ERIC ED482566: ENC Focus Review.

18 Pages·2003·0.57 MB·English

by  ERIC

DOCUMENT RESUME
ED 482 566
SE 068 331
AUTHOR
Thorson, Annette, Ed.
ENC Focus Review.
TITLE
INSTITUTION
Eisenhower National Clearinghouse for Mathematics and Science
Education, Columbus, OH.
SPONS AGENCY
Office of Educational Research and Improvement (ED),
Washington, DC.
REPORT NO ENC-03-003
2003-00-00
PUB DATE
NOTE
17p.
CONTRACT RJ97071001
AVAILABLE FROM
Eisenhower National Clearinghouse for Mathematics and Science
Education, 1929 Kenny Road, Suite 400, Columbus, OH 43210-
1079. Tel: [phone] (Toll Free); Fax: [phone]; e-
mail: [email protected]; Web site: http://www.enc.org.
PUB TYPE Reports Descriptive (141)
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DESCRIPTORS
*Beginning Teacher Induction; Elementary Secondary Education;
*Interdisciplinary Approach; *Literature; *Mathematics
Education; Mentors; Pictorial Stimuli; Teaching Methods
ABSTRACT
The mission of the Eisenhower National Clearinghouse (ENC) is
to identify effective curriculum resources, create high-quality professional
development materials, and disseminate useful information and products to
improve K-12 mathematics and science teaching and learning. This issue of
"ENC Focus" contains articles related to mathematics teaching and teacher
"Bringing Literature into the High
collaboration. Articles include:
(1)
School Math Class" (Laurie Pines)-- through a high school literacy program, a
program combining literature and mathematics is developed;
"Using Picture
(2)
Books in High School Math" (Judy Spicer)--high school students enjoy and
learn from picture books the same as younger 'students do; and (3)
"Collaborating with Colleagues to Improve Student Learning" (Harry Wong) --the
elements of effective programs for helping new teachers succeed is presented.
(MVL)
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Bringing LiteratUre into the
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High School Math Class
Through a high school literacy
program,teacher Laurie Pines
developed a program combining
iterature and mathematics. (Page 3)
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Collaborating with
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Colleagues to Improve
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Student Learning
Harry Wong, author of
.
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ipescribes the elements
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,DUCAT1ONAL RESOURCES INFORMATION
tiof effective programs for
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' elping new teachers
originating It
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a Minor changes have been made to
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The Mission of the Eisenhower
Len Mescals
EXECUTIVE DIRECTOR:
ASSOCIATE DIRECTORS
National Clearinghouse
Thomas Gadsden
Collaboration:
Kimberly S. Light le
lostrational Resources:
Gay Gordon
is to identify effective curriculum
Publishing:
STAFF
resources, create high-quality pro-
Tracy Crow
Publications Manager
fessional development materials,
Doug Line
Manager of Electronic Production:
Annette Thorson
Editor
and disseminate useful information
Carolyn Hamilton
Senior Editor
and products to improve KI2
Melanie Shreffler
Managing Editor
Brian Deep
Senior Graphic Designer
mathematics and science teaching
NagaraJan Gopalan
Interactive MedU Specialist:
Judy Duguid
Contributing Editors: and learning.
Julia Harris
Virginia Cook
Editorial Assistant:
Mark Holtman
Electronic Publishing:
To accomplish its mission,
Constance Reining
Deb Schneider
ENC... Acquires
Assistant Director
.
Judy Ridgway
and catalogs mathematics and science
of Instructional Resources:
Caro lee Barber
Content:
curriculum resources, creating the most comprehensive
Carol Damian
collection in the nation.
Jennifer Gonya
Terese Herrera
Judy Spicer
Provides the best selection of math and
science
Ed Coss
Evaluation Data:
education resources on the Internet.
Beth Brown
Cataloging:
Janet Kahkonen-Smith
Supports teachers' professional development
in
Jessica Pyle
Beth Stenger
math, science, and the effective use of technology.
Linda Trombetti
Un Zhang
Serves all KI 2 educators,
parents, and students
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HOW TO REACH
US:
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ENC Focus Is publithed by the Eisenhower National Clearinghouse
For Mathematics and Science Education. ENC Is funded at least In
part through Contract No. RJ97071001 with the U.S. Department of
Education. The contents of this publication do not necessarily reflect
the views or policies of the U.S. Department of Education nor does
the mention of trade names, commercial products, or organizations
The Eisenhower National Clearinghouse for Mathematics
Imply endorsement by the U.S. Government. ENC welcomes read-
and Science Education is funded by the U.S. Department
ers' comments and questions.
