Discovery Algebra: Graphing Linear Equations
David Thomas, Rex Thomas
One teacher's effort to change the classroom environment. It reveals a teacher, strongly motivated by dissatisfaction with existing practices, experimenting with a new approach to teaching. It shows that change can be made. The story is told through the teacher's perception of classroom events.
Broken-Line Functions with Unbroken Domains
Pavel Satianov, Michael Fried, Miriam Amit
Although we no longer doubt the legitimacy of split domains as a function, students still have difficulty perceiving a graph having a shape like that of Euler and d'Alembert's string as the graph of a single function rather than of several joined functions (Vinner 1989). Given the centrality of the function concept in the school curriculum (NCTM 1989; Amit and Koren 1993), one cannot underestimate the importance of exposing students to this type of function. A method of introducing students to this concept while furnishing the teacher with material that has its own intrinsic interest (Satianov 1995).
The Role of Instructors in Creating Math Anxiety in Students from Kindergarten through College
Carol Jackson, R. Leffingwell
"I just don't like math". How often have students uttered these anxiety-based words? The primary purpose of this research was to investigate the types of instructor behavior that created or exacerbated anxiety. In addition, the authors wanted to determine the grade levels (K–college) in which mathematics anxiety first occurred in these students. In this article, the term instructor includes anyone who teaches at any level, kindergarten through college.
Counting Triples, Triangles, and Acute Triangles
Activities involving counting triples, triangles, and acute triangles enrich the curriculum with excursions into modular arithmetic, the greatest-integer function, and summation notation. In addition, more advanced students can apply difference-equation techniques to find closed forms and can use mathematical induction to prove the formulas. Students may be learning about these topics for the first time, or they may be reviewing familiar ideas in different problem-solving contexts. In either situation, personal arsenals of problem-attacking skills are strengthened.
Exploring Hyperbolic Geometry with The Geometer's Sketchpad
Marlene Dwyer, Richard Pfiefer
This article explores some principles of, and shows several constructions in, hyperbolic geometry using script tools originally created by Mike Alexander and modified by Bill Finzer and Nick Jackiw for The Geometer's Sketchpad (Jackiw 1995). These tools are compatible with The Geometer's Sketchpad 3.0 and 3.05 for both Macintosh and Windows users.