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Al Cuoco

The views expressed in “Soundoff!” reflect the views of the author and not necessarily those of the Editorial Panel of the Mathematics Teacher or the National Council of Teachers of Mathematics. Readers are encouraged to respond to this editorial by sending doublespaced letters to the Mathematics Teacher for possible publication in “Reader Reflections.” Editorials from readers are welcomed.

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Al Cuoco

People all over the country are working on the restructuring of mathematics education. We are in the midst of the most serious and promising educational reform effort of the twentieth century.

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Al Cuoco and E. Paul Goldenberg

In a recent “Sound Off” in Mathematics Teacher, Robert Reys and Rustin Reys (2009) contrasted two curricular approaches, what they called “subjectbased” and “integrated.” They came down heavily in favor of the latter, arguing that many of the difficulties that students have with high school mathematics are consequences of the subject–based organization.

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Al Cuoco and Michelle Manes

How you can frequently use the memory limitations of a graphing calculator to teach important conceptual ideas.

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Al Cuoco and E. Paul Goldenberg

Welcome to “Delving Deeper,” a new department in the Mathematics Teacher. The concept for this department has been evolving for several years, but the basic goal is to provide teachers with a forum for their own mathematical investigations. Do you have an idea in your mind or on your computer that is based on one of your mathematical explorations? Here is a chance to get your idea off your hard drive and into print. Submissions of up to ten single-spaced pages are welcomed. Articles written jointly with others (including students or mathematicians) are encouraged.

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Al Cuoco and E. Paul Goldenberg

From the first time that we used such inter-active geometry programs as The Geometer's Sketchpad and Cabri Geometry, we were intrigued by their potential to help students develop ways of thinking that underlie calculus and analysis (Cuoco, Goldenberg, and Mark 1995; Cuoco and Goldenberg 1997). One theme in this approach has been to look at optimization problems as geometrically defined functions, for example, the sum of the distances from a point to three fixed points. In an interactive geometry world such as Sketchpad or Cabri, the user does not need to impose coordinates on the plane and specify the distances algebraically at the outset. He or she may define the function directly as a geometric relationship; manipulate its variable (the movable point); and observe, numerically or geometrically, the value (sum of distances) that results. The algebraic step is also valuable; both geometric and algebraic interpretations lead to important insights. But the geometric step is often a particularly productive starting place for generating the ideas that one may want to revisit algebraically.

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Al Cuoco, E. Paul Goldenberg and June Mark

“Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what the users and makers of mathematics do and what they say.” (Cuoco, Goldenberg, and Mark 1996, p. 376)

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E. Paul Goldenberg, June Mark and Al Cuoco

Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what the users and makers of mathematics do and what they say (Cuoco, Goldenberg, and Mark 1996, p. 376).

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June Mark, Al Cuoco, E. Paul Goldenberg and Sarah Sword

Mathematical habits of mind include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work (Cuoco, Goldenberg, and Mark 1996; Goldenberg 1996). Current recommendations emphasize the critical nature of developing these habits of mind: “Once this kind of thinking is established, students can apply it in the context of geometry, trigonometry, calculus, data and statistics, or other advanced courses” (Achieve 2008, p. 4).

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Sarah Sword, Ryota Matsuura, Al Cuoco, Jane Kang and Miriam Gates

Two high school classroom situations illustrate how routinely promoting the two practices of experimenting and describing in increasingly precise language can support students' modeling.