|
|
| Home | Textbook | Newsletter | Discussion Forum | Contact |
 Textbook
|
|
[1] Excerpts from the Curriculum Foundations Project — Voices of the Partner Disciplines
The Curriculum Foundations Project was a major undertaking of the MAA's CUPM
subcommittee on Curriculum Renewal Across the First Two Years (CRAFTY). The
objective was to hear the views of partner disciplines concerning the
mathematics curriculums for the first two years. This was accomplished through
eleven discipline-based workshops held during the period 1999-2001. Each
workshop brought together 20-35 faculty, most of whom represented the discipline under question with the remainder
chosen from mathematics. The purpose of each workshop was for members of the
partner discipline to dialogue about their mathematical needs (desires) while
the mathematicians listened and served as resources. The Summary and final
report of the Project, Curriculum Foundations Project, Voices of
the Partner Disciplines, was published by the MAA. The entire report is
available on-line at www.maa.org/cupm/crafty.
The reports from each of the workshops explicitly recommended problem solving
and modeling. The majority of the reports called for more emphasis on
developing communication skills and conceptual understanding. The specific
recommendations for college algebra as written in the Summary is reproduced
here.
"Replace traditional college algebra courses with courses stressing
problem solving, mathematical modeling, descriptive statistics, and
applications in the appropriate technical areas. De-emphasize intricate
algebraic manipulations.
College algebra courses serve two distinct student populations: the
overwhelming majority for whom this is a terminal course in mathematics, and
the relatively small minority for whom it is a gateway to further mathematics.
Neither group is well-served by the traditional version of the college algebra
course. Many of the disciplinary workshops recommended the reorganization of
college algebra and precalculus courses to better meet the needs of various
student populations. In particular, the obvious mismatch between a curriculum
designed to prepare students for calculus and the reality that very few of
these students subsequently enroll in calculus caused the Summary Curriculum
Foundations Conference participants to recommend changes stressing problem
solving, modeling, statistics, and applications."
With respect to technology, the Report states: "Technology should be used in
introductory mathematics courses to provide students with tools for solving
problems." However, the Report makes clear that teachers "must stress to
students the importance of choosing the appropriate method of calculation
(mental, paper-and-pencil, or technology) for the desired task." An
interesting outcome of the discussions on technology was the strong consensus
that spreadsheets are the technology of choice for many of the partner
disciplines. [2] The Wind Doth Blow
Wind power holds great potential as a major renewable source for electricity.
Although accounting for less than one percent of the country's energy
generation today, the development of wind farms is growing rapidly. Wind
Energy predicts that by 2020 up to six percent of our country's
electrical energy will be generated from wind-power. (Presently, 20% of
Denmark's electricity is generated from the wind.) The company claims that
with today's technology, wind power could generate enough electricity to
supply the country's needs. In fact, they predict that North Dakota alone
could supply 40% of today's needs. The fast growth of the industry is due
largely to technological improvements over the past twenty years that have
increased the efficiency of windmills and decreased the costs. For example, a
large windmill in 1980 stood about a 100 feet tall and had 40 foot blades.
Today, a large windmill stands about 350 feet tall and has 115 foot
blades. Because wind velocities are decreased near the ground due to friction
with the earth's surface, wind velocities at the high towers may be several
times as great as those near the surface. This increased velocity makes
today's larger windmills much more efficient and productive than those of a
few years ago.
The following data (taken from USA Today, January 5, 2005) measures the amount
of wind generated electricity in terms of the number of typical U.S.
Households supplied.
Plot this data and then determine a fourth degree polynomial whose graph
contains each data point in the scatter plot. Proceed in the following manner.
Let
Substituting a data point into this equation yields one equation in five
unknowns
(
For example, substituting the first data point, (1982, 302), yields the
equation
The five data points thus give a system of five equations in five unknowns. Solve this system for the five unknowns (the coefficients) by converting the system to a matrix equation and then using the reduced row echelon command applied to the augmented matrix.
Superimpose the graph of
Predict the number of households whose electricity needs will be met in 2010.
Explain the assumptions you made in forming your prediction. [3] Figuring the Cost of a Sail
(The first two parts of this problem are straight forward in terms of problem
solving, but the third part is not as there are several ways of
aligning/cutting the 6 foot wide material to form the sail.)
The Wind Sail Company charges $25 per square foot for a triangular shaped sail
with side lengths 33 feet, 27 feet, and 21 feet. a. Is the shape of the sail a right triangle? Explain your reasoning. b. Determine the cost of the sail. Using a sketch, explain how you obtained your answer.
c. If the sail material comes in 6 foot widths, how many feet of material
would you need? Illustrate your approach with a sketch and then explain your
reasoning? Is your answer the minimum necessary? Explain.
[4] Identifying Scatter PlotsA common modeling procedure is to gather data, plot the data, and then fit a curve to the resulting scatter plot. This last step depends, in part, on recognizing the shape of the scatter plot. The following is an interesting way to test our students' skills ability to recognize basic shapes. For each of the following scatter plots, identify a reasonable choice of function to fit the scatter plot.
[5] Request for Information on College Algebra Courses
The MAA, AMATYC, and NCTCM have joined forces to assess how well college
algebra courses meet the needs of the students who are taking them. In
particular, they are interested in collecting data on answers to the following
questions: Who are the students who take college algebra? What percentage of students are successful in college algebra? What percentage of college algebra students take additional mathematics courses and how well do the students do in these courses?
What percentage of college algebra students enter calculus I?
If you or your department has conducted any studies involving these questions
and are willing to share the results, please contact Sheldon Gordon
(gordonsp@farmingdale.edu) or Bill Haver (wehaver@vcu.edu) or Don Small
(don-small@usma.edu). [6] Quiz ActivityThis activity involves shifting and scaling a graph. Let the function f be defined by the following plot. Hand a copy of the graph of f to each pair of students and then have them superimpose the graphs of functions g1 through g4 defined below. (Copying the graph of f on a sheet of graph paper would probably yield better results.)
a.
c.
True merit is like a river, the deeper it is the less noise it makes.
Anon
[7] Notices
* Supported by the National Science Foundation and the U.S. Military Academy. |
|
| Home | Textbook | Newsletter | Discussion Forum | Contact |
