Argumentation is a process that occurs often in ill-defined domains and that helps deal with the ill-definedness. Typically a notion of "correctness" for an argument in an ill-defined domain is impossible to define or verify formally because the underlying concepts are open-textured and the quality of the argument may be subject to discussion or…

A number of studies have shown that spending time in nature produces cognitive benefits. What if a child's exposure to the out-of-doors is considered not just a beneficial extracurricular activity, but a fundamental building block to an elementary education in math and science? The Young Achievers Science and Math Pilot School operates a 9:30 a.m.…

Field studies are an excellent way for students to learn ecological concepts and practice doing science. This article presents an approach for the secondary science classroom that permits students to ask and answer their own questions, a prerequisite for truly experiencing the process of science. Students explore a local natural area and, in…

Encouraging students to make independent discoveries is an effective way to get them excited about mathematics, and sharing their triumphant moments (their light bulb moments) helps to spread this excitement to their peers. A Mathematics for the Liberal Arts course is a perfect venue for the sharing of light bulb moments, as it helps to correct…

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…

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…

"MathThematics" is a mathematics curriculum for grades 6 through 8 that combines activity-based, discovery learning with direct instruction. The textbook for each grade level has eight instructional modules, with each module focused on a theme. Open-ended questions and projects are utilized throughout the curriculum to assess…

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…

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,…

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 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 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…