a historical research: Margaret R. Sáraco

Historical
Research:
How to Fit Minority and Women’s
Studies into Mathematics Class
Ask middle school students to name
their favorite musicians, athletes, or
actors, and they will tell you everything about them: statistics, hair color,
who they are married to, where they
live, their accomplishments, and more.
Students are exposed to celebrities
every day through television, movies,
radio, and the Internet. Isn’t it time
we expose our students to some mathematical heroes?
Margaret R. Sáraco,
[email protected]
.nj.us, teaches sixth-,
seventh-, and eighthgrade mathematics at
Mount Hebron Middle School in Montclair,
New Jersey. She is interested in helping
students discover real-world applications
of mathematics.
70
The Heroes and Heroines
of Mathematics
In February and March, educators
teach history lessons on African
Americans and women in our various
subject areas, which take the form of
PowerPoint presentations and discussions. However, there is little opportunity for students to research these important historical figures, because of all
the material that teachers are expected
to cover and skills that the students
are expected to learn during the school
year. It is impossible to add one more
Mathematics Teaching in the Middle School
●
Vol. 14, No. 2, September 2008
Copyright © 2008 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.
This material may not be copied or distributed electronically or in any other format without written permission from NCTM.
item to our agendas. Or is it?
I would argue that students should
not learn mathematics in a vacuum.
In every other subject in their middle
school studieslanguage arts, social
studies, science, art, and music—students study the people who made and
make significant contributions to the
field. However, I was not surprised
when I asked my students to name
some mathematicians from history;
they had difficulty coming up with
five names. And of those five mathematicians named, none were female
or minority. If students can find
themselves reflected in the pages of
history, they may be inspired to pursue
a career in mathematics. By researching men and women who have made
contributions to the field of mathematics, our young scholars may find
a role model. In so doing, we may be
able to stem the tide of the shrinking number of students entering the
field of mathematics by helping them
become interested in its history.
Photographs by Alex Polner and Margaret R. Sáraco; all rights reserved
a
Margaret R. Sáraco
Vol. 14, No. 2, September 2008
●
Mathematics Teaching in the Middle School
71
Photographs by Alex Polner and Margaret R. Sáraco; all rights reserved
Further, the study of mathematics
history is imbedded in our national
and state-based mathematics standards. NCTM discusses the importance of reaching across other disciplines in understanding mathematics.
Many mathematicians who have
become part of the chronicles of history are also scientists, physicians, and
business executives, among other professions. NCTM’s Communication
and Connections strands and New
Jersey’s Mathematical Process strand
instruct us to teach our students to
recognize recurring themes across
mathematical domains; recognize
that mathematics is used in a variety
of contexts; trace the development
of mathematical concepts over time
and across cultures; recognize and
use connections among mathematical
ideas; understand how mathematical
ideas interconnect and build on one
another to produce a coherent whole;
and recognize and apply mathematics
in contexts outside of mathematics
(NCTM 2000; State of New Jersey
Department of Education).
72
Getting Started
To fit mathematics history into the
middle school classroom, I started with
an idea and a grant proposal. Through
grants made possible by the Montclair Fund for Educational Excellence
(MFEE) and the Montclair State
University Network for Educational
Renewal (MSUNER), history books
were made available to students in class.
Although it would be difficult to fit
additional work into a seventy-minute
block in which I see my students every
other day, I wanted to create a unit
plan that would use minimal time in
the classroom but would require more
preparation of students and teacher.
The unit, titled “Minorities’ and
Women’s Presence in Mathematics: A
Historical Perspective,” is a yearlong
project that can be adapted to many
different learning and teaching styles.
For instance, I repeat this project
annually with my students who loop
(students and teachers who move to
the next grade level together).
Attention to these mathematicians
need not be reserved for one month
Mathematics Teaching in the Middle School
●
Vol. 14, No. 2, September 2008
per school year. The project described
here begins in September and continues through May. Students research
their mathematician and create oral
presentations about one notable
individual. Each class hears between
fifteen and twenty presentations on
different mathematicians, depending
on the number of students in class.
This is an ideal project for an
interdisciplinary unit. Mathematics
teachers can team with a social studies teacher because of the historical
element or with the language arts
teacher because of the writing and
researching involved. Science is a
natural overlap, because many mathematicians are also scientists.
