Patent Publication Number: US-6212358-B1

Title: Learning system and method based on review

Description:
This application is a continuation of U.S. patent application Ser. No. 08/968,681, filed on Nov. 12, 1997, now abandoned, which is a continuation of U.S. patent application Ser. No. 08/675,391, filed on Jul. 2, 1996, now U.S. Pat. No. 5,863,208, and incorporated by reference into this application. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to education, and more particularly to using reviews to enrich the learning process in a computer-aided educational system and method. 
     Review is very important in any educational or training systems. Most of us have encountered situations where we have forgotten what we have learnt, and would appreciate some forms of review to refresh our memory. As subject matter becomes more complicated, our need for review increases, especially when we are learning an inter-disciplinary subject, or solving inter-disciplinary problems. For example, when we encounter the problem of performance degradation due to temperature increase in an integrated circuit, probably some of us would like to design a heat-sink with fins on the integrated circuit, and would like to have a review on the subject of heat-flow on a heat-sink with different types of fins. 
     In a typical computer-aided educational system, there is no review. Those systems assume the students remember everything they have learnt, and just keep on teaching new areas. If a student wants to review certain subject matter, she can always go back and search for it. However, most students generally do not go back; they typically proceed forward and believe that once they have learnt a subject, they will never forget. As forgetfulness and lack in understanding start to build up, not for long a typical student will be totally lost, with his interest in learning the subject significantly diminished. 
     There is one exception to the typical educational system; it provides students with reviews. However, those reviews are not dynamic—they are just fixed reviews, which are not personalized. Such a system provides a student a set of study-plan. After the system has presented the study-plan to the student, the system automatically provides a summary of what the student has just learnt. Such an approach is not useful. Since the student has just studied the material, the probability of the student to forget is quite low. Also, the student might understand fully what she has just studied. The system does not know, and does not care. The reviews are fixed. Under no condition would the system not present the review to the student. Such fixed reviews not catered to the needs of individual students are not very helpful to the students. 
     It should be obvious from the foregoing that there is still a need for a computer-aided educational system and method that is catered specifically to the needs of individual students, or the characteristics of the subject, through dynamic review so as to reinforce each student&#39;s learning in a subject. 
     SUMMARY OF THE INVENTION 
     The invented computer-aided educational system and method provide dynamic reviews for individual students. After a student has learnt certain areas in a subject, summarized learning materials on those areas are selectively generated for the student so as to reinforce the student&#39;s learning in the subject through reviews. Unlike prior systems, the reviews in the present invention are dynamic; they are specifically tailored to the needs of individual students, or the characteristics of the subject. 
     The present invention is applicable to any subject that can be taught by a computer. A subject in the present invention is divided into areas that the student has learnt and those that the student has not learnt; they are referred to as learnt line-items and un-learnt line-items respectively. The line-items are stored in a line-item storage-medium. 
     In one embodiment, the present invention selects an un-learnt line-item, and generates detailed learning materials for the un-learnt line-item. Then a learnt line-item is selected based on one or more learnt-line-item-selection rules, depending on factors such as the time elapsed from the time when the student learnt that line-item, the level achieved by the student in learning that line-item, its difficulty level, whether that learnt line-item is related to the selected un-learnt line-item, and whether that learnt line-item has been selected before. Then, the invention generates summarized-learning materials on the selected learnt line-item for the student to review. 
     Different materials are applicable for learning. The summarized-learning materials include study-plans. The detailed learning materials may further include questions, in addition to study-plans. 
     For an un-learnt line-item, after presenting the generated learning material to the student, the present invention assesses the student&#39;s understanding in the line-item. If the assessment is satisfactory, the un-learnt line-item is re-classified as a learnt line-item. 
     In another embodiment, the present invention accesses a line-item probability value, which is used to select a line-item. If the line-item is an un-learnt line-item, the invention generates detailed learning materials for the student; and if the student is successful in learning the materials, the invention re-classifies the line-item to a learnt line-item. If the line-item is a learnt line-item, the invention generates summarized learning materials for the student. The invention then repeats and selects another line-item. 
     Other aspects and advantages of the present invention will become apparent from the following detailed description, which, when taken in conjunction with the accompanying drawings, illustrates by way of example the principles of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows one embodiment of a line-item entry in the present invention. 
     FIG. 2 shows an embodiment of the present invention. 
     FIGS. 3A-B show one embodiment of a system implementing the present invention. 
     FIG. 4 shows a set of steps to implement one embodiment of the present invention 
     FIG. 5 shows an example of a difficulty hierarchy in the present invention. 
     FIG. 6 shows a set of steps to generate a detailed learning material in the present invention. 
     FIG. 7 shows a number of criteria to select a learnt line-item in the present invention. 
     FIG. 8 shows a set of steps to implement another embodiment of the present invention. 
     FIG. 9 shows a set of steps to select a line-item based on a line-item probability. 
    
