A Garden: A Metaphor for Learning
Betty Field, MCLI

Mathematics faculty, like other Maricopa faculty, welcome professional development opportunities. MCLI supports innovations, risk taking and cutting edge thinking and learning. So, last summer the MCLI seeded a project to support four sets of mathematics faculty to think, explore and learn plus provide information about ways to support faculty and facilitate faculty learning.

We chose people with different backgrounds, interests and experiences. They chose a variety of paths and projects: some projects were collaborative, others were not; two of the projects were very specific, two of the projects were very open ended.

The Seeding
From Scottsdale Community College, John Losse was invited to collaborate with Alan Levine from the MCLI on "something involving the World Wide Web."

From Scottsdale Community College, Edgar Chandler wanted to develop exploratory activities for College Algebra using the graphing calculator.

From Glendale Community College, Michael Holtfrerich decided to continue development of a polynomial manipulation program that is making Beginning Algebra more visual and manipulative for students through an innovative use of the computer.

From Phoenix College, Timothy Bryan and Andrew Conti wanted to examine the positive uses of scientific and graphing calculators in Arithmetic Review and Beginning Algebra, to do a literature search of existing reports, and to design some appropriate activities.

The Gardens Grows
John Losse started his project thinking he wanted to learn to write HTMLs so that he could do his own technical work. After some brainstorming with Alan Levine, both were convinced it was more productive for John to concentrate on mathematics and to discover something the Web could uniquely deliver that would be useful for learning and teaching mathematics. The result is a "Virtual Coin Toss" that has John continuously flipping a coin and recording the results. Students will be able to see the chain of tosses, search for patterns, find "x" number of continuous heads (or tails), see the results of the tosses from the Xth to the Yth, and so on. The site is limitless in its possibilities for use in mathematics learning and can be used in every mathematics course taught at our community colleges. And, the site is "almost ready."

Edgar Chandler knew exactly what he wanted to do with the ideas and resources he's been collecting for the last several years: develop student activities. He was so productive that he finished the College Algebra work and moved on to develop activities for Intermediate Algebra. He is using them in the classroom and sharing them with colleagues.

Michael Holtfrerich also knew exactly what he wanted to do; in fact, this is a continuation of some prior work. The program, developed with Toolbook, is a tutorial for students of Beginning Algebra. He completed the sections on the collection of like terms and the addition and subtraction of polynomials and started the section on multiplication and simplification of expressions. His goals included developing friendly, flexible programs that are considerate of the student.

The match of Timothy Bryan and Andrew Conti was sheer serendipity. Tim is young and energetic; Andy is one of our experienced (and energetic) evening instructors who also teaches at Alhambra High School. Their combined energy and thinking during their open ended project of examining positive uses of scientific and graphing calculators in Arithmetic Review and Beginning Algebra resulted in a resource notebook of articles and activities. They found the Internet useful for finding both research articles and materials. In addition to the research and reading, they talked with other instructors and wrote a set of appropriate student projects. Tim has already given workshops to mathematics instructors to share his knowledge and skills.

Harvesting The Garden
When I interviewed participants, I asked them to comment about the learning that took place as they did their projects.

John Losse appreciated the non structured, "no strings attached" project as he reminisced about the joy of "playing professionally" and then bringing his mathematical training into play. During the summer of 1995 John had worked on a project with a Computer Based Lab (CBL) instrument, a data gathering devise for the graphing calculator. John has shared this project widely with his colleagues and during this interview he shared the joy of watching his colleagues learn CBL and watching them "play professionally." It gave us the opportunity to "fiddle with mathematics in a new way . . . We have very little time to play professionally and to bring into play all of our professional training . . . I watched people pick up the equipment, experiment with it, have fun and also experiment with a lot of mathematics."

In describing his project John said, "We decided to set up a Web page that would do nothing more mundane than flip a coin and keep track of the results. As a teacher I knew some of the mathematical uses in the classroom but I realized quickly the importance of someone with the technical expertise for just this simple concept. "What I learned," John said, "was how difficult, but also how rewarding collaboration can be . . . when people bring two different kinds of outlooks and skills into a project."

Edgar Chandler drew on ideas from many sources as he developed the student activities. He spoke of the importance of "blocks of time" so that "I could make connections and follow the flow of thought from beginning to end." Ed spoke with a passion about "helping the student make connections between what we are doing in class and something that is real in their lives."

Mike Holtfrerich said, "I learned a lot about the thinking process . . . what [kind of] thinking process is trying to go through my students' minds . . . So, I had to think from the students' point of view . . . I had to think about the most concise way to show the student the concept, how the student will relate to this screen or how the screen would be easy to use. I think I learned about the thinking process."

Tim and Andy were emphatically positive about the collaboration process. They would meet in the Phoenix College Student Union and hash over journal articles they had read and student activities they had written. Tim said, "If you want to find better ideas for teaching, you talk to people . . . What we produced was a lot better because we worked together." Both agreed that calculators should be introduced early in the mathematics course sequence so students learn to use the technology and not to fear it. They said calculators must be "used in a positive way so students are required to learn and not just push buttons."

There was consensus about several things. One is the value of the summer project; that is, being able to work in the summer when you are not teaching. The ability to focus without distractions was productive for all. And, all agreed that 5 weeks was just about right. Another agreement was on the value of collaboration. Each collaborative project participant spoke of the value and excitement of working with someone else: John talked about how rewarding it was to collaborate, Mike knows that he would like to work with someone as he continues his project, and Ed spoke of having someone to give input and feedback.

Professional development is complex. It is a combination of individual and institutional decisions and support. The MCLI will continue to support learning -- both faculty learning and faculty developing innovative learning experiences for students.