Teaching Teachers in a
Research Mathematics
Department
Heather Calahan
Ted Gamelin
UCLA Mathematics Department
Course Structure
• Three quarter hybrid course integrating
mathematics and pedagogical content topics
• Co-taught by mathematician and mathematics
educator
• Guest presenters
• Includes classroom observation
• Culminates in presentation of portfolio
Course Features
• Connects undergraduate coursework to secondary
mathematics
• Deepens student understanding of secondary
mathematics
• Emphasizes problem solving, student presentation
of solutions, and multiple solutions
• Students learn new mathematics in the manner in
which they are being encouraged to teach
Course Mathematics Content
• Number
• Function
• Equation
• Axiomatic systems and proof
• Measure
• Transformations
• Trigonometry
• Probability and statistics
Course Pedagogical Content
• Assessment
• Connections
• Equity issues in the mathematics classroom
• Justification and proof
• Mathematical communication
• Problem solving
• Professional practice and growth
• Representation and interpretation
• Theories of learning
Axiomatic Systems Vignette
• Prove hyperbolic line theorem
• Define hyperbolic notions
• Consider parallelism and the parallel postulate
• Construct several hyperbolic triangles and
measure angle-sums
• Compare Euclidean, spherical, and hyperbolic
geometries
Mathematics for Teaching Major
• Two year calculus sequence, computer science course,
mechanics course
• 13 UD (1-quarter) courses
• hybrid capstone/methods sequence
• math history
• probability and statistics
• 7 “standard” courses
• 30 hours of observation
• Portfolio requirement (integrated into Math105)
Department Math/Ed Platform
• California Mathematics Project
• Mathematics Diagnostic Testing Project
• Math Content Program for Teachers
• Mathematics Teacher in Residence
• Joint Mathematics Education Program
• Subject Matter Preparation Program
Challenges
• Generating student interest in a teaching career
• Fitting teacher education into a mathematics
department
• The sociology gap between mathematics and
education
• Working in midst of giant school district with
giant problems
More Challenges
• Elimination of a waiver route to content
certification for elementary school teachers
• Barriers posed by CTC bean counters
• The changing shape of extramurally funded public
universities
• The department infrastructure for teacher
preparation and outreach
And Yet More Challenges
• Attuning hiring regulations of the College to
teacher preparation programs
• The view that any intelligent person can teach
mathematics