At their core, Intelligent Tutoring Systems consist of a student model and a policy. The student model captures the state of the student and the policy uses the student model to individualize instruction. Policies require different properties from the student model. For example, a mastery threshold policy requires the student model to have a way…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

Many science problems require students to convert units. While this skill may not get the attention that more central science concepts do, teachers in the middle school and early high school grades will be doing their students a great service by leaving them with a strong understanding of both the skill itself and the reasons behind it. When the…

Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

In eighth grade, students usually learn about forces in science class and linear relationships in math class, crucial topics that form the foundation for further study in science and engineering. An activity that links these two fundamental concepts involves measuring the distance a spring stretches as a function of how much weight is suspended…

In recent years, there has been some dispute over the appropriate way to model decision making in professional sports leagues. In particular, Szymanski and Kesenne (2004) argue that formulating the decision-making problem in a noncooperative game leads to radically different conclusions about the nature of competition in sports leagues. The author…

Shows that the experiment of the ancient Greek mathematician and geographer, Eratosthenes, can be replicated and used to teach geographic concepts. Eratosthenes calculated the most accurate ancient measurement of earth based on fundamental mathematics concepts and earth-sun relations. Includes instructions, illustrations, graphs, and historical…

The Beginning Teacher Evaluation Study (BTES), Phase II, was a research project on effective teaching behavior--what teachers do that significantly affects what and how pupils learn. The purposes of Phase II were to (1) develop an assessment system for measuring teacher and pupil behaviors and other factors which could influence each of them and…