Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics.

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- Author or Editor: Zalman Usiskin x

### Zalman Usiskin

A strong curriculum is not the sole reason for Singaporean students' success on international assessments.

### Zalman Usiskin

This article briefly describes the timing of the first concentrated study of algebra over the 100 years of NCTM, from a 9th-grade course taken by only about 1/5 of students to a course taken by virtually all students, with almost half taking it in 8th grade.

### Zalman Usiskin

In this article, two problems are called *equivalent* if they can be solved using the *same* mathematics.

### Zalman Usiskin

“Constructions are different!” “Constructions are interesting!”

### Zalman Usiskin

A thorough discussion of early appearances of approaches using transformations in geometry textbooks intended for use in high schools.

### Zalman Usiskin

Even under quite reasonable schemes for decision making some sets of preference choices may not obey transitivity. The specific examples of such sets given here give rise to paradoxes because we so strongly believe transitivity should hold.

### Zalman Usiskin

The subfield of pure mathematics that has grown most significantly in the past few decades is that of algebra, by which is meant “higher” or “abstract” algebra and linear algebra. Twenty years ago courses in algebra were at the advanced undergraduate and graduate level, and it was easy to become a certified mathematics teacher without having any knowledge of groups, rings, fields, or vector spaces. Today virtually all prospective teachers take a course in which some of these structures are studied.

### Zalman Usiskin

It is possible to form a set in an infinite additive group by beginning with any nonzero real *a* and adding it to itself over and over again, then including zero and the opposites of all numbers in the set. We call such a set the set of integral multiples of *a.* If *a =* 3, then here is such a set.