Highlights of two educational efforts
at the University of Minnesota

  1. Mastery learning and Calculus for Biologists

  2. The Math Insight web site

Duane Nykamp

University of Minnesota

PCCIW, November 2015

Math 1241: Calculus and Dynamical Systems in Biology

  • Nonstandard curriculum focused on dynamical systems
    (get to bifurcation analysis in first semester)

  • Flipped format (watch videos outside class, groupwork in class)

  • 170 students

  • Weekly schedule:

    • Two days in large active learning classroom
    • One day in small section with TA
    • One day for taking exams

Working toward mastery learning

  • Eventual goal: students work at own pace until develop mastery
    Eventual, eventual goal: students receive credit based on objectives mastered.

  • Technical, curricular, and bureaucratic obstacles
    • Delegation of grading of exams between computer and human
    • Sufficient exams variability and consistency for repeated attempts
    • Effective model for groupwork in an asynchronous setting
    • The ability to assign credit based on mastery

Working toward mastery learning, current state

  • Some degree of asynchrony allowed among students.

  • Weekly deadlines, but assignments available from beginning of class

  • Exams

    • Each exam can be taken twice (max score counts)
    • Everyone takes exams on same two days.
    • Exams are computer generated but hand graded

Immediate feedback to large numbers of students

Primary tool: printed worksheet, computer graded

Tour on Math Insight

Worksheet: Using cobwebbing as a graphical solution technique for discrete dynamical systems

Math Insight

Goals:

  • Publically available content

    • Allow any content, even assessments, to be public and readily assessable
    • Multiple threads through a corpus of content
    • Integrate applets, videos, text, assessments

  • Technology to facilitate mastery learning

    • Delegation of course tasks between human and computer
    • Instructor overrides if students demonstrate mastery in person
    • Robust probability distribution of exams

  • Research platform