ERIC ED390677: Teacher-Made Reform: Influences Shaping Curriculum in a High School Mathematics Department.

21 Pages·1995·0.38 MB·English

by  ERIC

DOCUMENT RESUME
ED 390 677
SE 057 308
AUTHOR
Meador, Elizabeth
TITLE
Teacher-Made Reform: Influences Shaping Curriculum in
a High School Mathematics Department.
PUB DATE
95
NOTE
21p.; Paper presented at the Annual Meeting of the
American Educational Research Association (San
Francisco, CA, April 1995).
PUB TYPE
Speeches/Conference Papers (150)
Reports
Research/Technical (143)
EDRS PRICE
MFOI/PC01 Plus Postage.
DESCRIPTORS
*Educational Change; Ethnography; High Schools;
*Mathematics Teachers; Professional Development;
*Secondary School Mathematics; Student Role; Teacher
Role; *Thinking Skills
IDENTIFIERS
*Reform Efforts; *Teacher Change
ABSTRACT
This paper is an ethnography of a high school
mathematics department that has been struggling with curriculum
change since 1977. A literature review of curriculum reform revealed
four elements of mathematics reform:
a focus on students' complex
(1)
thinking;
a change in locus of authority in the claEsroom;
(2)
(3) a
change in student roles; and (4) an emphasis on ongoing professional
development. These four elements were taken as the focus of this high
school mathematics department, either directly or indirectly. This
paper describes the following aspects of these four elements: the
focus on students' learning to think in complex ways that led
teachers tc search for materials that used this approach; the
negotiation that ensued around the locus of authority, as well as the
changes in roles of students and teachers; and finally, the informal,
national network of teachers and higher education professionals that
was import int to the professional development of the teachers. These
elements comprised the bulk of the reform efforts at this school.
(MKR)
Reproductions supplied by EDRS are the best
that can be made
from the original document.
TEACHER-MADE REFORM:
INFLUENCES SHAPING CURRICULUM
IN A HIGH SCHOOL MATHEMATICS DEPARTMENT
Elizabeth
Meador
University
of
Colorado
Paper
presented
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Introduction
The nature of curriculum reform
a fabric woven with
mathematics
in
is
The goal of this paper is to describe several of those strands
many strands.
from the perspective of those most intimately involved with mathematics
education on a day to day basis, teachers and students.
This is the tale of a high
has been
mathematics department
school
struggling
that
curriculum
with
change since
1977, close to twenty years.
These teachers began their struggle
without the benefit of the current school reform
No one handed
literature.
them a set of cutting edge curricular materials and said, "Here, implement this.
ready to go."
There was no principal well-versed in the "tribal
It's
all
1989, 266) of school
rhetoric" (Siemon
lead them through the
restructuring
to
many steps to effective schools.
The motivation to change was theirs, and
theirs alone.
Throughout this paper.
examine that struggle and ask:
what
I
were the forces and influences that
drove, shaped and impeded this effort?
A review of the
curriculum reform
literature
several key
reveals
in
elements of mathematics reform.
Four of those elements under consideration
here
arc:
a focus on student's learning to think in complex ways about
1.
mathematical situations
(Stephens, Lovitt, Clarke and Romberg 1989;
Math Sciences Education Board 1990; NCTM 1991; Anderson et al
1994;
Romagnano
1994);
a change in
locus of authority held strictly by the teacher to a
2.
tl:e
shared authority betweeo teacher and student (NCTM 1991; Romagnano
1994);
a change in
the student role from what is considered traditional to
3.
an
approach
negotiates meaning within
student
"where:1y
the
learning
a
community, makes connections with
understandings, and builds
past
new understandings within
a context" (Anderson et
1994,
2);
al
an emphasis on "appropriate and ongoing professional
4.
development" (NCTM 1991.
3).
These four elements were the
focus of this high school mathematics
department, directly and indirect!).
describe the
paper
this
following
In
1
aspects of these four elements: the
focus on student's learning
think
to
in
complex ways that
for materials
teachers
led used this
the
search
to
that
MFADOR
1
approach; the negotiation around the locus of authority,
as well
the change
as
roles of the student and the
teacher; and finally,
the informal, national
the
in
network of teachers
that was important
and higher education professionals
to
the professional development of the teachers.
These elements comprised the
bulk of the reform efforts
this school.
at
Methodology
Ethnographic methodology was used to collect data over a period of six
These data were in
the form of non-participant observations,
months.
of students,
interviews
faculty members and
administrators,
teachers,
former
community members, documents from
mathematics department and
the
thc
school district offices, and artifacts such as exams, student projects, and
student journals.
