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1. An analysis of students’ mathematical models for music

   Corum, K.; Kara, M.; Talbot, E.; Ilina, T. (January 2020, Proceedings of the Forty-Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   This paper describes a modeling task designed to improve students’ understanding of music and related unit structures (e.g., whole note, half note). Fourteen upper elementary students were asked to build models of melodies using Cuisenaire rods and make arguments about how their models represented what they heard. Our analysis of students’ models suggested four categories of models. Students exhibited one- or two-dimensional reasoning with either (or both) height and length correspondence that varied in terms of duration and/or pitch features. 

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2. An analysis of students’ mathematical models for music

   Corum, K.; Kara, M.; Talbot, E.; Ilina, T. (January 2020, Proceedings of the Forty-Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.)

   This paper describes a modeling task designed to improve students’ understanding of music and related unit structures (e.g., whole note, half note). Fourteen upper elementary students were asked to build models of melodies using Cuisenaire rods and make arguments about how their models represented what they heard. Our analysis of students’ models suggested four categories of models. Students exhibited one- or two-dimensional reasoning with either (or both) height and length correspondence that varied in terms of duration and/or pitch features. 

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3. Steerable Environmental Simulations for Exploratory Learning

   Zhu, M. (January 2019, In Proceedings of E-Learn: World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education)

   This paper presents the software design for three interactive simulations on the subject of Earth and Environmental science in grades 5, 6 and 7. These simulations together with some programming activities have been successfully integrated into a series of instructional modules for local New Jersey elementary and middle schools. The goal of these modules was for the students to explore the steerable parameters of the simulations and develop their computational and mathematical thinking. In this paper, we present three simulations we developed, discuss their design and examine student assessment results that were collected and analyzed using statistical inferences. Our findings illustrate the effectiveness of such enticing exploratory learning processes for developing students’ reasoning of Earth and Environmental science, computational thinking and mathematics. 

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4. Impact of blended immersive virtual world and programming curriculum on student perspectives about scientific modeling

   Kamarainen, A; Metcalf, S; Dickes, A; Gun-Yildiz, S; Brennan, K; Grotzer, T; Dede, C (April 2019, Annual meeting program American Educational Research Association)

   null (Ed.)

   EcoMOD uses a design-based research approach to develop and study an elementary curriculum that combines an immersive virtual environment with interactive computer programming interface to support computational modeling, ecosystem science understanding, and causal reasoning. Here we report on changes in students’ perspectives on modeling before and after use of the fifteen day interactive, technology-based curriculum in a 3rd and 4th grade classroom. Pre-post interviews were conducted with ten students, and preliminary results suggest that students demonstrated an increased awareness that models are designed for a purpose, and the purposes students described aligned more closely with scientifically relevant activities like prediction, investigation and explanation. Students also increased in their level of sophistication related to ecosystem science understanding and causal reasoning. 

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5. Examining students’ reasoning of multiple quantities.

   Panorkou, N.; Germia, E. F. (January 2020, Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A.I.; null; Ruiz-Arias, P.M. (Ed.)

   In this report, we discuss five forms of reasoning about multiple quantities that sixth-grade students exhibited as they examined mathematical relationships within the context of science. Specifically, students exhibited forms of sequential, transitive, dependent, and independent multivariational reasoning as well as relational reasoning. We use data from whole-class design experiments with students to illustrate examples of each of these forms of reasoning. 

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