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…

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…

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

In this article, we show a dynamic graphic in Excel that is used to introduce an important concept in our subject, Statistics I: the probability density function. This interactive graphic seeks to facilitate conceptual understanding of the main aspects analysed by the learners.

This article describes activities in which students deepen their relational understanding of the equals sign through exploring inequalities in a competitive dice game, built around the familiar fairy-tale "The Three Little Pigs" and "The Big Bad Wolf." The activity can be adapted to different abilities by choosing more or less…

In 2006, Marcus du Sautoy delivered the Royal Institution Christmas Lectures on the subject of mathematics. From this, a workshop was created using ideas illustrated in the programme. A group of mathematical students from the University of Oxford, known as Marcus' Marvellous Mathemagicians, were trained in this workshop and now travel to schools…

"We can never be sure that there is not some wild, untamed piece of mathematics ready to spring out on us... This is what keeps mathematics enchanting." This is how Jim Neyland, one of the contributing authors to this book, describes mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to…

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

This article describes several methods from discrete mathematics used to simulate and solve an interesting problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? (Contains 5 figures.)

Uses probability and Pascal's triangle to analyze the game Plinko from the game show "The Price Is Right." (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Analyzes how each of the three opponents could win on the game show "Jeopardy" regardless of their relative standing when they enter the Final Jeopardy round. Analyzes optimal strategies for each contestant using probabilities. (MKR)

Explains an application of matrix algebra which involves probability matrices and weather predictions. Using probabilities of sunny or cloudy weather students can determine the effect weather on day one will have on subsequent days. (DH)

Identifies key questions concerning children's intuitions and conceptions of probabilistic notions. Research on the theoretical framework for probability studies, misconceptions and strategies, and pupil attainment is reviewed, and the methodology is evaluated. Finally, implications for classroom practice are discussed. (MNS)