We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…

To determine whether having a program is sufficient one must first define what is meant by "program." If by program one refers to the pullout program in the elementary school, or the afterschool enrichment program in the middle school, or the Advanced Placement program in the high school, or the hockey program, then certainly having a "program" is…

Researchers, educators, and parents have long believed that children learn cause and effect relationships through exploratory play. However, previous research suggests that children are poor at designing informative experiments; children fail to control relevant variables and tend to alter multiple variables simultaneously. Thus, little is…

An experiment is described that allows students to experimentally determine an empirical formula for silver sulfide. At elevated temperatures, silver sulfide reacts in air to form silver, silver sulfate, and sulfur dioxide. At higher temperatures (960 [degree]C) silver sulfate decomposes to produce metallic silver. (Contains 1 figure and 1 table.)

This article draws on the 21st Century Skills Movement and the successful teaching practices of Asian schools in order to provide five suggestions that secondary math teachers can incorporate into their classrooms in order to promote the skill set necessary for an ever-changing global economy. Problem-based instruction, student-led solutions, risk…

The authors of the three papers in this issue discuss and analyze the practice underlying "critical exploration," a research pedagogy applied in common within their separate art, science, and teacher education classrooms. Eleanor Duckworth developed critical exploration as a method of teaching by involving students so actively and reflectively…

I discuss my experience with teaching an advanced undergraduate Real Analysis class using both lecturing and the small-group guided discovery method. The article is structured as follows. The first section is about the organizational and administrative components of the class. In the second section I give examples of successes and difficulties…

The "tabula rasa" of this article's title is a Latin term meaning "clean slate." For centuries before January 6, 1907, and continuing more than 100 years since, teachers have walked into classrooms of young children convinced they know full well what is good for them, and what should be poured into their minds and by what means. But on that day,…

This article outlines a method of conducting a laboratory designed to discover mathematical integration with students. The results are produced and verified in the laboratory by students. Understanding that an integral is defined by the area bounded by a function of x and the x-axis from a point a to a point b is challenging. Students often have…

In this article, the author discusses the advantages and the disadvantages of using surprise elements in teaching mathematics. According to the author, there are three key ideas concerning the element of surprise: (1) The ethical aspects of teachers' manipulation of their students in order to construct surprise; (2) Every mathematical task…

The article describes a new discovery experiment that uses thermodynamical analysis to study neutralization reactions based on neutralization of citric acid. The experiment would be able to reinforce students' understanding of stoichiometry and allow for the discovery of basic concepts of thermochemistry.

The manner in which teachers mediate children's learning varies across early childhood classrooms. In this study, we used a multi-element design to evaluate the efficacy of three commonly implemented strategies that varied in teacher directedness for teaching color- and object-name relations. Strategy 1 consisted of brief exposure to the target…

The author builds on arguments he has made elsewhere that good commercial video games foster deep learning and problem solving and that such games in fact promote mastery as a form of play. Here he maintains that some good video games engage players with an important type of play, namely of play as discovery, of play as surmising new possibilities…

When state and local standards drive instruction, teachers often worry about compromising their creativity for a prescriptive curriculum with predictable outcomes. It is possible for creative teaching to flourish by using touchstone texts, or mentor texts, that engage both teacher and student in exploratory yet purposeful learning. (Contains 1…

In the monograph The Math Teacher (following the Third International Scientific Colloquium Mathematics and Children in 2011), the term "teacher" designates a person who teaches mathematics, and the context of each article reveals whether this implies the teacher at a pre-school institution, a school or a university instructor. In…