Mathematica
 in High School
& College
by Duane Koets
Science Academy
South Texas ISD
	I have taught in high school as well as college and junior college.  I used math computerized  solving software.  At Heartland Community college, I used the available software of Converge and Derive.  Each had its capabilities but one had to switch from one to the other.  Three years ago I taught Calculus through a modem using Mathematica.  I did not use the hardware or software but instructed the students in the calculus part.  It was an experiment begun by and for two student s.  One student had a major family catastrophe and was unable to finish.  The other student got high school and college credit from the University  of  Illinois.  That student  is now a student at the Air Force Academy.  He is highly motivated  and competed in math contests amd various atheletics.
	For the last two years I have used Mathematica as part of my curriculum for Calculus II.  The students were very good with the TI82 through TI86 calculators;  they were introduced to the TI92 calculator the first six weeks.  By the third six weeks they were introduced to Mathematica.  Each student was given 10 short assignments to do using Mathematica.  At first, they did not like Mathematica and its structure.  I had expected that.  By about the third assignment the students were looking forward to the use of Mathematica.  I have had several students come back from college and express thanks that they had been introduced to Mathematica.  If they used a computer-aided math solving program, most used Mathematica.  One student  said his university  used  Maple because the professors helped develop it.  One used Matlab (matrix manipulation) and again because the professor helped develop it.  This year one student told me that every  university  to which he applied had Mathematica as part of the first freshman advanced courses.
	The students realize that they still must learn the math before then can effectively use Mathematica.   Several math teachers on staff are worried  that students will only  be able to push buttons to solve math problems.  If one teaches the math correctly, the students will learn the math and probably more because one will not have to learn all the “little tricks” to solve various calculus problems.  One can solve many more problems with the computer-aided program of Mathematica  thus exposing the students to more and more complex problems in the same time.
	I would like to extend the use of Mathematica to my  precalculus students and later my algebra II students.  They, of course, will solve different types of problems.  So far I have written my own problems for the students to solve.   Books may be available for this but I have not found them so far.  The colleges  are picking up on the computerized math solutions.  The high schools need to give the students some exposure to this type of thinking - it is the wave of the future.
	When the slide rule was put away for the calculator, that was a large step.  Now computerized math - Mathematica -  is here.  The graphing calculators will probably stay for quite some time but will  gradually  be put  away  for  computerized math - Mathematica.
	My  students and I  have found the student manual to be of great help  to set up  problems and learn the code of Mathematica.  Also of help has been a CD of Mathematica by Example to set up more complicated problems.  The students at first found the code a little time consuming.  But as they became familiar with the code, they  enjoyed the challenge.  We like the fact that one can print off the results.  With the graphing calculator, one can not print the results.  We like being able to take the formula right out the book, enter it into Mathematica and get the same pictures as the book.  We could rotate and see what the back  side looked like,  we could see the saddle points so clearly, and we were able to print the pictures in color.  Some calculus problems that seemed so hard were made easy and one had a better picture of what was going on.  It may take a little time to get good at using  Mathematica but the results are worth it.
	At an Advanced Placement conference, research had been done which showed that at least three Texas Universities students were denied advanced placement if they had not had Mathematica or knew how to use the TI92.  That was three years ago.  I  feel sure this trend is fast becoming the expected norm for colleges and universities.
	The colleges  at which  I have taught are Lincoln, MacMurray,  and also Heartland Community  College in  Illinois.  The high school where I am currently  teaching is the Science Academy  of South Texas Independent School District, Mercedes, Texas.  The Science Academy  is considered to be a magnet  school  and  is considered to be the top academic school in Texas and one of the top 10 high school of United States.   
 	Included in this presentation will be a list of exercises that I used to get students prepared for setting up Mathematica to solve problems.

Conclusion
	Mathematica has entered colleges to a large extent.  The use of Mathematica is constantly  growing.  The high schools are just beginning to use Mathematica.  The use of computerized math will greatly change the way  math is taught in the future.   Mathematica is, I believe, the standard  for the teaching of computerized  math.

Duane Koets

email addresses
personal	koets_1@acnet.net	
educational	koets_1@hotmail.com