Entropy-based sequences of educational modules

Abstract

Techniques disclosed herein can determine sequences for educational units by evaluating entropies of multiple potential sequences and biasing selection of next units towards those associated with high sequence entropies. Further, an analysis can determine which units are under-represented (relative to a target proportion) in a past sequence and bias towards inclusion of an under-represented unit in the sequence. The available units that are considered for potential selection can include those matched to a learner's skill (e.g., such that all pre-requisite units have been mastered but the unit itself has not been mastered). Thus, techniques can generate sequences of units that promote unit variation and nonetheless conform to relative unit frequencies and skill level appropriateness.

What is claimed is: 
     
         1 . A method for determining sequences for presentation of educational content objects or educational questions, the method comprising:
 identifying a set of educational-item types, each education-item type in the set of educational-item type including a type of educational content object or a type of educational question;   identifying a target proportion of representation of an educational-item type in the set of educational-item types;   accessing a past sequence of educational-item types, the past sequence of educational-item types including a series of identifiers of educational-item types in the set of educational-item types;   for each educational-item type in the set of educational-item types:
 appending an identifier of the educational-item type to the past sequence of educational-item types to produce a potential sequence; 
 determining an entropy of the potential sequence; 
 determining a proportion of the identifiers in the past sequence or potential sequence that identify the educational-item type; and 
 determining a score based on the entropy, the proportion and the target proportion for the educational-item type; 
   selecting an educational-item type from amongst the set of educational-item types based on the determined scores; and   appending the past sequence with the selected educational-item type.   
     
     
         2 . The method for determining sequences for presentation of educational content objects or educational questions as recited in  claim 1 , further comprising:
 determining a past-sequence entropy of the past sequence of educational-item types; and   defining an entropy-delta metric for each educational-item type in the set of educational-item types based on a difference between the determined entropy and the past-sequence entropy,   wherein the score for each educational-item type in the set of educational-item types is determined based on the entropy-delta metric for the educational-item type.   
     
     
         3 . The method for determining sequences for presentation of educational content objects or educational questions as recited in  claim 1 , further comprising:
 defining a proportion-delta metric for each educational-item type in the set of educational-item types based on a difference between the determined proportion and the target proportion for the educational-item type,   wherein the score for each educational-item type in the set of educational-item types is determined based on the proportion-delta metric for the educational-item type.   
     
     
         4 . The method for determining sequences for presentation of educational content objects or educational questions as recited in  claim 1 , further comprising, for each educational-item type in the set of educational-item types:
 generating a normalized entropy metric based on of the determined entropy and a normalization factor based on entropies determined for other educational-item types in the set of educational-item types; and   generating a normalized proportion metric based on of the determined proportion and a normalization factor based on proportions determined for other educational-item types in the set of educational-item types;   wherein the score is determined based on the normalized entropy metric and the normalized proportion metric.   
     
     
         5 . The method for determining sequences for presentation of educational content objects or educational questions as recited in  claim 1 , further comprising:
 identifying a content object from amongst the set of content objects that corresponds to the selected educational-item type; and   causing the identified content object to be presented .   
     
     
         6 . The method for determining sequences for presentation of educational content objects or educational questions as recited in  claim 1 , wherein each educational-item type in the set of educational-item types includes a type of educational content object. 
     
     
         7 . The method for determining sequences for presentation of educational content objects or educational questions as recited in  claim 1 , further comprising:
 determining that each educational-item type in the set of educational-item types is to be made accessible to a particular learner;   monitoring performance of the learner;   determining that a new educational-item type is to be added to the set of educational-item types or that an existing educational-item type in the set of educational-item types is to be removed from the set;   modifying the set of educational-item types to include the new educational-item type or remove the existing educational-item type; and   evaluating the modified set of educational-item types to select a second educational-item type for inclusion in the sequence.   
     
     
         8 . A system for determining sequences for presentation of educational content objects or educational questions, the system comprising:
 an educational-item type availer that identifies a set of educational-item types, each education-item type in the set of educational-item type including a type of educational content object or a type of educational question;   a target-proportion definer defines a target proportion of representation of an educational-item type in the set of educational-item types within a sequence of educational-item types;   an entropy-based sequence engine that:
 accesses a past sequence of educational-item types, the past sequence of educational-item types including a series of identifiers of educational-item types in the set of educational-item types; 
 for each educational-item type in the set of educational-item types:
 appends an identifier of the educational-item type to the past sequence of educational-item types to produce a potential sequence; 
 determines an entropy of the potential sequence; 
 determines a proportion of the identifiers in the past sequence or potential sequence that identify the educational-item type; and 
 determines a score based on the entropy, the proportion and the target proportion for the educational-item type; 
 
 selects an educational-item type from amongst the set of educational-item types based on the determined scores; and 
 appends the past sequence with the selected educational-item type. 
   
