REPORT ON MSRI WORKSHOP: TEACHING UNDERGRADUATE MATHEMATICS MIKE WILLS

Abstract In May 2009, the author attended an MSRI workshop entitled “Teaching Undergraduate Mathematics". These notes summarize the author's impressions of the workshop. The main department concern is with increasing enrollment in the mathematics majors at Weber. A secondary concern is how to adapt our teaching practices to deal with incoming freshman as we approach the second decade of the third millennium.

How do we increase enrollment in math? How do we adapt our teaching practices to today's students? How can we engage more effectively?

Houston axiom: We have a problem. Picard's theorem: Engage!

David Bressoud’s comments HS AP Calculus up College Calculus down Developmental enrollment up Worse situation if we exclude engineering schools Traditional calculus geared towards mathematicians and engineers. Number of engineering majors going down Biological science majors up. Proposals: Set up separate calculus geared for biological sciences Concentrate on what students do know MSRI.pdf

University of Michigan calculus Instructors run an “interactive engaged'' classroom. Instructor must ask well-posed questions. Instructor keeps the discussions moving. Preliminary indications Students seem to learn concepts better Students do no worse in computation Downside Significantly more preparation on the part of the instructor.

Good Questions Project “Good questions” asked by instructor Students vote (by clicker), and discuss in groups Second vote Approach works well with peer discussion. True/False: You were once exactly 3 feet tall. Result? Before: 80% /20% After: 90% /10% True/False: You were once exactly π feet tall. Result? Before: 40% /60% After: 85% /15%.

Key questions: What concepts from arithmetic are needed for calculus? Is the Archimedean property necessary for understanding limits? Good Questions project:

Wade Ellis tech recommendations Learning Management System: Angel Webwork up to QL Level Class response: use clickers. Math presentation: Beamer (which uses Latex). Software tutorial: ALEKS How can we get students to ``understand the math"? A/C/R principle: A= Act C= Context R= Relevant Chalkboard lectures?

Jerry Epstein’s Project Question: How much do student’s retain? Answer: Even less than we think they do. One question asked of students is to order five non-negative numbers. Typical mistake: 0.14>0.7

Questions to ask ourselves Question: What grade do we give ourselves in our pursuit of excellence in teaching first year students? Question: Are we viewed as a pump or a filter? Easy steps to improve teaching. Proper use of technology Strong department leadership.

Dan Teague’s comments 1 st Teir of HS Students: mathematicians regardless of what we do 2 nd Teir being taught away Perhaps should not make calculus testable

Marilyn Carlson’s comments Why have math ed ideas not penetrated more into math teaching? More than 20 years of qualitative work in math ed Small classes are not a panacea. ``Math isn't fun" is a big reason students give about why they stop taking math. An instructor's content knowledge is critical Individual h.s. teachers cannot be expected to rewrite their syllabi.

Relations with the Disciplines What should we know about other departments? What pedagogy works for students in other fields? How do we learn this? Comfort with symbols and graphs as a language ``listen to the equations" (Chemistry) Conceptual understanding Facility with applications Business and economics professors (especially) think in terms of logarithms Biology graphs are amenable to graph theory. Our texts have very little actual data. Adopt Polya's rule of four together with a fifth: experiential math.

My suggestions? More group learning and use of clicker technology