ERIC ED372298: Implementing the Massachusetts Adult Basic Education Math Standards: Our Research Stories. The ABE Math Standards Project. Volume 2.

264 Pages·1994·7.1 MB·English

by  ERIC

DOCUMENT RESUME
ED 372 298
CE 066 943
AUTHOR
Leonelli, Esther, Ed.; And Others
TITLE
Implementing the Massachusetts Adult Basic Education
Math Standards: Our Research Stories. The ABE Math
Standards Project. Volume 2.
INSTITUTION
Holyoke Community Coll., MA.; Massachusetts State
Dept. of Education, Quincy.
SPONS AGENCY
National Inst. for Literacy, Washington, DC.
PUB DATE
94
NOTE
264p.; For related documents, see CE 066 942-944.
PUB TYPE
Guides
Non-Classroom Use (055)
EDRS PRICE
MF01/PC11 Plus Postage.
DESCRIPTORS
Adult Basic Education; *Adult Literacy; *Classroom
Techniques; Curriculum Development; Educational
Research; Literacy Education; *Mathematical
Applications; *Mathematics Instruction; Research
Projects; State Curriculum Guides; *State Standards;
*Teaching Methods
IDENTIFIERS
*Massachusetts; NCTM Curriculum and Evaluation
Standards; NCTM Professional Teaching Standards
ABSTRACT
The product of a project conducted in Massachusetts
to apply the National Council of Teachers of Mathematics' (NCTM)
"Curriculum and Evaluation Standards for School Mathematics" to adult
basic education (ABE) learning environments, this volume is
a
collection of teacher-researchers' essays on field-based application
of the adapted standards. The following
essays are included: "Can the
Fear of Manipulatives Be Overcome?" (Debra Richard); "Making
Connections in Math and Science" (Karen DeCoster); "'It's Not through
the Book'" (Leonora E. Thomas); "Exploring the Metric System in
a
Workplace Education Class" (Judith Sulzbach); "Non-Traditional
Problems in the Forefront" (Marilyn Moses); "Learning to Learn. How
Long Does It Take?" (Leslie Arriola); "Manipulatives
vs. Rote Memory"
(Margaret Fallon); "When You Have
a Problem, Use Your Head (...and
Your Instinct)" (Thomson Macdonald); "'They Never Asked Me: Who Did
They Ask?'" (Shelley Bourgeois, Martha Merson); "'What If I Used
Research and the Scientific Method to Teach Problem Solving?'"
(Catherine M. Coleman); "Journey into Journal Jottings" (Donna
Curry); "Shapes and Stitches: Quilting in
an ABE Math Class" (Linda
Huntington); "When Students Work in Teams" (Barbara
Blake Goodridge);
"Learning by Doing, or What Happens When Students Write Their
Own
Math Word Problems?" (Tricia Donovan); "Evaluating Creative
Mathematical Thinking and the GED [General Educational
Development
Test]" (Sally Spencer); and "Adult Diploma
Program Math Research"
(Susan Barnard, Kenneth Tamarkin).
(KC)
Reproductions supplied by EDRS are the best that
can be made
from the original document.
***********************************************************************
THE ABE MATH
STANDARDS PROJECT
VOLUME 2:
IMPLEMENTING
THE MASSACHUSETTS
ADULT BASIC EDUCATION
MATH STANDARDS:
OUR RESEARCH STORIES
EDUCATION
U $ DEPARTMENT OF
Improvement
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INFORMATION
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THE ABE MATH
STANDARDS PROJECT
is a field-based research project for teacher development
based on the application of
The National Council of Teachers of Mathematics
CURRICULUM AND EVALUATION STANDARDS
FOR SCHOOL MATHEMATICS
to Adult Basic Education Learning Environments
The main funding came as an award from
THE NATIONAL INSTITUTE
FOR LITERACY GRANTS PROGRAM
to
Holyoke COmnaunity College
in collaboration with
SABES
Slow ier Atie Ow Gamow ii0.0
and
The Massachusetts Department of Education
Copyright c 1994 by The Massachusetts ABE MATH TEAM
Perrnissbn to phowoopy limited material from The ABE Math Standanla
Project, Volumes 1 and 2, is grunted for educational purposes. Permissbre
must be soughtfor commercial use of content from this publication. when the
material is quoted in advertising, when portions am used in other publicaticns,
or when charges for copies are made. Use of material other than those cases
described should be brought t o the attention of Me Massachusetts ABE Math
Team. c/o Mary Jane Schmitt. Massachusetts Department of Eclu...ition. 350
Main Street, Malden. MA 02148-5023.
