Computer simulation can be used to demonstrate why the unbiased sample variance uses degrees of freedom (n-1). This is first demonstrated for sampling from a normal random variable, and in additional simulations for some selected non-normal random variables, namely, chi-square and binomial.

In regression analysis courses, there are many settings in which the response variable under study is continuous, strictly positive, and right skew. This type of response variable does not adhere to the normality assumptions underlying the traditional linear regression model, and accordingly may be analyzed using a generalized linear model…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

The Hunger Games is an annual event in the fictional country of Panem. Each year, 24 children (tributes) are chosen by lottery from 12 districts to fight to the death in the arena for the entertainment of the Capitol citizens. Using statistical analysis and computer simulations, we will explore the possibility that the Gamemakers, those in charge…

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A…

In this article, Strayer and Matuszewski present a six-phase strategy that teachers can use to help students develop a conceptual understanding of inferential hypothesis testing through simulation. As Strayer and Matuszewski discuss the strategy, they describe each phase in general, explain how they implemented the phase while teaching their…

This exploratory study examined the influence of different virtual manipulative (VM) types on the nature of student pairs' techno-mathematical discourse (TMD). Three fifth-grade student pairs participated in 9 sessions of mathematics instruction using VMs. The study compared three VM types: linked, pictorial, and tutorial. Students' levels of…

As literature has reported, it is usual that university students in statistics courses, and even statistics teachers, interpret the confidence level associated with a confidence interval as the probability that the parameter value will be between the lower and upper interval limits. To confront this misconception, class activities have been…

The Analysis of Variance is often taught in introductory statistics courses, but it is not clear that students really understand the method. This is because the derivation of the test statistic and p-value requires a relatively sophisticated mathematical background which may not be well-remembered or understood. Thus, the essential concept behind…

Classification evaluation metrics are often used to evaluate adaptive tutoring systems-- programs that teach and adapt to humans. Unfortunately, it is not clear how intuitive these metrics are for practitioners with little machine learning background. Moreover, our experiments suggest that existing convention for evaluating tutoring systems may…

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

Prospective elementary teachers at three universities engaged in online modules called the Virtual Field Experience, created by the Math Forum. The prospective teachers learned about problem solving and mentoring elementary students in composing solutions and explanations to nonroutine challenge problems. Finally, through an asynchronous online…

Self-regulated learning (SRL) environments provide students with activities to improve their learning (e.g., by solving exercises), but they might also provide optional activities (e.g., changing an avatar image or setting goals) where students can decide whether they would like to use or do them and how. Few works have dealt with the use of…

The effect of simulation-based probability teaching on the prospective teachers' inference skills has been examined with this research. In line with this purpose, it has been aimed to examine the design, implementation and efficiency of a learning environment for experimental probability. Activities were built on modeling, simulation and the…

In schools, learning spatial geometry is usually dependent upon a student's ability to visualize three dimensional geometric configurations from two dimensional drawings. Such a process, however, often creates visual obstacles which are unique to spatial geometry. Useful software programs which realistically depict three dimensional geometric…