Literature Index

Understanding counting rules is challenging for students; in particular, they struggle with determining when and how to implement combinations, permutations, and the multiplication rule as tools for counting large sets and computing probability. We present an activity – using ideas from the games of poker and pinochle – designed to help students solidify and expand upon counting techniques while also promoting critical thinking in the classroom. While this activity has been used in college level courses, we believe it would also be applicable in a high school discrete mathematics class or in any probability course having substantial emphasis on these topics. We present and discuss the activity including desired learning outcomes, rationale, opportunities for teachable moments, and potential follow-up assignments.

Monte Carlo simulations (MCSs) provide important information about statistical phenomena that would be impossible to assess otherwise. This article introduces MCS methods and their applications to research and statistical pedagogy using a novel software package for the R Project for Statistical Computing constructed to lessen the often steep learning curve when organizing simulation code. A primary goal of this article is to demonstrate how well-suited MCS designs are to classroom demonstrations, and how they provide a hands-on method for students to become acquainted with complex statistical concepts. In this article, essential programming aspects for writing MCS code in R are overviewed, multiple applied examples with relevant code are provided, and the benefits of using a generate–analyze–summarize coding structure over the typical “for-loop” strategy are discussed.

The questionnaire survey was conducted among post-graduate and under-graduate students of two agricultural universities in Poland to study their basic knowledge of graphing. A smaller group of primary school pupils was also administered in the survey for comparison purposes. The survey consisted of only two questions concerning the choice of the best and the worst chart among three options: a piechart, a vertical barchart with three-dimensional columns, and a horizontal barchart. The charts were constructed in such a way that only one type - the horizontal barchart - could be considered a good chart. The results are worrying: among university students, both under- and postgraduate, quite often the three-dimensional barchart was chosen as the best one. Among the primary school pupils the piechart was most often chosen as the best one.

In this chapter, the process of developing a form of alternative assessment, the portfolio, will be described. The portfolio is a purposeful collection of student work that exhibits the student's efforts, progress and achievements over time. Portfolio develpment supports the assessment of long-term projects, encourages student-initiated revision and provides a context for presentation, guidance, and critique. The purpose of portfolio development is the same no matter the course or age of the students, to display the products of instruction in a way which challenges teachers and students to focus on meaningful outcomes. The context in which the use of portfolios is described here is a graduate level statistics course where an additional purpose is to provide students with an organized reference on statistical programming, analylsis, and interpretation. However, the process used in developing portfolios and the important issues surrounding portfolio assessment can easily be generalized to different educational levels and subject areas. Some of the questions addressed in this chapter are 1) What is the underlying belief concerning knowledge construction which guides portfolio assessment?, 2) How do you develop and use portfolios?, 3) What does a portfolio look like?, and 4) What are the major considerations in deciding to use portfolio assessment?