現行的深度學習方式的小學數學文字題解題系統，宛如「黑箱」一般只輸出計算結果，卻無法清楚得知系統是如何解題的，並且無法對其解題過程做出解釋說明。本論文基於簡化法以及計算概念框架的小學數學文字題解題系統，製作了模板式的解釋生成模組。與深度學習不同，其解題模型是仿效人類思考、理解的方式對題目進行分析與解題，因此能夠以此為據生成解釋。
　　此論文以小學數學文字題中的「基本題」與「應用題」為例，利用模板方式設計一個解釋生成模組。此生成模組可以根據不同的解題策略，設計不同的解釋模版。「基本題」是以句型為單位設計解釋模版，主要描述題目中語意與數學計算之間的關聯；「應用題」是類似於函式的概念設計函式節點。先從解題系統讀取資訊做連接，強調列舉出題目有哪些已知與未知的條件。接著依照系統解題的演算法流程，逐步從模板中輸出文字說明並顯示算式。最後還能根據題目有解還是無解的情況，顯示計算結果。
　　我們以問卷調查進行人工評估，探討生成的解釋是否具有邏輯性，讓人能夠理解解題系統的解題過程。結果呈現五點量表中，非常同意與同意占整體81.5%。大部分的受訪者皆認同本論文設計的解釋具有邏輯性，能夠清處描述系統的解題行為。

The current mathematics word problem solvers based on deep learning is like a "black box" and generally only generate calculation results. It is difficult to clearly know how the solvers solve the problems. This paper proposes an explanation generation module according to a mathematics word problem solver based on reduction-based approach (RBA) and frame. This solver can imitate the way of human thinking and understanding. Thus, we can analyze the problems and generate the explanation for them.
We use the template-based method to design an explanation generation module for “basic questions(基本題)” and “application questions(應用題)”. Due to the different problem-solving strategies of these two questions’ types, the generated explanations are also different. Templates of “basic questions” are designed by the units of sentence patterns and mainly describe the relationship between the question’s semantic meaning and mathematical calculations. And the idea of templates in the “application questions” is like functions. It emphasizes listing the known and unknown conditions in the problem. Those templates will follow the solution strategies to display the calculation formula, the explanations and the calculation result step by step.
The experiment is evaluated by a questionnaire survey to explore whether the generated explanations are logical. The results showed that 81.5% choose the strongly agree and agree. Most of the survey participants agree that the designed explanation is logical and can clearly describe the problem-solving behavior of the solver.

[1] K. Kukich, “Design of a knowledge-based report generator,” in Proc. 21st Annu. ACL Conf., USA, 1983, pp. 145–150.
[2] K. McKeown, Text generation: using discourse strategies and focus constraints to generate natural language text, USA: Cambridge University Press, 1985.
[3] N. Y. Liang, “書面漢語自動分詞系統—CDWS,” Journal of Chinese Information Processing, vol. 1, no. 1, pp. 44-52, 1993.
[4] E. Goldberg, N. Driedger and R. I. Kittredge, “Using natural-language processing to produce weather forecasts,” IEEE Expert: Intelligent Systems and Their Applications, vol. 9, no. 2, pp. 45-53, 1994.
[5] G. A. Miller, “WordNet: A Lexical Database for English,” Communications of the ACM, vol. 38, no. 11, pp. 39-41, 1995.
[6] E. Reiter and R. Dale, “Building applied natural language generation systems,” Nat. Lang. Eng., vol. 3, no. 1, pp.57-87, 1997.
[7] Y. K. Wang, W. L. Hsu, and Y. C. Chen, “The anaphoric expressions of Chinese algebraic word problem,” resented at the 1998 ISMIP Conf., China, 1998.
[8] D. Jurafsky and J. H. Martin, Speech and language processing: an introduction to natural language processing, computational linguistics, and speech recognition, Upper Saddle River, N.J.: Prentice Hall, 2000.
[9] F. Peng and D. Schuurmans, “Self-supervised Chinese word segmentation,” in Proc. 4th IDA Conf., Portugal, 2001, pp. 238–247.
[10] K. Papineni, S. Roukos, T. Ward, and W. J. Zhu, “BLEU: a method for automatic evaluation of machine translation,” in Proc. 40th Annu. ACL Conf., USA, 2002, pp. 311-318.
[11] G. Doddington, “Automatic evaluation of machine translation quality using n-gram co-occurrence statistics,” in Proc. 2002 HLT Conf., USA, 2002, pp. 138–145.
