|
Bayesian Knowledge Tracing
Bayesian knowledge tracing is an algorithm used in many intelligent tutoring systems to model each learner's mastery of the knowledge being tutored. It models student knowledge in a hidden Markov model as a latent variable, updated by observing the correctness of each student's interaction in which they apply the skill in question. BKT assumes that student knowledge is represented as a set of binary variables, one per skill, where the skill is either mastered by the student or not. Observations in BKT are also binary: a student gets a problem/step either right or wrong. Intelligent tutoring systems often use BKT for mastery learning and problem sequencing. In its most common implementation, BKT has only skill-specific parameters. Method There are four model parameters used in BKT: * p(L_0) or p\text, the probability of the student knowing the skill beforehand. * p(T) or p\text, the probability of the student demonstrating knowledge of the skill after an opportunity to apply it * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intelligent Tutoring Systems
An intelligent tutoring system (ITS) is a computer system that aims to provide immediate and customized instruction or feedback to learners, usually without requiring intervention from a human teacher. ITSs have the common goal of enabling learning in a meaningful and effective manner by using a variety of computing technologies. There are many examples of ITSs being used in both formal education and professional settings in which they have demonstrated their capabilities and limitations. There is a close relationship between intelligent tutoring, cognitive learning theories and design; and there is ongoing research to improve the effectiveness of ITS. An ITS typically aims to replicate the demonstrated benefits of one-to-one, personalized tutoring, in contexts where students would otherwise have access to one-to-many instruction from a single teacher (e.g., classroom lectures), or no teacher at all (e.g., online homework). ITSs are often designed with the goal of providing acces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Markov Model
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an observable process Y whose outcomes are "influenced" by the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about X by observing Y. HMM has an additional requirement that the outcome of Y at time t=t_0 must be "influenced" exclusively by the outcome of X at t=t_0 and that the outcomes of X and Y at t handwriting recognition, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics. Definition Let X_n and Y_n be discrete-time stochastic processes and n\geq 1. The pair (X_n,Y_n) is a ''hidden Markov model'' if * X_n is a Markov process whose behavior is not directly observable ("hidden"); * \operatorname\bigl(Y_n \i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Data
Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including ''bit'' (binary digit) in computer science, ''truth value'' in mathematical logic and related domains and ''binary variable'' in statistics. Mathematical and combinatoric foundations A discrete variable that can take only one state contains zero information, and is the next natural number after 1. That is why the bit, a variable with only two possible values, is a standard primary unit of information. A collection of bits may have states: see binary number for details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states of each variable. Ten bits have more () states than three decimal digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intelligent Tutoring Systems
An intelligent tutoring system (ITS) is a computer system that aims to provide immediate and customized instruction or feedback to learners, usually without requiring intervention from a human teacher. ITSs have the common goal of enabling learning in a meaningful and effective manner by using a variety of computing technologies. There are many examples of ITSs being used in both formal education and professional settings in which they have demonstrated their capabilities and limitations. There is a close relationship between intelligent tutoring, cognitive learning theories and design; and there is ongoing research to improve the effectiveness of ITS. An ITS typically aims to replicate the demonstrated benefits of one-to-one, personalized tutoring, in contexts where students would otherwise have access to one-to-many instruction from a single teacher (e.g., classroom lectures), or no teacher at all (e.g., online homework). ITSs are often designed with the goal of providing acces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computerized Adaptive Testing
Computerized adaptive testing (CAT) is a form of computer-based test that adapts to the examinee's ability level. For this reason, it has also been called tailored testing. In other words, it is a form of computer-administered test in which the next item or set of items selected to be administered depends on the correctness of the test taker's responses to the most recent items administered. How it works CAT successively selects questions for the purpose of maximizing the precision of the exam based on what is known about the examinee from previous questions. From the examinee's perspective, the difficulty of the exam seems to tailor itself to their level of ability. For example, if an examinee performs well on an item of intermediate difficulty, they will then be presented with a more difficult question. Or, if they performed poorly, they would be presented with a simpler question. Compared to static multiple choice tests that nearly everyone has experienced, with a fixed set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Item Response Theory
In psychometrics, item response theory (IRT) (also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is a theory of testing based on the relationship between individuals' performances on a test item and the test takers' levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics. Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, Likert scaling, in which ''"''All items are assumed to be replications of each other or in other words items are considered to be parallel instruments".A. van Alphen, R. Halfens, A. Hasman and T. Imbos. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Space
In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne, and remain in extensive use in the education theory. Modern applications include two computerized tutoring systems, ALEKS and the defunct RATH. Formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered. Not all concepts are interchangeable; some require other concepts as prerequisites. Conversely, competency at one skill may ease the acquisition of another through similarity. A knowledge space marks out which collections of skills are ''feasible'': they can be learned without mastering any other skills. Under reasonable assumptions, the collection of feasible competencies forms the mathematical structure known as an antimatro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latent Growth Modeling
Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectories. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of psychology, behavioral science, education and social science. It is also called latent growth curve analysis. The latent growth model was derived from theories of SEM. General purpose SEM software, such as OpenMx, lavaan (both open source packages based in R), AMOS, Mplus, LISREL, or EQS among others may be used to estimate growth trajectories. Background Latent Growth Models Tucker, L.R. (1958) Determination of parameters of a functional relation by factor analysis. ''Psychometrika'' 23, 19-23. Rao, C.R. (1958) Some statistical methods for the comparison of growth curves. ''Biometrics''. 14, 1-17. Scher, A.M., Young, A.C. & Meredith, W.M. (1960) Factor analysis of the electrocardiogram. ''Circulation Research'' 8, 519-526. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
