ERIC ED458716: Cognitively Guided Instruction & Systemic Reform.

32 Pages·2000·0.86 MB·English

by  ERIC

DOCUMENT RESUME
EA 031 434
ED 458 716
Cognitively Guided Instruction & Systemic Reform.
TITLE
Wisconsin Center for Education Research, Madison.
INSTITUTION
Office of Elementary and Secondary Education (ED),
SPONS AGENCY
Washington, DC.
PUB DATE
2000-00-00
32p.; Theme issue. Published biannually.
NOTE
AVAILABLE FROM Center Document Service, Wisconsin Center for Education
Research, School of Education, University of
Wisconsin-Madison, 1025 W. Johnson St., Room 242, Madison,
WI 53706. Tel: [phone] (Toll Free); Tel: [phone];
Fax: [phone]. For full text:
http://www.wcer.wisc.edu/publications/pub_online.htm.
Collected Works
Serials (022)
PUB TYPE
The Newsletter of the Comprehensive Center-Region VI; v5 n2
JOURNAL CIT
Fall 2000.
EDRS PRICE MF01/PCO2 Plus Postage.
*Academic Achievement; *Cognitive Development; Educational
DESCRIPTORS
Change; Educational Environment; Elementary Secondary
Education; Evaluation; *Instructional Design; *Instructional
Effectiveness; Limited English Speaking; *Professional
Development; Public Schools; Student Improvement; *Teacher
Effectiveness
ABSTRACT
This issue contains an interview with Elizabeth Fennema in
which she explains that decades of research on learning has had a minor
impact co what goes on in the schools. She and other researchers decided to
try to integrate the study of teaching along with the study of learning.
Their desire was to effect real change in the classroom and to enhance
mathematics learning and achievement for students. Two articles are included
by Gloria Ladson-Billings; one is a talk given at the 1999 Cognitively Guided
Instruction (CGI) Institute for Teachers in which she outlined how
incorporating CGI instructional practices can radically change education at
the school; the other article is her talk given at the 1998 CGI Institute for
Teachers. A CGI classroom vignette is presented that depicts how a teacher
might incorporate assessments into instruction and could make some decisions
based on what he or she is learning about students. Another article explains
how Fargo, North Dakota, has become a safe haven for Bosnians, Serbians,
Croatians, Albanians, and Macedonians, and how the ensuing problems related
to English-language learners have challenged the school district. A similar
situation applies to Dearborn, Michigan, which has experienced an influx of
Arabic-speaking pupils. CGI student-achievement evaluation findings for
Region VI are provided.
(DFR)
Reproductions supplied by EDRS are the best that can be made
from the original document.
THE NEWSLETTER OF THE COMPREHENSIVE CENTERREGION VI
I Cognitively Guided Instruction
Li
& Systemic Reform
Volume 5, No. 2
Fall 2000
REFORMING AN ECOSYSTEM
THE ROLE OF
PROFESSIONAL DEVELOPMENT
PERMISSION TO REPRODUCE AND
DISSEMINATE THIS MATERIAL HAS
f waiter g. secada
BEEN GRANTED BY
4.
111 CGI FROM THE BEGINNING
Per-ter
AN INTERVIEW WITH PROFESSOR
ELIZABETH FENNEMA
sherian e. foster I
TO THE EDUCATIONAL RESOURCES
INFORMATION CENTER (ERIC)
1
/1 DEVELOPING A "DANGEROUS"
_
PEDAGOGY
TALK GIVEN AT THE 1999 CGI
INSTITUTE FOR TEACHERS
[gloria ladson-billings
A PARENT'S EXPERERIENCE
10
TALK GIVEN AT THE 1998 CGI
INSTITUTE FOR TEACHERS
[gloria ladson-billings ]
CGI CLASSROOM VIGNETTE
INSERT
CGI STUDENT
ACHIEVEMENT IN REGION VI
FARGO, NORTH DAKOTA
16
A STORY OF TEACHER CHANGE
jonathan I. brendefur and
sherian e. foster
DEARBORN, MICHIGAN
20
A SYSTEM CHANGES
[ jonathan I. brerodefur and
sherian e. foster I
Ea FROM THE DIRECTOR
[waiter g. secada]
COMPREHENSIVE
CENTERREGION VI
WISCONSIN CENTER
EDUCATION RESEARCH
FOR
T H E SCHOOL OF EDUCATION
-±-UNIVERSITY
WISCONSIN-MADISON
OF
BEST COPY AVAILABLE
:.
1-
0 1025 W. JOHNSON ST.
