Teachers often rely on the use of a range of open-ended
problems to assess students’ understanding of mathematical
concepts. Beyond traditional conceptions of student open-
ended work, commonly in the form of textual short-answer
or essay responses, the use of figures, tables, number lines,
graphs, and pictographs are other examples of open-ended
work common in mathematics. While recent developments
in areas of natural language processing and machine learning
have led to automated methods to score student open-ended
work, these methods have largely been limited to textual an-
swers. Several computer-based learning systems allow stu-
dents to take pictures of hand-written work and include such
images within their answers to open-ended questions. With
that, however, there are few-to-no existing solutions that
support the auto-scoring of student hand-written or drawn
answers to questions. In this work, we build upon an ex-
isting method for auto-scoring textual student answers and
explore the use of OpenAI/CLIP, a deep learning embedding
method designed to represent both images and text, as well
as Optical Character Recognition (OCR) to improve model
performance. We evaluate the performance of our method
on a dataset of student open-responses that contains both
text- and image-based responses, and find a reduction of
model error in the presence of images when controlling for
other answer-level features.
more »
« less
HyperQuaternionE: A hyperbolic embedding model for qualitative spatial and temporal reasoning
Qualitative spatial/temporal reasoning (QSR/QTR) plays a key role in research on human cognition, e.g., as it relates to navigation, as well as in work on robotics and artificial intelligence. Although previous work has mainly focused on various spatial and temporal calculi, more recently representation learning techniques such as embedding have been applied to reasoning and inference tasks such as query answering and knowledge base completion. These subsymbolic and learnable representations are well suited for handling noise and efficiency problems that plagued prior work. However, applying embedding techniques to spatial and temporal reasoning has received little attention to date. In this paper, we explore two research questions: (1) How do embedding-based methods perform empirically compared to traditional reasoning methods on QSR/QTR problems? (2) If the embedding-based methods are better, what causes this superiority? In order to answer these questions, we first propose a hyperbolic embedding model, called HyperQuaternionE, to capture varying properties of relations (such as symmetry and anti-symmetry), to learn inversion relations and relation compositions (i.e., composition tables), and to model hierarchical structures over entities induced by transitive relations. We conduct various experiments on two synthetic datasets to demonstrate the advantages of our proposed embedding-based method against existing embedding models as well as traditional reasoners with respect to entity inference and relation inference. Additionally, our qualitative analysis reveals that our method is able to learn conceptual neighborhoods implicitly. We conclude that the success of our method is attributed to its ability to model composition tables and learn conceptual neighbors, which are among the core building blocks of QSR/QTR.
more » « less- Award ID(s):
- 2033521
- NSF-PAR ID:
- 10370839
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- GeoInformatica
- Volume:
- 27
- Issue:
- 2
- ISSN:
- 1384-6175
- Page Range / eLocation ID:
- p. 159-197
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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