following letter quoted from Beaver Area High School:

Monday, March 11, 1996

Charles A. Dana Awards for Pioneering Achievement in Education
Office of the President
Education Commission of the States
707 17th Street
Suite 2700
Denver, Colorado 80202-3427


Dear Office of The President,

This year, 1995-1996, I have been involved in the pilot of a new course at Beaver Area High School in Beaver Pennsylvania. The PUMP (Pittsburgh Urban Mathematics Project) curriculum is being field tested in out basic algebra courses. The curriculum contains two components -classroom curricular materials and the PUMP Algebra Tutor (PAT) for the computer. The second component of the program has been, in my professional opinion, the catalyst for a variety of developments in our basic algebra student.

Traditionally, algebra has been a course that many, if not most, high school students feared. The lack of real-world connections, the tedious mode of instruction and the theoretical basis for the traditional algebra curriculum has created an environment that students see as being intimidating and stuffy. This year I have witnessed the dissolution of these beliefs. The use of the computer tutor, or PAT, has created an environment where students are actually excited about mathematics, and more-so, they are excited about algebraic concepts!

The PAT allows the students to connect what they are doing in the classroom by presenting problems that are applicable to real life and which contain topics currently under study. The problems presented on PAT support the concepts of independent and dependent variables, scaling, creating a graphical representation of a pattern, expressing a pattern algebraically, and using algebraic skills to solve a variety of problems. The PAT computer component is definitely integrated with the classroom curricular materials, as well as other subject areas. The science curriculum is benefiting from the exposure students are receiving to independent/dependent variables, graphing, and scaling. I have received many comments in the second semester that indicate that material I am covering is carrying over into other classrooms.

The PAT creates an environment where the students are able to interact with their peers on a higher level than they were accustomed to in the "traditional" mathematics classes. This is one area where I am most impressed and excited with student progress. Students must depend on the computer or other classmates for guidance an a problem when I am not available. It is wonderful to stand in the background and listen to student comments such as:

     student 1: "Why is my graph all dark?"

     student 2: "Think about it, can you number by 10Ős when your graph needs to span from 0 to 81,000?" -Sims, Algebra 1, 3rd period

     "There are four quarters in one hour, so you would write 4 hours and 15 minutes as 4 and one-quarter or 4+1/4." -Sims, Algebra 1, 7th period

     "I just did that problem, let me help you...." -Sims, Algebra 1, 6th period

Students are taking control of their own learning when they are using the PAT. They are able to gain a varying level of assistance from their computer, are able to get help from their classmates, or may make a mistake and try another approach without a great deal of manipulation. Students are willing to help each other, and more-so, they are teaching each other. I hear similar questioning occurring between the students as I try to create when I am facilitating learning. Through the process of interacting with peers and exchanging conjectures, students have developed their own understanding of how to write an expression for a pattern or how to solve for 'x' -the independent variable when given 'y' -the dependent variable. This has more value than simply regurgitating an algorithm or following a memorized set of steps. Not only are students learning about algebraic concepts contained within the PAT, but they are gaining invaluable exposure to cooperating with peers, using computers, spreadsheets, and correcting possible system errors that might occur with the operation of the computer. Few, possibly none, of these would be occurring in the "traditional algebra classroom".

I would have to assert that the most profound affect of using PAT with my algebra students this year is the change in attitudes that I have witnessed. A young lady said to me one day, "My mother cannot believe that you are teaching me algebra, and neither can I. I am so proud that I am getting it!" -J. Hart, Sims, Algebra 1, 7th period. This student would more than likely have claimed a much different attitude had she been enrolled in the traditional algebra class. While the letter grade that a student receives is not necessarily a true reflection of the learning that has taken place, I have one student who received a D the first grading period, a C the second grading period, and an A for the third grading period. She told me that her mother is very proud of her. This, coupled with the fact that she rarely completed one problem on PAT during a single class setting at the beginning of the year and is now doing four or five problems (depending on the scope of the problem) while helping others, indicates that she has built up her self-confidence in her abilities. Students are excited about using the computer in their learning. This excitement has lead to a desire to be present on the days the class goes to the computer lab to use PAT. This has lead to an increase in attendance (roughly +12%) amongst students who are/were habitually absent.

In closing, the PAT computer component of the PUMP program creates an environment where All students can succeed. The mode of instruction is technologically rich and thus exciting to students and to me! I would have a very difficult time reverting back to my traditional method of instruction after this experience. Having seen the fertile gains made by students through the use of PAT, I count on the availability of other intelligent tutors for mathematics in future years.

Sincerely,

Lisa S. Sims
Teacher