Complete Description: At FSCJ exercises are being developed to demonstrate
critical thinking ability of the students in all of the general education
classes. Cognitive scientists define “critical thinking” as mental activity
associated with these types of thinking: a. applying reasoning; b. making
decisions; c. problem solving. This critical thinking project is a joint
effort to compare students in both College Algebra and Chemistry classes.
During the first weeks of a beginning or first semester of college chemistry
classes temperature scales are introduced as part of measurement. America
still lives with the out dated Fahrenheit scale while most of the world uses
the Celsius scale developed as the centigrade scale in the metric system of
measurement. Most textbooks demonstrate a graphic comparing three
thermometers: Fahrenheit, Celsius, and Kelvin. Then conversion formulas are
shown to calculate the corresponding temperature on one thermometer from a
temperature on another thermometer.
During the first weeks in a College Algebra Class linear equations are
introduced. Graphing linear data, the students sees the y=mx+b relationship. At an AMA summer math workshop at Duke
University, the participants were developing discovering learning projects to
introduce college algebra topics. The first project had a bank sign flashing
current temperatures, Fahrenheit and Celsius. Five data points were given for
the temperatures at five different times of day. Graphing the data the
student discovers that converting one temperature to another is a linear
function: F = 1.8C + 32 or C=0.556(F32). It was pointed out by the presenters
that every science student from the fifth or sixth grades and above has seen
the conversion formulas in one form or another.
One of the best web sites discussing temperature conversions is:
http://www.mathsisfun.com/temperatureconversion.html
In addition to the standard textbook formulas, this site has several
alternative formulas, one using the +40/40 process which is by far the best
formula for nonmathematical students to use because the conversion from F to
C and C to F uses the same order of operation: Add, multiple, then subtract.
The functional relationship between the Fahrenheit and Celsius Temperature
scales are derived using the corresponding boiling and freezing points of
water. However, to make the college algebra project more interesting, the
presenters developed a web site so that the each student creates a unique
Temperature scale using the student’s body weight and the student’s age as
the boiling and freezing points of water respectively. This “student” scale
is then compared to the Fahrenheit and Celsius scales. The resulting
functions are graphed and compared. Each student’s linear equation is a
unique formula to convert Student to Fahrenheit and Student to Celsius.
If you Google “temperature conversions” you find about 68 millions web pages.
However, the unique webpage developed by the presenters which generates the
data points is:
http://www.fscj.me/mathworkshop1/frametemp2.html
