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Finite mathematics & Applied calculus Instructor resources (7th Edition) |

We would like to introduce three texts that set new standards for current, reform-oriented, applied college mathematics. These high-quality texts meet the challenges of the most demanding student audiences, and completely integrate the use of graphing technology, spreadsheet technology (with Excel), and Internet resources.

Like the first six editions, the texts are filled with unrivaled pedagogy and applications based on real data with carefully references sources, and include integrated and extensive support for graphing calculator,spreadsheet, and Internet technologies. The seventh edition, a substantial revision of the sixth, continues to offer all these features but pays even more attention to algebraic preliminaries, with an expanded Precalclus Review and rewritten introductory chapter. Unlike any other texts on the market to date, the texts are supported by, and linked with, an extensive and highly developed student Website filled with interactive tutorials, randomized game tutorials, computational utilities, optional supplementary material, and much more.

Reform and the Rules of Three, Four and Five

We began writing our books around 1992 because we were dissatisfied with the books then available for finite math and applied calculus and had the idea that we could do a far better job by using innovative ideas being promoted by the “reform” movement in calculus at the time, exemplified by the “Harvard Calculus Consortium” [1]. The reform movement was a revolution in the presentation and conceptualization of calculus, where the so-called “rule of three” (presentation of mathematical concepts numerically, graphically, and algebraically) was introduced in the first edition of the Consortium’s Calculus book in 1993. In our first edition, called Finite Mathematics and Calculus Applied to the Real World (1995) we adopted this philosophy for both calculus and finite mathematics and extended it by introducing a fourth element which we felt was lacking in the “rule of three”, namely, the presentation of mathematical concepts verbally, and we are pleased to see that the “rule of four” is now widely adopted and considered an integral part of the reform approach to calculus. Moreover, our rule of four philosophy extends through all our subsequent editions. With the appearance of the second edition and the accompanying Website now at wanermath.com, we introduced a fifth element: presentation of mathematical concepts interactively.

Use of Spreadsheets

Another part of the reform movement that we thought useful to adopt was the use of technology, then typified by the newly-introduced Texas Instruments graphing calculators, to bring the numerical and graphical viewpoints to life. However, when planning our second edition, we realized that spreadsheet technology, largely neglected by the other textbooks at the time, was an even more powerful tool for the purpose and particularly useful for handling real datasets (see Real World Commitment below). It is also important for business math students to see, many of whom go on to rely heavily on spreadsheets in their professional careers. (See, for instance, [2] and [3]). So, starting with the second edition, we integrated comprehensive optional discussions of spreadsheets as a second technology alternative.

With the advent and growth of our Website, we have also included instructions on using the many resources available there, like two- and three-dimensional grahers, regression and curve-fitting calculators, linear programming utilities, and general matrix utilities, among others.

Keeping Important Traditional Approaches

As important and positive as the reform movement has been for the teaching of calculus, numerous schools became disillusioned with its rejection—and even derision—of anything that smacked of “drill.” Donald Estep writes in [4] that

“Once the drill in computation was removed, Calculus was completely stripped of its heart. In fact, most students passing through a reformed Calculus course neither understand the basic concepts of analysis and Calculus nor can compute derivatives and integrals with proficiency.”

Indeed, while drill and practice in mathematics does not teach the concepts, the manipulation and problem-solving techniques required for drill and practice provide a solid conceptual basis for abstracting the ideas ([5]). For instance, it can be pointless to talk about the algebraic approach to calculating limits unless the students have a good grasp of algebraic techniques that only drill and practice can provide.

In our books we have strived to strike a balance between the best of the reform movement and the best of the traditional approach. For instance, when we introduce the notion of the derivative algebraically—or any new concept for that matter—we immediately provide the student with a comprehensive list of basic “Quick Examples” to help them master the skills before we go on to discuss applications and real data. Similarly, our exercise sets—unlike the relatively small exercise sets found in purely reform books—are comprehensive, with emphasis on drill in the beginning exercises and on analyzing and using the newly-acquired algebraic techniques to understand what the concepts are about and how they apply to real world situations in the later ones.

Similarly, our organization of the main topics is traditional in content, with a reform philosophy in approach, so that instructors with varying attitudes toward reform can comfortably adjust to our approach.

Real World Commitment

In our own teaching we saw that students were not impressed with or engaged by obviously made-up examples; especially students in disciplines like business, in which mathematics is not front and center. We resolved to, as much as reasonable, base examples and exercises on real world data and scenarios, chosen for their relevance to student interests, to which the students can relate in their everyday lives. We are also, in our citation and source notes, careful to be honest and clear as to how we used, or in some cases, modified the original data. This allows us to tie the math we present to events in the news that students are likely already familiar with and, in general, show, rather than tell, the relevance of what they are learning.

Humor

Math books should not be dreary things to read. To the extent that we can slip it by our editors, we have added light touches and humorous references here and there. Where we do have to have made-up scenarios, we have at least tried to make them fun. In [6] it is observed that humor can enhance the learning of mathematics cognitively (through surprise and the rejection of standard ways of thinking), emotionally and motivationally (by the removal of stress), and developmentally (though sharpness of vision of the world and critical thinking), and also in other ways.

The humor in some of our chapter review application exercises—all of which involve the management of a fictitious online bookstore called OHaganBooks.com—is also designed to draw the motivated student into a hinted-at personal story going on just beneath the surface.

Online Resources

The student companion bilingual English-Spanish website here at www.wanermath.com includes everything from videos, resources such as graphers, linear algebra and linear programming calculators, to online interactive chapter reviews and optional extra sections, and detailed interactive section-by-section tutorials in the form of games, a growing number of which include adaptive practice sessions that adjust to a student’s performance and provide additional practice in necessary prerequisite skills when the student is observed to be struggling.

Browse: On Line Utilities | On Line Tutorials | Topic Summaries | Practice and visualize

References

[1]: On the Harvard Consortium Calculus http://www.math.harvard.edu/~knill/pedagogy/harvardcalculus/

[2]: Janet T. MacDonald, Integrating Spreadsheets into the Mathematics Classroom

[3]: Mathematics with Spreadsheets

http://archives.math.utk.edu/ICTCM/VOL10/P007/paper.html

[4]: An essay on Calculus reform

https://www.stat.colostate.edu/~estep/donproposal.html

[5]: Practice and drills are the keys to math success

[6]: Humour as a Means to Make Mathematics Enjoyable

http://ife.ens-lyon.fr/publications/edition-electronique/cerme6/wg1-12-shmakov-hannula.pdf