believe their students should “really understand” • Others desire their students to “internalize knowledge” • Still others want their students to “grasp the core or essence” or “comprehend” • Specifically, what does a student do who "really understands" which he does not do when he does not understand? There was no common vocabulary among teachers to discuss their curriculum outcomes with other teachers.

the teachers only catered to students low level of cognition. • In order for students to master or excel at a subject, they need to be taught lessons that would exercise their higher level of cognition. • Benjamin Bloom along with other fellow scientist’s developed a taxonomy • as a means for teachers to have a common vocabulary to define the curriculum outcomes in the cognitive area

and from concrete to abstract. • The taxonomy was assumed to have a cumulative hierarchy; • mastery of a simple category was a prerequisite to the mastery of the next more complex category.

and from concrete to abstract. • The taxonomy allowed for some overlaps across the categories relaxing the cumulative hierarchical assumption • mastery of a simple category was not necessarily a prerequisite to the mastery of the next more complex category.

computational model of student Cognition • Use this model as a virtual student – to simulate student behavior • Design and conduct experiments on this virtual student

• Knowledge Tracing Techniques • Bayesian Knowledge Tracing (BKT) • Performance Factor Analysis (PFA) • Item Response Theory (IRT) • None of these available Knowledge Tracing Techniques can capture • Dynamic relationships between different cognitive skills • Lack flexibility and predictive power

knowledge) • Hidden state is a function of itself and input • Hidden state evolves with student’s performance • LSTMs: maintain a memory like students do • Both short term and long term

• Models the knowledge acquisition process of the student • Even trying to consider the knowledge retention, long term memory, short term memory and practice effects • Explores and figures out the links and knowledge dependencies between different skills • The skills may be very distant and unrelated • Skill Discovery

• Grade 2 to 9 • More than 100,000 students • More than 100 schools across India • Subjects: Mathematics and Science • Indian Boards of Education: CBSE, KASB, ICSE, …

(having at least two btlos) • Btlo – (Revised) Bloom’s Taxonomy Learning Objective • 1,03,593 students • 10,158 problems • 41.7 million data points • 29.7 million solved (71 %) • 22.7 million solved-fast (54%)

btlos are used as features. • The input vector is a series of btlos (tagged to the problems attempted by the student) and their corresponding outcomes of the problem attempts: solved and solved-fast in our case. • For instance, if an ssc consists of three btlos, the input consists of three neurons per btlo, one representing whether the interaction belonged to that btlo, one for solved and one for solved-fast. • The model outputs the probability that the problem will be solved and solved-fast for each btlo, amounting to two output neurons per btlo.

the skills are judged on their relative (median) complexity. • Clearly observed in the lower learning objectives - Remember, Understand and Apply • But, it is not a strict hierarchy in the sense that it allows for overlaps even among the non-adjacent skills, ensuring higher order skills do not subsume lower order skills.

all the higher order skills. Understand might be force fitted and seems out of place. • Understand was not included in the Original Taxonomy for the very similar reason that, Understand for all the practical purposes actually means anything from Comprehension to Synthesis. • Despite of that, Understand was included in the Revised Taxonomy considering its widespread usage as a synonym of Comprehension.