Ethnographic methodology
qualitative
research
design
that
is
allows
a
focus on
researcher
the
context of educational phenomena
to
sociocultural
the
and the meanings that teachers and students bring to
that context,
this case
in
curricular reform
high school mathematics.
rests on
An analysis
in
that
ethnographic methodology
upon the
underlying values and
relics
beliefs of
the group to explain the actions of individuals.
"From this perspective
meanings and
actions, context and
situations
and make
inextricably
are
linked
no sense in
isolation from one another.
facts' of human activity are
The
they exist only by
social
constructions;
agreement or consensus among
social
participants in a context and situation" (Eisenhart
is this social
103).
1988,
It
construction of what
meant w reform the
teaching and learning of
it
mathematics
Fruitvale High School I
this paper will address by
at
that
examining thc
of individual
actions
mathematics teachers
their
students
and
the school context.
in
Selection
Site
Fru itvalc (population 55,000)
an agricultural
located
region.
in
The
iN
demographics of
this
the school population
roughly mirrored
small
city
arc
in
composed of 75% European American,
24% Mexican American, 1% Native
American, African American and Asian American.
Thc school hosts
1600
grades 9-12.
There are
students
ten departments at
in
Fruitvale High School
I The name of the school
and names of the
teachers throughout this paper
site
pseudonyms.
arc
MEADOR
2
nine of whom are members of the
and eighty-five persons on the
faculty,
mathematics
department.
site drew the
Several features of this
attention of the Curriculum
Project2, a research project whose purpose was 'to document the
Reform
process of reform
nine schools identified
at implementing
successful
in
as
reform. The unique features of the mathematics department
site
this
at
several winners o
tradition of piloting,
teaching awards;
included:
national
a
testing and adopting materials
that address mat.lematics as
integrated body
an
of knowledge and pose complex mathematical situations
for students to explore
and make sense of;
a computer laboratory devoted to
a library of mathematics
a variety of levels of
software; the extensive use of graphic calculators
at
teachers who had searched
funding from grants and
course offerings;
for
other sources within and outside of their district;
and a reliance on an
teacher-created,
informal,
collaborative
national
professional
network
for
development
personal support.
and
This site was also unique in
that Cie reform efforts were a result of
forces within the department of mathematics.
Other departments
this
high
at
school were relatively
and the principal described himself as
traditional,
a
"traditionalist who is uncomfortable with change" (Fieldnote 5-94).
Thus, the
change and improve came from
teachers of mathematics
impetus
individual
to
district
state,
rather
than
administrative
or
mandates.
Results
and
Discussion
will be initiated by looking
This discussion
the day-to-day practices
at
mathematics department
Fruitvale High
that
shaped
reform
the
the
in
at
These practices included the ongoing drive
School.
acquire materials that
to
focused on mathematical problem
of norms around
solving,
re-negotiation
thc
roles by students and teachers, and
classroom
participation by teachers
the
in
support network of mathematics educators.
national
informal
an
The
these practices sustained the
involvement
reform efforts
site,
in
this
at
yet
at
the same timc, kept educators suspended in motion.
There was no closure; no
reform was fully implemented or the job completely done.
sense
that
this
ln
2The Curriculum Reform Project
funded by the
U.S. Department of Education,
is
Office of Educational Research and Improvement. Office of Research, under
contract No. RR 91182001.
MEAIX)R
3
5
high school mathematics department, change was a part of the culture.
People
talked about it, looked for it, and expected it.
Materials
this high school began their efforts
The individuals
at
curriculum
at
reform when they
that most students were completing only the
realized
for high school
minimal mathematics requirements
graduation.
They
felt
the
sequence of classes and the materials used turned students off to mathematics,
that met the basic
the classes
particularly
requirements,
referred
to
as
"bonehead math".
One teacher, Howard Roseberry, describes the situation
in
the late
1970's:
"As you car. imagine, bonehead math was pretty boring.
We needed to
beef up the whole program.
We started using calculators, which was
unheard of back then, and we disguised skill
higher level
learning
in
problems that allowed kids to think, but also to practice their
they needed
fractions
practice their
fractions"
(Interview,
to
3-94).
if
These teachers had to put their beliefs about mathematics on the
line
at
a time when a hierarchical
sequencing of mathematics classes based on
student's ability was the norm.
Like most high schools in
the late
1970's, the
majority ot students enrolled
basic math, while a minority of students
in
in advanced math (Mathematical Sciences Education Board
enrolled
The
1990).
at Fruitvale High School saw mathematics as
teachers
a body of integrated
knowledge that
students could learn and they were willing
all
to challenge the
to implement their ideas.
Roseberry and one of his colleagues, Ted
list* ict
Wolfe, lobbied the district to reduce class sizes and allow the best math teachers
to work with the "low-end" classes.
