Suggestions for Improving Mathematics Learning Experiences:Cedar Crest

College

• Emphasizing creativity in mathematics

• Making connections to real life situations

• Permitting students to engage in problem posing

• Emphasizing group work

• Encouraging debates, discussions, and critiques of mathematical works.

http://www.maa.org/saum/maanotes49/149.html

Emphasizing Creativity in Mathematics

In Calculus II, I assigned students the task of making a model of an inverse function. One ingenious model was made from hospital-sized Q-tips. This student made a three dimensional cube using these over-sized Q-tips. Inside the cube she placed three axes. With wire, she constructed a physical representation of a function and its inverse. Another movable model was made from a pipe cleaner and ponytail beads. The function (a pipe cleaner attached to a piece of cardboard by the ponytail beads) was attached to a two-dimensional axes model. Then by lifting and rotating the pipe cleaner, a student could view a function and its inverse function by rotating the function (pipe cleaner) about the line y = x. One student brought in her lamp as an illustration since the contours of the lamp's shadow were representative of a function and its inverse function.

Regina Brunner of Cedar Crest Collegehttp://www.maa.org/saum/maanotes49/149.html

Making Connections to Real Life Situations

A group in Finite Math shared a counting technique they found on the Internet for making sand patterns in India. The class went to the blackboard to draw these patterns because they were intrigued with this concept and wanted to try it also. Wanting to learn more than is required by the coursework and bringing mathematics into their lives to me makes our students mathematically literate and aware of the power, beauty, and mystique of mathematics.

Regina Brunner of Cedar Crest Collegehttp://www.maa.org/saum/maanotes49/149.html

Permitting Students to Engage in Problem Posing

Students realize that I care about their learning because I require and grade their journals each week. In turn, they work harder and harder to understand mathematics. I will solve original problems that they pose in the journal. So the journals become written, one-on-one, semester-long conversations and dialogues.

Regina Brunner of Cedar Crest College

http://www.maa.org/saum/maanotes49/149.html

Emphasizing Group Work

Group work helps the teacher view the interactions within a group, notice which group members need additional help in graphing or algebra skills, and provide help while the group is problem solving. I find group work invaluable. I do not enjoy giving long lectures anymore. I want to present a concept briefly and then solve problems in groups at the blackboard for the rest of the class period. I teach individual groups and assess learning effectiveness as they learn in small groups. My students always write in their journals of the value of the board work. It prepares them for the homework for that night. They are successful on the homework assignments because of the struggles in class that day.

Regina Brunner of Cedar Crest College

http://www.maa.org/saum/maanotes49/149.html

Findings

In the fall of 1996, I used journals, group work, a group test, and creative projects in Calculus I and Finite Math. Final grades included two individual tests, one group test, and an individual comprehensive three-hour final. In comparing student grades on the first test of the semester to their final grades, I found that students performed substantially better on the final tests.

Written student final evaluations note that journal writing gives students time to reflect on how they learn best, a focus on class work, and a link between the professor and the student. In addition, journals provide the teacher an opportunity to view student thought processes and use this knowledge to teach more effectively. Group work increased student confidence in mathematics, replaced competition with cooperation, emphasized hands-on problem solving, and individual contact with the teacher. Projects enabled students to review and reflect on major concepts from the course.

Regina Brunner of Cedar Crest Collegehttp://www.maa.org/saum/maanotes49/149.html