Glenn Stevens Wayne Harvey Ryota 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 )‏ Boston University Education 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: Visit the programs: PROMYS (July 2 to August 10)‏ Focus on Math (all year)‏