Good number sense is fundamental for success in estimation, approximation, and problem solving. We need to develop a sense of large numbers because newspaper and television news reports contain many references to large quantities. The federal budget is expressed in billions and trillions of dollars, space distances in millions of light years or trillions of miles, computer speeds in nanoseconds (1 nanosecond = 1 billionth of a second), computer storage memory in gigabytes (1 gigabyte = 1 billion bytes), world populations in millions and billions of individuals, and nuclear weapons in millions of tons of TNT. Clearly, the average citizen needs a well-developed sense of large numbers to understand many of the news items that invade the home. Large-number concepts a re appropriate for development in upper elementary school, high school, and beyond. This article presents some examples to enhance a sense of large numbers in middle and high school students.

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### Robert N. Ronau

Authorities in the field of mathematical diagnosis have documented that diagnostic information is an essential and integral component of mathematics instruction (Ashlock 1976; Brueckner and Bond 1955; Buswell and Leonore 1926; Reisman 1972; and Underhill 1977). Yet partly because of time constraints and classroom-management difficulties, teachers often neglect formal diagnosis. This article presents a few examples of mathematical diagnosis by microcomputer and suggests possible future considerations for this field.

### Robert N. Ronau and Karen S. Karp

WE HEARD THAT REMARK OVER AND over when we visited a class of sixth graders for a week in a nearby middle school. Through an integrated approach that incorporated literature to define a topic—in this instance, garbage—we linked concepts and activities in mathematics and science. This article shares a strategy for teaching organization, analysis, and representation of data using manipulatives and graphing calculators.

### Karen S. Karp and Robert N. Ronau

Middle school students rank their birthday as being the most important day of the year for them and one that they eagerly anticipate, according to an informal poll. Teachers can capitalize on this interest by engaging them in the mathematical birth-date activities described in this article. Applications and tasks that are relevant to students' lives have been shown to motivate students at the middle school level, according to the *Curriculum and Evaluation Standards for School Mathematics* (NCTM 1989).

### Margaret Mohr-Schroeder, Robert N. Ronau, Susan Peters, Carl W. Lee and William S. Bush

This article describes the development and validation of two forms of the Geometry Assessments for Secondary Teachers (GAST), which were designed to assess teachers' knowledge for teaching geometry. Both forms were developed by teams of mathematicians, mathematics educators, psychometricians, and secondary classroom geometry teachers. Predictive validity for the GAST assessment was explored by observing and testing 157 teachers as well as administering pre– and post–tests to 3,698 students. The reliability coefficient for both GAST assessment forms was acceptable (r = .79). GAST assessment scores explained a statistically significant but small amount of the variance of student scores, demonstrating an effect that was greater than the number of years of teaching experience but smaller than the effect of having an advanced degree.