IXL is an end-to-end teaching and learning solution that engages learners in grades Pre-K through 12 with a comprehensive curriculum and a first-of-its-kind assessment suite. A core component of IXL's assessment suite is the IXL Diagnostic, an interim assessment designed by a team of educators and mathematicians that uses Item Response Theory…

Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of…

Probabilities tend to become an integral part of early childhood mathematics curricula. Research has shown that at the age of 4, children indicate basics of probabilistic reasoning and can engage with probabilistic tasks and uncertainty. The aim of this study is to examine whether methodological and design alterations influence children's…

This descriptive and correlational study investigated the effects of using PSPP in learning Statistics on students' attitudes and performance. The respondents of the study were 200 Grade 11 Senior High School students who were enrolled in Probability and Statistics subject during the Second Semester of School Year 2018-2019. The respondents were…

In this work we are going to present how an interactive platform can be used as a powerful tool to allow students to better explore a foundational problem in quantum chemistry: the application of the variational method to the dihydrogen molecule using simple Gaussian trial functions. The theoretical approach for the hydrogen atom is quite…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students' abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis…

Quantum mechanics (QMs) is a foundational subject in many science and engineering fields. It is difficult to teach, however, as it requires a fundamental revision of the assumptions and laws of classical physics and probability. Furthermore, introductory QM courses and texts predominantly focus on the mathematical formulations of the subject and…

In this paper, we explore the relationship between scaffolding, dialogue, and conceptual breakthroughs, using data from a design-based research study that focuses on the development of understanding of probability in 10-12 year old students. The aim of the study is to gain insight into how the combination of scaffolding for content using…

Whether through the use of online-only or hybrid/blended formats, colleges and universities across the country are increasingly utilizing online platforms as a medium for the delivery of instruction. At the same time, we know little about how student learning outcomes are related to students' engagement with online instructional formats. In…

The unexpectedness of the birthday problem has long been used by teachers of statistics in discussing basic probability calculation. An activity is described that engages students in understanding probability and sampling using the popular Facebook social networking site. (Contains 2 figures and 1 table.)

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships,…

This undergraduate physical chemistry laboratory exercise introduces students to the study of probability distributions both experimentally and using computer simulations. Students perform the classic coin toss experiment individually and then pool all of their data together to study the effect of experimental sample size on the binomial…