He states:
"Ted and
worked together to implement our ideas.
We convinced thc
I
district to let us limit class size to 22.
And then we had to argue pretty
hard to convince the
district that our strongest teachers should be
teaching thc lowest classes.
We had to convince them that the best
teachers could explain things in
a variety of ways" (Interview 3-94),
At the same time, there was concern that kids who were in thc honor's
were entering
calculus
track
without
conceptual
the
understanding
that
they
needed to he successful.
This concern led
the piloting of prc-calculus
to
1987 developed by a
materials
nationally recognized secondary school,
in
the
North Carolina School of Science and Mathematics (NCSSM).
Teachers also
MEADOR
4
persuaded the district to adopt a text book series in
1989 that presented
mathematics in
an integrated fashion,
the University of Chicago School Math
Program (UCSMP) materials (Usisken
These materials represented a
1990).
significant change
the way mathematics were presented, and rested on
in
about the purpose of learning mathematics, described
beliefs
fundamental
in
the NCTM standards as "an integrated set of intellectual tools for making
sense
of mathematical situations" (NCTM 1991, 2).
The teachers
this department were largely
their love
influenced by
in
of mathematics and their desire to see better materials in
the hands of their
Personal beliefs about mathematics as a system of knowledge,
students.
as
opposed to a segregated series of topics, and as an approach to problem solving,
as opposed to a computational
skill, drove them to search for materials that
reflected those beliefs, and when materials could not be found, to design their
Piloting new materials was exciting and transforming.
own.
One teacher, Mr.
Wolfe, spoke of the personal and professional challenge that
piloting
lie
in
fel*
the NCSSM pre-calculus materials (Barret et l 1991).
"Piloting the North Carolina materials really changed me.
was team
I
teaching with Mr. Davis, and we were holding each other's hand.
Teaching these materials made me see math in a different
way.
I
could be
realized
Ione differently"
it
(Interview 3-94).
The years spent on the search for better materials also drove them to
search
creatively
for
funding,
were reasonably
and
they
successful,
resulting
the purchase of state-of-the-art materials and technology.
in
Grants from
such sources
Hewlett-Packard, Trout Unlimited, General Telephone and
as
Electric, the State Department of Education, Tech Prep and the Woodrow Wilson
were used to buy graphic calculators, computers, televisions, VCRs,
Institute
to pay
tables,
chairs,
travel expenses and conference registration
and
for
fees.
The personal
that these teachers held about what constituted
beliefs
good mathematics influenced the reform
site and led them to embrace
this
at
key components
of
current
the
agenda advancing curriculum
national
reform
Such important
mathematics.
criteria
in
of mathematical
the
integration
as
substantive use of calculators and computers, student experience with
topics,
a
genuine problems, and the exploration and use of real
data were in place
at
as early
this
1980, criteria that can n.ow he found in numerous
site
as
MEADOR
5
7
statements on the
for mathematics education (Mathematical Sciences
standards
Education Board 1990; NCTM 1991). As a result of these efforts, the students at
site had the
interact with
interesting mathematical
this
opportunity
to
problems in a range of courses offered by the high school.
However, this
interaction with the materials was limited by the traditional nature of the
roles assumed by teachers and students.
Roles
Key to
the reform of mathematics currici!lum
the shift
the
is
in
role from locus of authority and trasmitter of knowledge to
that of
teacher's
problem poser and manager of the ensuing discussion, with an explicit
deflection of the role of teacher as keeper of the knowledge (Anderson et
al
This new role assumes a teacher's ability to establish
1994; Romagnano 1994).
norms of discourse (NCTM 1991) while engaging the students in
a verbal and
mental exploration of a mathematical problem.
(in Von Glaserfeld
Richards
nature of traditional classroom discourse
1991) describes
the
information
as
an
transfer in which the subject
is presented as a collection of facts.
this
In
teacher controk ttm classroom dynamics,
because the
traditional
setting,
a
a creativt
mathematical discussion
of spontaneous
true
that
involves
series
responses does not occur.
The re-negotiation of norms of discourse to allow for spontaneity,
inquiry and discussion was a difficult
shift for teachers and students at
this
and the high school context may be particularly
site;
resistant
pedagogical
to
Talbert and McLaughlin reflect on the conditions that promote
change.
in which the teacher acts
as a guide
for understanding"
"teaching
in
a
community of learners who together co-construct knowledge,
description
of
a
the classroom that
is echoed
the NCTM standards
for teaching mathematics
in
(1991).
