ElEmEntary mathEmatics laboratory
ElEmEntarymathEmatics laboratory
What is involved in holding
high expectations for every
student and in enabling complex
mathematical work?
How can professional educators
make the skilled and often
“invisible” work of teaching available
to and learnable by novices?
How can teachers work to reverse
patterns of inequity related to race,
family income, language, and gender
in their teaching of mathematics?
What does it take to build a
respectful and mathematically-
focused learning environment?
These are just several of the questions on which researchers and teacher educators are working through the Elementary Mathematics Laboratory (EML) at the University of Michigan School of Education. Teaching is notoriously difficult to study and to improve, and numerous educational interventions in the United States have failed to influence teachers’ work at the level of individual classrooms. This is especially true in mathematics. The United States has worried about the quality of math instruction in its public schools for decades. And despite efforts to increase funding for special curricula and raise standards for teachers and students alike, American children continue to lag behind their peers in other countries on international exams. In the EML, we put teaching––particularly elementary mathematics teaching––under a magnifying glass.
Our goal is to slow down and make visible every aspect of this complex work––instructional planning, the design and preparation of materials, improvisational decision-making, the arrangement of board space, analysis of students’ mathematical ideas, and consideration of the crucial relational aspects of classroom instruction, to name just a few examples. The EML offers a rare opportunity for researchers, teachers, and other observers to unpack and study the often “invisible” elements of teachers’ work and to collaborate in tackling the challenge of improving mathematics instruction.
The EML is part of the Teacher Education Initiative (TEI), a project housed in the School of Education to redesign how teachers are prepared for practice at the University of Michigan and to build knowledge and tools that will inform the field of teacher education more broadly. Through work on the Initiative, researchers and educators at Ann Arbor are developing instructional materials and activities that will prepare teachers to carry out the core tasks of their work effectively with all American schoolchildren.
The Inner CIrCle: The FIFTh-Grade MaTheMaTICs Class
The fifth-grade mathematics class offers a chance for students from public schools in southeast Michigan to work with University of Michigan faculty members on important and challenging topics in mathematics. The class is designed for all incoming fifth grade students, and no special interest or skill in mathematics is required. Most of our students come from the neighboring city of Ypsilanti, Michigan. This year just as last year, the class will focus on several topics important for doing well in fifth grade, including fractions, permutations, number lines, equivalence, and place value. We will also help students develop core mathematical practices, including explaining, representing, proving, and defining, as well as practices of learning math, including recording, summarizing, attending to language, and studying. Students will participate in highly interactive activities each day, and will have opportunities to use a variety of mathematical manipulatives and tools such as overhead calculators and Cuisenaire rods. For the first time this year, students will have the benefit of a full-day program which will include daily opportunities to participate in hands-on art activities with professional art instructors and to improve their mathematics skills in afternoon workshops. At the conclusion of the two-week program, students invite their family and friends to a celebration at which they demonstrate the mathematical activities that they have been working on during the two weeks.
The OuTer CIrCles: TeaCher and researCh
Professionals travel to Ann Arbor from all over the country and from several foreign nations to observe the EML and
eduCaTIOn
K-12 Teachers
Preservice Teachers
M
athe
mat
ics
Educ
ators
Teacher Educators Mathematicians
Unive
rsity
Res
earc
hers
Math Clinicwith Students
Professional Development Courses
Course with Professor Hyman Bass
Research GroupMeetings
Docum
etation & Record Collection
Elem
enta
ry M
at
hematics Laboratory (EML) C
lass
Vide
otaping
Stud
ent Work
The EML math teacher Dr. Deborah Ball purposefully strives to make her work and that of the entire instructional team visible and available to the wide variety of professionals who come to
observe the class every day and actively
solicits ideas, suggestions, and feedback
from everyone.
contribute to the research and activities that surround the fifth-grade math class. On any given day the observers include research mathematicians, often of international renown; education researchers studying different aspects of mathematics instruction as well as investigating questions about achievement among children from
various racial, ethnic, and socioeconomic backgrounds; veteran teachers aiming to improve their own instruction; and student teachers studying expert practice together as part of their professional training. The discussions range across many topics but focus on mathematics teaching and children’s mathematical thinking.
dOCuMenTaTIOn and reCOrds COlleCTIOn
To enable close study of the course
from multiple perspectives (and with
the permission of the students and
their families), the laboratory class is
videotaped every day and careful records
are made of the children’s work and of
the lesson plan and other elements of
the instructor’s work. All of the records
that we collect are labeled, catalogued,
and made available (again with the
permission of the students and their
families) for review, commentary from
multiple perspectives, and deeper study
by different kinds of professionals.