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What's New with ENC Focus?
I
written articles, sometimes you'll see
pages will continue to provide inspiration
f you are a long-time ENC subscriber,
compilations of curriculum resources or
and resources to help you with your
you've noticed by now that this issue of
web links. Throughout this print issue,
teaching. Second, with each page of the
looks quite different
ENC Focus Review
you'll see information about the topics we
publication we are building a bridge to
from what you've seen in the past. The
have online already.
ENC Online.
changes to our print publication go hand
To see everything we have to offer,
Every article you see here is available
in hand with the changes to ENC Online
you'll need to check back with ENC
ENC Focus
online, as always. But now
(www.enc.org). ENC Online now presents
Online frequently. This print publication
is just a taste of what you can find
Review
fresh new content every week!
is one way to learn about and share what
online. Each week, the online version
ENC
From now on, ENC will publish
of
ENC offers. Our new email newsletter is
(www.enc.org/focus/)
ENC Focus
in print six times during the
Focus Review
another way to stay in touch (see inside
highlights a different important topic for
school yearyou'll be receiving valuable
front cover for details).
math and science teachers, with much
information even more often than you did
We always welcome comments or
more information than we could ever
before. We chose the new name because
feedback on our products and services.
publish in print.
the print publication is a sampler of what
And we still look for teacher-written
For each online topic, ENC offers a
you'll find online.
articles, on any topic of your choice.
carefully crafted selection of relevant
We have two big goals for this new
Contact [email protected] with your ideas
materialsometimes you'll find teacher-
print publication. First, we hope that these
or suggestions.
Laurie Pines has developed a variety of tools for using literature with her students. See the online version of this article for
a sample reading graphic organizer, a list of reading prompts for Fermat's Enigma, and a term paper assignment sheet, as
well as a list of the teacher and student resources she finds particularly helpful. The online article is one portion of the full
ENC Focus issue on Literature in High School Mathematieswww.enc.org/focus/mathlit/.
Bringing
This high school teacher developed
a program that uses literature to build
mathematics interest and understanding
Literature
in her students.
by Laurie Pines, Fremont High School,
Sunnyvale, California
into the
Six years ago, I became involved in the Secondary
School Literacy Project, a program of the Bay
Area Coalition of Essential Schools in the San
Francisco area. Being the only math teacher in
the group, I did not think that teachers of other disciplines
High School
would be interested in a math literacy program.
But soon I realized that my project was not a solo
affair. My English and social studies colleagues helped
me find relevant literacy tools and reading techniques,
Math Class
and they provided suggestions for books to use with my
math classes.
Today I have the beginnings of a successful mathemat-
ics literacy program: it is fun, relevant, and a great learn-
ing tool for my students. I have found a plethora of stories
and creative methods to approach the task. Literature in
mathematics class is not an oxymoron, but a viable and
motivating activity to pursue with your students.
Begin with Reading Comprehension
I adapt the program for use with different mathematics
classes, but generally, I begin by helping students improve
their reading comprehension. They are taught and prac-
tice different reading techniques with the assignments.
An excellent resource for these techniques is Reading
Reminders, Tips, Tools and Techniques (Burke, 2000).
One of the most useful reading-improvement tech-
niques is a two-column graphic organizer that helps
my students become aware of their own metacognitive
processes. I explain to the students that they are becom-
ing aware of the conversation happening in their heads as
they read.
As they find thought-provoking material in their
reading, students record the words from the text on the
left-hand column of the graphic organizer. Then they
write their own thoughts and questions triggered by the
text on the right. Students are introduced to this graphic
organizer while reading Stories to Solve (Shannon, 1985).
(See the Reading Graphic Organizer for an example,
3
Focus on Literature in High School Math
www.enc.orgifocus/mathlit/
included online at www.enc.org/focus/
mathlit/.)
