CORE MATHEMATICS AT THE UNITED STATES MILITARY ACADEMY: LEADING INTO THE 21st CENTURY

Abstract

The Department of Mathematical Sciences at the United States Military Academy is prepared to lead the young minds of America into the 21st century with a bold and innovative curriculum coupled with student and faculty growth models and interdisciplinary lively applications. In 1990, the mathematics department began its first iteration of their "7 into 4" core curriculum. Each year improvements have been incorporated into the core mathematics program. In 1992 , interdisciplinary applications appeared in the core program as an opportunity t o communicate and work with the academic disciplines. Our core curriculum is tied together both vertically and horizontally with threads. These threads tie together both the content within each course as well as among all the courses. Student attitudes are measured through course surveys as we attempt to develop "life long learners". Student performance is measured or calibrated throughout their four years.

Aiding Undergraduate Understanding of Covariance and Correlation

“…Unlike some other texts, Devore [2] points out that a major defect of using the covariance to define the degree of association between two random variables is that the computed value depends critically on the units measured. This unit dependence follows clearly from the definition in (1).…”

Classical Probability Application: A Discrete Dynamical System Defined by a Markov Chain

“…These threads include: writing in mathematics, nature and history of mathematics, analysis, scientific computing, connectivity and modeling [1]. The student growth model provides progressively less guidance and progressively higher expectations on individual learning and written presentations as the student passes through the core mathematics curriculum.…”

“…Our students are required to maintain portfolios for their core courses [1]. The use of the portfolios is extremely helpful for a student to review previous core mathematics projects in order to recall the experience.…”

“…It can be traced back to approximately 1830 as being part of the curriculum [1]. Today, our topical coverage includes: descriptive statistics, classical probability, discrete random variables, continuous random variables, jointly distributed random variables, estimation, hypothesis testing, and simple linear regression .…”

Chalkboard vs. Paper: Technique for Improving Collaboration in Active Learning Activities

“…After conversations with colleagues about this challenge, we decided to experiment with a change in group-work format designed to encourage greater engagement among group members. The use of chalkboards or whiteboards to encourage student participation and collaboration is not a new approach, and benefits have been documented by other educators (Arney et al, 1995;Graham et al, 1999;Khalid et al, 2011;Subramanian et al, 2009). Our intention is to compare the outcomes of small-group, collaborative problem-solving when groups work at the board on a common solution versus when groups work at tables, with instructions to collaborate on solving the problems together, yet ultimately recording the solutions on individual paper worksheets.…”