数学 & 统计项目

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分会报告8A -海报展示

Addition is regarded as a fundamental part of mathematical practice. Yet, we do not understand how students construct their understanding of this operation. This project will look at three methods of addition and then discuss the underlying logical systems that give rise to these methods. We will then consider the cognitive neuroscience and the human reasoning in mathematics behind one of these methods. 最后, we will consider some teaching methods and strategies that align with a supposed model of student learning.

The Kaplan Meier Estimator is the most well-known survival curve estimator in the branch of biostatistics. 然而, when the Kaplan Meier estimator is found for two datasets assuming a certain condition known as stochastic order, the estimator can violate the assumption, which presents some issues of bias and mean squared error. 例如, we would expect a Degree 1 Carcinoma Cancer patient to have higher survival probabilities and an increased likelihood of living longer than a Degree 2 Carcinoma Cancer patient because of their slightly healthier condition. 然而, the survival functions we derived from Carcinoma Cancer datasets (survival package in R studio, 斯坦福大学, 1977) cross over each other with respect to survival probability and time, which is a violation of stochastic ordering. 在这个项目中, we will consider an estimator proposed by Rojo (2004) to force stochastic ordering as we evaluate the Carcinoma Cancer data in the two-sample case as well as look into a theoretical three-sample case using exponential data created using R studio.

在这个项目中 we investigate the benefits of incorporating movement into the mathematics classroom. We also look at methods for implementing movement into a secondary mathematics lesson with a focus on pedagogical techniques that include active and tactile learning.

Having the energy and supplies to get to their destination and back is important to hikers and hunters alike. There are times where hunters are successful in their efforts, and they are far from their base camp. How far can they hike so that they can still not only get back, but also bring back their harvested animal? 在这个项目中, we will seek to find the answer in order to help hunters and hikers know their limits while they enjoy the beautiful scenery.

在这个项目中, we consider spatial relationships between a variety of variables at the county level in Colorado based on data collected from the United States Congress Joint Economic Committee. These spatial relationships are considered for both raw data and residuals of linear models. Analysis of the linear model residuals can be used to determine whether a spatial term belongs in each model.