ObservaTIOn and dIsCussIOn
Each morning interns from the
Elementary Master of Arts with
Certification (ELMAC) program observe
the fifth-grade mathematics laboratory
class and use it as a common text for
studying teaching and mathematics. The interns participate directly in the Laboratory as part of their summer
hO
w I
T w
Or
ks Before Class
Each morning Dr. ball meets with observers in a “pre-class briefing,” during
which she presents the day’s lesson plan, explains the goals and activities
for the class, and raises any concerns she and other lesson-planners
have about the lesson or particular students in the class. observers
are invited to share ideas, make suggestions, and ask questions.
During Class
During the two and a half hour instructional period, observers are seated
either on risers in the back of the laboratory classroom or in an adjacent
classroom where they can observe live video feeds from the class in
a more relaxed setting that allows them to talk among themselves.
in the laboratory classroom each child and the teacher speak into
microphones, and technicians engineer the sound system in the room
so that observers can hear important parts of the classroom dialogue.
course on mathematics content and teaching methods. Through a concentrated course structure organized around the EML, the interns will develop mathematical knowledge, skills, and ways of reasoning needed for teaching while learning to enact high-leverage practices of teaching mathematics.
A live video feed allows classroom
events to be paused and replayed,
creating an environment in which the
complex practice of teaching can be
slowed down and discussed to make
it more available for learning. These
daily observations create a rich site
for collectively investigating problems
of practice, anticipating and listening
closely to student thinking, studying
teaching moves and their consequences,
tracking student learning over time,
and experimenting with the design of
instruction and assignments.
MaTh ClInIC
In the afternoon the interns play a
central role in a new component of
the EML: the “Math Clinic.” During
Math Clinic interns teach the children
who participated in the morning math
class, implementing instructional
activities that deepen and broaden
students’ engagement with mathematics.
Interns lead large-group problem
solving activities, direct small-group
learning stations, and develop targeted
instruction for individual students based
on their homework from the math class.
Interns also have daily opportunities
to learn from records of their own
teaching, from a variety of teaching
materials and resources, and from peers
and instructors who are part of the
professional community engaged in
the clinic.
PrOFessIOnal develOPMenT OPPOrTunITIes FOr TeaChers and TeaCher eduCaTOrs
We offer several formal learning
experiences for educators who
participate in the EML. This year three
courses and workshops are available.
One is a mathematics course taught by
Dr. Hyman Bass, University of Michigan
mathematician, mathematics educator,
During Class
During the two and a half hour instructional period, observers are seated
either on risers in the back of the laboratory classroom or in an adjacent
classroom where they can observe live video feeds from the class in
a more relaxed setting that allows them to talk among themselves.
in the laboratory classroom each child and the teacher speak into
microphones, and technicians engineer the sound system in the room
so that observers can hear important parts of the classroom dialogue.
after Class
after students leave the classroom at the conclusion of each lesson,
the observers are invited to study the students’ work in their notebooks and on
the whiteboards. they may then participate in a one-hour “debriefing” session
with Dr. ball during which everyone assembled analyzes the morning’s lesson and
makes preliminary suggestions for the next day. the group often deliberates over
instructional issues such as how to phrase a question to students or what to do to
help a child who is reluctant to go to the board to demonstrate his or her work.
and recent winner of the National
Medal of Science. Another is a workshop
for practicing teachers taught by Dr.
Alison Castro-Superfine, mathematics
educator and education researcher at the
University of Illinois – Chicago. A third
is a workshop for University of Michigan
graduate students who are preparing
to be “field instructors” in teacher
education programs––i.e. to support
student teachers as they observe and
practice teaching in actual elementary,
middle, and secondary schools.
