數學文字題是一種以文字來描述數學問題的題目，因此它比起一般的數學計算式題目更像是一種情境描述的表達。小朋友必須把在學校所學習到的基本數學運算、邏輯推演以及日常生活中的綜合知識融合成解題所需要的概念，才能夠有系統的解決問題。

近幾年來，隨著對個體差異的重視，客製化的教學方式日益興盛。因為每個人的學習能力有所不同，標準化的教學方式，並不一定能夠適用於每一位學習者。因此若要讓學習者的學習效益最大化，客製化的教學就顯得格外重要。此外又因為全球疫情的影響，許多學生沒有辦法獲得充足的教育資源，因此本研究希望能夠透過設計一套自動的客製化數學文字題生成系統來幫助學生的學習。

我們透過成分句法剖析將數學文字題中的實體進行初步分析，並且針對數學文字題中常見的特定實體，如物件、量詞、動詞、地點以及行為者(Agent)透過知識本體來進行更進一步的語義分析。本論文的貢獻如下： (1)提出了一個基於剖析結果的抽取方法，其能夠有效地擷取出題目中的物件及量詞，並同時獲得量詞與對應物件的所屬關係。(2)加入適性化學習的元素來評估生成題目的難易度。(3)設計一套情境詞系統，能夠讓使用者透過自然語言來指定題目的生成方向。在生成的過程中我們使用核取樣(Nucleus Sampling)，能夠在避免長尾效應的同時，也確保生成數學文字題的多樣性。
實驗結果顯示，我們系統生成的數學文字題的對數困惑度得到了3.593，並且在自雙語替換評測(self-BLEU)中得到了0.747的分數。此外我們也透過問卷調查的方式來收集使用者回饋，得到4.3/5分的使用者喜好度，顯示本研究生成的結果具有相當的成效。

Math Word Problem is a kind of math problem which uses words to describe the problem. Compared to the math formula problem, it is more like a scenario description in our life. The students should combine the basic math operation, logic inference learned from school, and general knowledge in daily life to solve the math word problem systematically and effectively.

In recent years, with the emphasis on individual differences, customized instruction education has become increasingly prosperous. Because the learning abilities of each learners are different, standardized teaching methods might not be suitable for everyone. In order to maximize the benefit of learners, customized instruction education is important. In addition, many students cannot obtain sufficient educational resources since the global pandemic. Therefore, this research aims to design an automatic customized math word problems generation system to help the students.

We conduct a preliminary analysis of the entities in math word problems through constituent parsing, and further semantic analysis on specific entities, such as Object, Quantifier, Verb, Location, and Agent by the ontology. The contributions of this thesis are: (1) Proposed an extraction method based on the parsing results, which can effectively extract the objects and quantifiers, and obtain the dependency relation between quantifiers and corresponding objects at the same time. (2) Added the consideration of adaptive learning to evaluate the difficulty of the generated math word problems. (3) Designed a scenario word system that allows users to specify the generation direction through natural language. In the process of generating, we use Nucleus Sampling, which can avoid the long tail effect while ensuring the diversity of the generated math word problems.
The experimental result shows that, the proposed generation system achieve 3.593 of logarithm perplexity score and 0.747 of self-BLEU. Besides, we carry out a questionnaire survey to collect user feedback, and receive 4.3/5 of user preference. These can illustrate the system is quite effective.