MADISON, WI 53706-1796
608.263.4220
888.862.7763
FAX: [phone]
E-MA1L: [email protected]
WEB: www.wcer.wise.edu/ccvi/
'
THE NEWSLETTER OF THE COMPREHENSIVE CENTERREGION VI
I Cognitively Guided Instruction
& Systemic Reform
Volume 5, No. 2
Fall 2000
REFORMING AN ECOSYSTEM
FORPANG AN ECOSYS
THE ROLE OF
EM
PROFESSIONAL DEVELOPMENT
I- wafter g. secatta ]
Ro__E OF
_ME
CGI FROM THE BEGINNING
DEMOPMEN
AN INTERVIEW WITH PROFESSOR
PRoOssilo_NAL
ELIZABETH FENNEMA
[ sherian e.
foster ]
wafter g. secada
DEVELOPING A "DANGEROUS"
PEDAGOGY
TALK GIVEN AT THE 1999 CGI
/'
HE MOST COMM/ONLy.-,EXPRESSED IDEAS ABOUT SYSTEMIC REFORM SEEM TO IMPLY
INSTITUTE FOR TEACHERS
THAT-SCHOOL SYSTEMS:(01E LITTLE MORE THAN HUGE MACHINES WHICH CAN BE CHANGED
]
[ gloria
BY: A. MODIFyING WHAT THE MACHINERY WORKS \ ON (INPUT), B. CHANGING HOW THE,
A PARENT'S EXPERERIENCE
10
MACHINERY- WORKS (RROCESS), OR C. BY BETTER SPECIFYING OR REDEFINING WHAT THE
CGI
TALK GIVEN AT THE 1998
MACHINERY IS SUPPOSE6 TO PRODUCE (DESIRED OUTPUT). 1NDEED UNTIL RECENTLY,-
INSTITUTE FOR TEACHERS
POLICYMAKEAS -AND DISTRiCT ADMINISTRATORS HAVE TRIED TO REFORM ENTIRE SCHOOL
[ gloria ladson-bitlings ]
SYSTEMS, BY,M'ANIPULATING INPUTS ANCOR PROCESSES
FOR EXAMPLE, BY SPECIFYING
"
VIGNETTE
CGI CLASSROOM
0 0
\\\''
.
..HOW 'MUCH MONEY,SCHOOLS RECEIVE PER PUPIL- (INPUT), WHAT MATERIALS AND CURRICU-'\
Ei
CGI STUDENT
INSERT
LOM-GUIDES WILL BE ADOPTED1INPUT), THE INSTRUCTION THAT STUDENTS RECEIVE(PROCESS),
VI
ACHIEvEMENT IN
REGION
OR THE CATEGORICAL PROGRAMS FOR WHICH STUDENTS ARE ELIGIBLE (PRoCESS). RECENTLY
,
HOWEVER, THROUGH-THE STANDARDS AND ACCOUNTABILITY MOVEMENTS, POLICYMAKERS
FARGO, NORTH DAKOTA
A STORY OF TEACHER CHANGE
SHIFTED TO A FOCUS ON THE SCHOOL SYSTEM'S OUTCOMES AND ON IMPOSED CONSE-
and
[ jonathanl. brenclefur
QUENCES FOR SUCCESS OR FAILURE IN ACHIEVING SPECIFIED OUTCOMES.
sherian e. foster ]
More-complex ideas about school
system so conceived? If school systems are
DEARBORN, MICHIGAN
systems seem to suggest that
A SYSTEM CHANGES
machines, then it would seem that pro-
brendefur and
[ jonathan 1.
school systems are like huge Rube
fessional development faces the choice of
sherian e. foster ]
Goldberg machines. That is, school
working on one piece of the system at a
systems are thought to operate as loosely
time (inputs, processes, or outputs) or of
NI FROM THE DIRECTOR
coupled machines in which there is
[ waiter g. secada]
trying to change the entire system at once.
slippage between levels of interest. One
These choices capture the stereotypical
set of outcomes serves as input for
dichotomy between providing profes-
multiple other processes, and things work
sional development (usually in the form
in complex and somewhat mysterious
of workshops or conferences) to many
ways. Almost like magic, the product pops
teachers
either in rapid succession or
out at the end of a long, convoluted pro-
all at once
versus working with a few
COMPREHENSIVE
cess. A Rube Goldberg machine may be
teachers in great depth. In the latter case,
CENTERREGION VI
complex, but it is a machine nonetheless.
when one is finished working with those
How can professional development
few teachers, it is time to move on.
WISCONSIN CENTER FOR EDUCATION RESEARCH
THE SCHOOL OF EDUCATION
drive, or even support, the reform of a
(continued on next page)
CLINIVERSITY OF WISCONSIN-MADISON
-
)
1025 W. JOHNSON ST.
MADISON, WI 53706-1796
608.263.4220
888.862.7763
FAX: [phone]
WEB: www.wcer.wisc.edukcvi/
E-MAIL: [email protected]
3
larger syste'm by introducing either a
creation of a niche environment in which
SCHOOL SYSTEMS AS
new species or a variant of an existing
CGI can take root by actively encourag-
ECOSYSTEMS
ing teachers to work together
in this case a new practice for
some-
species
thing they promise to do upon sending
into the
the teaching of mathematics
Suppose that, instead of thinking of
ecosystem. Hence, we think of the
groups of teachers to the CGI Institute.
a school system as a machine turning
CC-VI work with individual schools as
This is indeed what has happened in
out specified output, we think of it as an
Fargo, North Dakota and Dearborn,
seeding change. We strategically introduce
ecological system much as we think of the
Michigan (districts featured in this news-
new ways of teaching mathematics, sup-
world's great ecosystems. An ecosystem
port teachers and their schools in imple-
letter) and in other districts that have sent
is home to many species that are in
large numbers of teachers to the CGI
menting those ideas, then depend on the
complex relationships with one another.
