The authors present a new classroom-tested lesson that was designed to engage students in the joy of mathematical inquiry through a card game, Frustration, while building number sense, understanding of uncertainty, statistical reasoning, and discourse skills. The purpose in developing and sharing these lessons is to highlight how games of chance…

To facilitate people using mathematical reasoning to compare risks associated with the COVID-19 pandemic, the National Science Foundation (NSF) funded the COViD-TASER (Creation of Visualizations of Data: The Application of STEM Education Research) research team to create the COVID-19 Relative Risk Tool (RRT). The RRT uses an interactive bar chart…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and…

The Common Core State Standards for Mathematics have a widespread impact on children's statistical learning opportunities. The Grade 6 standards are particularly ambitious in the goals they set. In this critique, experiences helping children work toward the Grade 6 Common Core statistics expectations are used in conjunction with previous research…

Teachers often use number talks at the beginning of class to hear the ways that students understand mathematical topics so that they can base future instruction on student thinking. Students who engage in number talks become accustomed to thinking about mathematics in multiple ways, sharing their thoughts and critiquing the thoughts of others. The…

By focusing on a particular alteration of the comparative likelihood task, this study contributes to research on teachers' understanding of probability. Our novel task presented prospective teachers with multinomial, contextualized sequences and asked them to identify which was least likely. Results demonstrate that determinants of…

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.

The objective of this article is to contribute to research on teachers' probabilistic knowledge and reasoning. To meet this objective, prospective mathematics teachers were presented coin flip sequences and were asked to determine and explain which of the sequences was least likely to occur. This research suggests that certain individuals, when…

This study investigated prospective elementary (PEMTs) and secondary (PSMTs) school mathematics teachers' statistical reasoning. The study began with the adaptation of the Statistical Reasoning Assessment (Garfield, 2003) test. Then, the test was administered to 82 PEMTs and 91 PSMTs in a metropolitan city of Turkey. Results showed that both…

In Maori medium schools, research that investigates children's mathematical computation with number and connections they might make to mathematical ideas in other strands is limited. This paper seeks to share ideas elicited in a task-based observation and interview with one child about the number ideas she utilises to solve a problem requiring…

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…

Within the limited field of research on teachers' probabilistic knowledge, incorrect, inconsistent and even inexplicable responses to probabilistic tasks are most often accounted for by utilizing theories, frameworks and models, which are based upon heuristic and informal reasoning. More recently, the emergence of new research based upon informal…

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

There is much to be learned and pondered by reading "Proofs and Refutations" by Imre Lakatos (Lakatos, 1976). It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning…