Cooperative Learning and Reinforcing Effort

Cooperative Learning:

A few years ago, I created an assignment that involved students cooperatively building a bridge made of popsicle sticks, string, construction paper and elmer’s glue. The ultimate goal of the assignment was to show students how algebraic formulas work and what factors (variables, mathematical operations and their locations in the formula) influence the output of the “bridge equation. So I developed a formula that I thought encompassed all of the parameters. In a flash of inpiration, I included an aesthetic multiplier in the formula. This aesthetic multiplier was an average of a rating each student assigned to a finished bridge by secret ballot.

I arranged students in groups of 3 to 4 members. One of the problems that I encountered was too few jobs for too many people. What I mean by that is, I found in some of my groups the vast majority of the work was done by 1 or 2 of the group’s members. I enacted this lesson in a class that some students have excessive absences and I although I clearly spelled out the points awarded to the group for the finished product, I did not address how individual grades would be affected by absence(s).

Where the assignment was effective:
In the formula that I developed as the assessment tool, I placed the length of the bridge (minimum 24 inches) and the load (weight in pounds) it could support “cubed” in the numerator and the number of popsicle sticks “squared” times the number of bottles of glue “to the fourth” times in the denominator (I didn’t buy alot of glue and did not wish to have the students douse their bridge with glue prior to presenting to the class, a practical lesson in the cost of materials). The students were witness to how the materials in the denominator (to various powers) would detract from their “bridge index” and how strong their bridge was and its length would increase the index. Before construction began, I introduced the formula to them and gave them example numbers to “plug in” to the formula to see how the output index was calculated. After showing example pictures of bridges I stressed how aesthetically pleasing the bridges were. One of the best outcomes that I did not foresee was how honest (and critcal) the aesthetically pleasing factor played out. The ratings by secret ballot were from 1 to 5 with 5 being the most pleasing to the eye. The ratings were very uniform even when the students rated their own work.
The stress test was an exciting day for the groups presenting as well. I hung a 5 gallon bucket with dumb bell weights from the center of their bridges to find the maximum load sustained by their bridge. The student were witness to how their efforts and attention to detail in construction paid off in finding the critical load and ultimate failure of their bridge.

Where the assignment broke down:
Since individual job titles were not defined or assigned, I did not account for how the students would be individually affected by lack of effort or absence. If and when I choose to use this lesson again, I will have job titles assigned by the group’s members and address the absence issue. Clearly defined titles, responsibilities and an individual post stress test evaluation form will promote active engagement and learning by all.

Reinforcing Effort:

After writing so much for the cooperative learning prompt, I'll keep this short.

During my teaching career, I have always tried to put myself into my students shoes and try to remember what was occupying my thoughts while a high school student. I must admit it wasn't always on my studies, but school came easy for me for the most part. In reading the first part of the reinforcing effort chapter, there is a scenario in which a student blames his genetics on the fact that he is not succeeding in mathematics. In particular, he says his mom wasn't good at math either. (My mother was not the best math student either, but she did instill in me the importance of education.) I believe some of the problem with this student could also be that neither the student or his mother see the importance of learning math. This defeatist attitude and indifference to learning math that occurs more often than I'd like to admit is all the more reason for me to reinforce any effort put forth.