Institutes. As these teachers went back to
system's own internal mechanisms to help
Some species are in constant competition;
their schools and implemented CGI, the
spread the innovation
while still lend-
some create codependent relationships
Center provided on-site technical assis-
ing our support.
with one another, and some simply ignore
tance. During these site visits, CC
The Comprehensive Center assumes
VI
one another almost all of the time. Even
staff a) conducted workshops and facili-
that professional development will affect
within a single species, relationships are
tated teacher meetings, b) discussed
the balance of a school's ecosystem and
complex. In some species there are strict
student work samples with teachers,
that forces from within the system will act
hierarchies, while in others status and
c) helped teachers present word problems
to strike a new balance. Our goal is to help
roles are much more slippery.
orally to individual students and listen as
create the conditions for that new balance
One critical feature of an ecosystem,
a balance in which the introduced
they solved the problems so as to better
moreover, is that its components are in
species can survive and eventually
understand the student's reasoning, and
dynamic balance. This means that any-
d) discussed any other concerns that
spread throughout the system. Once the
thing that has an impact on one part of
Cognitively Guided Instruction (CGI)
teachers might have had.
the system also has an impact on other
Recently, the Comprehensive Cen-
mathematics program, for example, has a
parts, upsetting that dynamic balance
foothold that will allow it to spread
Region VI introduced a specialized
ter
which the system then moves to reestab-
web site (www.wcer.wisc.edu/ccvi/
throughout the system, we have
lish. The new balanced state is, by defini-
according to our view of schools as
cgispider/) with bulletin boards where
tion, different from before by having
teachers can pose questions that will be
engaged in systemic reform.
ecosystems
incorporated a new species or by having
answered by their friends and colleagues
adjusted to new or changing conditions.
from throughout the region. The web site
The idea that schools function as
CREATING A NICHE ENVIRONMENT
provides a means for CG1 teachers to dis-
ecosystems is not new. This conception
cuss ideas for lessons and stay connected.
For a new species to successfully
has been invoked to explain the complex,
All these actions helped to establish in
enter an ecosystem, it must find a niche,
and often contradictory, ways in which
schools the niche environments within
a haven, in which to first establish itself.
school policies interact with one another
which new ways of teaching mathematics to
By obtaining commitments from school
and ways in which school personnel be-
at-risk students could take root and flourish.
principals that participating teachers will
have. From the very start of our efforts to
be encouraged to try the ideas they
help schools improve how at-risk students
encounter in the CGI Institutes and by
are taught mathematics, we at the Com-
EXPANDING THE ENVIRONMENT
prehensive Center Region VI (CC VI)
limiting Institute participation to teams of
teachers, the Comprehensive Center_
Once a new species,_or variant, has
have operated on the premise that school
_
entered an ecosystem, either it a) is driven
encourages the creation of such niches.
systems are ecosystems, giving us a differ-
When the teacher teams return to
ent way of thinking about professional
out of the system altogether, b) stabilizes in
its small niche environment and does not
their districts, they themselves create those
development. In designing our work with
supportive niches by meeting together to
spread, or c) expands
slowly at first
teachers, their schools, and their districts,
discuss how their students solve math-
throughout the system. In the districts (eco-
we expect to find the kinds of competing
ematical word problems, to plan lessons,
and often contradictory
systems) into which CGI was originally in-
policies,
troduced (seeded) two years ago, it has been
practices, and complex relationships that
to discuss their classroom instruction, and
to address questions as they arise. Such-
spreading throughout those -districts. This
one finds within an ec-osystem. As in the
is due, in large part, to the complex rela-
case of an ecosystem, we expect these
discussions provide a time and a safe place
tionships among the school systems' own
competing demands to be in a dynamic
for teachers to learn from one another as
they work with a common mission
personnel and the infectious enthusiasm of
balance among themselves.
enhanc i ng students' learning of
the first group of CGI teachers.
Professional development upsets this
balance within a school and within its
How did this happen? Teachers who
mathematics. Principals also support the
[2]
4
not impossible, to change inputs or tinker
taught next door to the first year's CGI
LESSONS LEARNEd
with the inner process or redefine the de-
teachers noticed that something had
sired output and get massive systemic
changed. Their colleagues were excited by
Thinking in terms of an ecosystem
changes. Yet, the same collegial friendships
how they were teaching. Students were
and how it changes, the CC VI has been
and professional relationships that can
joyfully and successfully solving word
supporting systemic reform in those school
work to stifle innovation in a machine can
problems
including difficult and non-
ecosystems in which CGI has taken root
allow it to take root and spread in an
routine problems. Non-CGI teachers were
and is spreading. Though Cognitively
ecosystemprovided that teachers see the
recruited to help make classroom sets of
Guided Instruction is a professional de-
value in that-innovation.
