Project Goals:
We proposed to create a problem-selection-based critiquing and tutoring system for college algebra students. We planned for the critiquing portion of the program to allow a user to type in his or her work for each question and will point out on which step he or she made a mistake. We planned for the tutoring aspect of the program to monitor what types of mistakes the user commonly makes and create new problems to test those skills. Our chief hypothesis was that students who study with our intelligent tutoring system will yield a greater improvement in their college algebra test scores than will students who study with only a representative set of multiple choice questions.

Project Process:
We began the fall semester doing extensive research on similar critiquing systems. We met weekly and discussed relevant books and papers that we had each found in the previous week. We soon discovered that while there are many critiquing systems in disciplines such as trigonometry or calculus, there is no system like the one we were proposing for colllege algebra. There are many different orders in which students can simplify algebraic expressions, and students can also skip multiple steps. We also discovered that a good critiquing and tutoring system would be able to tell if a student was not making progress, even if each of their steps were correct. We spent much meeting time discussing this issue. We closed out the fall semester by drawing up the design of our user interface and developed a grammar for algebraic expressions.

In the spring semester, we began by using JCup and JLex (parsing and lexing tools for Java) to parse algebraic expressions and convert them to our internal format. We had never used a parser/lexer generator before, so this took much more time than we anticipated. For the remainder of the semester, Lindsey analyzed student work that had been gathered in college algebra classes in the fall to attempt to classify the types of mistakes students made. Julie extended the system to be able to provide the correct answer to a problem involving simplification of an algebraic expression. The simplification rules she included were combining like terms and simplification of exponents.

Conclusions and Results Achieved:
We were unable to test our system on any college algebra students because the actual development took much longer than we expected. We still have much more that could be done with the project -- first, we could very easily generate an algebraic expression, have a student type in his or her simplification, and then check whether this final answer is correct. At that point, we could extend our system to analyze steps of a student's work to see if they are still algebraically equivalent to the original expression. Finally, we could classify the student's mistakes as one of our "common mistakes" we found from student's work using something such as ID3 and then generate similar problems to test that skill. Because Julie will be a graduate teaching assistant for the mathematics department in the fall (and will most likely be teacing college algebra), she plans to continue work on the system over the summer to implement the above features.

Publications:
We (with the help of Julie's husband) turned our program into an applet and put in on our CREW website: http://www.cis.ksu.edu/~jas3466/CREW. The website contains instructions for use. This website also contains our original proposal, a Power Point presentation we made on the project in the fall, our progress report from January, and this final report. After continuing work on the project over the summer, Julie plans to write up the project results for a conference such as IAAI (Innovative Applications of Artificial Intelligence) or a conference on tutoring and critiquing.