[12] C. Y. Lin, “ROUGE: a package for automatic evaluation of summaries,” in Proc. 42th Annu. ACL Conf., Spain, 2004, pp. 74–81.
[13] S. Banerjee and A. Lavie, “METEOR: an automatic metric for MT evaluation with improved correlation with human judgments,” in 2005 Proc ACL Workshop., USA, 2005, pp. 65-72.
[14] K. J. Chen, “Lexical semantic representation and semantic composition: an Introduction to E-HowNet,” CKIP, Institute of Information Science, Academia Sinica, Taiwan, 2009.
[15] A. Belz and E. Kow, “System building cost vs. output quality in data-to-text generation,” in 2009 Proc ENLG Conf., Greece, 2009, pp. 16–24.
[16] P. Liang, M. Jordan and D. Klein, “Learning semantic correspondences with less supervision,” in 2009 Proc joint Annu. ACL Conf. and IJCNLP Conf., Singapore, 2009, pp. 91–99.
[17] B. Langner, S. Vogel and A. Black, “Evaluating a dialog language generation system: comparing the mountain system to other NLG approaches,” in 2010 Proc INTERSPEECH Conf., Japan, 2010, pp. 1109–1112.
[18] J. Turian, L. Ratinov, Y. Bengio, “Word representations: a simple and general method for semi-supervised learning,” in Proc. 48th Annu. ACL Conf., Sweden, 2010, pp. 384-394.
[19] I. Adeyanju, “Generating weather forecast texts with case based reasoning,” IJCA., vol. 45, no. 10, pp. 35-40, 2012.
[20] T. Mikolov, K. Chen, G. Corrado and J. Dean, “Efficient estimation of word representations in vector space,” presented at the 2013 ICLR Workshop, USA, 2013.
[21] J. Pennington, R. Socher, and C. Manning, “GloVe: global vectors for word representation,” in 2014 Proc EMNLP Conf., Qatar, 2014, pp. 1532-1543.
[22] M. J. Hosseini, H. Hajishirzi, O. Etzioni and N. Kushman, “Learning to solve arithmetic word problems with verb categorization,” in 2014 Proc EMNLP Conf., Qatar, 2014, pp. 523-533.
[23] J. Chung, C. Gulcehre, K. Cho and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” presented at the 2014 NIPS Workshop, Canada, 2014.
[24] J. C. Pereira, A. Teixeira and J. S. Pinto “Towards a hybrid NLG system for data2text in Portuguese,” in 2015 Proc CISTI Conf., Portugal, 2015, pp. 1-6.
[25] C. T. Huang, Y. C. Lin, C. C. Liang, K. Y. Hsu, S. Y. Miao, W. Y. Ma, L. W. Ku, C. J. Liau and K. Y. Su, “Designing a tag-based statistical math word problem solver with reasoning and explanation,” in 2015 Proc ROCLING Conf., Taiwan, 2015, pp. 58–63.
[26] C. T. Huang, Y. C. Lin and K. Y. Su, “Explanation generation for a math word problem solver,” IJCLCLP, vol. 20, no. 2, pp. 27-44, 2015.
[27] R. Lebret, D. Grangier and M. Auli, “Neural text generation from structured data with application to the biography domain,” in 2016 Proc EMNLP Conf., USA, 2016, pp. 1203–1213.
[28] C. C. Liang, Y. S. Wong, Y. C. Lin and K. Y. Su, “A goal-oriented meaning-based statistical multi-step math word problem solver with understanding, reasoning and explanation,” in 2017 Proc IJCAI Conf., Australia, 2017, pp. 5235-5237.
[29] S. Wiseman, S. M. Shieber and A. M. Rush, “Challenges in data-to-document generation,” presented at the 2017 EMNLP Conf., Denmark, 2017.
[30] T. Liu, K. Wang, L. Sha, B. Chang and Z. Sui, “Table-to-text generation by structure-aware seq2seq learning,” in 2018 Proc AAAI Conf., USA, 2018, pp. 4881-4888.
[31] M. E. Peters, M. Neumann, M. Iyyer, M. Gardner, C. Clark, K. Lee and L. Zettlemoyer, “Deep contextualized word representations,” in 2018 Proc NAACL Conf., USA, 2018, pp. 2227–2237.
[32] C. C. Liang, Y. S. Wong, Y. C. Lin and K. Y. Su, “A meaning-based statistical English math word problem solver,” in 2018 Proc NAACL Conf., USA, 2018, pp. 652–662.