VOLUME 2:
IMPLEMENTING THE
MASSACHUSETTS ADULT BASIC
EDUCATION MATH STANDARDS:
OUR RESEARCH STORIES
Edited by Esther Leone Ili, Martha W Merson,
and Mary Jane Schmitt
and members of the Massachusetts ABE Math Team
William Arcand
Martha W. Merson
PROJECT CO-D1RECTOR
ADULT LITERACY RESOURCE INSTITUTE,
SABES WESTERN REGIONAL SUPPORT CENTER,
BOSTON
HOLYOKE COMMUNITY COLLEGE
Adrienne Monis
Leslie Arriola
PROJECT ASSISTANT
HOLYOKE ADULT LEARNING OPPORTUNITIES
SASES WESTERN REGIONAL SUPPORT CENTER,
(HALO) CENTER
HOLYOKE COMMUNITY COLLEGE
Shelley Bourgeois
Marilyn Moses
JACKSON-MANN COMMUNITY CENTER,
BROCKTON ADULT LEARNING CENTER
ALLSTON
Debra Richard
Catherine Coleman
ADULT BASIC EDUCATION PROGRAM,
WORCESTER ADULT LEARNING CENTER
QUINSIGAMOND COMMUNITY COLLEGE,
WORCESTER
Donna Curry
Mary Jane Schmitt
SKILLS DEVELOPMENT PROGRAM,
DIGITAL EQUIPMENT CORPORATION
PROJECT CO-DIRECTOR
MASSACHUSETTS DEPARTMENT OF EDUCATION
Karen DeCoster
Ruth Schwendeman
HOLYOKE ADULT LEARNING OPPORTUNITIES
(HALO) CCNTER
PRODUCT COORDINATOR
OFFICE OF WORKPLACE EDUCATION,
Tricia
Donovan
QUINSIGAMOND COMMUNITY COLLEGE,
FRANKLIN/HAMPSHIRE EMPLOYMENT &
WORCESTER
TRAINING CONSORTIUM, GREENFIELD
Sally Spencer
Margaret Fallon
THE CARE CENTER, HOLYOIC
LAWRENCE ADULT LEARNING CENTER
Judith Sulzbach
Barbara Blake Goodridge
QUINSIGAMOND COMMUNITY COLLEGE,
LOWELL ADULT EDUCATION
WORCESTER
Hunthigton
Linda
Kenneth Tamarkin
COMMUNITY LEARNING CENTER, CAMBRIDGE
SOMERVILLE CENTER FOR ADULT LEARNING
Esther D. Leonelli
EXPERIENCES (SCALE)
Leonora Thomas
PRODUCT COORDINATOR
COMMUNITY LEARNING CENTER, CAMBRIDGE
NEW BEDFORD ADULT EDUCATION PROGRAM/
Thomson Macdonald
ADULT LEARNING CENTER
HAITIAN MULTI-SERVICE CENTER,
DORCHESTER
4
ACKNOWLEDGMENTS
The Massachusetts ABE Math Team teachers wish
to acknowledge the two hundred adult learners who
explored strategies for teaching and learning mathemat-
ics during this year-long project.
We thank them for their support and healthy skepti-
cism as we tried to create environments that were unlike
the math classes any of us had known in our youth. The
names of all learners referred to or quoted in this docu-
ment have been changed to respect their privacy.