    
     Same numerals in FIGS. 1-9 are assigned to similar elements in all the figures. Embodiments of the invention are discussed below with reference to FIGS. 1-9. However, those skilled in the art will readily appreciate that the detailed description given herein with respect to these figures is for explanatory purposes as the invention extends beyond these limited embodiments. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is applicable to teach any subject that can be taught by a computer. The subject may be a subject taught in one-semester or in a year, or in just one class session. The subject may cover inter-disciplinary areas, such as electrical engineering and thermodynamics, or computer networking and programming techniques. In the following, mathematics is the subject used to illustrate the present invention. 
     In one embodiment, the subject is divided into major-topics, with each major-topic subdivided into minor-topics, and with each minor-topic further subdivided into line-items. Each line-item typically covers one well-defined area in the subject. In another embodiment, the subject is further divided into more levels below the line-items; and in a third embodiment, the subject is just divided into line-items. 
     As an example of line-items, if the major-topic is high school algebra, then it can be divided into the following line-items, with bracketed terms served as comments: 
     High School Algebra (the major-topic) 
     (Minor-topics under the major-topic) 
     Decimal Numbers 
     Polynomials 
     Linear Equations 
     Quadratic Equations 
     . . . 
     Integers 
     (Line-items under the minor-topic of integers) 
     Addition &amp; Subtraction (Difficulty level 1) 
     Multiplication (Difficulty level 2) 
     Division (Difficulty level 2) 
     Prime Numbers (Difficulty level 3) 
     Factorization (Difficulty level 3) 
     Common Divisor (Difficulty level 4) 
     . . . 
     Fractions 
     (Line-items under the minor-topic of fractions) 
     Addition &amp; Subtraction (+/−) with Common Denominator (Difficulty level 3) 
     +/− with Integers (Difficulty level 4) 
     +/− without Common Denominator (Difficulty level 5) 
     Multiplication and Divisions (*,/) with Integers (Difficulty level 5) 
     *,/ with fraction (Difficulty level 6) 
     Compound Fractions (Difficulty level 6) 
     Fraction Reduction (Difficulty level 7) 
     Ratios and Proportions (Difficulty level 7) 
     Another example with the minor topic being differential calculus is as follows: 
     Calculus (major topic) 
     Differential calculus (minor topic) 
     Fractions (Difficulty level 1) 
     Polynomials (Difficulty level 1) 
     Exponential Functions (Difficulty level 1) 
     Differentiation (Difficulty level 2) 
     Differentiate a sum (Difficulty level 3) 
     Differentiate a product (Difficulty level 3) 
     Differentiate a quotient (Difficulty level 4) 
     In one embodiment, each line-item has a difficulty level. The bracketed difficulty level next to each line-item in the above example indicates how difficult one line-item is relative to other line-item in the subject, or how significant one is relative to another. A line-item whose difficulty level is at a low number implies that it is a relatively easy line-item, or that it is a relatively less important line-item. Typically, a student learning a subject starts from learning line-items at the lowest difficulty level. 
     The lists of items in the above examples are generated based on expert knowledge on the subject of mathematics. With the proper instruction, such as through reading the present specification, generating such lists with the difficulty levels should be obvious to experts in the subject. The more knowledgeable the expert, the more complete the sets of items. 
     When the student starts learning the subject, all the line-items are classified as un-learnt line-items. As the student progresses through the subject, he would have learnt some of the line-items, and those un-learnt line-items would then be re-classified as learnt line-items. 
     Different criteria may be used to evaluate if the student has learnt a line-item. Generally, learning implies achieving a preset mastery level. This level depends, for example, on the subject and the line-item, and is determined by education experts in that subject and in the behavior of human learning. In the present invention, one does not have to totally understand every aspect of a line-item before he is considered to have learnt that line-item. For example, achieved a passing grade in a line-item may indicate having learnt that line-item. In one embodiment, as long as there is an evaluation based on a preset level, and the student has reached or exceeded that level, the student is considered to have learnt that line-item. In another embodiment, as long as there are two types of learning materials on a line-item for the student (detailed learning materials and summarized learning materials), the present invention assumes that there is a preset level in learning that line-item. As the student progresses from the detailed learning materials to the summarized learning materials, the student has achieved the preset level in the detailed learning materials, with the summarized learning materials serving as a review for the line-item. 
     FIG. 1 shows one embodiment  50  of a line-item entry E representing a line-item. For the sake of clarity, that line-item is known as a parent line-item in this example. The entry E includes a line-item-root  52 , an associated line-item-root list  54 , and line-item attributes  56 . 
     The line-item root  52  includes the corresponding line-item  64  (the parent line-item) and its root, which in one embodiment includes its subject  58 , its major topic  60 , and its minor topic  62 . The associated line-item-root list  54  may include one or more associated line-item roots, such as  66 , with each representing a line-item (a child line-item) that is related to the parent line-item. For example, if the parent line-item is differentiation, the children line-items may include exponential functions, logarithmic functions and hyperbolic functions. 
