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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden
Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden
Mathematics
Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.
Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez
Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez
Mathematics
Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking, …