Again, we wish to thank the agencies which finan-
cially supported our efforts: the National Institute for
Literacy which provided the main funding; the Massa-
chusetts Department of Education's Project PALMS
(Partnerships Advancing the Learning of Mathematics
and Science) which funded one co-director's time and
contributed to five of the team members' stipends; the
SABES Regional Support Center at Holyoke Community
College which funded the other co-director's time; and
the SABES Central Resource Center at World Education
which helped us conceptualize the project and write our
initial proposal.
Thanks, too, to the agencies and individuals who
lent moral support, encouragement, and endorsement at
key points: the SABES Regional Support Centers, Susan
Lytle, and advisory committee members John Comings,
Myrna Manly, William Masalskt, Bonnie Mullinix (also
an honorary team member), and Sally Waldron.
Finally, we thank Mary Lindquist, the President
of the National Council of Teachers of Mathematics,
who encouraged us. We are indebted to our partners,
spouses, and children for support during long days and
late nights.
DESIGN MD PRODUCTION BY RICK SCHWARTZ/COMMUNICATIONS
FOREWORD
By Susan L. Lytle, Graduate School of Education.
University of Pennsylvania
()ver the past decade there has been growing
support for the notion that research by
teachers about their own classroom prac-
tices can function as a powerful means of
professional development and also contribute to knowl-
edge generation in the field of education. The terms
"teacher research" or "teacher inquiry" have been used
as umbrellas to describe a range of activities in which
teachers draw on their intellectual histories and close
observations of learners to identify questions critical to
teaching in specific contexts. Traceable to the writing of
educators early in the century, the current efforts of
teacher researchers echo John Dewey's belief in the
importance of teacher's reflecting on their practices and
integrating their observations into their emerging theo-
ries of teaching and learning. In his writing, Dewey urges
educators to be both consumers and producers of
knowledge about teaching, both teachers and students
of classroom life.
As more teachers at all levels have come to regard
themselves as researchers in their classrooms, schools
and programs, they have also begun to explore innova-
tive forms and formats for documenting their own work
an for making visible the ways students and teachers
together construct knowledge and curriculum. Writing
about classrooms as sites of inquiry has thus begun to
make accessible some of the interpretive frames of
teachers largely missing to date from the literature on
teaching. From their 'ernic' or insider perspectives,
teachers are now examining what happens when inquiry
is both subject and method, i.e., when teachers inquire
with their students in ways that generate knowledge
useful to themselves and their immediate communities
as well as potentially useful to the wider field.
In our recent collaborative work, Marilyn Cochran-
Smith and I have posited a working definition of teacher
research as "systematic and intentional inquiry carried
out by teachers." By "systematic," we refer primarily to
ways of gathering and recording information, document-
ing experiences inside and outside of classrooms, and
making some kind of written record. The word 'system-
atic' also indicates ordered ways of recollecting, rethink-
ing, and analyzing classroom events for which there may
be only partial or unwritten records. "Intentionar signals
that teacher research is an activity that is planned
rather than spontaneous, and the use of the term
"inquiry" emphasizes that teacher research both stems
from and generates questions and reflects teachers'
desires to make sense of their experiences by adopting
a learning stance toward classroom life.
Despite the growing interest in the movement for
teacher research and an expanding arena for publica-
tion, however, there continue to be several local and
natioral obstacles, including the isolation of teachers,
their occupational socialization as self-sufficient and
independent, and the prevalence of a technical model of
professionalization in which teachers are expected to be
consumers of outside-expert knowledge. In the field of
adult literacy education these issues of teacher culture
and the dramatic differences among learners and pro-
gram structures and settings makes the generation of
knowledge by field-based practitioners extremely com-
plex. There is much that works against raising questions
and against taldng the risks of interrogating assump-
tions and common practices. Overcoming obstacles such
as these requires support for groups of adult literacy
teachers to come together as inquiry communities that
function as intellectually stimulating and challenging
context within which to conduct significant research
designed primarily to improve daily practice.
