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--- leveling [2022/09/23 22:57] – [Calculate level of all words in the dictionary] jhagstrand
+++ leveling [2023/01/12 11:08] (current) – removed jhagstrand
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-====== Mai Leveling ======
-===== Recommendation =====
-A typical recommendation engine would choose stories with similar content.
-We leave that to the student to judge by reading the story titles.
-Leveling is one of the tools we use.
-student: vocabulary size, average level \\
-each story: average level, number of mastered words, number of new words, ratio, total number of words
-find stories with words that the student should know by now to be at this level.
-Goal.  Introduce vocabulary to the student gradually, more common words first, more advanced words later. \\
-Always reinforcing and building upon what the student already knows.
-totally wrong.  stories are recommended based on specific vocabulary comparison of known and unknown words.
-leveling is a vague way of sorting stories and words and students and choosing what to offer to the student next.
-the level of a student can be used to as motivational, but would be better to just use size of mastered vocabulary.
-controlled vocabulary.  stories or paragraphs can be designed with specific level of words.
-The goal of leveling is to recommend appropriate stories to a student depending on his vocabulary.  An appropriate story is one that has many known words and a few new words.  (Coach and student are expected to sometimes override these recommendations and instead choose stories based on the student's interest in the subject matter.)
-The "level" of a word is an index from 1 to 100. \\
-A lower level indicates a more common word. \\
-A higher level is more advanced, rarely-used word.
-The level of a story is the weighted average of the levels of all the words used in the story.
-The levels of words and stories are re-calculated on the server once each day.
-The level of a student is the average level of all the mastered words in his vocabulary.
-===== Calculate level of all words in the dictionary =====
-  - Make the mean-table in memory with an entry for every word/mean in the dictionary.  Each entry in the table contains word, mean, old-count, old-level, new-count, new-level.
-  - Read all the stories.  For each:
-    * open the consolidated words field into an array
-    * (the number of loc items in the array is the use-count for that word/mean)
-    * add the use-count to the new-count in the master word table
-  - Loop thru the mean table saving lowest and highest use-count.
-  - Loop thru the mean table again.  For each entry:
-    * calculate and set the level for the mean, by interpolating an index from 1 to 100 as follows:
-      * level = 100 - (use-count * (high-low)/high)
-      * max/min : 1/100
-      * freq/max-min = 100-level/100
-      * 100 * (freq/max-min) = 100-level
-      * level + (100 * (freq/max-min)) = 100
-      * level = 100 - (100 * (freq/max-min))
-    * Update mean table record setting count and level if changed.
-===== Calculate level of all stories =====
-  - Read all stories.  For each:
-    * open the consolidated words field into an array
-    * get the level of each word from the dictionary
-    * save total-use-count
-    * save total-level as level*use-count
-  -  Calculate average-level.
-    * average-level = total-level / total-use-count
-    * update the story record, setting level
-For each story
-  * Num words
-  * Num uniques
-  * Avg level
-For each story per student
-  * Num mastered
-  * Num new words
-  * Num working
-  * % new / uniques
-Calc avg level for each user
-New table, story-user