TY - GEN
T1 - Interpreting freeform equation solving
AU - Rafferty, Anna N.
AU - Griffiths, Thomas L.
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - Learners’ step-by-step solutions can offer insight into their misunderstandings. Because of the difficulty of automatically interpreting freeform solutions, educational technologies often structure problem solving into particular patterns. Hypothesizing that structured interfaces may frustrate some learners, we conducted an experiment comparing two interfaces for solving equations: one requires users to enter steps in an efficient sequence and insists each step be mathematically correct before the user can continue, and the other allows users to enter any steps they would like. We find that practicing equation solving in either interface was associated with improved scores on a multiple choice assessment, but that users who had the freedom to make mistakes were more satisfied with the interface. In order to make inferences from these more freeform data, we develop a Bayesian inverse planning algorithm for diagnosing algebra understanding that interprets individual equation solving steps and places no restrictions on the ordering or correctness of steps. This algorithms draws inferences and exhibits similar confidence based on data from either interface. Our work shows that inverse planning can interpret freeform problem solving, and suggests the need to further investigate how structured interfaces affect learners’ motivation and engagement.
AB - Learners’ step-by-step solutions can offer insight into their misunderstandings. Because of the difficulty of automatically interpreting freeform solutions, educational technologies often structure problem solving into particular patterns. Hypothesizing that structured interfaces may frustrate some learners, we conducted an experiment comparing two interfaces for solving equations: one requires users to enter steps in an efficient sequence and insists each step be mathematically correct before the user can continue, and the other allows users to enter any steps they would like. We find that practicing equation solving in either interface was associated with improved scores on a multiple choice assessment, but that users who had the freedom to make mistakes were more satisfied with the interface. In order to make inferences from these more freeform data, we develop a Bayesian inverse planning algorithm for diagnosing algebra understanding that interprets individual equation solving steps and places no restrictions on the ordering or correctness of steps. This algorithms draws inferences and exhibits similar confidence based on data from either interface. Our work shows that inverse planning can interpret freeform problem solving, and suggests the need to further investigate how structured interfaces affect learners’ motivation and engagement.
UR - http://www.scopus.com/inward/record.url?scp=84949057530&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84949057530&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-19773-9_39
DO - 10.1007/978-3-319-19773-9_39
M3 - Conference contribution
AN - SCOPUS:84949057530
SN - 9783319197722
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 387
EP - 397
BT - Artificial Intelligence in Education - 17th International Conference, AIED 2015, Proceedings
A2 - Conati, Cristina
A2 - Heffernan, Neil
A2 - Mitrovic, Antonija
A2 - Felisa Verdejo, M.
PB - Springer Verlag
T2 - 17th International Conference on Artificial Intelligence in Education, AIED 2015
Y2 - 22 June 2015 through 26 June 2015
ER -