manipulatives to support children's prob-
velopment program with a proven track
Third, we learned, once again, the
lem solving in CGI classrooms. Other
record of increasing student achievement
importance of providing the opportunities for
teachers and school administrators
in mathematics, it is still important to
teachers to study and to improve their own
noticed that children of CGI teachers
continuously monitor its progress. After
practice. As we seeded CGI, schools
showed a new interest in mathematics.
all, educational reform is full of stories
provided planning time, and we, from the
CGI teacher teams enthusiastically shared
about innovative programs that fail be-
Center, visited and provided what help we
their plans and teaching strategies with
cause they simply do not work with one
could, but it was teachers who effected
colleagues who visited their classrooms to
or another population. Our evaluation
change. They met, diagnosed student
see what was happening. Impressed at see-
evidence, based on students' performance
reasoning, planned lessons, and
in a word
ing CGI students solving problems that
in solving word problems and in compu-
did the hard work that spread this
seemed beyond the reach of typical at-risk
tation, shows that students whose teach-
program and made it a success. Yet, with-
students, non-CGI teachers asked
and
ers taught using CGI principles learned
out ongoing research-based support and
to go to the
in some cases demanded
more than a comparable group of students
evidence of increased student achievement,
following year's CGI Institute. They too
whose teachers did not.
(See Student
it is doubtful that the program would have
wanted in on this new way of teaching
Achievement insert.)
succeeded. Competing species (ideologies,
for the benefit of their students.
The first lesson we learned is how im-
regulations, traditions), with political or
Purposefully planning to expand the
portant it is to start small and seed change.
emotional support, could have prevented
reach of its mathematics initiative, the
Too often, people want to implement
the new species (reformed thinking and
Comprehensive Center
Region VI
change immediately and throughout a
practice in teaching mathematics) from
offered an Advanced CGI Institute so that
school system. The alternative trap is to
or even from surviving.
spreading
teachers who had been teaching CGI for
give up on systemic change in the face of
Fourth, we learned that it is important
at least one year could learn about how
what look like insurmountable odds and
to put into place, almost from the very
children engage in more advanced math-
to create what are, at best, demonstration
start, the environmental structures that
ematical topics
the ideas of algebra, for
sites where teaching is exemplary. Think-
will encourage an innovation to grow. In
example. They also learned how to present
ing of school systems as ecosystems coun-
seeding CGI, the Comprehensive Center
the ideas of CGI to their colleagues. Be-
seled against both extremes and enabled
obtained commitments from principals
yond this, a few teachers were invited to
us to think about reform as a process
that teachers would be encouraged to
co-present
with the people who had,
whereby the improvement of teaching
share what they had learned with their
just the year before, been their own men-
takes root then spreads
slowly but
colleagues. We told teachers that we
at the beginning CGI Institute.
tors
throughout the system. In addi-
surely
would offer Advanced COI Institutes so
These schools and districts themselves
tion, the hoped-for change accelerated as
that they, too, could help other teachers
took steps to expand the reach of the math-
it took on a life of its own. As teachers
learn from what they had done. We
ematics program. Dearborn sent a large
became interested in what they saw in
invited some CGI teachers to co-present
contingency of teachers to talk about their
their colleagues' classrooms, they became
at CGI Institutes offered in Madison by
experiences at the 1999 Improving America's
excited at the prospect of creating similar
the CC VI. We also helped districts plan
Schools Chicago Regional Conference. At
classrooms themselves. Teachers also be-
and implement their own CGI profes-
least two districts are planning to conduct
came learners as they focused on how their
sional development opportunities.
their own CGI Institutes so that all the
students reasoned when solving problems.
Finally, the metaphors we use often
district's teachers can learn about the pro-
Second, we learned it that it is impor-
define how we see and solve problems.
gram. One state education agency has taken
tant to realize that school ecosystems have
Our thinking of school systems as ecologi-
an active interest in supporting teachers'
the kinds of complex relationships among
cal systems gave us a different way of
travel to and participation in the Compre-
their staff that allow innovations to spread.
hensive Center's CGI Institutes. Another
thinking about professional development
A common complaint often found within
thinking of it as a way to introduce a
school made it a condition of employment
a school system is its resistance to change.
Certainly, with a machine it is difficult, if
that new teachers receive CGI training.
(continued on page 23 ...)
3 ]
CGI FROM THE BEGINNING
AN INTERVIEW WITH PROFESSOR ELIZABETH FENNEMA
I sherian e. foster ]
Elizabeth Fennema is Professor Emeritus in the School of Education and Director of the Spencer Research Training Grant.
In the seventies and early eighties, the research of Professor Fennema and her colleagues contributed important information about gender equity
in mathematics. Here she talks about the foundational Cognitively Guided Instruction research and the importance of that work.
ROFESSOR FENNEMA EXPLAINED THAT, IN THE MID 19805, IN SPITE OF ALL THAT WAS KNOWN ABOUT GENDER INEQUITIES IN MATHEMATICS,
"EVERY INTERVENTION WE HAD TRIED [TO REDUCE THE ACHIEVEMENT GAP BETWEEN BOYS AND GIRLS] WAS NOT PARTICULARLY SUCCESSFUL."