At Mount Hebron Middle School,
the Science and Technology magnet
school for our district, our students
take a technology class as a core
subject and have access to a computer lab. For this project, students
are required to use the Internet and
find at least one online source that is
helpful to them, so they are allowed
to conduct some research online at
school. If these resources are not
available at your school, this project
can be completed without the online
research component. (However, you
will probably be satisfying your state’s
mathematics and technology requirements by having students work on this
project using the Internet.)
You can also ask the school media
specialist or librarian to help obtain
resources for this mathematics project. This staff member can also assist
the students, by class or individually,
when researching their topics. (This
individual may also be a good resource
when investigating grant money for
future projects.)
Setting up the Lesson
I begin in September by introducing
the project to my students. They pick
a number out of a hat to determine the
order of their presentations. The due
Fig. 1 This rubric sets the parameters for grading.
Mathematics History Project Rubric
Student’s name ___________________________________ Teacher’s name _______________________________
Category
4
3
2
1
Research
subject
Student shows a full
understanding of his or
her research topic.
Student shows a good
understanding of his or
her research topic.
Oral
presentation
Student is completely
prepared and has
rehearsed the
presentation.
Student is mostly
The student is
Student is unprepared.
prepared but needs more somewhat prepared, but
practice rehearsing.
it is clear that rehearsal
is lacking.
Question
and answer
Student is able to
accurately answer most
questions about his or
her research topic.
Student is able to
answer some questions
about his or her
research topic.
Student is able to
Student is unable to
answer a few questions answer any questions.
about his or her
research topic.
Biographical
form
Form is complete;
contains two citations
from book sources and
one online source.
Form is partially
complete; contains two
citations from book
sources and one online
source.
Form is partially
Form is not complete.
complete; contains two
or fewer citations from
book and online sources.
Poster
Poster is extremely well Poster is well
constructed.
constructed.
dates and the time-to-begin-research
dates are posted on a big calendar by
their name. Students choose a mathematician to research from a list of 150
mathematicians generated from book
resources compiled for the project.
Students are assigned a female or
a minority mathematician to research.
At first, I was going to limit their
research subjects to African American
and female mathematicians. However, while doing my own research, I
discovered many mathematicians who
have been delegated to the outskirts of
society based solely on race, ethnicity,
or gender, so I widened the search.
The challenges I face with a
middle school population are (1)
the reading difficulty of the material and (2) the level of complexity
of the mathematicians’ discoveries
or inventions. I sometimes suggest
particularly accessible mathematicians
to various students. Another approach
Student shows some
understanding of his or
her research topic.
Poster is not well
constructed.
is to assign a research subject and a
specific discovery or invention. For
example, someone could research
Benjamin Banneker and his invention of a wooden clock that ran for
fifty years. Each student is required
either to submit a one-page written
report or complete the Mathematicians Biography Form (see activity
sheet 1), according to skill and grade
level. The report assignment requires
that the bibliography include at least
two books and one Web site reference.
Students give a five- to ten-minute
oral presentation to the class, which
includes a brief question and answer
session about the mathematician they
researched. Additionally, each student
produces a poster or other visual aid
about their mathematician. A “Famous Mathematicians from History”
bulletin board displays all the projects
to date. Students are given a rubric
designed for this project (see fig. 1).
Vol. 14, No. 2, September 2008
●
Student does not show
any understanding of his
or her topic.
Form is not complete.
The grade for the project is equivalent
to one test grade.
Helping Students
Research THEIR
MATHEMATICIAN
To get involved and help students
with the research process, create lunch
or study groups with several students
every month. This is an opportunity to
teach them how to help each other and
that research can be fun. In addition,
five minutes during class or lunch can
be reserved for one-on-one conferences on students’ progress. Although
this sounds like a lot of time, if different students work on their project
throughout the year, and you have 100
students, you will be seeing approximately 10 students each month.