     
     
         9 . The system for determining sequences for presentation of educational content objects or educational questions as recited in  claim 8 , wherein the entropy-based sequence engine further:
 determines a past-sequence entropy of the past sequence of educational-item types; and   defines an entropy-delta metric for each educational-item type in the set of educational-item types based on a difference between the determined entropy and the past-sequence entropy,   wherein the score for each educational-item type in the set of educational-item types is determined based on the entropy-delta metric for the educational-item type.   
     
     
         10 . The system for determining sequences for presentation of educational content objects or educational questions as recited in  claim 8 , wherein the entropy-based sequence engine further:
 defines a proportion-delta metric for each educational-item type in the set of educational-item types based on a difference between the determined proportion and the target proportion for the educational-item type,   wherein the score for each educational-item type in the set of educational-item types is determined based on the proportion-delta metric for the educational-item type.   
     
     
         11 . The system for determining sequences for presentation of educational content objects or educational questions as recited in  claim 8 , wherein the entropy-based sequence engine further, for each educational-item type in the set of educational-item types:
 generates a normalized entropy metric based on of the determined entropy and a normalization factor based on entropies determined for other educational-item types in the set of educational-item types; and   generates a normalized proportion metric based on of the determined proportion and a normalization factor based on proportions determined for other educational-item types in the set of educational-item types;   wherein the score is determined based on the normalized entropy metric and the normalized proportion metric.   
     
     
         12 . The system for determining sequences for presentation of educational content objects or educational questions as recited in  claim 8 , further comprising a content manager that:
 identifies a content object from amongst the set of content objects that corresponds to the selected educational-item type; and   causes the identified content object to be presented .   
     
     
         13 . The system for determining sequences for presentation of educational content objects or educational questions as recited in  claim 8 , wherein each educational-item type in the set of educational-item types includes a type of educational content object. 
     
     
         14 . The system for determining sequences for presentation of educational content objects or educational questions as recited in  claim 8 , wherein the educational-item type availer further:
 determines that each educational-item type in the set of educational-item types is to be made accessible to a particular learner;   monitors performance of the learner;   determines that a new educational-item type is to be added to the set of educational-item types or that an existing educational-item type in the set of educational-item types is to be removed from the set; and   modifies the set of educational-item types to include the new educational-item type or remove the existing educational-item type;   wherein the entropy-based sequence engine further evaluates the modified set of educational-item types to select a second educational-item type for inclusion in the sequence.   
     
     
         15 . A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, including instructions configured to cause one or more data processors to perform actions including:
 identifying a set of educational-item types, each education-item type in the set of educational-item type including a type of educational content object or a type of educational question;   identifying a target proportion of representation of an educational-item type in the set of educational-item types within a sequence of educational-item types;   accessing a past sequence of educational-item types, the past sequence of educational-item types including a series of identifiers of educational-item types in the set of educational-item types;   for each educational-item type in the set of educational-item types:
 appending an identifier of the educational-item type to the past sequence of educational-item types to produce a potential sequence; 
 determining an entropy of the potential sequence; 
 determining a proportion of the identifiers in the past sequence or potential sequence that identify the educational-item type; and 
 determining a score based on the entropy, the proportion and the target proportion for the educational-item type; 
   selecting an educational-item type from amongst the set of educational-item types based on the determined scores; and   appending the past sequence with the selected educational-item type.   
     
     
         16 . The computer-program product as recited in  claim 15 , wherein the actions further include:
 determining a past-sequence entropy of the past sequence of educational-item types; and   defining an entropy-delta metric for each educational-item type in the set of educational-item types based on a difference between the determined entropy and the past-sequence entropy,   wherein the score for each educational-item type in the set of educational-item types is determined based on the entropy-delta metric for the educational-item type.   
     
     
         17 . The computer-program product as recited in  claim 15 , wherein the actions further include:
 defining a proportion-delta metric for each educational-item type in the set of educational-item types based on a difference between the determined proportion and the target proportion for the educational-item type,   wherein the score for each educational-item type in the set of educational-item types is determined based on the proportion-delta metric for the educational-item type.   
     
     
         18 . The computer-program product as recited in  claim 15 , wherein the actions further include, for each educational-item type in the set of educational-item types:
 generating a normalized entropy metric based on of the determined entropy and a normalization factor based on entropies determined for other educational-item types in the set of educational-item types; and   generating a normalized proportion metric based on of the determined proportion and a normalization factor based on proportions determined for other educational-item types in the set of educational-item types;   wherein the score is determined based on the normalized entropy metric and the normalized proportion metric.   
     
     
         19 . The computer-program product as recited in  claim 15 , wherein the actions further include:
 identifying a content object from amongst the set of content objects that corresponds to the selected educational-item type; and   causing the identified content object to be presented.   
     
     
         20 . The computer-program product as recited in  claim 15 , wherein each educational-item type in the set of educational-item types includes a type of educational content object.