{"id":162576,"date":"2012-04-01T00:00:00","date_gmt":"2012-04-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/automatically-generating-algebra-problems\/"},"modified":"2018-10-16T22:24:47","modified_gmt":"2018-10-17T05:24:47","slug":"automatically-generating-algebra-problems","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/automatically-generating-algebra-problems\/","title":{"rendered":"Automatically Generating Algebra Problems"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We propose computer-assisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the from &#8220;Left-hand-side-term = Right-hand-side-term&#8221;), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in making examinations where they need to test students on problems similar to what they taught in class, and students in generating practice problems tailored to their specific needs. Our first insight is that we can generalize p syntactically to a query Q that implicitly represents a set of problems [Q] (which includes p). Our second insight is that we can explore the space of problems [Q] automatically, use classical results from polynomial identity testing to generate only those problems in [Q] that are correct, and then use pruning techniques to generate only unique and interesting problems. Our third insight is that with a small amount of manual tuning on the query Q, the user can interactively guide the computer to generate problems of interest to her. We present the technical details of the above mentioned steps, and also describe a tool where these steps have been implemented. We also present an empirical evaluation on a wide variety of problems from various sub-fields of algebra including polynomials, trigonometry, calculus, determinants etc. Our tool is able to generate a rich corpus of similar problems from each given problem; while some of these similar problems were already present in the textbook, several were new!<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We propose computer-assisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the from &#8220;Left-hand-side-term = Right-hand-side-term&#8221;), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in making examinations where they need to test students [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-162576","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"Microsoft Research","msr_edition":"","msr_affiliation":"","msr_published_date":"2012-04-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"AAAI","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"491435","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"aaai12-full","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2012\/04\/aaai12-full.pdf","id":491435,"label_id":0},{"type":"file","title":"aaai12","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2012\/04\/aaai12.pptx","id":491444,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":491444,"url":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2018\/06\/aaai12.pptx"},{"id":491435,"url":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2018\/06\/aaai12-full.pdf"}],"msr-author-ordering":[{"type":"edited_text","value":"Sriram Rajamani","user_id":33711,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Sriram Rajamani"},{"type":"edited_text","value":"Sumit Gulwani","user_id":33755,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Sumit Gulwani"},{"type":"text","value":"Sriram Rajamani","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[171112,361034],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":171112,"post_title":"Automated Problem Generation for Education","post_name":"automated-problem-generation-for-education","post_type":"msr-project","post_date":"2013-02-25 15:56:26","post_modified":"2017-06-01 17:56:30","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/automated-problem-generation-for-education\/","post_excerpt":"Intelligent Tutoring Systems (ITS) can significantly enhance the educational experience, both in the classroom and online. A key aspect of ITS is the ability to automatically generate problems of a certain difficulty level and that exercise use of certain concepts. This can help avoid copyright or plagiarism issues and help generate personalized workflows. This project develops technologies for problem generation in various subject domains including math, logic, and even language learning. Team This is an&hellip;","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/171112"}]}},{"ID":361034,"post_title":"Program Synthesis","post_name":"program-synthesis","post_type":"msr-project","post_date":"2017-02-02 13:37:27","post_modified":"2020-01-24 08:27:25","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/program-synthesis\/","post_excerpt":"Introduction Program synthesis is the task of automatically discovering an executable piece of code given user intent expressed using various forms of constraints such as input-output examples, demonstrations, natural language, etc. Program synthesis has direct applications for various classes of users in the technology pyramid: (100s of millions of) End Users (people who have access to a computational device but are not expert programmers): Helping them to create small snippets of code for performing repetitive&hellip;","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/361034"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/162576"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/162576\/revisions"}],"predecessor-version":[{"id":491441,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/162576\/revisions\/491441"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=162576"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=162576"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=162576"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=162576"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=162576"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=162576"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=162576"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=162576"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=162576"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=162576"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=162576"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=162576"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=162576"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=162576"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=162576"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=162576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}