Michael Fried's ``A Vision for Enhancing the Teacher as a Resource''

A Vision for Enhancing the Teacher as a Resource

Michael Fried, Professor of Mathematics, UCI and MSU-Billings, July 2004mfried@math.uci.edu mfri4@aol.com (especially when I'm traveling)

GOALS

Mathematics is an enormously important skill. Our students can learn to use this skill in one-on-one learner-teacher situations. Technology is the one classroom resource that has increased over the last ten years. We must use that resource to efficiently simulate one-on-one learning situations.

Evaluate the places where computer mediated communications can assist learner-teacher and learner-learner interaction/communication.
Structure student-instructor electronic interactions to reduce the burden on the instructor, increase responsiveness to individual needs. Enhance the process for all.
Don't replace the teacher, help the teacher work more effectively with the heterogeneous body of students. Teacher work is work with students.
Provide incentive to create evaluative tools that can raise student initiative and faculty hope for teaching success. INTERACTION PORTFOLIOS, electronically formatted and archived essences of student-instructor interaction, provide the raw material for teachers to know their students. With these they can evaluate their students' progress over time.
(Click portfol_eval_grfx.gif to see a portfolio evaluation graphic. To see an explanation of the graphic, click portfol_eval_grfx.html.) Dynamic learning curves: DynLearnGph07-14-04.gif >shows how wrong teacher expectations of final student performance can be when we don't reckon with the actual stages of learning. DynLearnGph07-14-04.html gives more explanation of the graphic.
- Teacher assumption: Topic, being a regular part of classroom prior to midterm, then students can handle it from then on their own.
- What is wrong with the teacher assumption: Several steps needed for independent response to topic
  a. Respond to strongly telegraphed prompts – the teacher gives key words to enhance the significance of the topic.
  b. Responds to embedded prompts – the teacher enhances notation to prompt for the topic.
  c. Retrieve from memory without outside prompts – the student finds a way to recall without teacher-initiated prompts.
Use student-student interactions as a resource. Help teachers model their most effective methods so transparently our most successful students can use the same resources to help fellow students.

Warning: When I discuss Interaction Portfolios, the emphasis is on student-teacher interaction. It is not a repository, say, for student multi-media projects.

SUBJECT MATTER VISION

Recognize that encouraging teacher success, without also encouraging vision, will persuade teachers to limit, rather than expand, their teaching concern territory.
Encourage faculty to document subject matter vision that encompasses more expertise than one course.

Example from Mathematics: Many dedicate their lives to improving first year calculus teaching. Teaching that material, however, by contrast to vector calculus, has an advantage: engineers, physics people, chemistry people, math people, all agree what is its essence. That agreement disappears when you cross into the spatially oriented vector calculus. Especially difficult is how to entwine the necessary algebra and geometry thinking.

The problem: 9th and 10th grade algebra texts have yet to show teachers how put the algebra and geometry modes of thinking together into one classroom. First year Calculus, in a practical sense, is mostly algebra. Failure to deal with algebra and geometry together has meant an almost total wipe out of minority students, for their teachers also stopped with the algebra viewpoint.

Warning: It is nice to think that teachers can apply the materials of their own classroom to outside classrooms. Alas, there is little evidence for this. All teachers would have to grow some, most of them significantly, to use the material they habitually teach in topics from other courses. This holds even in cases where the topics would be almost the same if the vocabulary changed slightly.

Analogy: If you give a left-handed potato pealer to a right-handed person – who knows it is supposed to be a potato pealer – at first they will say it doesn't work right. If you tell them they must use their other hand, you are giving a clue that the change is slight. Switching between the modes of the math and science view of equations and variables can often be compared with switching between right and left-handed potato pealers. If everything is memorized as if the names of variables must be kept intact, you can't switch. If, however, it is understood that mathematics must include all possible variables, and science names its variables significantly, then there is a way to translate between them. Much independent problem solving in math or science depends only on this interchange.