[1] A. A. Bekele, “Automatic generation of amharic math word problem and equation,” Journal of Computer and Communications, vol. 8, no. 8, pp. 59–77, 2020.
[2] C.­-C. Liang, K.­-Y. Hsu, C.­-T. Huang, C.­-M. Li, S.­-Y. Miao, and K.­-Y. Su, “A tag­-based statistical english math word problem solver with understanding, reasoning and explanation.,” in IJCAI, pp. 4254–4255, 2016.
[3] M. O. Riedl, “Human­-centered artificial intelligence and machine learning,” Human Behavior and Emerging Technologies, vol. 1, no. 1, pp. 33–36, 2019.
[4] P. I. Pavlov, “Conditioned reflexes: an investigation of the physiological activity of the cerebral cortex,” Annals of neurosciences, vol. 17, no. 3, p. 136, 2010.
[5] S. F. Maier and M. E. Seligman, “Learned helplessness: theory and evidence.,” Journal of experimental psychology: general, vol. 105, no. 1, p. 3, 1976.
[6] Y. H. Ting and F. Bond, “Comparing classifier use in chinese and japanese,” in Proceedings of the 26th Pacific Asia Conference on Language, Information, and Computation, pp. 264– 271, 2012.
[7] Q. Hu, The acquisition of Chinese classifiers by young Mandarin­-speaking children. PhD thesis, Boston University, 1993.
[8] M. S. Erbaugh, “Taking stock: The development of chinese noun classifiers historically and in young children,” Noun classes and categorization, pp. 399–436, 1986.
[9] C. N. Li and S. A. Thompson, Mandarin Chinese: A functional reference grammar, vol. 3. Univ of California Press, 1989.
[10] S. E. Robertson and S. Walker, “Some simple effective approximations to the 2­-poisson model for probabilistic weighted retrieval,” in SIGIR＇94, pp. 232–241, Springer, 1994.
[11] M. Zhang, “A survey of syntactic­-semantic parsing based on constituent and dependency structures,” Science China Technological Sciences, pp. 1–23, 2020.
[12] H. Zhang, D. Duckworth, D. Ippolito, and A. Neelakantan, “Trading off diversity and quality in natural language generation,” arXiv preprint arXiv:2004.10450, 2020.
[13] A. Fan, M. Lewis, and Y. Dauphin, “Hierarchical neural story generation,” arXiv preprint arXiv:1805.04833, 2018.
[14] A. Holtzman, J. Buys, L. Du, M. Forbes, and Y. Choi, “The curious case of neural text degeneration,” arXiv preprint arXiv:1904.09751, 2019.
[15] G. A. Miller, “Wordnet: a lexical database for english,” Communications of the ACM, vol. 38, no. 11, pp. 39–41, 1995.
[16] B. Xu, Y. Xu, J. Liang, C. Xie, B. Liang, W. Cui, and Y. Xiao, “Cn­-dbpedia: A neverending chinese knowledge extraction system,” in International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, pp. 428–438, Springer, 2017.
[17] Z. Dong and Q. Dong, “Hownet­-a hybrid language and knowledge resource,” in International Conference on Natural Language Processing and Knowledge Engineering, 2003. Proceedings. 2003, pp. 820–824, IEEE, 2003.
[18] K.­-J. Chen, S.­-L. Huang, Y.­-Y. Shih, and Y.­-J. Chen, “Extended­-hownet: A representational framework for concepts,” in Proceedings of OntoLex 2005­-Ontologies and Lexical Resources, 2005.
[19] W.­-Y. Ma and Y.­-Y. Shih, “Extended hownet 2.0–an entity­-relation common­-sense representation model,” in Proceedings of the Eleventh International Conference on Language Resources and Evaluation (LREC 2018), 2018.
[20] S. R. Maetschke, M. Simonsen, M. J. Davis, and M. A. Ragan, “Gene ontology­-driven inference of protein–protein interactions using inducers,” Bioinformatics, vol. 28, no. 1, pp. 69–75, 2012.
[21] V. Tresp, M. Bundschus, A. Rettinger, and Y. Huang, “Towards machine learning on the semantic web,” in Uncertainty reasoning for the Semantic Web I, pp. 282–314, Springer, 2006.
[22] S. E. Middleton, D. De Roure, and N. R. Shadbolt, “Ontology­-based recommender systems,” in Handbook on ontologies, pp. 477–498, Springer, 2004.
[23] W. H. Gomaa, A. A. Fahmy, et al., “A survey of text similarity approaches,” International Journal of Computer Applications, vol. 68, no. 13, pp. 13–18, 2013.
[24] Y. Xu, J. Liu, W. Yang, and L. Huang, “Incorporating latent meanings of morphological compositions to enhance word embeddings,” in Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 1232– 1242, 2018.
[25] T. K. Landauer and S. T. Dumais, “A solution to plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge.,” Psychological review, vol. 104, no. 2, p. 211, 1997.
[26] P. D. Turney, “Mining the web for synonyms: Pmi­-ir versus lsa on toefl,” in European conference on machine learning, pp. 491–502, Springer, 2001.
[27] E. Reiter and R. Dale, Building natural language generation systems. Cambridge university press, 2000.
[28] K. R. McKeown, “The text system for natural language generation: An overview,” in 20th Annual Meeting of the Association for Computational Linguistics, (Toronto, Ontario, Canada), pp. 113–120, Association for Computational Linguistics, June 1982.
[29] A. Gatt and E. Krahmer, “Survey of the state of the art in natural language generation: Core tasks, applications and evaluation,” Journal of Artificial Intelligence Research, vol. 61, pp. 65–170, 2018.
