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## Richard Baraniuk Mr. Lan , Andrew Waters, Christoph Studer

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**learning and contentanalytics**Richard Baraniuk Mr. Lan, Andrew Waters, ChristophStuder**learning analytics**Goal:assessand track student learning progress by analyzing their interactions with content data(massive, rich, personal) close the learning feedback loop**content**learninganalytics assess and track student learning progress by analyzingtheir interactions with content**content**learninganalytics assume contentis organized(“knowledge graph”)**“While such results are promising, perhaps it's a little**soon to crown Inquire the future of textbooks. For starters, after two years of work the system is still only half-finished. The team plan to encode the rest of the 1400-page Campbell Biology by the end of 2013, but they expect a team of 18 biologists will be needed to do so. This raises concerns about whether the project could be expanded to cover other areas of science, let alone other subjects.” http://www.newscientist.com/article/mg21528765.700-the-intelligent-textbook-that-helps-students-learn.html**content**learninganalytics contentanalytics**standard practice**Johnny Eve Patty Neelsh Nora Nicholas Barbara Agnes Vivek Bob Fernando Sarah Hillary Judy Janet**standard practice**Johnny Goal: using only “grade book” data, infer: • the concepts underlying the questions (content analytics) • each student’s “knowledge” of each underlying concept (learning analytics) Eve Patty Neelsh Nora Nicholas Barbara Agnes Vivek Bob Fernando Sarah Hillary Judy Janet**from grades to concepts**students data • graded student responses to unlabeled questions • large matrix with entries: white: correct responseblack: incorrect responsegrey: unobserved standard practice • instructor’s “grade book” = sum/average over each column goal • infer underlying concepts and student understanding withoutquestion-level metadata problems**from grades to concepts**students data • graded student responses to unlabeledquestions • large matrix with entries: white: correct responseblack: incorrect responsegrey: unobserved goal • infer underlying concepts and student understanding without question-level metadata key observation • each question involves only a small number of “concepts” (low rank) problems**statistical model**students converts to 0/1(probitor logisticcoin fliptransformation) red = strong ability blue = weak ability ~ Ber problems estimate of each student’s ability to solve each problem(even unsolved problems)**SPARse Factor Analysis**students ~ + Ber problems**SPARFA**each problem’s intrinsic “difficulty” concepts students each problem involves a combination of a small number of key “concepts” students ~ + Ber problems each student’s knowledge of each “concept”**solving SPARFA**students factor analyzing the grade book matrix is a severely ill-posed problem significant recent progress in relaxation-based optimization for sparse/low-rank problems • matrix based methods (SPARFA-M) • Bayesian methods (SPARFA-B) similar to compressive sensing problems**standard practice**Johnny Grade 8 science • 80 questions • 145 students • 1353 problems solved (sparsely) • learned 5 concepts Eve Patty Neelsh Nora Nicholas Barbara Agnes Vivek Bob Fernando Sarah Hillary Judy Janet**Grade 8 science**• 80 questions • 145 students • 1353 problems solved (sparsely) • 5 concepts**questions(w/ estimated inherent difficulty)**concepts 87 55 23 93 62 studentknowledgeprofile**summary**scaling up personalized learning requires that we exploit the massive collection of relatively unorganized educational content can estimate content analytics on this collection as we estimate learning analytics related work: Rasch model, IRT integrating SPARFA into**.com**Mr. LanAndrew WatersChristophStuder