PROFESSOR FENNEMA SAID THAT SHE AND PENELOPE PETERSON HAD WORKED TOGETHER DOING RESEARCH ON TEACHING AND THAT SHE AND
THOMAS CARPENTER HAD TALKED "FOR MANY, MANY YEARS ABOUT THE IMPORTANCE OF RESEARCH ON LEARNING." (SEE SUGGESTED READING.)
"BUT," SHE SAID,"WE HAVE HAD DECADES AND DECADES OF RESEARCH ON LEARNING THAT HAS NOT MADE MUCH OF AN IMPACT ON WHAT GOES
ON IN THE SCHOOLS." FENNEMA, CARPENTER, AND PETERSON, THEREFORE, DECIDED TO "TRY TO INTEGRATE THIS STUDY OF TEACHING ALONG
WITH THE STUDY OF LEARNING." THEIR DESIRE, ULTIMATELY, WAS TO EFFECT REAL CHANGE IN THE CLASSROOM AND TO ENHANCE MATHEMATICS
LEARNING AND ACHIEVEMENT FOR STUDENTS.
project we realized that [telling teachers
THE ORIGINAL PLAN
AMAZING CLASSROOMS
what to do with knowledge we gave them]
was basically in conflict with what we
Professor Fennema explained: "The
Professor Fennema explained that
knew about learning and what we knew
overall purpose of CGI, originally, was to
the principal investigators did not go into
about teachers." She pointed out that
do a three-year research project in which
the classrooms because "it would have
"the fundamental assumption underlying
we would study the impact on teachers of
really influenced the results of the study."
CGI is that you have to make instruc-
their learning about what we knew from re-
Near the end of the study, however, after
tional decisions based upon each child's
the data were collected, Fennema,
search about children's learning and thinking
thinking" and added, "It would have been
in mathematics. It was not enough to just
Carpenter, and Peterson decided that they
a little bit arrogant of us to think that, be-
study the teaching. We also wanted to
themselves had to see what was happen-
fore we knew the children, we could tell
study the impact on learning of the children
ing in classrooms in which teachers had
the teachers what to do in the classroom!"
in these teachers' classrooms. .
research-based knowledge about how
."
.
"This went along about as expected
Professor Fennema said that the prin-
children think and solve problems.
cipal investigators "realized that, indeed,
for the first couple of years. We had long,
Professor Fennema said, "We could
involved discussions about how we would
we did not know what teachers should do
believe our eyes at the quality of the
not
help teachers learn about children's learn-
with this material. It had never been tried
teaching that was going on. We realized, at
ing and what we would tell teachers to do
that time, that we had a great deal more
before." She continued: "We decided, as a
because almost all curriculum devel-
in our hands than just a research study.
upon really examining our own
result
Op-ment projects try to tell teachers what
We were arriazed: 7 .. "The Classrborns that
that
knowledge of teaching and learning
to do with information. And that's what
we first saw do not begin to compare with
the only thing we could do was to help teach-
we planned to do. We planned to develop
compared to
what we see today, but
ers learn about how children learn and then
some kind of a curriculum based on what
what we had both seen before in the el-
to study what they did with that knowledge."
we knew about children's thinking, teach
they were amazing."
ementary schools
"It turned out to be the best decision
it to teachers, and assume they would do
we ever made, to be very truthful with you.
and that
what we had told them to do
Teachers have so much knowledge about
CHILDREN LEARN MATHEMATICS
would be it."
the practicalities of teaching and about
The most important effect of CGI for
children that they were much better able
A CHANGE IN PLANS
to implement something than if we had
children, Professor Fennema said, is that
told them what to do."
they are learning and "taking a different
Professor Fennema continued, "But
kind of look at mathematics [than. they
along about the first six months of the
(continued on page 6...)
141
6
DEVELOPING A "DANGEROUS" PEDAGOGY
TALK GIVEN AT THE 1999 CGI INSTITUTE FOR TEACHERS
gloria ladsonbillings ]
A
THOUGH I FEEL LIKE MY COLLEAGUES HERE AT UW-MADISON IN MATHEMATICS EDUCATION HAVE ACCEPTED ME AS AN HONORARY MATH EDUCA-
TOR, I DO HAVE A CURRICULUM HOME IN SOCIAL STUDIES. MY TRAINING IN SOCIAL STUDIES PROMPTS ME TO LOOK AT MOST ISSUES THROUGH HISTORI-
CAL, GEOGRAPHIC, SOCIAL, POLITICAL, ECONOMIC, OR CULTURAL LENSES. I EVEN SEE OTHER SUBJECT AREAS THROUGH THOSE SOCIAL STUDIES FILTERS.
SO,TONIGHT I WANT TO SHARE WITH YOU WHY I THINK INCORPORATING CGI IN YOUR CLASSROOM IS POTENTIALLY A DANGEROUS PEDAGOGICAL MOVE.
