[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125667-en":3,"doc-seo-125667-105":30,"detail-sidebar-cat-0-en-105":95},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125667,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Integration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System - PhD dissertation","Computer-based feedback is widely used in mathematics education, from correctness indicators to worked solutions and practice suggestions. Intelligent Tutoring Systems (ITS) extend this by providing feedback repeatedly during problem solving. Developing step-level feedback for specific topics can be time-intensive, and machine learning has only recently entered the ITS authoring process. This dissertation presents the SANYMS ITS, combining a Computer Algebra System for correctness at each step with machine learning to measure equation similarity and graph-based expert next-step hints.","Chapman University Digital Commons  \n\n| Computational and Data Sciences (PhD) Dissertations | Dissertations and Theses |\n| --- | --- |\n| Spring 5-2023\u003Cbr>Integration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System\u003Cbr>Sam Ford\u003Cbr>Chapman University, [samford@chapman.edu](samford@chapman.edu)\u003Cbr>Follow this and additional works at: [https://digitalcommons.chapman.edu/cads_dissertations](https://digitalcommons.chapman.edu/cads_dissertations)\u003Cbr> Part of the Data Science Commons, and the Educational Technology Commons |  |\n\nRecommended Citation  \nS. Ford, \"Integration of computer algebra systems and machine learning in the authoring of the SANYMS Intelligent Tutoring System,\" Ph. D. dissertation, Chapman University, Orange, CA, 2023. [https://doi.org/](https://doi.org/)[ ](https://doi.org/)[10.36837/chapman.000469](10.36837/chapman.000469)  \nThis Dissertation is brought to you for free and open access by the Dissertations and Theses at Chapman University Digital Commons. It has been accepted for inclusion in Computational and Data Sciences (PhD) Dissertations by an authorized administrator of Chapman University Digital Commons. For more information, please contact [laughtin@chapman.edu](laughtin@chapman.edu).  \nIntegration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System  \nA Dissertation by  \nSam Oliver Ford  \nChapman University  \nOrange, CA  \nSchmid College of Science and Technology Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computational and Data Sciences  \nMay 2023  \nCommittee in charge:  \nMohamed Allali, Ph.D., Chair  \nErik Linstead, Ph.D.  \nAdrian Vajiac, Ph.D.  \nIntegration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System  \nCopyright © 2023  \nby Sam Oliver Ford  \nACKNOWLEDGEMENTS  \nFirst and foremost I would like to thank my advisor Dr. Allali. Your classes were the highlight of my undergraduate career at Chapman, and without your encouragement I never would have embarked on this endeavor. Your support has been invaluable and I take inspiration from you in my teaching. I would also like to thank my other committee members Dr. Linstead and Dr. Vajiac, whose teaching and support was likewise integral. Thank you also to Chelsea Parlett, Chris Watkins, and Viseth Sean for helping me always find my motivation. To my wonderful colleagues at Sequoyah: thankyou for your endless encouragement and your willingness to offer your support, even as your work kept you busy.  \nFinally, thank you to my family. To my mom, who has always believed I could do anything I set my mind to, and to my partner Elliott, without whose support I would not have made it this far.  \nLIST OF PUBLICATIONS  \nSam Ford & Mohamed Allali (2022)“Using a constraint-based expert model to provide step-level feedback for user-inputted mathematics equations,” International Journal of Mathematical  \nEducation in Science and Technology, DOI: 10.1080/0020739X.2022.2035000  \nABSTRACT  \nIntegration of Computer Algebra Systems and Machine Learning in the Authoring of the  \nSANYMS Intelligent Tutoring System  \nby Sam Oliver Ford  \nComputer-based feedback is an increasingly common tool in mathematics education. The feedback that such programs provide can range from indicating whether an answer was correct, to giving an answer or worked out solution or suggesting a similar practice problem. One type of computerbased feedback, the Intelligent Tutoring Systems (ITS), is able to provide feedback not just once per problem, but at multiple points during the process of solving a problem. Creating an ITS that gives feedback for even a narrow topic is often a time-intensive process, and machine learning is only recently being integrated into the ITS authoring process.  \nWe introduce the Show and Name your Math Steps (SANYMS) ITS, which uses a Computer Algebra Sy","cbCaitCs9pukruVp","https://ap.wps.com/l/cbCaitCs9pukruVp","pdf",2298667,1,116,"English","en",105,"# Acknowledgements\n# List of Publications\n# Abstract\n# List of Tables\n# List of Figures\n# List of Abbreviations\n# 1 Introduction\n## 1.1 Intelligent Tutoring Systems\n## 1.1.1 General Structure","[{\"question\":\"What educational need does the dissertation address?\",\"answer\":\"It addresses the need for interactive, step-level feedback in mathematics education, especially within Intelligent Tutoring Systems.\"},{\"question\":\"How does the proposed SANYMS system provide feedback during problem solving?\",\"answer\":\"It uses a Computer Algebra System to produce correctness feedback at every step for equations chosen by the user.\"},{\"question\":\"What role does machine learning play in the dissertation’s approach?\",\"answer\":\"Machine learning is used to develop a metric that measures similarity between equations after generalizing algebraic expressions.\"},{\"question\":\"How are expert solutions used to generate next-step hints?\",\"answer\":\"A small set of expert-solved equations is incorporated into a directed graph to provide next-step hints for equation types and solution paths the system has not previously seen.\"}]","Integration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System - PhD dissertation | PDF",1785900533,292,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":90,"head_meta":92,"extra_data":94,"updated_unix":28},"integration-of-computer-algebra-systems-and-machine-learning-in-the-authoring-of-the-sanyms-intelligent-tutoring-system-phd-dissertation","",{"@graph":36,"@context":89},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/integration-of-computer-algebra-systems-and-machine-learning-in-the-authoring-of-the-sanyms-intelligent-tutoring-system-phd-dissertation/125667/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"What educational need does the dissertation address?","Question",{"text":75,"@type":76},"It addresses the need for interactive, step-level feedback in mathematics education, especially within Intelligent Tutoring Systems.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed SANYMS system provide feedback during problem solving?",{"text":80,"@type":76},"It uses a Computer Algebra System to produce correctness feedback at every step for equations chosen by the user.",{"name":82,"@type":73,"acceptedAnswer":83},"What role does machine learning play in the dissertation’s approach?",{"text":84,"@type":76},"Machine learning is used to develop a metric that measures similarity between equations after generalizing algebraic expressions.",{"name":86,"@type":73,"acceptedAnswer":87},"How are expert solutions used to generate next-step hints?",{"text":88,"@type":76},"A small set of expert-solved equations is incorporated into a directed graph to provide next-step hints for equation types and solution paths the system has not previously seen.","https://schema.org",{"og:url":52,"og:type":91,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":93,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":96},[97,101,105,109,114,119,124,127,132,135,139],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},"Exam",70,"exam",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},5,"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},6,"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":125,"slug":126},30,"research-report",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":130,"slug":131},9,"Religion & Spirituality",20,"religion-spirituality",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":130,"slug":134},"World Cup","world-cup",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":136,"slug":138},10,"Lifestyle","lifestyle",{"id":140,"doc_module":4,"doc_module_name":46,"category_name":141,"show_sort_weight":110,"slug":142},19,"General","general"]