Knowledge of probability is perceived as valuable in the 21st century. This knowledge enables people to understand and make informed decisions relating to uncertain events that occur in real life. Hence, many educational authorities have considered the inclusion of the teaching of probability important in their school curricula. This study…

We have extended two perspectives of proportional reasoning to solve problems based in probability. Four future middle grade teachers were enrolled in a mathematics content course that emphasized reasoning about multiplication with quantities. The course expected future teachers to generate and explain methods for solving proportions. Probability…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN ? QUAL) was used to examine students' reasoning processes when solving…

Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

The authors explored whether a testing effect occurs not only for retention of facts but also for application of principles and procedures. For that purpose, 38 high school students either repeatedly studied a text on probability calculations or studied the text, took a test on the content, restudied the text, and finally took the test a second…

Online learning from video modeling examples, in which a human model demonstrates and explains how to perform a learning task, is an effective instructional method that is increasingly used nowadays. However, model characteristics such as gender tend to differ across videos, and the model-observer similarity hypothesis suggests that such…

This article explores integrating place-based education with critical mathematics toward teaching mathematics for spatial justice. "Local Lotto," a curricular module with associated digital tools, was designed to investigate the lottery as a critical spatial phenomenon and piloted in urban high schools. This article describes findings…

This study is an exploration of teachers' engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an "unknown percentage" problem, which required the application…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

In this article, the authors discuss how acknowledging and embracing that the sample space is one of many ways to partition the set of all possible outcomes impacts the teaching and learning of sample space and probability. After recounting an exchange surrounding two viable answers to a probability question, the authors detail how developments…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

The goal of this geometry project is to use Voronoi diagrams, a powerful modeling tool across disciplines, and the integration of technology to analyze spring rainfall from rain gauge data over a region. In their investigation, students use familiar equipment from their mathematical toolbox: triangles and other polygons, circumcenters and…