Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that...Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.展开更多
By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong...By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong inhibition of the same time, support the weak” (抑强扶弱) based on “Yin Yang Wu Xing” Theory in image mathematics of Traditional Chinese Mathematics (TCMath). We defined generalized relations and generalized reasoning, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the intervention principle in image mathematics of TCMath and treated the research object of the image mathematics as a steady multilateral system, it has been proved that the mathematical intervening principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.展开更多
近年来,得益于人工智能技术(Artificial Intelligence,AI)的快速发展,关于自动求解数学应用题(Math Word Problem,MWP)的研究越来越趋向成熟。在自动求解数学应用题任务中,对问题文本进行建模至关重要。针对这一问题,文章提出了一个基...近年来,得益于人工智能技术(Artificial Intelligence,AI)的快速发展,关于自动求解数学应用题(Math Word Problem,MWP)的研究越来越趋向成熟。在自动求解数学应用题任务中,对问题文本进行建模至关重要。针对这一问题,文章提出了一个基于循环神经网络(Recursive Neural Network,RNN)和Transformer编码网络的双路文本编码器(Dual Channel Text Encoder,DCTE):首先,使用循环神经网络对文本进行初步的编码;然后,利用基于自注意力(Self-attention)机制的Transformer编码网络来获得词语的远距离上下文语义信息,以增强词语和文本的语义表征。结合DCTE和GTS(Goal-Driven Tree-structured MWP Solver)解码器,得到了数学应用题求解器(DCTE-GTS模型),并在Math23k数据集上,将该模型与Graph2Tree、HMS等模型进行了对比实验;同时,为探讨编码器配置方法对模型效果的影响,进行了消融实验。对比实验结果表明:DCTE-GTS模型均优于各基准模型,答案正确率达到77.6%。消融实验结果表明双路编码器的配置方法是最优的。展开更多
近几年,数学应用题自动解答(Math Word Problems,MWP)的研究受到越来越多学者关注,大多数研究的重点是对编码器的改进。然而目前的研究在编码器的改进方面还存在以下问题:(1)输入文本的颗粒度一般是字级别,这会导致泛化能力不足;(2)大...近几年,数学应用题自动解答(Math Word Problems,MWP)的研究受到越来越多学者关注,大多数研究的重点是对编码器的改进。然而目前的研究在编码器的改进方面还存在以下问题:(1)输入文本的颗粒度一般是字级别,这会导致泛化能力不足;(2)大多数模型对文本信息的挖掘没有充分利用文本内实体、词性等信息,只是停留在时序信息层面。该文针对以上问题,在双向GRU(Gated Recurrent Unit)的基础上提出了一种新颖的基于多粒度分词和图卷积网络的编码器结构(Multi-grained Graph Neural Networks,MGNet)。多粒度分词是通过对文本的每个词进行不同颗粒度的分词,增加了样本容量,并且通过引入一些噪声样本,提高了模型的泛化能力。图卷积神经网络通过构建文本内实体、数字、日期之间的不同的属性图,对它们之间隐含的关系进行建模。在Math23K和Ape210K数据集的实验显示,该文提出的模型MGNet准确率分别达到77.73%和80.8%。展开更多
文摘Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.
文摘By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong inhibition of the same time, support the weak” (抑强扶弱) based on “Yin Yang Wu Xing” Theory in image mathematics of Traditional Chinese Mathematics (TCMath). We defined generalized relations and generalized reasoning, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the intervention principle in image mathematics of TCMath and treated the research object of the image mathematics as a steady multilateral system, it has been proved that the mathematical intervening principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.