Teachers must be knowledgeable
about the subjects they are assigning,
which requires preparation. Before the
school year starts, decide which
Mathematics Teaching in the Middle School
73
Fig. 2 Famous women and minority mathematicians
ANCIENT WORLD
Female Mathematician
Hypatia
EIGHTEENTH CENTURY
Minority Male Mathematician
Benjamin Banneker
Female Mathematicians
Maria Gaetana Agnesi
Émilie de Breteuil du Châtelet
Sophie Germain
Caroline Herschel
Mary Fairfax Greig Somerville
NINETEENTH CENTURY
Minority Male Mathematicians
Edward Alexander Bouchet
Patrick Francis Healy
Kelly Miller
James Joseph Sylvester
Female Mathematicians
Mary Everest Boole
Susan Cunningham
Ruth Gentry
Ellen Amanda Hayes
Sofia Kovalevskaya
Christine Ladd-Franklin
Ada Lovelace
Maria Mitchell
mathematicians you would like to
assign. It could be as few as 20 and as
many as 100. Take some time to read
about the mathematicians and build
your knowledge base. The summer
before I began this project, I read
numerous biographies, which I
enjoyed immensely. Every year that
this project takes place, you will have
done a lot of the background work.
The hardest part of a new lesson is
the first year of implementation.
If you have little preparation time,
try a limited version. When students
ask for extra-credit projects, assign
them a person from the list of “Famous Minority and Women Mathematicians” (see fig. 2). In addition, for
students working on this project who
74
Mary Frances Winston Newson
Charlotte Angas Scott
Alicia Boole Stott
Mary Watson Whitney
TWENTIETH CENTURY
Minority Male Mathematicians
Manuel Berriozábal
Albert Turner Bharucha-Reid
David Harold Blackwell
Elbert Frank Cox
Philip Emeagwali
Jonathan David Farley
Lee Lorch
Ronald Elbert Mickens
Luna Isaac Mishoe
Luis Ortiz-Franco
Srinivasa Ramanujan
Abdulalim A. Shabazz
Richard Tapia
William Vélez
Jesse Ernest Wilkins Jr.
Scott Warner Williams
Female Mathematicians
Elayne Arrington
Lida Kittrell Barrett
Dorothy Lewis Bernstein
Lenore Blum
Marjorie Lee Browne
Fan King Chung
are looking for extra credit, have a list
of other famous mathematicians ready,
such as Fibonacci, Ptolemy, Pythagoras, and so on. Save these projects over
the summer and post them in the fall;
they make wonderful bulletin board
displays for September’s Back-toSchool events.
the Mathematicians’ Library
on Wheels Book Cart
The success of this project requires that
books be purchased for classroom use.
The Resources section at the end of
this article lists some books you may
want to purchase. Some books contain
general information; other books about
individual mathematicians are excellent
resources for middle school students.
Mathematics Teaching in the Middle School
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Vol. 14, No. 2, September 2008
Christine Mann Darden
Mary Lovenia Deconge-Watson
Etta Zuber Falconer
Lillian Moller Gilbreth
Meredith Charles Gourdine
Evelyn Boyd Granville
Euphemia Lofton Haynes
Grace Brewster Murray Hopper
Fern Hunt
Katherine G. Johnson
Eleanor Green Dawley Jones
Barbara Lee Keyfitz
Vivienne Malone-Mayes
Cleopatria Martinez
Susie Johnson McAfee
Shirley Mathis McBay
Fanya Montalvo
Cathleen Synge Morawetz
Caryn Navy
Emmy Noether
Kathleen Adebola Okikiolu
Edna Lee Paisano
Theoni Pappas
Mina Rees
Ida Rhodes
Julia Bowman Robinson
Myra (and David) Sadker
Pauline Sperry
Olga Taussky-Todd
Anna Johnson Pell Wheeler
Grace Chisholm Young
However, if your budget is limited,
start with these titles. Make sure you
include several books to reach students
at their particular reading skill level.
Once you assemble your book cart,
make it available in your room to your
students at all times. Although sharing
resources with other teachers is preferable, the students are better served if
the books and materials are available
in your classroom only. When students
complete an assignment, they should
be able to work on their mathematician from the book cart available in
your room. At Mount Hebron, we
have regularly scheduled DEAR (Drop
Everything and Read) periods; I sometimes offer a book to a student who has
forgotten it that day. What a pleasure
Student Responses
and Results
I am thrilled by my students’ investment in the project and their reactions
to the mathematicians they present.
One question that comes up in every
class, regardless of the mathematician’s gender, is this: “Were they married, and did they have any children?”
I inquire why they deem that so important. Their response in all classes
is that they are not sure if they would
have time in their own lives to have a
family and produce that kind of work.
