We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during...We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.展开更多
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
Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This pap...Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.展开更多
In primary school maths, CIRCLE is one of the most important units. Some of the students would think it would be okay to be able to understand the relationship between the diameter or the radius and the circumference ...In primary school maths, CIRCLE is one of the most important units. Some of the students would think it would be okay to be able to understand the relationship between the diameter or the radius and the circumference or the area of a circle.Here is a word problem:Choose the correct option A, B or C.Inthesquare,thereisaquartercircleandasmallcircle.展开更多
This thesis is about the E-C translation of The Innocent.This novel is the prequel by M.R.Hall,a famous British playwright,for his another novel Tlze Clzosen Dead.Through this thesis,the author here aims to use some t...This thesis is about the E-C translation of The Innocent.This novel is the prequel by M.R.Hall,a famous British playwright,for his another novel Tlze Clzosen Dead.Through this thesis,the author here aims to use some typical examples to illustrate the application of such translation methods and strategies as choice of word,meaning extension and transformation of part of speech to solve the difficulties and problems she encountered during the translation of this detective novel.In order to achieve the similar reading effect between the target and the original readers,the author,under the guidance of functional equivalence theory,also adopts other translation strategies and techniques to solve the problems in translation,striving for maintaining the writing style of the source text,expecting to provide some reference for other texts alike.展开更多
尽管使用思维链(chain of thought,CoT)的大模型(large language model,LLM)在单未知数的数学问题求解(math word problem,MWP)任务上取得了显著成果。但是,目前的研究缺乏适用于方程数学问题的方法。由于数学问题求解对推理步骤具有很...尽管使用思维链(chain of thought,CoT)的大模型(large language model,LLM)在单未知数的数学问题求解(math word problem,MWP)任务上取得了显著成果。但是,目前的研究缺乏适用于方程数学问题的方法。由于数学问题求解对推理步骤具有很高的敏感性,列方程出错会导致后续步骤连环出错,所以提出一种渐近式验证纠正的方法2ERP,一边验证一边纠正步骤错误,输出最有可能的正确答案。在验证环节使用等式和答案的双重验证,回代答案到等式确保计算的正确,从数学表达式获取数值关系来验证等式的正确性。在纠正流程中,根据回代的结果和双重验证的一致性排除错误的推理路径,逼近正确结果。与其他CoT方法相比,2ERP方法在6个数据集上均取得了性能上的提升,平均准确率达到了66.2%,尤其是方程问题的数据集上,平均提高了6.9百分点。2ERP方法是一种设计提示的零样本方法,通过多次迭代提高数学问题的准确率,并输出具有详细步骤的求解过程,该方法在方程问题上的提升更加明显。展开更多
文摘We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.
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.
基金The National Natural Science Foundation of China(No.61977029)supported the worksupported partly by Nurturing Program for Doctoral Dissertations at Central China Normal University(No.2022YBZZ028).
文摘Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.
文摘In primary school maths, CIRCLE is one of the most important units. Some of the students would think it would be okay to be able to understand the relationship between the diameter or the radius and the circumference or the area of a circle.Here is a word problem:Choose the correct option A, B or C.Inthesquare,thereisaquartercircleandasmallcircle.
文摘This thesis is about the E-C translation of The Innocent.This novel is the prequel by M.R.Hall,a famous British playwright,for his another novel Tlze Clzosen Dead.Through this thesis,the author here aims to use some typical examples to illustrate the application of such translation methods and strategies as choice of word,meaning extension and transformation of part of speech to solve the difficulties and problems she encountered during the translation of this detective novel.In order to achieve the similar reading effect between the target and the original readers,the author,under the guidance of functional equivalence theory,also adopts other translation strategies and techniques to solve the problems in translation,striving for maintaining the writing style of the source text,expecting to provide some reference for other texts alike.
文摘尽管使用思维链(chain of thought,CoT)的大模型(large language model,LLM)在单未知数的数学问题求解(math word problem,MWP)任务上取得了显著成果。但是,目前的研究缺乏适用于方程数学问题的方法。由于数学问题求解对推理步骤具有很高的敏感性,列方程出错会导致后续步骤连环出错,所以提出一种渐近式验证纠正的方法2ERP,一边验证一边纠正步骤错误,输出最有可能的正确答案。在验证环节使用等式和答案的双重验证,回代答案到等式确保计算的正确,从数学表达式获取数值关系来验证等式的正确性。在纠正流程中,根据回代的结果和双重验证的一致性排除错误的推理路径,逼近正确结果。与其他CoT方法相比,2ERP方法在6个数据集上均取得了性能上的提升,平均准确率达到了66.2%,尤其是方程问题的数据集上,平均提高了6.9百分点。2ERP方法是一种设计提示的零样本方法,通过多次迭代提高数学问题的准确率,并输出具有详细步骤的求解过程,该方法在方程问题上的提升更加明显。
