The Impact on Teachers of
Immersion in Mathematics
Glenn Stevens
Ryota Matsuura
Steve Rosenberg
Wayne Harvey
Al Cuoco
Sarah Sword
(Boston University)
(Education Development Center)
Focus
on
Mathematics
Focus
on Mathematics
(NSF/EHR-0314692)
a Wide-Ranging Partnership of Grade 5-12 Teachers,
Administrators, University Educators and Professional
Mathematicians
Boston University
Education Development Center, inc
and five school districts
Immersion in Mathematics
Three examples:
• PROMYS for Teachers
• FoM “Study Groups”
• PCMI’s “Developing Mathematics”
The Immersion Experience
Teachers experiencing mathematics
•
•
•
•
as exploration and problem-solving
as an empirical science
as a community activity
as mathematicians experience it
Key Features
• emphasis on learning and doing mathematics
• strengthening mathematical habits of mind
• low threshold, high ceiling
• deeply personal engagement in mathematical
ideas
PROMYS for Teachers
• Immersion experience of mathematical exploration
– six week summer component
• Reflection on classroom practice
– 5 daylong workshops in academic year
– Doing mathematics together
– Sharing classroom experiences
• More immersion in mathematics in second summer (six
weeks)
– advanced mathematics seminars
– more reflection on practice
Habits of Mind
• Acquiring experience
– numerical experimentation
– alert observation
• Good use of language
– asking good questions
– formulating conjectures
– proofs and disproofs
• Review
– identifying important ideas
– Formalization
– looking for connections
• Generalization
– broadening applicability
– questioning answers
Culture of Exploration
• Immersion in new ideas
• Necessity for open communication
• Acquiring taste for hard problems
• The central role of experience
– empirical basis of mathematical knowledge
– personal experience as guide for new explorations
• Learning good judgement in recognizing significant ideas
• Sharing ideas with others
– in writing
– in seminars
• Questioning answers
Methods
• Rich mathematical content
- number theory
- discrete mathematics
- geometry
- analysis
• Intense problem solving
- problem-solving seminars
- independent work and in groups
• Multi-tiered structure
• History and tradition
• Open-ended explorations
- teacher/student teams
- final papers
- oral presentations
To think deeply of
simple ideas
Arnold Ross
The Mathematics
The PROMYS Community
• First year participants
• 20 teachers
• 8 pre-service teachers
• 45 high school students
• Returning participants
• 8 teachers
• 20 high school students
• Counselors
• 6 graduate students
• 6 teachers (alumni)
• 15 undergraduates (for students)
• Faculty
• 5 mathematicians
• 2 math educators
PROMYS for Teachers
• Stand-alone course for graduate
credit in mathematics
or
• The entry level course for the Master
of Mathematics for Teaching degree
at Boston University
Focus on Mathematics
Masters Degree in
Mathematics for Teaching
Designed to develop and sustain:
• School-based intellectual leadership in mathematics
• Learning cultures in school settings involving
–
–
–
–
Students
Teachers
Educators
Mathematicians
Masters Degree in
Mathematics for Teaching
Elements of the Program:
• Immersion Experience of Mathematics
(Entry Level Course!)
• Mathematics in the Curriculum
• Research experience in mathematics
• Classroom Connections Seminars
• Leadership Experiences (Capstone Course!)
The Experience
“The first weeks of the program, I could connect to
things I knew. Even if I was frustrated one day, the next
day I'd have an epiphany - there were lots of ups and
downs. Understanding math concepts was not enough,
you had to look at things in different ways. It's not
necessarily intuitive. I learned a lot about my own
patience. Every time I felt frustrated, I realized
something that I wouldn't have realized without being
frustrated.”
FoM Middle School Teacher
“A lot of us didn't feel we were prepared
for the summer program . . .
Afterwards we felt we could do anything.”
FoM Middle School Teacher
What lessons are to be learned?
• What is it in the structure of PROMYS that makes it possible
to “succeed” with such disparate audiences?
– the genius of Arnold Ross’s problem sets;
– low threshold, high ceiling;
– the depth of the traditions and the community.
• Are these teachers “special” before they begin the program?
Undoubtedly, “yes”!
– What is special about them?
– How rare is this brand of “specialness”?
• What relationship does this have with leadership?
• How does the immersion experience affect teachers’ work in
the classroom?
• Can we replicate (generalize) key elements of the program?
Remarks
•
The number of “special” mathematics teachers having both significant
talent and significant interest in mathematics is significantly higher than
is commonly believed.
•
Helping these teachers is work that mathematicians are uniquely
prepared to do.
•
The mathematical habits of thought required for excellence in teaching
are similar to those required for excellence in research.
•
Mathematicians can benefit AS MATHEMATICIANS from engagement
in issues of mathematics education.
An Open Invitation
Visit the programs: PROMYS (July 2 to August 10)
Focus on Math (all year)
Visit our websites:
http://www.promys.org
http://www.focusonmath.org
http://www2.edc.org/cme/showcase
http://math.bu.edu/study/mmt.html