Teaching across the curriculum is encouraged by the
standards, and students benefit when relevant literature is
Next: Stories That
used to illustrate mathematics concepts. Many resources
Require Deductive Rea-
are available for bringing literature into math in elementary
school, but not nearly so much for using literature in
soning
middle school, and very little for including it in high
FERMAT'S
(NIGMA
Stories to Solve requires deductive
school math courses.
reasoning, an important skill in math-
ematics. I also use Sir Arthur Conan
This online feature takes a step toward filling that gap! The
Doyle's Sherlock Holmes stories for
article here by Laurie Pines is just one piece of this online
this purpose.
feature. Additional resources include other teacher-written
I introduce the readings with the
articles about classroom-tested ways to use literature
game 221B Baker Street. This interest-
in high school math, and book suggestions from one of
ing game uses deductive reasoning and
SIMON
ENC's math education specialists (see page 5). Finally, link
can easily be adapted to groups of four
0
hl
I
k.
to ENC's Classroom Calendar entries for more ideas and
players.
resources to use with your students.
The problem with Holmes stories
is the difficult language. To make the
reading more accessible to my stu-
dents, I have them skim the story and
record any unfamiliar words. We then,
MATH=
EUCLID'S
as a class, research the words and dis-
cuss the meanings that would best fit
WINDOW
,
the context of the story.
111,1:101,Cr
140,441.01.1.1SE
Another option is to use stories
CUR/SE
from a book that is easier to read. The
Man Who Counted by Malba Tahan
works well with my students.
1011 SCIDIXA LAU SMITH
I
I
-
(Editor's Note: Sophisticated teen-
aged readers who enjoy Sherlock
et!*a
11.% 400
Holmes stories will benefit from the
strong mathematics component in
ing Prompts for Fermat's Enigma for samples of read-
the final mystery solved in The Beekeeper's Apprentice,
ing questions and methods.)
a 1994 historical mystery novel by Laurie R. King. In
The students are assigned the term paper midway into
addition to Holmes and Watson, characters include a
the semester. I require each student to choose a math-
teenaged girl, making the book more appealing to girls.
ematician from his or her log and research that person.
Reviews are available online at www.mysteryguide.com/
Students write a term paper based on their research and
bkKingApprentice.html.)
also prepare a short oral report that introduces his or her
Finally: A Mathematical Enigma
mathematician to the class. (See Term Paper Assign-
ment Sheet online.)
Fermat's Enigma by Simon Singh is the last book my
Students are often creative with their oral reports. Two
students read. It tells the story of the quest to solve Pierre
years ago a student began his report on Archimedes by
de Fermat's Last Theorem.
saying, "Archimedes is the man who invented streaking."
For more than three centuries, professional and ama-
The program ends with the video Fermat's Last
teur mathematicians alike searched for the elusive proof
Tango, a musical based on this quest to find a solution to
that Fermat himself claimed to have solved, but never
Fermat's Last Theorem. The video is well worth the time
recorded. The book takes the reader through thousands
to view and enjoy.
of years of mathematical history and discoveries. It con-
Laurie Pines was a 2002-2003 Albert Einstein Dis-
cludes with Professor Andrew Wiles from Princeton Uni-
tinguished Educator Fellow in Washington, D.C. She
versity publishing a correct proof.
teaches mathematics at Fremont High School in Sunny-
I introduce the book by showing the video The Proof
vale, California, and at San Jose State University.
which provides an excellent overview of the Last Theo-
Email: [email protected]
rem story. The students then read the book, keeping a log
of all the mathematicians they encounter. As they proceed
References
through the book, I continue to introduce various reading
Burke, Jim. (2000). Reading Reminders, Tips, Tools and Techniques.
techniques. (In the online version of the article, see
Read-
Portsmouth, NH: Boynton/Cook Publishers.
Shannon, George. (1985). Stories to Solve.New York: HarperCollins.
7
ENC 2003 v.ww.encerg
BEST COPY
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Using Picture Books
Books in the ENC
,Collection
in High School Math
Note: Web addresses are included
for each full ENC catalog record;
links to the records are quick and
easy in the full online feature at
by Judy Spicer, ENC Instructional Resources
www.enc.org/focus/mathlitt.
When we decided to create
the online feature Focus on
The Librarian Who Measured the
I.
HOW
Earth
Literature in High School Math,
by Kathryn Lasky (Little,
Brown, 1994).
we assumed we would emphasize
MUCH 15
books written for teens and adults.
This is a story made for students
A MILLION?
