is at its initial phases. The two ...
HMM Based Online Handwritten Bangla Character Recognition Using Dirichlet Distributions
ICFHR '12: Proceedings of the 2012 International Conference on Frontiers in Handwriting RecognitionA reasonably large database of online handwritten Bangla characters has been developed. Such a handwritten character sample is composed of one or more strokes. Seventy five such stroke classes have been identified on the basis of the varying handwriting ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
September 2023
532 pages
ISBN:9798400709111
DOI:10.1145/3629296
Copyright © 2023 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 15 January 2024
Check for updates
Author Tags
Qualifiers
- Research-article
- Research
- Refereed limited
Conference
ICETC 2023
ICETC 2023: The 15th International Conference on Education Technology and Computers
September 26 - 28, 2023
Barcelona, Spain
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 28Total Downloads
- Downloads (Last 12 months)24
- Downloads (Last 6 weeks)6
Reflects downloads up to 18 Feb 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign inFull Access
View options
View or Download as a PDF file.
PDFeReader
View online with eReader.
eReaderHTML Format
View this article in HTML Format.
HTML Format