[33] S. Wiseman, S. Shieber and A. Rush, “Learning neural templates for text generation,” in 2018 Proc EMNLP Conf., Belgium, 2018, pp. 3174–3187.
[34] A. Amini, S. Gabriel, S. Lin, R. Koncel-Kedziorski, Y. Choi, H. Hajishirzi, “MathQA: towards interpretable math word problem solving with operation-based formalisms,” in 2019 Proc NAACL Conf., USA, 2019, pp. 2357–2367.
[35] T. R. Chiang and Y. N. Chen, “Semantically-aligned equation generation for solving and reasoning math word problems,” in 2019 Proc NAACL Conf., USA, 2019, pp. 2656–2668.
[36] J. Devlin, M. W. Chang, K. Lee and K. Toutanova, “BERT: pre-training of deep bidirectional transformers for language understanding,” in 2019 Proc NAACL Conf., USA, 2019, pp. 4171–4186.
[37] N. Mathur, T. Baldwin and T. Cohn, “Putting evaluation in context: contextual embeddings improve machine translation evaluation,” in Proc. 57th Annu. ACL Conf., Italy, 2019, pp. 2799–2808.
[38] B. Dhingra, M. Faruqui, A. P. Parikh, M. W. Chang, D. Das and W. W. Cohen, “Handling divergent reference texts when evaluating table-to-text generation,” in Proc. 57th Annu. ACL Conf., Italy, 2019, pp. 4884–4895.
[39] J. Li, L. Wang, J. Zhang, Y. Wang, B. T. Dai and D. Zhang, “Modeling intra-relation in math word problems with different functional multi-head attentions,” in Proc. 57th Annu. ACL Conf., Italy, 2019, pp. 6162–6167.
[40] L. Wang, D. Zhang, J. Zhang, X. Xu, L. Gao, B. T. Dai and Heng Tao Shen, “Template-based math word problem solvers with recursive neural networks,” in 2019 Proc AAAI Conf., USA, 2019, pp. 7144-7151.
[41] Z. Xie and S. Sun, “A goal-driven tree-structured neural model for math word problems,” in 2019 Proc IJCAI Conf., China, 2019, pp. 5299-5305.
[42] J. Gu, C. Wang and J. Zhao, “Levenshtein transformer,” presented at the 2019 NeurIPS Conf., Canada, 2019.
[43] R. Tian, S. Narayan, T. Sellam and A. P. Parikh, “Sticking to the facts: confident decoding for faithful data-to-text generation,” presented at the 2020 ICLR Conf., Ethiopia, 2020.
[44] T. Zhang, V. Kishore, F. Wu, K. Q. Weinberger and Y. Artzi, “BERTScore: evaluating text generation with BERT,” presented at the 2020 ICLR Conf., Ethiopia, 2020.
[45] M. Danilevsky, K. Qian, R. Aharonov, Y. Katsis, B. Kawas and P. Sen, “A survey of the state of explainable AI for natural language processing,” in 2020 Proc AACL-IJCNLP Conf., China, 2020, pp. 447-459.
[46] A. V. Mota, T. L. C. D. Silva and J. Macêdo, “Template-based multi-solution approach for data-to-text generation,” in 2020 Proc ADBIS Conf., France, 2020, pp. 157-170.
[47] B. Luo, Z. Bai, K. Lai and J. Shen, “Make templates smarter: a template based data2text system powered by text stitch model,” in 2020 Proc EMNLP Conf., 2020, pp. 1057–1062.
[48] A. Mishra, M. F. M. Chowdhury, S. Manohar, D. Gutfreund and K. Sankaranarayanan, “Template controllable keywords-to-text generation,” Computer Research Repository, vol. 2011.03722, 2020.
[49] H. Harkous, I. Groves and A. Saffari, “Have your text and use it too! end-to-end neural data-to-text generation with semantic fidelity,” in 2020 Proc COLING Conf., Spain, 2020, pp. 2410–2424.
[50] A. B. Sai, A. K. Mohankumar and M. M. Khapra, “A survey of evaluation metrics used for NLG systems,” arXiv preprints, 2020.
[51] E. Chang, X. Shen, D. Zhu, V. Demberg and H. Su, “Neural data-to-text generation with LM-based text augmentation,” in 2021 Proc EACL Conf., 2021, pp. 758–768.
[52] J. D. Chen, “Incorporating Reduction-Based Approach and Frame into Chinese Math Word Problem Solver,” M.S. thesis, Data Science Degree Program, National Taiwan University and Academia Sinica, Taiwan, 2021.