About the Booklet
College Mathematics with Technology - A Project Approach by M.B. Ulmer is a booklet originally written to support Mathematics 120, College Mathematics, at the University of South Carolina Spartanburg. It can also be used to lend structure to a post-algebra course at the secondary level. Now in its fifth revision, it is available packaged with a hard copy set of activities like those on this web site. The following is excerpted from the introduction to the booklet.
This booklet provides background material and structure for a project-based course for liberal arts majors. It is not intended to be a textbook. It cannot be used effectively as the sole source of information for such a course, but must be combined with projects that include significant writing components. Students for whom Algebra II is not fresh are encouraged to select an ancillary text for reference. Most any college algebra or college mathematics text will suffice as reference for the foundation mathematics needed in this course. An inexpensive, used text is suggested. The use of technology is an important part of the course design. Students need access to a word processor and technology for graphing and regression. Minimally, a graphing calculator with polynomial and exponential regression features should be required. (The TI-82 and TI-83 were used to develop these materials.) If possible, students should have access to a spreadsheet that does multivariable regression. (Quattro Pro and Excel were used in this development.)
It should be remembered that this course is designed to enhance the student's ability to use quantitative reasoning and communication in other disciplines. As such, it has been an effective preparation for elementary statistics. It is not intended to provide the algebraic, analytical or trigonometric skills needed for calculus.
The course for which this material is written has been successful in its first semesters of use. We think the success is due primarily to the use of projects, cooperative group work, writing to learn, lab availability, and adherence to the principle that practice should occur, insofar as possible, in the context of real data.
Although we have inconclusive data at this writing, there is sufficient evidence to question whether math skill practice may actually be detrimental to lasting learning. Specifically, students from sections of College Mathematics in which there was much reliance on practice sheets for learning such topics as graphing and data transformations have the lowest success rates in subsequent statistics courses. This seems to indicate that when one spends time practicing, it is "thinking in context" that one should be practicing - not math skills. After all, students at this level have had two years of algebra. Most have skills of sorts, but few know when to use them.
The booklet is therefore written without sufficient practice sets to support the instructor who wishes to engage students in out-of-context drill. Students are thus encouraged to use the activities distributed with the booklet or found on this web site for practice that requires thinking mathematically in context. At this writing, it is the students from sections that used no practice beyond that in the text who have the highest success rates in subsequent statistics courses.
College Mathematics with Technology is available from the USCS Bookstore. Also see the Table of Contents.