Glenn Stevens Wayne HarveyRyota Matsuura Al Cuoco Steve Rosenberg Sarah Sword (Boston University) (Education Development Center)

The Impact on Teachers of Immersion in Mathematics

Focus on

Mathematics

a Wide-Ranging Partnership of Grade 5-12 Teachers, Administrators, University Educators and

Professional Mathematicians

Focus on

Mathematics(NSF/EHR-0314692)

Boston UniversityEducation Development Center,

inc and five school districts

• PROMYS for Teachers

• FoM “Study Groups”

• PCMI’s “Developing Mathematics”

Three examples:

Immersion in Mathematics

The Immersion Experience

• as exploration and problem-solving• as an empirical science• as a community activity• as mathematicians experience it

Teachers experiencing mathematics

• emphasis on learning and doing mathematics• strengthening mathematical habits of mind• low threshold, high ceiling• deeply personal engagement in mathematical

ideas

Key Features

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

• The entry level course for the Master of Mathematics for Teaching degree at Boston University

or

• School-based intellectual leadership in mathematics

• Learning cultures in school settings involving – Students– Teachers– Educators– Mathematicians

Designed to develop and sustain:

Focus on Mathematics

Masters Degree in Mathematics for Teaching

• Immersion Experience of Mathematics (Entry Level Course!)

• Mathematics in the Curriculum

• Research experience in mathematics

• Classroom Connections Seminars

• Leadership Experiences (Capstone Course!)

Elements of the Program:

Masters Degree in Mathematics for Teaching

“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

The Experience

“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 our websites:

http://www.promys.org

http://www.focusonmath.org

http://www2.edc.org/cme/showcase

http://math.bu.edu/study/mmt.html

Visit the programs: PROMYS (July 2 to August 10)

Focus on Math (all year)