But using picture books written for
of trigonometry. The illustrated
younger children is also an excel-
by Daykl AA Schwartz
biography describes how
lent way to explore topics in high
pictures by Steven Kellogg
Eratosthenes, the head librarian of
school mathematics. It is amazing
the Alexandria Museum in Ancient
how artwork can make mathematics
Egypt, measured the circumference
of the Earth with amazing accuracy.
concepts real for students.
(www.enc.orgirecords/015932/)
According to mathematics educa-
tion professor and former high school
For an online version of this story
math teacher Jennifer Bay-Williams,
and a related web project, check
"opening a mathematics lesson with
out The Noon Day Project at
a children's book sparks enthusi-
www.k12science.org/noonday/.
asm.... Weeks after the activity,
(www.enc.orgirecords/0 I 8207/)
students will remember the story and
2. Sir Cumference and the
its related investigation, and this will
First Round Table by
Cindy
help them to remember the math-
Neuschwander (Charlesbridge,
ematics." (See Bay-Williams's article online for details of two literature-based
1997).
activities.)
Another, similar comment came from the web site of the National Council
This clever tale uses math
of Teachers of English. In response to a question on the site's interactive area
(which is no longer archived), Lind Williams, a teacher at Provo, Utah, High
Sir Cumference
School, wrote:
and the
"I would suggest that the tenth grade math teacher use picture books
First Round Table
rather than short stories. There are a plethora of picture books on math-
A hlailAikamst
related topics, and tenth graders would love them. What you do is just
joke around about the fact that these are children's books and then ham
up the reading. Once you start reading the books, the tenth graders will
love it." (Contact Williams via email: [email protected].)
Based on these recommendations, we searched the ENC collection and
elsewhere for picture books that we would recommend to high school math
teachers. We also discovered that the books may be for children on one level,
but on other levels they speak to older students and adults. For example,
The
vocabulary as Sir Cumference and
Librarian Who Measured the Earth
can be enjoyed as a history or biography,
his son Radius investigate a variety
or the reader can focus on and develop the trigonometry involved.
The Dot and
of geometric shapes to find the best
the Line: A Romance in Lower Case Mathematics
is designed to appeal to the
design for the king's table.
romantic in us all and offers a different take on geometrical relationships.
(www.enc.org/records/009844/).
As with any teaching technique, there is more than one way to present
picture books in a high school math class. A teacher can choose one book to
3. Sir Cuinference and the Dragon
of Pi by
read aloud to a class to introduce or reinforce a mathematics topic, or even to
Cindy Neuschwander
(Charlesbridge, 1999).
encourage students to think differently about the topic. Or if a learning goal is
mathematical communication, students can select a book from the list, report
Here is another clever tale for
on the story (characters and setting), and explain the related mathematics.
geometry students. In the story,
Another idea, depending on the book, might be to have students write sequels
Sir Cumference's son Radius
or prequels based on the mathematical story line.
must measure the circumference
The mathematics in the picture books listed here is realas well as being
and diameter of many circles to
beautifully illustrated and accessible. Have some fun with it!
determine the value of pi and
CEST COPY
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It describes the world population
This book tells a tale about
relationships on two levelsit is the
in terms of a more easily
understandable concept, a global
anguished story of incompatible love
village of 100 people. Using the
and an exploration of the possibilities
January 2002 world population
for geometric shapes!
(www.enc.org/records/021266/) of 6,200,000,000 people, the
author calculated the nationalities,
languages, education levels, and
Is a Blue Whale the Biggest Thing
7.
ages for the 100 residents of the
There Is? by Robert E. Wells (Albert
global village, in which each person
Whitman, 1993).
represents 62,000,000 people. The
number of people living in the
111111111111131
global village who have clean water,
I
electricity, and sufficient food was
xs A BLUE WHALE
A
also calculated. The results will
-OE BIGGEST T141140
shock students.
olERE IS?
rescue his father from a curse.
(www.enc.org/records/026534/)
(www.enc.org/records/014832/)
10. G is for Googol: A Math Alphabet
fkl,u.trin11
4 . Math Curse by Jon Scieszka
Book by David M. Schwartz (Tri-
(Penguin/Putnam, 1995).
cycle, 1998).