MY REMARKS THIS EVENING ARE ENTITLED: "COGNITIVELY GUIDED INSTRUCTION: DEVELOPING A 'DANGEROUS' PEDAGOGY." I THINK THERE ARE AT
LEAST FIVE REASONS WHY INCORPORATING CGI INTO YOUR INSTRUCTIONAL PRACTICES REPRESENTS A DANGEROUS PEDAGOGY.
chores this afternoon? Does it make more
Danger Number 2:
Danger Number 1:
sense to continue to play in the orchestra
Encouraging Students to Think
Challenging the Status Quo
or should I try out for the basketball team?
CGI's oft heard question, "How did
Second, incorporating CGI into the
First, incorporating CGI is dangerous
you come up with that solution?"
because it challenges the status quo.
classroom is dangerous because it encour-
provides a criterion that students can
ages students to think. Now that might
Schools are organized to maintain social and
and should use for a variety of problems.
cultural norms. One of those norms is that
sound paradoxical, but I argue that schools
Of course, our parents were more likely
are not places where we encourage students
mathematics is a subject area organized to sift
to ask us, "What in the world were you
out the best from the rest. While schools
to think. Indeed, the late James Baldwin,
thinking?" but the cognitive demands are
an esteemed novelist and civil rights
will accept some minimal level of math-
equivalent
how do we come up with the
ematics competence for all students, high
activist, argued that no society really wants
solutions to our problems?
thinking people. Thinking people raise
level functioning in mathematics seems
reserved for an elite few. And, that elite
uncomfortable questions. Thinking people
Danger Number 3:
group is restricted to white middle class
ask for explanations to the contradictions
Changing the Curriculum
male students and some Asian American that exist between what we say and what
students. Female students, poor and work-
we do. Students who are thinking are quick
Third, incorporating CGI into the
to ask, "How come...?" "How come our
ing class students, African American and
classroom is dangerous because it precipi-
school doesn't have enough books for all
Latino students, and students who are sec-
the kids? How come we don't have any
tates a change in the curriculum. Most of
ond language learners often are relegated
the research that has investigated the
teachers who can speak our language?
to a cycle of failure in mathematics.
state of elementary mathematics in the
CGI represents an attempt to inter-
How come only a few kids from our school
U.S. indicates that our elementary
rupt the status quo. This interruption will
graduate from high school?"
mathematics curriculum is filled with
not sit well with traditional school offi-
The kind of thinking that students are
rote learning of low level arithmetic.
cials. If everyone can demonstrate greater
encouraged to do through CGI is the kind of
The Mathematics in the elementary
mathematics understanding, who will be
thinking we hope that students will do in
curriculum is formulaic. Students are
left to fill in the spaces reserved for "basic
every aspect of problem solving they encounter.
math," "eonsumer math," and "math for
required to learn algorithms and rules for
Mathematical problems are but a few of
basic operations of addition, subtraction,
math phobics?" How will we be able to
the problems that students work to solve
multiplication, and division. Most
continue to rank and rate students?
each day. How can I stop a big kid from
picking on me without looking like a
students learn how to do those algorithms,
How will we know who is "better?" Yes, a
serious incorporation of CGI into a
follow those rules, and remember rote
wimp? How can I get my homework done,
operations. However, most students do not
classroom is bound to upset the status quo.
go to soccer practice, and finish all my
(continued on page 8 .. .)
7
5 .1
AN INTERVIEW WITH PROFESSOR ELIZABETH FENNEMA
continued from page 4
have before]. It gives them the ability to
know that the responsibility [for student
Teachers are instrumental in bring-
learning] is theirs
understand that they can makes sense of
they've always
ing administrators along in their under-
mathematics and that how they make
known that
but now they have the
standing of CGI by involving them in the
sense of mathematics is important."
knowledge with which to take that re-
change, said Professor Fennema, and she
Kindergarten children in CGI class-
sponsibility and do something with it."
gave an example. Some teachers "quite
rooms can, for example, solve a problem
o " They have changed the way they teach
often send a child to the principal's office
such as this:
dramatically." Professor Fennema
to explain how they solved a problem."
This has several benefits. The child is
Our class has 3 pages with stickers on them.
noted that all teachers with whom
There are 4 stickers on each page. How many
"feeling extremely important because she
they have worked changed, albeit to
solved a difficult problem, and she is
stickers do we have?
varying degrees.
In CGI classes, much attention is
going down to tell the principal about how
Professor Fennema is passionate on
she solved it. It only takes two or three
given to each student's thinking and prob-
this point. She reiterated, "The knowledge
minutes for a child to come in and
lem solving strategies, and multiple strate-
of children's thinking is powerful. It's
gies are encouraged. Professor Fennema
explain a solution strategy, and principals
extremely powerful. It's enabling." With
continued: "As [students] communicate
have an interaction that's pleasant with
a twinkle in her eye, Professor Fennema
their strategies
sometimes quite simple
children. They, also, can see what the
recalled teachers who have become
strategies, sometimes very complicated
children are thinking. I think that what
national leaders and said, "Torn [Carpenter]
they begin to feel that
strategies
really hooks teachers is children's thinking
calls me a 'born-again cockamamie scien-
mathematics is an understandable body
but I think it hooks principals, too ."
