مقایسهٔ روش‌ها

	منحنی یادگیری (قانون توان تمرین)	تحلیل یادگیری (Learning Analytics)	برنامه‌ریزی غیرخطی
حوزه	تحلیل‌گری آموزشی	تحلیل‌گری آموزشی	بهینه‌سازی
خانواده	Regression model	Process / pipeline	Process / pipeline
سال پیدایش	1936	2011	2006
پدیدآور	Theodore Wright	George Siemens & Phil Long	Jorge Nocedal & Stephen Wright
نوع	Power-law regression model	data-driven educational process pipeline	Continuous mathematical optimization
منبع بنیادین	Wright, T. P. (1936). Factors affecting the cost of airplanes. Journal of the Aeronautical Sciences, 3(4), 122–128.	Siemens, G., & Long, P. (2011). Penetrating the fog: Analytics in learning and education. EDUCAUSE Review, 46(5), 30–40.	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1
نام‌های دیگر	Power Law of Practice, Experience Curve, Wright's Law, Öğrenme Eğrisi	Educational Data Mining, Academic Analytics, Learning Data Analytics, Öğrenme Analitiği	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
مرتبط	3	3	3
خلاصه	The learning curve models how performance improves predictably as cumulative experience accumulates. Formalized by Theodore Wright in 1936 using aircraft manufacturing data, it expresses the relationship between the number of practice trials (or production units) and the time or cost per unit as a power-law function. It is widely applied in educational psychology, industrial engineering, health professions training, and human factors research whenever repeated task execution is the mechanism of skill acquisition.	Learning Analytics is the measurement, collection, analysis, and reporting of data about learners and their contexts, with the purpose of understanding and optimizing learning and the environments in which it occurs. Formally introduced by George Siemens and Phil Long in 2011, the approach draws on data generated in digital learning environments to provide educators, institutions, and learners with evidence-based feedback for improving educational outcomes.	Nonlinear programming (NLP) is a branch of mathematical optimization concerned with problems in which the objective function or at least one constraint is nonlinear. Formalized comprehensively by Jorge Nocedal and Stephen Wright in their seminal 2006 text, NLP encompasses gradient-based algorithms — including sequential quadratic programming (SQP), interior-point methods, and quasi-Newton approaches — for finding locally or globally optimal solutions to continuous decision problems arising across engineering, economics, and the physical sciences.