Computer-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 computer-based 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.
We introduce the Show and Name your Math Steps (SANYMS) ITS, which uses a Computer Algebra System to provide correctness feedback at every step of problem-solving on a wide variety of equations of the user’s choice. Using the data obtained by this novel structure, we use machine learning to develop a metric that measures the similarity between equations. After using a process to generalize equations and other algebraic expressions, we incorporate a small set of expert-solved equations into a directed graph to provide next-step hints for a wide variety of equations and solution paths that SANYMS has never seen. The final SANYMS ITS combines the versatility of online equation solvers that provide full solutions, with the important benefits of users constructing their own solutions.
","abstract_html":"<p>Computer-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 computer-based 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.</p> <p>We introduce the Show and Name your Math Steps (SANYMS) ITS, which uses a Computer Algebra System to provide correctness feedback at every step of problem-solving on a wide variety of equations of the user’s choice. Using the data obtained by this novel structure, we use machine learning to develop a metric that measures the similarity between equations. After using a process to generalize equations and other algebraic expressions, we incorporate a small set of expert-solved equations into a directed graph to provide next-step hints for a wide variety of equations and solution paths that SANYMS has never seen. The final SANYMS ITS combines the versatility of online equation solvers that provide full solutions, with the important benefits of users constructing their own solutions.</p>","abstract_has_math":false,"creators":["Ford, Sam"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Computational and Data Sciences","degree_department":null,"school":null,"contributors":["Mohamed Allali","Erik Linstead","Adrian Vajiac"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-05-01T07:00:00Z","date_published":"2023-05-01T07:00:00Z","updated_at":"2026-07-24T01:38:31Z","subjects":["Computer Algebra System","Intelligent Tutoring System","Machine Learning","Embedding","Metric Learning","Data Science","Educational Technology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.chapman.edu/cads_dissertations/33","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mohamed Allali","Erik Linstead","Adrian Vajiac"]},{"key":"dc:creator","label":"Author","values":["Ford, Sam"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2025-05-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computational and Data Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Algebra System","Intelligent Tutoring System","Machine Learning","Embedding","Metric Learning","Data Science","Educational Technology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.chapman.edu/cads_dissertations/33"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Computer-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 computer-based 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.
We introduce the Show and Name your Math Steps (SANYMS) ITS, which uses a Computer Algebra System to provide correctness feedback at every step of problem-solving on a wide variety of equations of the user’s choice. Using the data obtained by this novel structure, we use machine learning to develop a metric that measures the similarity between equations. After using a process to generalize equations and other algebraic expressions, we incorporate a small set of expert-solved equations into a directed graph to provide next-step hints for a wide variety of equations and solution paths that SANYMS has never seen. The final SANYMS ITS combines the versatility of online equation solvers that provide full solutions, with the important benefits of users constructing their own solutions.
"]},{"key":"dc:source","label":"Dc Source","values":["S. 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/10.36837/chapman.000469"]},{"key":"dc:title","label":"Title","values":["Integration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System"]}]}],"canonical_facts":{"dc:contributor":["Mohamed Allali","Erik Linstead","Adrian Vajiac"],"dc:creator":["Ford, Sam"],"dc:date.available":["2025-05-01T07:00:00Z"],"dc:description.abstract":["Computer-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 computer-based 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.
We introduce the Show and Name your Math Steps (SANYMS) ITS, which uses a Computer Algebra System to provide correctness feedback at every step of problem-solving on a wide variety of equations of the user’s choice. Using the data obtained by this novel structure, we use machine learning to develop a metric that measures the similarity between equations. After using a process to generalize equations and other algebraic expressions, we incorporate a small set of expert-solved equations into a directed graph to provide next-step hints for a wide variety of equations and solution paths that SANYMS has never seen. The final SANYMS ITS combines the versatility of online equation solvers that provide full solutions, with the important benefits of users constructing their own solutions.
"],"dc:identifier":["https://digitalcommons.chapman.edu/cads_dissertations/33"],"dc:source":["S. 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/10.36837/chapman.000469"],"dc:subject":["Computer Algebra System","Intelligent Tutoring System","Machine Learning","Embedding","Metric Learning","Data Science","Educational Technology"],"dc:title":["Integration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System"],"thesis:degree_discipline":["Computational and Data Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T01:38:31Z"}