The authors set out to develop a series of mathematical games that could be played 'openhanded' over zoom using only a virtual deck of cards (deck.of.cards). This article briefly describes three games they have developed that other teachers might find valuable, whether for use in a remote learning environment or back in the classroom. Each game…

It is well known that two events A and B are independent if and only if . Here, we derive a condition for independence not well known. We then extend the condition for independence of n events.

Many people are unduly intimidated by the thought of teaching probability. At its most basic level, probability revolves around being able to predict whether a future event is certain, possible, or impossible. These basic concepts grow and develop into a more mathematical understanding of likelihood as children learn to quantify that…

We consider here two questions posed by first-year undergraduate students in a statistics tutorial session. These questions are related, and each concerns an aspect of independence in probability. The notion of independence does tend to be a little less intuitive than some of the other elementary probabilistic concepts, thereby providing students…

This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…

During the 2021-22 school year, the Mathematics Standards Review Committee reviewed the 2007 Minnesota K-12 Academic Standards in Mathematics, other states' recently revised standards, current academic research, K-12 instructional best practices and public feedback. This review process followed the guidelines in Minnesota Statutes 2023, section…

Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

The Price is Right Bidder's Row and games provide many opportunities for mathematical connections. The Price is Right website has videos or pictures for students to see how each game is played (http://www.priceisright.com/games/). This article will describe the mathematics of probability and statistics that is integrated in the famous television…

The Monte Carlo method and related multiple imputation methods are traditionally used in math, physics and science to estimate and analyze data and are now becoming standard tools in analyzing business and financial problems. However, few sources explain the application of the Monte Carlo method for individuals and business professionals who are…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

A classic TV commercial once asked, "How many licks does it take to get to the center of a Tootsie Roll Tootsie Pop?" The narrator claims, "The world may never know" (Tootsie Roll 2012), but an Internet search returns a multitude of answers, some of which include rigorous systematic approaches by academics to address the…

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…

Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.