Using Natural Language as Knowledge Representation in an Intelligent Tutoring System

Knowledge used in an intelligent tutoring system to teach students is usually acquired from authors who are experts in the domain. A problem is that they cannot directly add and update knowledge if they don’t learn formal language used in the system. Using natural language to represent knowledge can allow authors to update knowledge easily. This thesis presents a new approach to use unconstrained natural language as knowledge representation for a physics tutoring system so that non-programmers can add knowledge without learning a new knowledge representation. This approach allows domain experts to add not only problem statements, but also background knowledge such as commonsense and domain knowledge including principles in natural language. Rather than translating into a formal language, natural language representation is directly used in inference so that domain experts can understand the internal process, detect knowledge bugs, and revise the knowledgebase easily. In authoring task studies with the new system based on this approach, it was shown that the size of added knowledge was small enough for a domain expert to add, and converged to near zero as more problems were added in one mental model test. After entering the no-new-knowledge state in the test, 5 out of 13 problems (38 percent) were automatically solved by the system without adding new knowledge

Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists' language encodes different varieties of analogical models through the use of grammar and conceptual metaphor. We hypothesize that students categorize concepts into ontological categories based on the grammatical structure of physicists' language. We also hypothesize that students over-extend and misapply conceptual metaphors in physicists' speech and writing. Using our theory, we will show how, in some cases, we can explain student difficulties in quantum mechanics as difficulties with language.Comment: Accepted for publication in Phys. Rev. ST:PE

Investigating Student Understanding of Vector Calculus in Upper-Division Electricity and Magnetism: Construction and Determination of Differential Element in Non-Cartesian Coordinate Systems

Differential length, area, and volume elements appear ubiquitously over the course of upper-division electricity and magnetism (E&M), used to sum the effects of or determine expressions for electric or magnetic fields. Given the plethora of tasks with spherical and cylindrical symmetry, non-Cartesian coordinates are commonly used, which include scaling factors as coefficients for the differential terms to account for the curvature of space. Furthermore, the application to vector fields means differential lengths and areas are vector quantities. So far, little of the education research in E&M has explored student understanding and construction of the non-Cartesian differential elements used in applications of vector calculus. This study contributes to the research base on the learning and teaching of these quantities. Following course observations of junior-level E&M, targeted investigations were conducted to categorize student understanding of the properties of these differentials as they are constructed in a coordinate system without a physics context and as they are determined within common physics tasks. In general, students did not have a strong understanding of the geometry of non-Cartesian coordinate systems. However, students who were able to construct differential area and volume elements as a product of differential lengths within a given coordinate system were more successful when applying vector calculus. The results of this study were used to develop preliminary instructional resources to aid in the teaching of this material. Lastly, this dissertation presents a theoretical model developed within the context of this study to describe students’ construction and interpretation of equations. The model joins existing theoretical frameworks: symbolic forms, used to describe students’ representational understanding of the structure of the constructed equation; and conceptual blending, which has been used to describe the ways in which students combine mathematics and physics knowledge when problem solving. In addition to providing a coherent picture for how the students in this study connect contextual information to symbolic representations, this model is broadly applicable as an analytical lens and allows for a detailed reinterpretation of similar analyses using these frameworks

Primary Physical Science for Student Teachers at Kindergarten and Primary School Levels: Part II—Implementation and Evaluation of a Course

AbstractThis is the second of two papers on a novel physical science course for student teachers that develops and uses an imaginative approach to Primary Physical Science Education. General philosophical, cognitive, developmental, and scientific issues have been presented in the first paper; here, we briefly recapitulate the most important aspects. In the main part of the current paper, we present in some detail concrete elements of the implementation of the course at three Italian universities where Primary Physical Science Education has been taught for more than 6 years. After a brief description of the course structure, we discuss which parts of macroscopic physics are taught, and how this is done in lectures and labs. Most importantly, we show how the science is entwined with methods related to pedagogy and didactics that (1) help our students approach the science and (2) can be transferred quite readily to teaching children in kindergarten and primary school. These methods include the design of direct physical experience of forces of nature, embodied simulations, writing and telling of stories of forces of nature, and design and performance of Forces-of-Nature Theater plays. The paper continues with a brief description of feedback from former students who have been teaching for some time, and an in-depth analysis of the research and teaching done by one of the students for her master thesis. We conclude the paper by summarizing aspects of both the philosophy and the design of the course that we believe to be of particular value

Varieties of Mathematics in Economics- A Partial View

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.

Language of physics, language of math: Disciplinary culture and dynamic epistemology

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we suggest that a fundamental issue has received insufficient exploration: the fact that in science, we don't just use math, we make meaning with it in a different way than mathematicians do. In this reflective essay, we explore math as a language and consider the language of math in physics through the lens of cognitive linguistics. We begin by offering a number of examples that show how the use of math in physics differs from the use of math as typically found in math classes. We then explore basic concepts in cognitive semantics to show how humans make meaning with language in general. The critical elements are the roles of embodied cognition and interpretation in context. Then we show how a theoretical framework commonly used in physics education research, resources, is coherent with and extends the ideas of cognitive semantics by connecting embodiment to phenomenological primitives and contextual interpretation to the dynamics of meaning making with conceptual resources, epistemological resources, and affect. We present these ideas with illustrative case studies of students working on physics problems with math and demonstrate the dynamical nature of student reasoning with math in physics. We conclude with some thoughts about the implications for instruction.Comment: 27 pages, 9 figure