The sampling (probability) distribution for the sum of dice is presented graphically as a compelling demonstration of the Central Limit Theorem.

Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original…

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

The Landau-Zener formula provides the probability of non-adiabatic transitions occurring when two energy levels are swept through an avoided crossing. The formula is derived here in a simple calculation that emphasizes the physics responsible for non-adiabatic population transfer. (Contains 2 figures.)

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Mathematics teachers, researchers and specialists in educational technology from Quebec, Canada developed virtual tools that make interactive simulations of games of chance. These tools were presented to a group of teachers from New Brunswick through workshops and they then got to test and validate them with their students. Semi-structured…

The phenomenon of cheating on exams, which harms both the reputation of an academic institution and the students who don't cheat, is becoming increasingly common. We attempt to shed light on this phenomenon using data from a survey of graduates of the College of Management Academic Studies in Israel. Three aspects of the problem are examined: 1)…

Mike Shaughnessy is Professor Emeritus of Mathematics and Statistics at Portland State University in Oregon. He served as co-chair for the Board for the Special Interest Group for Research in Mathematics Education of the American Educational Research Association from 2005-2007. A member of the Board of Directors of the National Council of Teachers…

This mixed-methods study examines the effects of rating scale length and rater experience on listeners' judgments of second-language (L2) speech. Twenty experienced and 20 novice raters, who were randomly assigned to 5-point or 9-point rating scale conditions, judged speech samples of 38 newcomers to Canada on numerical rating scales for…

This article reports the findings from a comparative analysis that examined several mathematical content strands, reasoning processes, and emphasis on technology in prior K-8 state mathematics standards and the Common Core State Standards for Mathematics (CCSSM). Various methodological tools were utilized to compare and contrast CCSSM with prior…

Acknowledging the powerful that role formative feedback plays in learning, students who are training for professions in the clinical setting and learn while working alongside professionals in their field report that they receive limited feedback. Formative feedback helps students gauge progress, identify weaknesses, and improve performance as well…

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning.…

Government policies that promote Year 12 completion are based on a recognition that, on average, the completion of senior secondary schooling leads to better labour market outcomes. Completing senior secondary schooling is not, however, for everyone, particularly not for those who are less academically inclined or who are unsuited to the…

The documentary film "The Lottery" focuses on the battle between advocates for a New York City charter school provider, Harlem Success Academy Charter Schools (HSA), and those presented as charter school opponents. It uses the struggle of four students who hope to get into a charter school as a vehicle to examine how difficult it is for…

This presentation focuses on the quasi-experimental methods used to select comparison schools for an evaluation of a federal investing in innovation (i3) validation grant. The Northeast Tennessee College and Career Ready Consortium (NETCO) consists of 29 high schools participating in a five-year program to expand students' access to rigorous…