The essays included in this collection by teachers of
adults in Massachusetts demonstrate the cumulative
power of such collaborative inquiry. Building on a Na-
tional Institute for Literacy grant and embracing a
shared overarching question
what happens when
adult education teachers try to implement their NCTIVI-
based Massachusetts Adult Basic Education Math
Standards in a range of communities and program
these educators construct specific questions
contexts?
from the particulars of their settings, providing richly
detailed accounts of the origins of these concerns, the
processes of teacher planning, and the fascinating
nuances of student response. Based on close observa-
tions of classrooms and students' processes of learning,
these narratives capture the energy of highly dedicated
and risk-taking professionals by showing how innovation
leads not just to decentering the teacher-led classroom
or to more student-student interaction but to the devel-
opment of an inquiry stance that aims to embrace teach-
ers and learners in a common endeavor. From case
studies of individuals and projects, close descriptions of
collaborations with learners and other teachers, and
analyses of efforts to build meaningful cross-disciplinary
linkages, we see the many innovative ways that math-
ematics teachers in diverse communities in Massachu-
setts are struggling against the powerful legacy of
student histories and expectations to integrate the
content of math into learners' real-life situations and
needs.
As teacher inquiry, this collection contributes to
research on adult literacy education by making the
distinctive perspectives and knowledge of committed
teachers accessible to the field. Using a wide range of
interpretive strategies for data collection, including
observations, field notes, interviews, audiotape record-
ing, and think-aloud protocols, these descriptions reveal
the profound diversity of adult students' needs and
interests, the salience of aintext to teaching method and
outcome, and the critical need for educators to interro-
gate and find alternatives to conventional modes of
curriculum and testing. Through their writing, these
teachers also disclose how they are learning about the
subject of mathematics from looking closely at their own
curriculum and interactions with learners.
By connecting this community of teacher research-
ers with others across the country, this publication
strengthens the possibilities for generating useful knowl-
edge from a field-based perspective. It is extremely
important that adult educators make visible their work
in progress in collections that reinforce the need for local
rather than monolithic solutions to thc challenges a
educating adults through the words of these teachers
and learners using the NCTM and their own standards
as a heuristic to interrogate and document their daily
work, so that others in the field of adult literacy educa-
tion
including teachers, learners, administrators,
can
university-based researchers and policy-makers
understand what it means to use a powerful overarching
framework to improve practice in ways that are respect-
ful of and responsive to differences among learners,
teachers and communities.
INTRODUCTION
By Martha Merson, Athzt Literacy Resource Institute
teachers read the NCIM Curriculum
and Evaluation Standards for School
When
Mathematics or the Massachusetts Adult
Basic Education Math Standards drafted
by the Massachusetts ABE Math Team, they might have
mixed reactions. While many of us on the Math Team
were at once excited by new possibilities when we heard
of or read the NCTM Standards, we also felt awed or even
resigned ahead of time that such a different way of
teaching and learning could ever occur in our own
classrooms. The teachers who have written for this book
have overcome those fears. They've attempted changes
in the format, the content, the very spirit of their classes.
In this volume we've outlined our journeys. Each article
tells the story of a question. These questions go to the
very heart of our teaching. We ask ourselves to question
our "best practice
to risk disrupting our own status
quos in order to create mathematical communities where
we problem-solve, reason, seek connections, and com-
municate with one another.
Be aware that the changes discussed here were not
implemented in ideal settings by privileged teachers. In
almost every article, teachers remind us of the con-
straints common to most adult literacy and basic educa-
tion: shaky attendance patterns, lack of prep time, open
entry and open exit enrollment, and multi-level classes.
This was the norm. Nevertheless, teachers who had a
choice among classes, and those who didn't, worked with
some of what one might in advance have labeled the
hardest cases: the strictly individualized GED class
became teams, the beginning level math and reading
students learned geometry and statistics, and students
who were loyal to the culture of schooling that had
trained them to compute answers began to write ques-
tions and demonstrate reasoning.
When teachers began initiating changes in their
classes, they did so with (some) guidance from me de-
signed to facilitate their growth into teacher researchers.