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Physical Sciences and Mathematics Commons™

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Mathematics

Utah State University

Publications

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Full-Text Articles in Physical Sciences and Mathematics

Facilitating Mathematics And Computer Science Connections: A Cross-Curricular Approach, Kimberly E. Beck, Jessica F. Shumway, Umar Shehzad, Jody Clarke-Midura, Mimi Recker Jan 2024

Facilitating Mathematics And Computer Science Connections: A Cross-Curricular Approach, Kimberly E. Beck, Jessica F. Shumway, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Publications

In the United States, school curricula are often created and taught with distinct boundaries between disciplines. This division between curricular areas may serve as a hindrance to students' long-term learning and their ability to generalize. In contrast, cross-curricular pedagogy provides a way for students to think beyond the classroom walls and make important connections across disciplines. The purpose of this paper is a theoretical reflection on our use of Expansive Framing in our design of lessons across learning environments within the school. We provide a narrative account of our early work in using this theoretical framework to co-plan and enact …

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Geometry And Coding: Introducing An Interactive And Integrated Mathematics-Computer Science Unit, Kimberly Beck, Jessica F. Shumway Apr 2023

Geometry And Coding: Introducing An Interactive And Integrated Mathematics-Computer Science Unit, Kimberly Beck, Jessica F. Shumway

Publications

As part of a collaborative project between Utah State University, the Cache County School District, and Stanford, instructional units were designed for fifth-grade students. These units integrated math concepts of geometrical shapes and computer science concepts of sequences, conditionals, and loops. One component of the unit was implemented in math classrooms by math teachers, and the other component was implemented in computer labs. This presentation will focus on the math unit as presented at the National Council of Teachers of Mathematics (NCTM-V).

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An Exploration Of Computational Text Analysis Of Co-Design Discourse In A Research-Practice Partnership, Mei Tan, Victor R. Lee Apr 2023

An Exploration Of Computational Text Analysis Of Co-Design Discourse In A Research-Practice Partnership, Mei Tan, Victor R. Lee

Publications

In combination with contextualized human interpretation, computational text analysis offers a quantitative approach to interrogating the nature of participation and social positioning in discourse. Using meeting transcript data from the development of a co-design research-practice partnership, we examine the roles and forms of participation that contribute to an effective collaboration between a multileveled school system and researcher partners. We apply computational methods to explore the language of co-design and multi-stakeholder perspectives in support of educational improvement science efforts and our theoretical understanding of partnership roles. Results indicate participation patterns align with documented roles in co- design partnerships and highlight the …

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Co-Designing Elementary-Level Computer Science And Mathematics Lessons: An Expansive Framing Approach, Umar Shehzad, Jody Clarke-Midura, Kimberly Beck, Jessica Shumway, Mimi Recker Jan 2023

Co-Designing Elementary-Level Computer Science And Mathematics Lessons: An Expansive Framing Approach, Umar Shehzad, Jody Clarke-Midura, Kimberly Beck, Jessica Shumway, Mimi Recker

Publications

This study examines how a rural-serving school district aimed to provide elementary-level computer science (CS) by offering instruction during students’ computer lab time. As part of a research-practice partnership, cross-context mathematics and CS lessons were co-designed to expansively frame and highlight connections across – as opposed to integration within – the two subjects. Findings indicated that most students who engaged with the lessons across the lab and classroom contexts reported finding the lessons interesting, seeing connections to their mathematics classes, and understanding the programming. In contrast, a three-level logistic regression model showed that students who only learned about mathematics connections …

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Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway Sep 2022

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

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A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Ian M. Anderson, Charles G. Torre Jan 2022

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Ian M. Anderson, Charles G. Torre

Publications

We find a new homogeneous solution to the Einstein-Maxwell equations with a cos- mological term. The spacetime manifold is R × S3. The spacetime metric admits a simply transitive isometry group G = R × SU(2) and is Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non- null and non-inheriting: it is only invariant with respect to the SU(2) subgroup and is time-dependent in a stationary reference frame.

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Spacetime Groups, Ian M. Anderson, Charles G. Torre Jan 2019

Spacetime Groups, Ian M. Anderson, Charles G. Torre

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A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …

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Technology And Mathematics Standards: An Integrated Approach, Chris Merrill, Mark Comerford Jan 2004

Technology And Mathematics Standards: An Integrated Approach, Chris Merrill, Mark Comerford

Publications

The article focuses on the use of standards-based teaching and learning that has been gaining significant attention in the education world. State and national associations now base their specific subject area or discipline solely on standards, i.e., International Technology Education Association (ITEA), National Council of Teachers of Mathematics (NCTM), National Science Education Association (NSEA). Moreover, at the public school level, state boards of education are holding school districts accountable for teaching standards-based curricula. It is with the latter definition in mind that the authors created a standards-based, integrated technology and mathematics lesson using the design and construction of stair systems.

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