An official website of the United States government
Tracing Student Learning Outcome at Historically Black Colleges and Universities via Deep Knowledge Tracing
More Like this
-
Roll, I; McNamara, D; Sosnovsky, S; Luckin, R; Dimitrova, V. (Ed.)Knowledge tracing refers to a family of methods that estimate each student’s knowledge component/skill mastery level from their past responses to questions. One key limitation of most existing knowledge tracing methods is that they can only estimate an overall knowledge level of a student per knowledge component/skill since they analyze only the (usually binary-valued) correctness of student responses. Therefore, it is hard to use them to diagnose specific student errors. In this paper, we extend existing knowledge tracing methods beyond correctness prediction to the task of predicting the exact option students select in multiple choice questions. We quantitatively evaluate the performance of our option tracing methods on two large-scale student response datasets. We also qualitatively evaluate their ability in identifying common student errors in the form of clusters of incorrect options across different questions that correspond to the same error.more » « less
-
Reconstructing and designing media with continuously-varying refractive index fields remains a challenging problem in computer graphics. A core difficulty in trying to tackle this inverse problem is that light travels inside such media along curves, rather than straight lines. Existing techniques for this problem make strong assumptions on the shape of the ray inside the medium, and thus limit themselves to media where the ray deflection is relatively small. More recently, differentiable rendering techniques have relaxed this limitation, by making it possible to differentiably simulate curved light paths. However, the automatic differentiation algorithms underlying these techniques use large amounts of memory, restricting existing differentiable rendering techniques to relatively small media and low spatial resolutions. We present a method for optimizing refractive index fields that both accounts for curved light paths and has a small, constant memory footprint. We use the adjoint state method to derive a set of equations for computing derivatives with respect to the refractive index field of optimization objectives that are subject to nonlinear ray tracing constraints. We additionally introduce discretization schemes to numerically evaluate these equations, without the need to store nonlinear ray trajectories in memory, significantly reducing the memory requirements of our algorithm. We use our technique to optimize high-resolution refractive index fields for a variety of applications, including creating different types of displays (multiview, lightfield, caustic), designing gradient-index optics, and reconstructing gas flows.more » « less
-
Reconstructing and designing media with continuously-varying refractive index fields remains a challenging problem in computer graphics. A core difficulty in trying to tackle this inverse problem is that light travels inside such media along curves, rather than straight lines. Existing techniques for this problem make strong assumptions on the shape of the ray inside the medium, and thus limit themselves to media where the ray deflection is relatively small. More recently, differentiable rendering techniques have relaxed this limitation, by making it possible to differentiably simulate curved light paths. However, the automatic differentiation algorithms underlying these techniques use large amounts of memory, restricting existing differentiable rendering techniques to relatively small media and low spatial resolutions. We present a method for optimizing refractive index fields that both accounts for curved light paths and has a small, constant memory footprint. We use the adjoint state method to derive a set of equations for computing derivatives with respect to the refractive index field of optimization objectives that are subject to nonlinear ray tracing constraints. We additionally introduce discretization schemes to numerically evaluate these equations, without the need to store nonlinear ray trajectories in memory, significantly reducing the memory requirements of our algorithm. We use our technique to optimize high-resolution refractive index fields for a variety of applications, including creating different types of displays (multiview, lightfield, caustic), designing gradient-index optics, and reconstructing gas flows.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1109/ACCESS.2025.3557316