     Each associated line-item-root list  54  denotes the corresponding child line-item, its roots, and its association factor, such as  88 . The association factor represents the degree of relatedness of each child line-item with the parent line-item  64 . For example, the parent line-item  56  is computer network modeling using Poisson process; the children line-items may include the stochastic process and the Guassian process. The stochastic process is more related to the Poisson process than the Guassian process. Thus, the association factor of the stochastic process has a higher value than the association factor of the Guassian process. 
     The line-item attributes  56  describe a number of attributes for the parent line-item. In one embodiment, the attributes of the parent line-item include, for example, its mode  70 , its difficulty level  72 , its mastery level  74 , its time-stamp  76 , and its review-counter  78 . The mode  70  denotes whether the student has learnt the line-item (the learnt mode), or the student has not learnt the line-item (the un-learnt mode). The difficulty level  72  denotes the level of difficulty of the parent line-item as compared to other line-items. If the line-item is a learnt line-item, the mastery level  74  denotes the level achieved by the student in learning that line-item; the time-stamp  76  denotes the time when the student achieved that mastery level; and the review-counter  78  denotes the number of times that line-item has been reviewed. Initially, all line-items are in the un-learnt mode, with the mastery levels and the time-stamps not being set, and with the review-counter being zero. 
     FIG. 2 shows one embodiment of the computer-aided-educational system  100  of the present invention. As an overview of some of its major components, the system  100  includes a line-item storage-medium  106 , which stores the learnt and un-learnt line-items of the subject. A selector  102  in the system  100 , based on some rules from a rules storage-medium  104 , selects a line-item from the line-item storage-medium  106 . For the selected line-item, a learning-material generator generates learning materials for the student. In one embodiment, the generator includes a study-plan generator  108 , which accesses a study-plan from a study-plan storage-medium  116  for a presenter  114  to present to a student. In another embodiment, the learning material generator further includes a question generator  110 . The question generator  110  accesses a set of questions from a question storage-medium  118  and sends the questions to the presenter  114  to be presented to the student. Then, an assessor  112  analyzes the student&#39;s perforrnance, and sends the results to the selector  102 , which then selects another line-item for the student. 
     FIG. 3A shows one embodiment of a system  150  implementing the present invention, preferably in software and hardware. The system  150  includes a server computer  152  and a number of client computers, such as  154 . Each client computer communicates to the server computer  152  through a dedicated communication link, or a computer network  156 . 
     FIG. 3B shows one embodiment of the client computer  154 . It typically includes a bus  159  connecting a number of components, such as a processing unit  160 , a main memory  162 , an I/O controller  164 , a peripheral controller  166 , a graphics adapter  168  and a network interface adapter  170 . The I/O controller  164  is connected to components, such as a harddisk drive  172  and a floppy disk drive  174 . The peripheral controller  166  is connected to components, such as a keyboard  176 . The graphics adapter  168  is connected to a monitor  178 ; and the network interface adapter  170  is connected to the network  120 . The network includes the internet, an intranet, the world wide web and other forms of networks. 
     Different components of the present invention can be in different elements shown in FIGS. 3A-B. For example, the presenter  114  and the assessor  112  can be in a client computer; the selector  102 , the question generator  110 , the study-plan generator  108 , and the line-item storage-medium  106  can be in the server computer  152 . In another embodiment, the selector  102 , the question generator  110  and the study-plan generator  108  are also in a client computer. A number of operations in the present invention can be implemented by software, which is controlled, for example, by the processing unit  160 . In yet another embodiment, the number of operations implemented by software can be stored in a storage-medium, which can be, for example, the main memory  162  or a CD read-only-memory. 
     FIG. 4 shows a set of steps  200  to implement one embodiment of the present invention. First, an un-learnt line-item is selected (step  202 ), and detailed learning materials on the un-learnt line-item is generated (step  204 ) for the student. Then a learnt line-item is selected (step  206 ), and summarized learning materials on the learnt line-item is generated (step  208 ). The following further describes each of the above steps. 
     Different methods may be used to select an un-learnt line-item (step  202 ). In one embodiment, the selector  102  first isolates the one or more un-learnt line-items that is at the lowest difficulty level among all the un-learnt line-items. Then out of the one or more isolated un-learnt line-items, one is randomly selected. 
     In another embodiment, all the line-items of a subject form a difficulty hierarchy, with the subject itself at the top of the hierarchy, and the one or more easiest line-items at the lowest level of the hierarchy. Selecting an un-learnt line-item starts from the bottom of the hierarchy on up. If there are a number of un-learnt line-items at the same level of the hierarchy, one of them is randomly selected. FIG. 5 shows an example of such an hierarchy with some of the terms in the figure defined as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Int 
                 Integer 
               
