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This paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot’s poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.
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A modified depth of knowledge framework for word problems.
Depth-of-knowledge (DOK) is a means to communicate the cognitive demand of tasks and is often used to categorize assessment items. Webb’s (2002) framework has been applied across content areas. The aim of this two-phase iterative study was to modify Webb’s DOK framework for word problems. Through work with school partners, this iterative design-research based study provides supportive evidence for a modified DOK framework reflecting levels of complexity in word problems. The resulting modified DOK framework presents an opportunity for mathematics educators to reflect on various aspects of cognitive complexity.
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- PAR ID:
- 10517399
- Editor(s):
- Lamberg, Teruni; Moss, Diana
- Publisher / Repository:
- PMENA
- Date Published:
- Page Range / eLocation ID:
- 228-233
- Subject(s) / Keyword(s):
- problem solving assessment
- Format(s):
- Medium: X
- Location:
- Reno, NV
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Proceeding:
- The DOI is not currently available.
