This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

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### Thomas G. Edwards

Without question, mathematics in general, and algebra in particular, have served as “gatekeepers” to the study of other academic fields, such as engineering, the physical sciences, computer science, and medicine, as well as to increased vocational opportunities in technical support fields. As a result, middle school teachers have felt increased pressure both to teach algebraic concepts directly and to develop mathematical concepts in ways that will support students' formal study of algebra in the future. A recent call for manuscripts in *Mathematics Teaching in the Middle School* noted that “the rate of students' success with this subject has been linked to the careful, planned development of algebra as a way of thinking about and modeling various phenomena at every grade level” (NCTM 1999). Such a careful, planned development requires clearly identifying the “big ideas” of algebra that are appropriate to middle school.

### Thomas G. Edwards

A number of years ago in geneva, switzerland, Barbel Inhelder and Jean Piaget (1958) conducted a series of experiments to study the development of logical thinking in young children. One of those experiments involved rolling balls of different masses down inclines of varying heights. The object was to see if young children could make appropriate inferences regarding the relationship among the variables in the problem.

### Thomas G. Edwards

During my twenty-four years as a middle school and high school teacher, I observed that students were often fascinated by vignettes from the history of mathematics. When the vignette had an ancient Egyptian setting, that background added a certain mystique.

### Thomas G. Edwards

Much of What We Know Today About the mathematics of ancient Egypt is contained in a papyrus scroll that was copied from an earlier scroll by the scribe Ahmes in about 1650 BME (before the modern era) (Boyer 1968). A fascinating feature of ancient Egyptian mathematics is its treatment of common fractions. In most cases, the Egyptians used only unit fractions, that is, fractions with numerators of 1. The one common exception is 2/3, and they would occasionally use fractions of the form *n*/(*n* + 1). However, both forms are complements of unit fractions.

### Thomas Edwards

Given the recent public mania over bungee jumping, stimulating students' interest in a model of that situation should be an easy “leap.” Students should investigate the connections among various mathematical representations and their relationships to applications in the real world, asserts the *Curriculum and Evaluation Standards for School Mathematics* (NCTM 1989). Mathematical modeling of real-world problems can make such connections more natural for students, the standards document further indicates. Moreover, explorations of periodic real-world phenomena by all students, as well as the modeling of such phenomena by college-intending students, is called for by Standard 9: Trigonometry.

### Thomas G. Edwards

A variety of instructional methods should be used in classrooms in order to cultivate students' abilities to investigate, to make sense of, and to construct meanings from new situations; to make and provide arguments for conjectures; and to use a flexible set of strategies to solve problems,” according to the NCTM's *Curriculum and Evaluation Standards for School Mathematics* (1989, 125). This article examines a way to recycle and enrich an old idea—exploring the effects of varying the coefficients in the general quadratic function—by using graphing calculators.

### Thomas G. Edwards and S. Aslı Özgün-Koca

Using quadratic functions as an example, see how the evolution of technology has altered the expectations of students' understanding and critical thinking.

## Mathematical Explorations: Interpreting Box Plots with Multiple Linked Representations

### classroom-ready activities

### S. Asli Özgün-Koca and Thomas G. Edwards

A box plot activity is driven by a TI-Nspire calculator.