               
                   
                 +/− 
                 Addition and subtraction 
               
               
                   
                 * 
                 Multiplication 
               
               
                   
                 / 
                 Division 
               
               
                   
                 w/ 
                 With 
               
               
                   
                 w/o 
                 Without 
               
               
                   
                 Frt 
                 Fraction 
               
               
                   
                 Comm Denom 
                 Common Denominator 
               
               
                   
                   
               
            
           
         
       
     
     After the un-learnt line-item has been selected, a learning material generator then generates detailed learning materials (step  204 ) for the student. FIG. 6 shows a set of steps  250  to generate detailed learning materials in the present invention. The selector  102  sends to the study-plan generator  108  the selected un-learnt line-item. The generator  108  accesses (step  252 ) from the study-plan storage medium  116  a set of detailed study-plan on the un-learnt line-item. 
     In one embodiment, the selector  102  sends the line-item entry E to the study-plan generator  108  to retrieve the corresponding study-plan from the study-plan storage-medium  116 . Typically, there are a number of study-plan entries in the storage-medium  116 , and they can be in the following format: 
     (line-item root, mode, study-plan) 
     The following serves as examples of a detailed study-plan for differentiating polynomial: 
     First, the system teaches the approach to generate derivatives based on the basic principle in differentiation, such as: 
     
       
           df ( x )/ dx=lim   h→0 (( f ( x+h )− f ( x )) /h )  
       
     
     Then the system teaches the generalized equation, such as: 
     
       
         (( dΣa   i   x   i ) /dx )=(Σ i*a   i   x   i−1 )  
       
     
     Finally, the system teaches the importance of and the way to find optima and minima by solving the following equation: 
     
