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Physical Sciences and Mathematics Commons™

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Western Michigan University

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Mathematics

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Full-Text Articles in Physical Sciences and Mathematics

Alternating Connectivity In Random Graphs, Patrick Bennett, Ryan Cushman, Andrzej Dudek Mar 2020

Alternating Connectivity In Random Graphs, Patrick Bennett, Ryan Cushman, Andrzej Dudek

Faculty Research and Creative Activities Award (FRACAA)

Many problems in graph theory are so hard in general that they seem hopeless. So sometimes mathematicians lower our expectations a bit, and try to prove that a statement is true for "almost all graphs" (for some reasonable interpretation of what that means) rather than insisting on proving it for all graphs. One way to address questions about about almost all graphs to use a random graph model, the first of which is due to Erdos, Rényi and Gilbert in the 1950's. Since then many more models have been introduced, but they all generate graphs according to the outcome of …

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Elementary/Middle School Pre-Service Teachers’ Understanding Of Variability And The Use Of Dynamical Statistical Software, Yaomingxin Lu Apr 2018

Elementary/Middle School Pre-Service Teachers’ Understanding Of Variability And The Use Of Dynamical Statistical Software, Yaomingxin Lu

Research and Creative Activities Poster Day

A primary purpose of the study was to examine the effects of using dynamical statistical software (DSS) on prospective teachers’ (PSTs) understanding of statistical concepts, especially variability. Data were collected from PSTs enrolled in a probability and statistics course designed for prospective K-8 teachers. After initial analysis of the data using coding and classification schemes, we found the need to develop a more targeted framework to analyze students’ different levels of understanding. The variability framework (Garfield & Ben-Zvi, 2005) and the Structure of Observed Learning Outcomes (SOLO) taxonomy were then used in combination to develop a revised framework in order …

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