Participants in these courses observe
the mathematics class every day, take
part in the pre- and post-class briefings,
and then attend their own course
or workshop meetings later in the
afternoon.
For more information about the
Elementary Mathematics Laboratory:
sitemaker.umich.edu/mathlab2008/
To learn more about the Teacher
Education Initiative:
www.soe.umich.edu/tei/
researCh sTudIes
Each group of participants in the EML brings its own set of research and study questions to the laboratory every summer. In 2008, members of three formal research projects are using the EML as a site for investigation and data collection:
InsTruCTIOnal PraCTICes In eleMenTary MaTheMaTICs
Principal Investigators: Deborah Loewenberg Ball Hyman Bass (University of Michigan-Ann Arbor)
This study seeks to understand the challenges that elementary mathematics teachers face, what kinds of mathematical work is possible for upper elementary students, and how teachers can help students engage in challenging mathematical work. Research questions for 2008 include the following:
What does it mean to expect and •enable complex mathematical work for all children?
How can teachers build connections •among and coordinate students’ home, school, and mathematical languages?
How can teachers use contexts •for mathematical problems with sensitivity and in ways that draw on students’ funds of knowledge while maintaining the integrity of the mathematics involved?
How can teachers create a respectful, •mathematics-focused learning environment?
suPPOrTInG ChIldren’s undersTandInG OF FraCTIOns
Principal Investigator: Geoffrey Saxe (University of California-Berkeley)
Fractions are a continuing challenge for many children through middle school and often high school. This project seeks to develop a research-based curriculum unit for fifth grade students on integers and fractions using the number line as a central representational context. Our coordinated studies involve (a) student interviews, (b) student tutorials, and (c) analyses of classroom practices.
Research questions keyed to interview, tutorial, and classroom studies that support the development of the unit include the following:
Interview Studies: • What are students’ intuitions about important mathematical ideas such as order, equivalence, and negative numbers when these ideas are represented on the number line?
Tutorial Studies: • What are the hurdles to learning as students work to make sense of core ideas central to fractions on the number line?
Classroom Studies:• What are useful teaching practices in whole class, small group, and individual work that support rich learning opportunities for diverse students? How do students build off of their peers’ ideas in their developing understanding of concepts involving fractions and integers?
analyzInG The uses OF The labOraTOry Class
Principal Investigator: Deborah Loewenberg Ball (University of Michigan-Ann Arbor)
This study examines the features of the laboratory class and the observational structures that surround it – including the pre- and de-briefing sessions, the professional development courses, and the Math Clinic – in order to better understand the ways in which the elementary mathematics class serves as a “laboratory” for the study of teaching. Specific research questions include the following:
How do different groups of •observers, including the professional development course instructors, use the laboratory class?
What work is involved for both •professional development course instructors and the laboratory course instructor in making elements of teaching visible to and learnable by all observers?
In what ways does concentrated •engagement with pupils in the math clinic support student teachers’ learning?
In what ways does concentrated •engagement with a particular strand of mathematics content support the use of mathematics in teaching?
What techniques or technologies •can be used to “pause” live teaching practice in ways that allow observers to reflect on and discuss what they have seen?
The COre PrOjeCT TeaM
The Elementary Mathematics Laboratory is collaboratively designed and executed by a team of researchers and teacher educators at the University of Michigan-Ann Arbor. Core team members include the following:
Deborah Loewenberg baLL is the teacher of the fifth-grade mathematics class at the heart of the EML and the director of the Laboratory. She is Dean of the School of Education and William H. Payne Collegiate Professor of Education at the University of Michigan. Drawing on her many years of experience as an elementary classroom teacher, her research focuses on improving the quality and effectiveness of mathematics instruction. She is also an expert on teacher education, and directs the Teacher Education Initiative, a comprehensive effort to improve the way that teachers are prepared for practice at the University of Michigan and to build knowledge and tools that will serve the field more broadly. Ball received her PhD from Michigan State University.
hyman bass, in addition to advising on the curriculum of the EML lab class, teaches a special mathematics course for mathematics educators in conjunction with the EML. He is the Samuel Eilenberg Distinguished University Professor, based in both the School of Education and the Department of Mathematics at the College of Literature, Science and the Arts at the University of Michigan.