       
         (( dΣa   i   x   i )/ dx )=0  
       
     
     Based on the line-item root and its mode in the line-item entry E, and with one set of detailed study-plan per un-learnt line-item, the generator  108  retrieves from the study-plan storage-medium  116 , the corresponding detailed study-plan. Creating detailed study-plans for a subject should be obvious to experts in the subject, and will not be further discussed in this application. 
     The generator  108  then sends the retrieved study-plan with the line-item entry E to the presenter  114 , which presents (step  254 ) the study-plan to the student. The study-plan can be a document containing studying materials for the un-learnt element. The document can be arranged as a list of screens, each of which covering part of the material. The presenter  114  typically includes the monitor  178 , which presents the study plan to the student, who can go from one screen to another with the keyboard  176 , or a mouse device. In another embodiment, the study plans are broadcast through a radio, or presented through a facsimile machine. 
     In this embodiment, as long as the study-plan has been presented to the student, it is assumed that the student has mastered the line-item. After the presentation, the study plan generator sends a mission-accomplished signal with the line-item entry E to the assessor  112 . Presumably, the student, by going through the study plan, should have learnt the line-item. 
     Then, the assessor  112  verifies the mission-accomplished signal, and sends it with the line-item entry E to the selector. The selector, based on rules in the rules-storage medium  104 , determines that the un-learnt line-item has been learnt. In the present situation, the rule is simply that once the study-plan has been presented, the line-item has been learnt. The selector  102  then re-classifies the mode in the entry E from un-learnt to learnt, stores the time when the line-item is re-classified in the time-stamp, and stores an identifier, such as “pass”, in the mastery level. The line-item with its modified entry E is stored in the line-item storage-medium  106 . 
     In another embodiment, after presenting to the student the detailed study-plan, questions are generated (step  256 ) and presented (step  258 ) to the students. Typical, students gain a better understanding on a subject through actively working on questions, than just through passively reading study plans. 
     In this embodiment, after the student indicates that he has finished studying the study-plan, the generator  110  accesses a set of questions from the question storage medium  118 , and sends the questions to the presenter  114  to be presented (step  258 ) to the student. In one embodiment, each question is embedded in a question entry, which is of the following format: 
     (line-item root, mode, question-body, answer). 
     The term “question-body” describes the body of a question. The following serves as an example: 
     Subject: Mathematics. 
     Major-topic: High School Algebra. 
     Minor-topic: Fraction. 
     Line-item: +/− with common denominator 
     Mode: Un-learnt 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Answer 
                 Question-body 
               
               
                   
                   
               
               
                   
                 28/37 
                 What is the sum of 2/37, 3/37, 8/37 and 15/37? 
               
               
                   
                 −2/43 
                 17/43 − 25/43 + 6/43 = ? 
               
               
                   
                   
               
            
           
         
       
     
     The selector  102  sends to the question generator  110  the line-item entry E. The question generator  110 , by matching the line-item root and the mode in the line-item entry E with the line-item root and the mode in the question entries, selects one or more question entries. For each question-entry selected, it is sent to the assessor  112 , with its question-body sent to the presenter  114  to be presented to the student. The student answers the questions, for example, by entering his answers through the keyboard  176  to the presenter  114 , and the results are sent to the assessor  112 . In another embodiment, the correct answers to the questions together with the student&#39;s answers are sent by the presenter  114  to the assessor  112 . 
     In yet another embodiment, the learning materials only include questions. For example, the learning materials are for the un-learnt line-item of differentiating exponential functions. A number of questions are generated, including the question on expanding an exponential function based on Taylor expansion, the question on differentiating the Taylor-expanded exponential function, whose answer is the original Taylor-expanded exponential function, and the question on differentiating the exponential function, whose answer is the exponential function. The presenter  114  bypasses study plans, and receives the questions, which are presented to the students. 
     Note that the formats of the learning materials may change as the student is learning. The student can learn one line-item based on questions, and another based on study-plans. As an example, in the above example of a minor topic being differential calculus, for the different line-items, all of them can be learnt through both study-plans and questions, except for the line-item of differentiation, which is typically learnt through a study-plan. That study-plan covers the general differentiation concept, such as the following: 
     
       
           df ( x )/ dx=lim   h→0 (( f ( x+h )− f ( x )) /h )  
       