Talbert and McLaughlin state
their
research,
are many
that
In
there
model of teaching
constraints
that
prevent
this
learning from
occurring,
and
particularly
character of
high
school level,
including
the
at
routine
"the
classrooms, watered down subject matter curriculum,
teaching
school
high
in
and transmission oriented pedagogy" (Talhcrt and McLaughlin
1991,
1 li2).
High schools have a
tradition of teaching as
a transmission of
',Ing
information influenced
that performance on standardized
the
by
tests
idea
is
the amount of factual knowledge the student has received from
linked
to
their
One of the teachers at Fruitvale High School spoke of the students as
teacher.
"a product that we have to put out that has to do well on the SAT for the
community" as a reason
to avoid too much experimentation with pedagogy
(Fieldnote
11).
At Fruitvale High School, student expectations of teachers to
act
in
traditional ways were also a source of constraint
to teaching for
roles of both teacher and student were being
Thus, the
understanding.
re-
negotiated, yet neither had clear ideas about the purpose or structure of the
new roles.
Romagnano characterizes one type of student response to
this
re-
disengagement.
curricular changes cal led
negotiation
analysis,
his
as
the
In
the reform of mathematics "substantially changed both the
for
nature and
in
the amount of expectations placed on our students" (Romagnano 1994, 63),
in disengagement or resistance on the part of the students.
esulting
The
the changing nature
vignette
following
describes
negotiation
around
of
the
teacher-student
relationship
classroom.
the
the
in
Vignette
to their Algebra class and take their places at one of the
Students file
in
nine tables arranged around the
The walls are hare
large, sunny classroom.
except for
string of pictures showing men and women mathematicians
a
A student walks in, Sandra, and says to no one in
throughout history.
particular but in hearing range of her teacher Mr. Davis,
the worst day of
"It's
my life."
"You always say that," responds Mr. Davis.
"No I
I've never said that before," she replies
don't!
testily.
"It's only nine o'clock in thc morning.
How can
already he the worst
it
day of your life?" Mr. Davis asks.
"Last night my sister's dog ate my curling iron, so
look like crap.
And
I
I'm not speaking to half my friends.
Well, two of them."
"You only have four friends?"
Mr. Davis is
teasing her, as he often does
with the
students, who seem to enjoy these exchanges with
thcir teacher.
Sandra finishes the conversation saying
"It's
really
0.1(.?"
bad,
"O.K. people, listen up."
This time Mr. Davis is speaking to the entire
"You only have five days to finish up the chapter.
class.
You're going to
class next term, so we have to get you through chapter four by
someone else's
MEADOR
7
next Tuesday. [They had spent three weeks outside the text working with codes]
I've prepared
a summary for you."
Most of the students in
this Algebra class are sophomores.
The trimester
about to end and they will continue in Algebra, but with a different teacher.
is
Mr. Davis takes a seat at his desk while the kids settle in at their tables, get out
their books and begin to work. They talk quietly among themselves.
Some read
books from other classes.
reads Glamour Magazine with a defiant look
One girl
on her face; most are working in their math books (UCSMP materials).
Oc ...asionally someone raises a hand and asks for help.
Mr. Davis walks around
class talking quietly
in on their progress.
with students, checking
the
Suddenly a student challenges Mr. Davis as he walks by her table.
"Why
don't you teach us?"
"It's not my responsibility to just sit here
is Sandra.
It
and look at this stupid book.
You should be teaching us."
Mr. Davis replies.
"It's not my responsibility to learn
material.
the
It's
your responsibility
learn
to
material."
the
Sandra implores him, "But why don't you lecture us?
We need you to
lecture
us."
lecture you privately right here any time you ask me to.
"Ell
But I'm
not going to stand at the chalk board and lecture you.
That's not how kids
learn best,"
Mr. Davis answers.
Sandra is not finished.
That is what a teacher is supposed to
"Yes it
is.
Every teacher stands up and gives a lecture but you."
do.
"We just do it
Another student, Maria, chimes in.
all by ourselves and
there's no help.
You say we don't
listen anyway when you lecture, but this
way is too boring.
I should have to ask for help.
don't think
You should be
I
able to tell us exactly what we're doing and how to do it."
A third student, Brad, says "You don't make us do anything.
Wc need
somebody to push us.
And if you don't,
don't do it."
I
The girl who was reading Glamour magazine adds, "We need
a teacher
who'll say,
'If you don't get this done by tomorrow, then you'll get a zero.
And
if you get zeroes for the whole trimester, you'll
fail.'"
Mr. Davis is used to these attacks on his teaching style.
I-Ic describes
as
it
a function of age.
"They haven't figured out
responsible for
they're
that
their
Own learning yet."
Or hc blames himself saying, "I'm not thc
hest teacher.
others arc
better teachers than
The.
am."
I
MEADOR
iO