I have found a few students already
imagining what it might be like to be
a mathematician. Some students ask
about the mathematician’s discoveries and inventions or about how and
when he or she died. Many students
report on inventions or ideas not often
discussed in a middle school mathematics class, such as high-end calculus
and Boolean geometry. The students
find it interesting even if they cannot
understand all of it.
It is not uncommon for students to
complain to me about the inability to
find material on their subject. I use this
as an opportunity to discuss how some
people have been written out of history
and suggest that we can help write them
back into history by presenting them to
our classmates and posting something
about them on our history wall.
CONCLUSION
As with any undertaking, the hardest part is getting started. This article
contains the groundwork to get
teachers started. The best lessons I
have created or worked with are those
that are collaborative, and this project
encourages students to work together.
RESOURCES
Baumgart, John K., Duane E. Deal, Bruce
R. Vogeli, and Arthur E. Hallerberg,
eds. Historical Topics
for the Mathematics Classroom. 2nd
ed. Reston, VA: National Council of
Teachers of Mathematics, 1989.
Grinstein, Louise S., and Paul J. Campbell, eds. Women of Mathematics : A
Biobibliographic Sourcebook. New York:
Greenwood Press, 1987.
Johnson, Art. Famous Problems and Their
Mathematicians. Englewood, CO:
Teacher Ideas Press, 1999.
Morrow, Charlene, and Teri Perl, eds.
Notable Women in Mathematics: A
Biographical Dictionary. Westport, CT:
Greenwood Press, 1998.
National Council of Teachers of Mathematics. “Focus Issue: History.” Mathematics Teacher 93 (November 2000).
Osen, Lynn M. Women in Mathematics.
Cambridge, MA: MIT Press, 1974.
Perl, Teri. Math Equals: Biographies of
Women Mathematicians + Related
Activities. Menlo Park, CA: AddisonWesley Publishing Co., 1978.
. Women and Numbers: Lives of
Women Mathematicians Plus Discovery
Activities. 3rd ed. San Carlos, CA:
Wide World Publishing/Tetra, 1997.
Reimer, Luetta, and Wilbert Reimer.
Mathematicians Are People, Too: Stories
from the Lives of Great Mathematicians.
Palo Alto: CA: Dale Seymour Publications, 1995.
. Mathematicians Are People, Too:
Stories from the Lives of Great MathVol. 14, No. 2, September 2008
●
Photograph by Alex Polner and Margaret R. Sáraco; all rights reserved
it is to see students engrossed in a book
about a mathematician.
ematicians, Volume 2. Palo Alto: CA:
Dale Seymour Publications, 1995.
Reimer, Wilbert. Historical Connections
in Mathematics: Resources for Using
History of Mathematics in the Classroom.
Fresno, CA: AIMS Education Foundation, 1992.
Smith, Sanderson. Agnesi to Zeno: Over
100 Vignettes from the History of Math.
Emeryville, CA: Key Curriculum
Press, 1996.
Spangenburg, Ray. African Americans in
Science, Math, and Invention. New
York: Facts On File, 2003.
. Kid’s Guide to African American
History. New York: Facts On File, 2003.
Yount, Lisa. A To Z of Women in Science
and Math. New York: Facts On File,
1999.
references
National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston,
VA: NCTM, 2000.
State of New Jersey Department of Education. www.state.nj.us/education.
Ed. note: If you would like to contact
the author about the lesson, ideas for
changes, or reactions to implementing
it, send an e-mail message to msaraco@
montclair.k12.nj.us and write “Historical
Research Lesson” in the subject line. l
Mathematics Teaching in the Middle School
75
activity sheet
Name _____________________________________
Mathematician Biography Form
Approach this research as if you were a newspaper reporter. Follow the who, what, when, where, why, and how format to
look for important information to share with your classmates.
1. Who is the mathematician that you have been assigned to research?
2. What did he or she do?
3. When did he or she live?
4. Where was he or she born?
5. Where did he or she live?
6. Why has his or her work been important to the field of mathematics?
7. How did he or she make the discoveries?
8. List at least three of the major discoveries or inventions attributed to your mathematician:
9. Choose one of his or her discoveries or inventions from above, and explain the discovery or invention in detail.
10. Why did you choose this discovery to discuss?
11. What did you find interesting about this mathematician’s life or work?
from the September 2008 issue of