     
     For the embodiment where the learning materials include questions, the assessor  112  assesses (step  260 ) the student&#39;s answers by comparing the student&#39;s answers to the answers in the question entries previously received. Through the analysis, the assessor  112  determines the student&#39;s learning progress. 
     In one embodiment, the assessor  112  receives question entries from the question generator  110 . The assessor  112  also receives the student&#39;s answers with their corresponding question-bodies from the presenter  114 . For each question, using the question-body as a key, the assessor  112  evaluates the student&#39;s answer by matching it with the answer in the corresponding question-entry. 
     Note that generating the questions should be obvious to experts in the subject, and will not be further discussed in this application. 
     After the assessment, the assessor  112  sends the student&#39;s assessed results on the line-item back to the selector. If the study materials include questions, the student&#39;s assessed results can be in the form of a score, or a grade. If the study materials are study-plans only, the student&#39;s performance is an indicator depending on whether the plans have been presented to the student. The selector  102  based on rules stored in the rule storage-medium  104  determines if the assessed results are satisfactory or not (step  262 ). For example, a score of 70 or higher is satisfactory, and 69 or lower is unsatisfactory; a grade of C or better is satisfactory, and D or lower is unsatisfactory; or a study-plan, after presentation, is considered as satisfactory. If the assessed results are unsatisfactory, then the system proceeds as if the student has not learnt that line-item. 
     If the selector  102  is satisfied with the student&#39;s assessed results in the selected un-learnt element, as discussed above, the selected un-learnt line-item is re-classified as a learned line-item, by having its mode field changed to the learnt mode, with the time when this occurs stored in the time-stamp, and with the student&#39;s assessed results stored in the mastery level, such as  74 . The modified entry E is re-stored in the line-item storage medium  106 . 
     In one embodiment, the assessor  112  passes an assessment entry back to the selector  102 . The format of an assessment entry is similar to that of a line-item entry, except the mastery level field is replaced by the student&#39;s assessed results in the corresponding line-item. 
     After the generation of the detailed learning materials (step  204 ), the selector  102  selects a learnt line-item (step  206 ) based on one or more learnt-line-item-selection rules stored in the rules storage-medium. FIG. 7 shows examples of factors affecting such rules to select a learnt line-item in the present invention. 
     In one embodiment, the learnt line-item is selected depending on the time elapsed from the time when the line-item is re-classified from the un-learnt to the learnt mode (box  300 ). The selection process dis-favors the line-item that has just been re-classified because presumably the line-item is still fresh in the student&#39;s mind. As time passes, the student&#39;s memory begins to fade, and should be refreshed. Typically, a student starts to forget what he has learnt a number of weeks, such as three, after he has learnt it. Thus, in one embodiment, the selection process starts favoring reviewing the line-item that has been re-classified three weeks ago. 
     In another embodiment, the selection process dis-favors the line-item that has been re-classified long time ago because presumably the student has learnt other more difficult line-item during the interim period. This is similar to a student learning a subject in a semester. After the end of the semester, the student stops reviewing the subject, and starts studying a more difficult subject. Typically, a semester is about three months or twelve weeks. Thus, in one embodiment, the selection process begins to dis-favor reviewing the line-item that has been re-classified more than twelve weeks ago. 
     In one embodiment, the above elapsed time dependency in selection is embedded in a rule that is represented by the following equation: 
     
       
         Weight  w ( t )= k* e   −at *(1− e   −t ) b    
       
     
     where k, a, and b&gt;0. Here the time t starts counting from the time when the line-item is re-classified. Initially, the weight function w(t) increases as time t increases, peaking with time being equal to 1n ((a+b)/a). From that point onwards, the function decreases as time further increases. The values for a and b are chosen to determine the position of the peak, and the value for k is used to adjust the variance of the function. 
     The bigger the weight of a line-item, the better the chance for that line-item to be selected. As an example, the weight is chosen to peak when t is between three weeks (or 21 days) and twelve weeks (or 84 days), which averages to 53 days. Thus, w(t) peaks around 53 days, implying that: 
     
       
         1 n (( a+b ) /a )=53.  
       
     
     The above exponential weight function is just an example representing the dependency on time. Other weight functions are also applicable, such as the Chi&#39;s Square functions. 
     In another embodiment, selecting a learnt line-item depends on the mastery level achieved by the student (box  302 ) when the line-item was changed from the learnt mode to the un-learnt mode. The lower the grade or the level achieved by the student, the higher the chance to select that line-item because the educational system should reinforce the student&#39;s weaker areas. Again, this can be represented by a weight function, which depends on the mastery level achieved by the student. 
     In yet another embodiment, selecting a learnt line-item depends on the characteristics of the line-item, such as the difficulty level of the line-item (box  304 ). The more difficult the line-item, the higher the probability to select that line-item because it is more likely for the student to be weak in that line-item, or that line-item is more significant than other line-items. Again, the dependency on difficulty level can be represented by a weight function, which tracks the difficulty level of the line-item. 
     For another different embodiment, selecting a learnt line-item depends on whether that line-item is related to the most recently selected un-learnt line-item (box  306 ). This embodiment favors a learnt line-item that is related to the un-learnt line-item because the student may form the relationship himself through working on both of them. For example, the un-learnt line-item just learnt is differentiating exponential functions. Then one learnt item to review may be the hyperbolic sine and cosine functions. The idea is for the student to form the relationship himself that differentiating hyperbolic sine is the hyperbolic cosine, and vice versa. Typically, a student enjoys learning a subject and remembers it better if he thinks that he, by himself, has developed some insights in the subject. 
     One way to identify related line-items is from the line-item entry shown in FIG.  1 . Each line-item in an associated line-item root, such as  66 , is related to the line-item in the parent line-item root  52 . The degree of relatedness is represented by the association factor, such as  88 . The line-item that is more closely related to the parent line-item has a larger association factor than a line-item that is not as closely related. Line-items not listed in the associated line-item root-list are either not related or too remotely related to the line-item in the parent line-item  56 . In one embodiment, the weight w depends on the association factor. 
     In yet another embodiment, selecting a learnt line-item depends on whether that learnt line-item has been selected before, as shown in the review-counter (box  308 ). The value in the review-counter does not include one or more prior selections of the line-items when the line-item was in its un-learnt mode. The selection process discourages re-selecting a line-item that has been selected before. One way to achieve this result is to multiply the weight factor affecting which line-item to select by 
     