This book is sure to generate a gasp
of amazement and moments of
This book illustrates and explains
thought in mathematics students.
mathematical vocabulary from
Illustrations help the reader perceive
abacus, binary, and cubit to zillion.
the size of the blue whale, the
Information gives insight into the
sun, and maybe even the universe.
place of mathematics in our world
Thinking about the size of a jar
today.
of blue whales, a stack of Mount
(www.enc.org/records/016027/)
Everests, or a crateful of sun-sized
Bonus Books
oranges can help students realize the
importance of scientific notation for
These excellent books are not in the
large numbers.
ENC Collection, but they are available in
(www.enc.org/records/014682/)
libraries.
8. The Token Go by Hugh William
The Missing Piece by Shel Silver-
II.
McKibbon (Annick, 1996).
This story begins with the challenge
stein (HarperCollins, 1976).
from a teacher, Mrs. Fibonacci,
This book presents the dilemma
that a person can think of almost
of an incomplete circle. For the
anything as a math problem. Using
mathematically inclined reader,
math that ranges from arithmetic to
the question can be how big is
the quadratic formula, the humorous
the missing piece in addition
book leads readers to discover math
to questions of friendship and
problems everywhere in the course
loneliness addressed by the author.
of one school day.
(See the Bay-Williams article online
(www.enc.org/records/009867/)
for activities related to this book.)
5. How Much Is a Million? by David
12. Socrates and the Three Little Pigs by
M. Schwartz (Lothrop, Lee &
Tuyosi Mori (Putnam, 1986).
Shepard, 1985).
If you are teaching probability,
This book takes the reader into
combinations and permutations, and
the world of large numbers. It
tree diagrams, this illustrated book is
offers comparisons that can help
perfect for your students. It clearly,
conceptualize the meaning of a
and cleverly, illustrates the possible
million, a billion, and a trillion. Here
The story, set in India, tells of the
arrangements of pigs in houses and
is one example of how magnitude
development of the game of chess.
shows the related tree diagrams.
is examined: If a billion kids could
The story can be used to explore the
Artwork is by the renowned
stand on each others' shoulders, the
meaning of growth by doubling.
illustrator Mitsumasa Anno. (This
tower would reach past the moon.
(www.enc.org/records/017323/)
book is now out of print but it is so
(www.enc.org/records/001299/)
excellent for math class that it is
9. If the World Were a Village by David
worth a search of your district and
6. The Dot and the Line: A Romance
J. Smith (Kids Can, 2002).
public libraries.)
in Lower Mathematics by Norton
This is a perfect book for linking
Juster (SeaStar Book, 2001).
mathematics and social studies.
A
6
ENC 2003 www.enc.org
BEST COPY AVAILABLE
What are the U.S. Department of Education's
top priorities in mathematics and science?
V
Tisit.the online ENC Focus issue covering the Mathematics and Science
V Initiative of the U.S. Department of Education to learn about its three
broad goals for improving mathematics and science:
Informing the public, including parents, about the pressing need for
better math and science education in the nation's schools.
Starting a campaign aimed at recruiting, preparing, training, and retain-
ing teachers with strong backgrounds in mathematics and science.
Developing a research base to help educators understand what improves
student learning in mathematics and science.
Online, you'll find more about how the department intends to accomplish
these goals. We have included a comprehensive list of specific programs from
agencies and organizations across the country working to support the depart-
ment in this effort.
See www.enc.org/focus/edinitiative/ for the full content of this issue.
Did you know that:
there are octopuses
that live in trees
and fields of Velcro
growing in California?
t's true, according to the web. In some cases, we
I
instantly know not to believe what we read online, but
most of the time, inaccurate information, author bias, or
commercial purposes of web sites are hidden beneath the
surface.
In this online issue of ENC Focus, we explore the
unique challenges the web poses as teachers search for
information. The full contents of the issue include:
An overview on the importance of
critically examining web sites
The web is a crazy and wonderful new medium, which
Quick routes to sources of filtered web sites
is just one reason you need to be careful, especially when
ENC does a lot of work finding high-quality web sites
your students are involved.
that teachers should know about, and we aren't the only
Teacher-specific criteria for evaluating web
ones!
sites
A chance to weigh in on what matters to you
In addition to key criteria to use as you examine web
Vote in our poll asking what you look for in web sites.
sites, some web-savvy teachers share what they care
about.
Find all of this online at www.enc.org/focus/webeval/.
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