His primary interests in education are mathematical knowledge for teaching, the education and development of mathematics teachers, and mathematical reasoning in elementary classrooms. He has also worked to build bridges between diverse professional communities and stakeholders involved in mathematics education. Professor Bass is past president of the International Commission on Mathematical Instruction and of the American Mathematical Society, and formerly chaired the Mathematical Sciences Education Board at the National Research Council. He recently received the U.S. National Medal of Science. His PhD is from the University of Chicago.
TimoThy boersT directs the Math Clinic associated with the EML and co-teaches the course for University of Michigan teacher education students that is offered in conjunction with the laboratory class. He is a research area specialist in the Teacher Education Program at the University of Michigan, working on several teacher education-related research projects and leading the development of new settings for teacher learning. He is concurrently involved in elementary classroom teaching, recently renewing the National Board for Professional Teaching Standards Certification that he has held since 1998. Boerst received his PhD from the University of Michigan.
aLison CasTro-superfine teaches a special professional development course for practicing teachers in conjunction with the EML. She is Assistant Professor of Mathematics Education and Learning Sciences at the University of Illinois at Chicago. Castro Superfine received her PhD from the University of Michigan.
franCesCa forzani studies the observational structures that surround the EML and what observers notice and discuss, and assists with public visits to the program. A former high school English teacher, she is the project manager of the Teacher Education Initiative at the School of
Education. Forzani is an advanced doctoral student in education at the University of Michigan.
Laura roop studies the overall design of the EML and works to educate the public about learning, teaching and the role of research. She is Director of Communications and Outreach for the School of Education. She received her PhD in English and Education from the University of Michigan.
Laurie sLeep co-teaches the course for University of Michigan teacher education students that is offered in conjunction with the laboratory class, supervises student teachers in the Math Clinic, and assists Deborah Ball in planning the fifth-grade class at the heart of the EML. She is an advanced doctoral student in mathematics education at the University of Michigan.
Kara suzuKa directs the execution and documentation of the EML. She draws on her years of experience with documenting and studying classrooms to coordinate a team to capture detailed records of classroom practice during the EML and make them available for a variety of purposes. She is a research scientist at the University of Michigan School of Education. Suzuka received her PhD from Michigan State University.
meri Tenney-muirheaD teaches a special workshop for current and prospective field instructors in conjunction with the EML. She has served as a field instructor for ten years and has developed and facilitated learning experiences for field instructors in the Teacher Education Program at the University of Michigan. She is an advanced doctoral student in education at the University of Michigan.
Deborah zopf assists Hyman Bass in planning and teaching the course for mathematics educators offered in conjunction with the EML. She is an advanced doctoral student in mathematics education at the University of Michigan.
The reGenTs OF The
unIversITy OF MIChIGan
Julia Donovan Darlow, ann arbor laurence b. Deitch, bingham Farms olivia P. maynard, Goodrich rebecca mcGowan, ann arbor andrea Fischer newman, ann arbor andrew c. richner, Grosse Pointe Park s. martin taylor, Grosse Pointe Farms Katherine E. White, ann arbor mary sue coleman, ex officio
nOndIsCrIMInaTIOn POlICy sTaTeMenT
the University of michigan, as an equal opportunity/affirmative action employer, complies with all applicable federal and state laws regarding nondiscrimination and affirmative action, including title iX of the Education amendments of 1972 and section 504 of the rehabilitation act of 1973. the University of michigan is committed to a policy of nondiscrimination and equal opportunity for all persons regardless of race, sex, color, religion, creed, national origin or ancestry, age, marital status, sexual orientation, gender identity, gender expression, disability, or Vietnam-era veteran status in employment, educational programs and activities, and admissions. inquiries or complaints may be addressed to the senior Director for institutional Equity and title iX/section 504 coordinator, office of institutional Equity, 2072 administrative services building, ann arbor, michigan 48109-1432, 734-763-0235, tty 734-647-1388. For other University of michigan information call 734-764-1817.
University of michigan school of Educationoffice of communications and outreach610 E. Universityann arbor, mi 48109(734) [email protected]
Elementary mathematics laboratory: sitemaker.umich.edu/mathlab2008/
teacher Education initiative: www.soe.umich.edu/tei/