       
         1/(the value in the review-counter of that line-item+1).  
       
     
     The higher the factor, the lower the probability that the corresponding line-item is selected. Thus, the above equation reduces the probability of selecting a line-item that has been reviewed before. 
     One or more of the above factors may be combined in a learnt-line-item selection rule to influence the selection of a learnt line-item. The combination process can simply be based on a weight factor that depends on one or more of the above factors. 
     After selecting the learnt line-item, summarized learning materials are generated (step  208 ) to be presented to the student. Generally, summarized learning materials are more concise than the detailed learning material. In one embodiment, summarized learning materials do not include any questions to test the student. In terms of the process, in one embodiment, the selector  102  sends the line-item entry E to the study-plan generator  108  to retrieve the corresponding summarized study plan from the study-plan storage-medium  116 . Typically, there are a number of study-plan entries in the storage-medium  116 , and they can be in the following format: 
     (line-item root, mode, study-plan) 
     If the mode is a learnt mode, the study-plan is a summarized study-plan. The following serves as an example of a summarized study-plan for differentiating polynomial: 
     The system teaches the generalized equation: 
     
       
         (( dΣa   i   x   i )/ dx )=(Σ i*a   i   x   i−1 )  
       
     
     The system also teaches the following equation, which is used to find optima and minima: 
     
       
         (( dΣa   i   x   i )/ dx )=0  
       
     
     Based on the line-item root and its mode in the line-item entry E, and with one summarized study plan per learnt line-item, the generator  108  retrieves from the study-plan storage-medium  116 , the corresponding summarized study-plan. Creating summarized study-plans for a subject should be obvious to experts in the subject, and will not be further discussed in this application. 
     In another embodiment, summarized learning materials also include a number of questions to test the student. These questions may be different from those in one embodiment of the detailed learning materials. The answers are used to assess the understanding level of the student in that line-item. 
     In the above embodiments, the detailed learning materials are generated before the summarized learning materials. In another embodiment, detailed learning materials for an un-learnt line-item are generated (step  204 ) after the generation of the summarized learning materials (step  208 ). This allows the student to review a learnt line-item before studying detailed learning materials on an un-learnt line-item. This different approach is applicable if the learnt line-item is related to the un-learnt line-item. A review helps to prepare the student for the un-learnt line-item. 
     In one embodiment, after a line-item has been reviewed, its review factor  78  is incremented by one. For that embodiment, the selection of a line-item to be reviewed is inversely proportional to the review factor. Thus, the probability of again selecting a line-item which has previously been reviewed is reduced. 
     The steps shown in FIG. 4 can be repeated. FIG. 8 shows a set of steps to implement another embodiment of the present invention, where there is repetition in selecting line-items. This embodiment starts from selecting an un-learnt line-item (step  352 ). Then, a line-item probability value is accessed (step  354 ) from the rules storage medium  104  to select a line-item (step  356 ). That value can be set by an instructor through a councilor  120 . Note that there may be a number of steps in between the step of selecting (step  352 ) an un-learnt line-item and the step of accessing a line-item probability value (step  354 ). Anyway, typically, when a student is learning a subject, he starts with working on an un-learnt line-item. But it is not necessary to start the process with selecting an un-learnt line-item. 
     FIG. 9 shows one embodiment of a set  400  of steps to select an un-learnt line-item or a learnt line-item in the present invention based on the line-item probability P. From the value P, an un-learnt line-item is selected (100*P)% of the time and a learnt line-item (100*(1−P))% of the time. Then, for the selection process, the selector  102  generates (step  402 ) a random number between 0 and 1, and compares (step  404 ) the random number with P. If the number is smaller than P, the selector selects (step  406 ) an un-learnt line-item. If there is no more un-learnt line-item, the student has mastered the subject, and can proceed to another, or the system can select learnt-line-items for review. If the number is bigger than or equal to P, the selector selects (step  408 ) a learnt line-item. If there is no learnt line-item, the selector  102  selects (step  412 ) an un-learnt line-item. 
     In one embodiment, one characteristic of the probability P is that the higher the value of P, the more likely the selector  102  selects an un-learnt line-item. Such a system/method favors teaching new concepts. The smaller the value of P, the more likely the selector  102  selects a learnt line-item. Such a system/method favors reviews to reinforce the understanding of the learnt line-items before attempting new concepts. 
     In another embodiment, the selector  102  automatically selects the probability P, which changes as the student is working through the subject. The probability P depends on its previously selected item. To illustrate such an embodiment, suppose P(n) is the line-item probability after selecting n line-items, then 
     
