In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this…

A derivation of the Maxwell Boltzmann distribution without using the Lagrange method of undetermined multipliers is represented. (Contains 1 figure and 2 notes.)

Real numbers are often a missing link in mathematical education. The standard working assumption in calculus courses is that there exists a system of "numbers", extending the rational number system, adequate for measuring continuous quantities. Moreover, that such "numbers" are in one-to-one correspondence with points on a "number line". But…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

In this article we discuss an approach to the critical problem of student retention and the high school-college transition. The context of the discussion is centered on science and engineering students for whom calculus in the first year in college is an essential requirement for on-time graduation. This transition/retention problem has become…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

This article offers an introductory activity for the limit concept with a geometrical and historical foundation. A connection among Geometry, Measurement and Calculus is highlighted with the help of technology. The geometrical drawing, measurement and graphing capabilities of both TI-89 and Geometer's Sketchpad make it possible for students to…

Research on the impact of Standards-based, K-12 mathematics programs (i.e., written curricula and associated teaching practices) and of reform calculus programs has focused primarily on student achievement and secondarily, and rather ineffectively, on student attitudes. This research has shown that reform programs have competed well with…

Principle of duality and numerical calculation of income and substitution effects under Hicksian Compensation are often left out of intermediate microeconomics courses because they require a rigorous calculus based analysis. But these topics are critically important for understanding consumer behavior. In this paper we use excel solver--a…

As the use of web-based homework delivery and checking systems expands, we have greater need to evaluate how students engage with these systems and how changes in the systems influence student behavior. Reported here is the assessment of WeBWorK, an open-source web-based homework program used largely in postsecondary math and science courses, with…

This study sought to gather empirical evidence of the effectiveness of calculus instruction like that used in the Calculus and Mathematica project by examining and comparing the effects of three different instructional approaches to calculus on students' (n=100) abilities to use and understand connections between numerical, graphical, and symbolic…

Presented is the work of the calculus group of SMSG. The Advisory Board expressed a desire for a suitable high school calculus text. The calculus group surveyed available texts and, finding none which met advisory board requirements, outlined a suitable course. This outline was annotated for use by future writers. Some group members felt a more…

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

The purpose of this investigation was to examine the interactive effects of prior mathematics preparation and instructional method on achievement in an introductory calculus course taught by both Personalized System of Instruction (PSI) and conventional approaches. Subjects were 248 university students, 60 from the self-paced method and 188 from…