I say, 'Maybe I am!" She quickly
tist.'
of content, that they, indeed, can learn and
Professor Fennema said that she
added, with professional sincerity, "But
that it's important to learn. It somehow
feels having administrators attend CGI
I'm not that kind of researcher."
makes them feel so good about mathemat-
workshops is important so they can
ics and about themselves. Plus, obviously,
understand "what CGI really means."
they learn to dO mathematics! We must never
CHANGING A SYSTEM
That, she said, "means more than just
forget that the bottom line is that students learn
reading about it."
When asked what recommendations
to do mathematics in a way that we had never
Teachers play a key role in helping
she would give to a school or district try-
really thought that children could."
parents understand what their children
ing to implement CGI, Professor Fennema
are learning in a CGI mathematics class.
made several points.
Again, Professor Fennema gave an
TEACHERS ARE PROFESSIONALS
example. One teacher, she said, "would
Change will come through
When asked about the most impor-
have the children and their parents come
teachers' professionalism.
tant effect CGI has had on teachers,
to school one night, and everybody solved
Professor Fennema said: "I think the most
problems. Then the children would come
Professor Fennema said she supports
important thing for CGI for teachers is that
the approach that Walter Secada and
up in front to the overhead and explain
the Comprehensive Center are taking.
they have been given the opportunity and have
acquired the knowledge that makes them truly
She ethphasize-dthat schools Shot-ild "hot
professional. They, by understanding the
to go into full-scale implementation the
Schools should not go
children's thinking, are able to make decisions
first year." Rather, she said, it is impor-
into full-scale implementation
that improve learning."
tant "to get a core group of teachers that
Professor Fennema said, "I feel
the first year. It is important
and the only
understand it fairly well
strongly about the impact I've seen on
way to truly understand [COI] is to teach
to get a core group of teachers
teachers who've become truly profes-
then facilitate letting
it a year or so
that understand ICGI]
sional," and shetnentioned several impor-
those teachers disseminate it to the rest
tant changes they saw in CGI teachers:
of the school system." This is possible
and the only
fairly well
,
o "Certainly they know their children
Professor Fennema said
because teachers
,
way to truly understand it is
much better."
are professionals who know their schools
to teach it a year or so.
o "They begin to think a great deal differ-
and know how to implement new things in
ently about themselves as teachers. They
their own settings
.
8
6
grades will be important. Specifically in
[their solutions]. She had to tell the
And a Teacher Said...
terms of CGI, she said she would like to
parents, 'Now don't you tell the children
see someone investigate the effects of
. You sit
how to solve these problems. .
"They must be able to
.
actively moving students toward using
and see if you can solve them a different
witness success in those
something CGI,
more mature strategies
way." Some teachers "send newsletters
classroomssee the outcome
to date, has not encouraged teachers to do.
home to parents with a solution strategy."
of learning in
With parents, as with administrators
and teachers, it is children's thinking that
A PASSION FOR EQUITY
CGLclassrooms verses
"hooks them," Professor Fennema said.
the non-CGI classrooms.
getting the parents
"Once again
Professor Fennema indicated that the
If that doesn't sell a teacher,
help-
intrigued with children's thinking
latter suggestion for further research stems
ing them know that teaching is not telling
well, I don't know
from her deep and abiding concern for the
[but is] letting the children have an oppor-
mathematics learning and achievement of
what else will."
tunity to do the exploration on their own."
all students in general and her concern for
Furthermore, at parent-teacher confer-
gender equity in particular. She said
She emphasized that the role of those
that girls tend to stay with less-mature
ences, "many of the teachers have used the
who lead CGI workshops and the CGI
children's thinking in mathematics as a
modeling strategies, while boys move to
Institutes is to share what they know
indicating
good communication device with parents
more-complex strategies
research-based information on how
rather than talking about some [of the
more mathematical understanding. Also,
children think and learn mathematics.
she pointed out, "girls are not doing as
usual] things." Because teachers keep care-
When asked how they help teachers
ful track of children's solution strategies,
well as we would like to have them do in
learn to keep track of every child's think-
Professor Fennema said, "They can show
complex reasoning."
ing or get common planning time, Profes-
growth from the beginning of the school
Professor Fennema added, "I should
sor Fennema answered, "We don't talk
year to the end of the school year."
really emphasize is that girls are doing much,
about the details of teaching. Teachers do."
much better than they ever did before. It's not
Change takes time.
