My project involved teaching two sections of Math 070 Intermediate Algebra using two different formats.  One class was taught using a traditional lecture and the other using a brief lecture with a class assignment completed by groups of students working together. The two classes covered the same material and were given similar tests and final exams.  Both classes met at the same time of day.  I wanted to do this project because I have usually taught classes at this level using mostly lecture but I have not been satisfied with the results.  I hoped that the groupwork class would do much better than the lecture class, but was afraid that they might do much worse.  As it turned out, neither extreme turned out to be the case.  The classes did about the same—based on my experience, the small differences were well within typical variation for any two sections of the same course. For this reason, and because the samples were small and not truly random, I did not apply any of the usual statistical tests to the data. (Subjectively my impression is that the groupwork class had a higher proportion of young, relatively immature students). 

How the groupwork was implemented:  The first day of class I divided the students into groups. I did this by handing out copies of the Greek alphabet and had the students count off using the first half of the alphabet instead of numbers.  This gave about 12 groups with 2 to 4 students in each group.  Each day in class I would give a quick mini-lesson with a few example problems.  Then I would give the groupwork assignment for that day—problems chosen from the homework problem page.  I usually assign the odd-numbered problems for homework and a subset of the even numbered problems for the classwork. (Math textbooks usually have the solutions to only the odd numbered problems in the back of the book.)  I believe that students should normally have the solutions to their homework problems so they can check their answers.  They did not have the answers to the classwork problems so that they would be responsible for discussing and agreeing on the correct solutions.  I would walk around the room giving helpful hints.  It was gratifying to see some of the mathematical arguments that ensued.  I feel that something important was learned from the group which is not reflected in the test scores.  When the assignment was completed to the satisfaction of all members of the group, they compiled one group paper to turn in to me. The assignment was graded and each group member received equal credit for that day’s assignment. (The groupwork was 10% of the student’s course grade).  I was really impressed with the quality of the group discussions and written work.  After the first week, most groups received full credit for almost all of their assignments. (This is not to say that all of the answers were correct-- I gave full credit for the assignment even if some of the answers were wrong as long as the correct methods were used. For the groupwork part of the class I was looking for an understanding of the correct methods even if a few mistakes were made.)  I encouraged groups to do their work on the whiteboard.  There was one group that always did their work on the board.  Members of the other groups could look at it and try to decide whether it was correct or not. 

Problems encountered:  The problems I encountered in implementing the groupwork were minor.   Several students had the instructor’s edition of the textbook which has all of the solutions.  I did not allow these to be used during class. There were a few instances of inappropriate comments, students standing on chairs to write on the board, or of group “members” not really participating.  Most of these were dealt with easily and not on-going problems.  However teaching a groupwork class does require the instructor to be alert to possible conflicts that could arise.  Also, some groups finished their assignment quickly and left class. Personally, this doesn’t bother me since I want students to develop a “goal-oriented” work ethic rather than a “time-clock” work ethic.  But this is something to consider for those instructors who want their entire class to be there at the end of the scheduled time. One of the difficulties in conducting this type of class in a lecture-style classroom is that the desks need to be moved into the group position and then returned to the normal position at the end of class.  It would be much better to find a classroom with tables and chairs, although the students did a good job of returning the desks to the normal location at the end of class.

Inclusion of survey.

As an instructor, I found the classes to be different but equally challenging.  For the lecture class, I needed to be prepared and energetic, but there was nothing unexpected. The students in the groupwork class always amazed me.  They were usually on task, discussing mathematics and I could see them learning from each other.  The best way to learn mathematics is through discovery and I could see this process taking place every day.  I am somewhat disappointed that this was not reflected in the test scores.
  The results were not really surprising.  I have always believed that that a student’s success in this course is determined by the time and effort the student spends on the homework.  What we do in class is only an introduction to the material and is not sufficient, in itself, for complete understanding. The conclusion I draw from this project is that an instructor should feel free to use whatever techniques he or she feels will be effective.  Student success is determined more by the student’s effort than by what we do in class.  There is one other possibility to be considered—probably neither of these extremes is optimal.  The best class would combine both lecture and groupwork in a balanced way.  I pan to use a groupwork component in my future classes at this level.