[30] A. B. Sai, A. K. Mohankumar, and M. M. Khapra, “A survey of evaluation metrics used for nlg systems,” arXiv preprint arXiv:2008.12009, 2020.
[31] T. Mikolov, K. Chen, G. Corrado, and J. Dean, “Efficient estimation of word representations in vector space,” arXiv preprint arXiv:1301.3781, 2013.
[32] T. Mikolov, M. Karafiát, L. Burget, J. Černockỳ, and S. Khudanpur, “Recurrent neural network based language model,” in Eleventh annual conference of the international speech communication association, 2010.
[33] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” in Advances in neural information processing systems, pp. 5998–6008, 2017.
[34] Z. Hu, Z. Yang, X. Liang, R. Salakhutdinov, and E. P. Xing, “Toward controlled generation of text,” in International Conference on Machine Learning, pp. 1587–1596, PMLR, 2017.
[35] K.­-H. Zeng, M. Shoeybi, and M.­-Y. Liu, “Style example­-guided text generation using generative adversarial transformers,” arXiv preprint arXiv:2003.00674, 2020.
[36] N. Dai, J. Liang, X. Qiu, and X. Huang, “Style transformer: Unpaired text style transfer without disentangled latent representation,” arXiv preprint arXiv:1905.05621, 2019.
[37] J. Li, R. Jia, H. He, and P. Liang, “Delete, retrieve, generate: A simple approach to sentiment and style transfer,” arXiv preprint arXiv:1804.06437, 2018.
[38] K. Nandhini and S. R. Balasundaram, “Math word question generation for training the students with learning difficulties,” in Proceedings of the International Conference & Workshop on Emerging Trends in Technology, pp. 206–211, 2011.
[39] D. M. Rembert, N. A. Mack, and J. E. Gilbert, “Exploring the needs and interests of fifth graders for personalized math word problem generation,” in Proceedings of the 18th ACM International Conference on Interaction Design and Children, pp. 592–597, 2019.
[40] Q. Zhou and D. Huang, “Towards generating math word problems from equations and topics,” in Proceedings of the 12th International Conference on Natural Language Generation, pp. 494–503, 2019.
[41] R. Koncel­-Kedziorski, I. Konstas, L. Zettlemoyer, and H. Hajishirzi, “A theme­-rewriting approach for generating algebra word problems,” arXiv preprint arXiv:1610.06210, 2016.
[42] B. Goodman and S. Flaxman, “European union regulations on algorithmic decisionmaking and a “right to explanation＂,” AI magazine, vol. 38, no. 3, pp. 50–57, 2017.
[43] A. Adadi and M. Berrada, “Peeking inside the black­-box: a survey on explainable artificial intelligence (xai),” IEEE access, vol. 6, pp. 52138–52160, 2018.
[44] Y.­-M. Hsieh, D.­-C. Yang, and K.­-J. Chen, “Improve parsing performance by self­-learning,” International Journal of Computational Linguistics & Chinese Language Processing, vol. 12, no. 2, pp. 195–216, 2007.
[45] Y.­-M. Hsieh, M.­-H. Bai, J. S. Chang, and K.­-J. Chen, “Improving PCFG chinese parsing with context­-dependent probability re­-estimation,” in Proceedings of the Second CIPSSIGHAN Joint Conference on Chinese Language Processing, pp. 216–221, 2012.
[46] D.­-C. Yang, Y.­-M. Hsieh, and K.­-J. Chen, “Resolving ambiguities of chinese conjunctive structures by divide­-and­-conquer approaches,” in Proceedings of the Third International Joint Conference on Natural Language Processing, 2008.
[47] C. K. I. P. Group, “中文詞類分析 (三版) 技術報告 93­-05,” tech. rep., Academia Sinica Institute of Information Science, 1993.
[48] W.­-Y. Ma and K.­-J. Chen, “Introduction to ckip chinese word segmentation system for the first international chinese word segmentation bakeoff,” in Proceedings of the second SIGHAN workshop on Chinese language processing, pp. 168–171, 2003.
[49] A. C. Graesser, D. S. McNamara, M. M. Louwerse, and Z. Cai, “Coh­-metrix: Analysis of text on cohesion and language,” Behavior research methods, instruments, & computers, vol. 36, no. 2, pp. 193–202, 2004.
[50] 蔡筱倩 et al., 兒童文本詞頻詞彙指標分析系統建置與應用. PhD thesis, Graduate Institute of Educational Information and Measurement, National Taichung University of Education, 2013.
[51] Z. S. Harris, “Distributional structure,” Word, vol. 10, no. 2­-3, pp. 146–162, 1954.
[52] E. Fredkin, “Trie memory,” Communications of the ACM, vol. 3, no. 9, pp. 490–499, 1960.
[53] E. Montahaei, D. Alihosseini, and M. S. Baghshah, “Jointly measuring diversity and quality in text generation models,” arXiv preprint arXiv:1904.03971, 2019.
[54] Y. Zhu, S. Lu, L. Zheng, J. Guo, W. Zhang, J. Wang, and Y. Yu, “Texygen: A benchmarking platform for text generation models,” in The 41st International ACM SIGIR Conference on Research & Development in Information Retrieval, pp. 1097–1100, 2018.
[55] J. Li, Y. Lan, J. Guo, and X. Cheng, “On the relation between quality­-diversity evaluation and distribution­-fitting goal in text generation,” in International Conference on Machine Learning, pp. 5905–5915, PMLR, 2020.