She continued, "I don't think anybody
as if the boys have been the ones who have
Implementing CGI involves dramatic
should trivialize what a complex kind of
been learning. Everybody's moved along,
changes, Professor Fennema pointed out,
an activity this is." Teachers and their
but there's still a gap in learning between
but teacher change "doesn't take place in
administrators know best how to solve
the girls and the boys and between
a week, or a month or a year... . The most
those problems in their own situations,
African-Americans and white, and
growth will take place over a period of sev-
she said.
between Hispanics and white, between
eral years." She continued, "one nice thing
Native Americans and white. So we've got
is that we do see rather immediate growth in
NEXT STEPS
to somehow do something there."
children's learning, so they [teachers and schools]
As for Professor Fennema, she will not
can at least be accountable to their parents and
Professor Fennema explained that, af-
be satisfied until all achievement gaps have
to their public that ICGI] is effective."
ter the first three-year project, they con-
been closed. She concluded hopefully,
Professor Fennema cautioned, how-
expanding CGI
tinued the research
saying, "I think that we have enough
ever, that "principals often go with some-
through grade three, exploring "the impact
information that we can begin to make some
thing for two or three years, and, if they're
of CGI in schools that were basically
intelligent recommendations on interventions
not seeing dramatic results, they say, 'well,
made up of African-American children,"
and to study those interventions."
we are going to try something else." But,
conducting a three-year longitudinal study
Thank you, Professor Fennema, for
because change takes time, she advises that
in Madison of the impact of CGI, and
your years of dedication and research and
"as long as [principals] see growth in their
"trying to put it into pre-service teacher
for your time in granting this interview.
children and their teachers, they should
education." She emphasized that "the
stick with it."
National Science Foundation ... has been
Change requires a joint effort.
very, very generous, in their funding of
[ about the interviewer ]
this all the way through."
With conviction, Professor Fennema
SHERIAN E. FOSTER is a Math-
When asked about the next research
said that implementing CGI and effecting
ematics Education Specialist and
to be done, Professor Fennema said that
change is " a cooperative venture between the
Editor of this Comprehensive Cen-
she feels the work Tom Carpenter and his
expert on children's thinking and the people who
colleagues are undertaking to study
Region VI Newsletter.
are out on the firing line of teaching, and we
ter
children's algebraic reasoning in the early
both know important things."
7 ]
DEVELOPING A "DANGEROUS" PEDAGOGY
continued from page 5 ]
to be 100 years old?" This one question
plunged the students into in-depth stud-
ies of actuarial tables, family histories and
genealogies, genetic diseases and heredi-
tary chronic conditions. The curriculum
lost its rigid boundaries and fixed shape.
Some problems evoked by this question
prompted the use of mathematics skills.
Others required students to use their
literacy skills. Still others required the
cultivation of research skills. In the end,
the students began to exhibit the kind of
critical thinking that we might expect
from much older students.
Danger Number 4:
Rendering Instruction
Unpredictable
The thinking that students develop
learn what these operations mean. They
Fourth, incorporating CGI into your
in a CGI classroom is not likely to
do not learn how such operations might
classroom is dangerous because it makes
be constrained to mathematics. Its in-
instruction less predictable. In today's
help them solve the kinds of problems that
urban classroom, the last thing many
fluence may spread to literacy, science,
are important in their lives.
teachers and administrators want is
social studies and other subject areas
We know that the elementary math-
.
ematics curriculum is vacuous, but
Students may begin to ask new questions
unpredictability. So-called well run urban
we aren't sure why the curriculum is
schools are characterized by their strict
about the nature of all sorts of social and
disciplinary standards, regimentation, and
vacuous. My hunch is that we permit such
scientific phenomena. This "bleeding" over
a redundant and intellectually weak
routine. Teachers in such schools are
into other subject fields is exactly what
mathematics curriculum because we
expected to write out daily objectives and
not the
integrated education should be
ensure that the students pass state and
know that we do not prepare elementary
festival of teddy bears or dinosaurs we see
local assessments. The atmosphere in
level teachers well enough in mathemat-
in many classrooms.
ics to be able to answer the kinds of
schools like this is oppressive. The em-
Instead, the curriculum might be more
important mathematical problems that
phasis is not on student learning; rather
like that of one of our former graduate
children pose.
it is on improving the previous year's test
students, Barb Brodhagen. Barb and her
_
_
scores to minimize-the personal sanctions
teaching partner teach in a seventh grade
Ifa student were to ask how many cats
are in her town, would most elementary
and public critique.
classroom. Each year they begin the school
Teachers who incorporate CGI are
year by asking the students, "What do you
teachers know how to go about solving that
willing to be less governed by routine and
want to know about yourself and what do
problem or helping the student to solve the
regulation in their teaching. They are likely
problem? These are the kinds of problems you want to know about the world?" After
that students want answers to. They could
to be more open and flexible to new ways of
students individually answer the questions,
teaching because they will experience
care less if Tim has 5 apples and Sue has 4 they meet in small groups to decide which
questions the group thinks are worth
apples. Most savvy elementary school
students' novel ways_of thinking. This is not
to suggest that CGI teachers do not plan
students probably look at a word problem
investigating. Finally, the entire class hears
and prepare their mathematics lessons.
the specific group questions and votes on
like that and say to themselves, "can't those
But, within that planning they are will-
idiots tell how many apples they have
those questions that most interest them.
ing to allow student thinking to guide the
One year, one of the questions that
and if they can't then maybe they shouldn't
even have any apples." lessons in a variety of directions, because
most interested the group was "Will I live
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