The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Math Problem Generator <s> This paper presents a semi-automated methodology for generating geometric proof problems of the kind found in a highschool curriculum. We formalize the notion of a geometry proof problem and describe an algorithm for generating such problems over a user-provided figure. Our experimental results indicate that our problem generation algorithm can effectively generate proof problems in elementary geometry. On a corpus of 110 figures taken from popular geometry textbooks, our system generated an average of about 443 problems per figure in an average time of 4.7 seconds per figure. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Math Problem Generator <s> We describe a framework that combines a combinatorial approach and automated deduction to generate geometry problems which require implicit constructions for their solution. This is an extension of our framework developed for generating geometric questions without construction. Such a system would help teachers to quickly generate large numbers of questions involving implicit construction on a geometry topic. Students can explore, revise and master the specific topics covered in classes and textbooks based on construction-based generated ::: ::: questions. This system may also help standardize tests such as GMAT and SAT. Our novel methodology uses (i) a combinatorial approach for generating geometric figures and objects for construction (ii) automated deduction to generate new questions and solutions. By combining these methods, we are able to generate questions involving finding or proving relationships between geometric objects based on a specification of the geometry objects, concepts, theorems and construction object to be covered by the questions. Experimental results show that a large number of questions can be generated in a short time. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Math Problem Generator <s> Word problems are an established technique for teaching mathematical modeling skills in K-12 education. However, many students find word problems unconnected to their lives, artificial, and uninteresting. Most students find them much more difficult than the corresponding symbolic representations. To account for this phenomenon, an ideal pedagogy might involve an individually crafted progression of unique word problems that form a personalized plot. ::: ::: We propose a novel technique for automatic generation of personalized word problems. In our system, word problems are generated from general specifications using answer-set programming (ASP). The specifications include tutor requirements (properties of a mathematical model), and student requirements (personalization, characters, setting). Our system takes a logical encoding of the specification, synthesizes a word problem narrative and its mathematical model as a labeled logical plot graph, and realizes the problem in natural language. Human judges found our problems as solvable as the textbook problems, with a slightly more artificial language. <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Math Problem Generator <s> This paper presents an intelligent tutoring system, GeoTutor, for Euclidean Geometry that is automatically able to synthesize proof problems and their respective solutions given a geometric figure together with a set of properties true of it. GeoTutor can provide personalized practice problems that address student deficiencies in the subject matter. <s> BIB004 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Math Problem Generator <s> Mathematical Word Problems (MWPs) are important for training students' literacy and numeracy skills. Traditionally MWPs have been manually designed; an effective automated MWP generator can significantly benefit education and research. The goal of this work is to efficiently synthesize MWPs that are authentic (i.e., similar to manually written problems), diverse (i.e., covering a wide range of mathematical tasks), and configurable (i.e., varying difficulty levels and solution characteristics). This is challenging because a generated problem needs to both exhibit a well-founded mathematical structure and also an easily understood natural language story. Our key insight is to leverage the important role that dimensional units play in MWPs, both textually and symbolically. We first synthesize a dimensionally consistent equation and then compose the natural language story via a bottom-up traversal of the equation tree. We have realized our technique and extensively evaluated its efficiency and effectiveness. Results show that the system can generate hundreds of valid problems per second with varying levels of difficulty. More importantly, we show, via a user study with 30 students from a local middle school, that the generated problems are statistically indistinguishable from actual textbook problems for practice and examination. <s> BIB005 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Math Problem Generator <s> Texts present coherent stories that have a particular theme or overall setting, for example science fiction or western. In this paper, we present a text generation method called {\it rewriting} that edits existing human-authored narratives to change their theme without changing the underlying story. We apply the approach to math word problems, where it might help students stay more engaged by quickly transforming all of their homework assignments to the theme of their favorite movie without changing the math concepts that are being taught. Our rewriting method uses a two-stage decoding process, which proposes new words from the target theme and scores the resulting stories according to a number of factors defining aspects of syntactic, semantic, and thematic coherence. Experiments demonstrate that the final stories typically represent the new theme well while still testing the original math concepts, outperforming a number of baselines. We also release a new dataset of human-authored rewrites of math word problems in several themes. <s> BIB006
We also review automatic math word problem generators that can efficiently produce a large, diverse and configurable corpus of question-answer database. The topics covered in this survey include algebra word problems with basic operators {+, −, ×, ÷} and geometry problems. In BIB005 , Wang et al. leveraged the concept of expression tree to generate a math word problem. The tree structure can provide the skeleton of the story, and meanwhile allow the story to be constructed recursively from the sub-stories. Each sub-story can be seen as a text template with value slots to be filled. These sub-stories will be concatenated into an entire narrative. Different from BIB005 , the work of BIB006 rewrites a given math word problem to fit a particular theme such as Star War. In this way, students may stay more engaged with their homework assignments. The candidate are scored with the coherence in multiple factors (e.g., syntactic, semantic and thematic). BIB003 generates math word problems that match the personal interest of students. The generator uses Answer Set Programming  , in which programs are composed of facts and rules in a first-order logic representation, to satisfy a collection of pedagogical and narrative requirements. Its objective is to produce coherent and personalized story problems that meet pedagogical requirements. In the branch of geometry problem generator, GeoTutor BIB001 , BIB004 is designed to generate geometry proof problems for high school students. The input contains a figure and a set of geometry axioms. The output is a pair (I, G), where I refers to the assumptions for the figure and goals in G are sets of explicit facts to be inferred. Singhal et al. also tackled the automated generation of geometry questions for high school students BIB002 ,  . Its input interface allows users to select geometric objects, concepts and theorems. Compared with BIB001 , BIB004 , its geometric figure is generated by the algorithm rather than specified by the user. Based on the figure, the next step of generating facts and solutions is similar to that in BIB001 , BIB004 . It requires pre-knowledge on axioms and theorems and results in the formation capturing the relationships between its objects.