       
           P ( n+ 1)= F ( P ( n ))n&gt;0  
       
     
     where F is a function operating on P(n). The initial value P(0) is randomly set by the system to be between 0 and 1. The idea is that the invented system tends to switch to teach a learnt line-item after teaching one or more un-learnt line-items, and vice versa. To increase the probability of choosing a learnt line-item after selecting one or more un-learnt line-items, the function F produces a value smaller than its argument P(n). Similarly, to increase the probability of choosing an un-learnt line-item after selecting one or more learnt line-items, the function F produces a value larger than its argument P(n). The following serves as an example for this embodiment, with PI being the previously selected line-item: 
     
       
           P ( n+ 1)=Max(0,  P ( n )− c ) if PI is an un-learnt line-item.  
       
     
     
       
           P ( n+ 1)=Min(1,  P ( n )+ d ) if PI is a learnt line-item.  
       
     
     “Min” denotes “The minimum of.” “Max” means “The maximum of” Both c and d are constants between 0 and 1; they are chosen to reflect how quickly the invented system selects a different type of line-item. Each time a learnt line-item is selected, P is increased by an amount of d, until P reaches 1. Similarly, each time a un-learnt line-item is selected, PI is reduced by an amount of c, until P becomes 0. 
     After the line-item is selected, if it is an un-learnt line-item, detailed learning material is generated (step  358 ). If the student is satisfactory in learning the detailed learning material, the un-learnt line-item is re-classified (step  362 ) as a learnt line-item. On the other hand, if the selected line-item is a learnt line-item, then summarized learning material is generated (step  360 ). The process then repeats to select another line-item. The generation of learning materials and the re-classification process are as described above. 
     Conclusion 
     In the above examples, initially the modes of all line-items are classified as un-learnt. In one embodiment, even initially, the modes of some of the line-items are classified as learnt, which can be done by the instructor through the councilor  120 . In another embodiment, initially all line-items are classified as learnt line-items. In such an embodiment, the student has previously learnt the subject, and the embodiment is just for reviews, which is suitable for one to prepare for an examination. Thus, only summarized learning materials are generated for the student, with no initial step of selecting an un-learnt line-item. 
     In the specification, learning materials can be study-plans, or questions, or study-plans with questions. In the embodiment where the learning materials only include study-plans, at least one line-item&#39;s learning materials include questions to more accurately assess the student&#39;s level in learning that line-item. 
     In a number of the above embodiments, rules are accessed from the rule storage medium. In another embodiment, those rules have previously been embedded in the programs implementing the present invention. With rules already embedded in the program, there is no need for accessing the rules. 
     Finally, a number of the above embodiments involve a number of steps that seem to have a specific sequence. For example, the step of generating detailed learning-material for an un-learnt line-item can comprise the steps of generating a detailed-study plan for the un-learnt line-item, presenting the detailed-study-plan to the student, generating questions on the un-learnt line-item for the student, and presenting the questions for the student. In the present invention, those embodiments include reshuffling the steps as long as there is no inherent dependency among those reshuffled steps. For example, one can reshuffle some of the steps of generating detailed learning-material for an un-learnt line-item to read: generating a detailed-study plan for the un-learnt line-item, generating questions on the un-learnt line-item for the student, presenting the detailed-study-plan to the student, and presenting the questions for the student. 
     Other embodiments of the invention will be apparent to those skilled in the art from a consideration of this specification or practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with the true scope and spirit of the invention being indicated by the following claims.