Keywords: Connections, Activities, Geometry
Ref: Jamie1
Author(s): Pacyga, Robert
Date: 1994
Title: Making Connections by Using Molecular Models in Geometry
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol.87, No.1,p.43-46
Reviewer: Jamie
Date of Review: March 3, 1999
This article presents an activity which connects the academic areas of math and science. The activity involves both independent and group work for students. Initially, work is done alone as students are instructed to cut a polystyrene ball into eight equal parts. They then reassemble these parts so that the resulting shape is a cube with empty space in the center. When they are finished, each student is in the possession of a model simple cube of a crystalline structure. The students are then instructed to join forces with seven other cube-holders. As the eight cubes are attached to one another a unit cell will reveal itself. Throughout the activity, students will be required to note the volumes of the initial sphere, the cube's empty space, and the volume of the empty space in the unit cell. Surprisingly, the empty space in the unit cell is an identical sphere to the initial sphere.
Having created and studied the molecular make-up of crystals in math class, the students will make important connections between the two disciplines of math and science. In addition, hands-on learning and applied mathematics are memorable and valuable to students. Therefore, I would certainly incorporate this activity into my unit plan. I think that it would be great for a high school geometry class during a unit on volume.
Keywords: Activities, Problem Solving, Communication
Ref: Jamie2
Author(s): Gonzales, Nancy; Fernandez,Albert; Knecht, Corine
Date: 1996
Title: Active Participation in the Classroom Through Creative Problem Generation
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol.89, No.5, p.383-385
Reviewer: Jamie
Date of Review: March 3, 1999
How do teachers get students to go from "passive recipients to active participants in the creation of mathematics problems?"This question, tackled by the authors of "Active Participation in the Classroom through Creative Problem Solving," has resulted in an activity which forces students to be the involved inventors of mathematical word problems. Here's how it works: The class is responsible for developing a problem in a step-by-step fashion. Each progressive step is an additional phrase or statement for the problem given by a single student or by a small group of students (either is fine, but be consistent). The first group sets the stage and the last group provides closure, or the final question.
This activity is incredibly beneficial in that it is necessary for students to communicate with each other for their problem to make sense. They also have to contiuously critique themselves and the suggestions of their classmates to ensure that the numerical values and the sequence of events are appropriate. If everything seems to be workable, the class then solves their problem.
This activity addresses many of the issues that the Standards
encourage. We see freedom of creativity, maximal students
involvement, minimal teacher involvement, and an unspoken
reinforcement for students and teachers to face unpredictable
situations. I would problably have a create-a-problem day once
for every unit and require that the problems involve at least a
few of the concepts covered in our unit.
Keywords: Activities, Measurement, Manipulatives
Ref: Jamie3
Author(s): Edwards, Thomas
Date: 1995
Title: Students as Researchers: An Inclined-Plane Activity
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol.1, No.7, pages 532-535
Reviewer: Jamie
Date of Review: March 15, 1999
Thomas Edwards presents a classroom activity for middle school
students in a upper-level algebra class. It would fit nicely into
a unit involving plotting data and finding functional
relationships to fit the data. The actvity requires students to
explore different measurements that can made with a ball and
inclined plane--when both can be altered in weight and height or
length respectivly. The class should brainstorm what they should
take note of, what they should change, and what they should leave.
The teacher should validate their ideas and lead them to focus on
feasible variables. The teacher should also provide various
weighted balls, inclines of different lengths, materials to change
the steepness of the inclines, and stop watches. Edwards also
suggests suggesting that students organize material in data tables
and encouraged to think about the importance of averages.
The class should be given 15 to 20 minutes to do the measuring
and varying themselves. This engages students in thinking and
hands-on learning. As a result, there is a higher potential for
retaining the implications of their results. I like this activity
because of the hands-on aspect as well as the connection to
physical science.
Keywords: Activities, Connections
Ref: Jamie4
Author(s): Miller, Louis
Date: 1995
Title: My Way and the Highway
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol.1, No.7, pages 550-551
Reviewer: Jamie
Date of Review: March 15, 1995
This is a short article, but it contains a valuable idea. If
you're working on patterns at a middle school level and need an
activity...here's a great one: use maps of our country's major
highways and freeways to discover patterns. Kids seem to have a
fascination with cars and traveling, so this is a good way to hold
their attention. Present the maps to your class and have them
work in groups to find patterns in the ways the roads are
numbered. To make geographical connections, ask them why certain
highways and freeways are placed the way they are. The article
also suggests incorporating patterns in area codes and zip codes.
This activity is interactive and it gives the class some
intersting information to tuck away in the growing knowledge-
files.
Keywords: History, Teaching Strategies
Ref: Jamie5
Author(s): Katz, Victor J.
Date: 1998
Title: History or Mythology?
Journal or Publisher: Math Horizons
Volume, Issue, Pages: pages 22-23
Reviewer: Jamie
Date of Review: March 15, 1999
Katz highlights a few mythological events in association with theorems or those who wrote the theorems. However, he questions presenting these stories due to there fabrications. On the other hand, knowing them still has value. For example, the story behind Newton's Apple grabs student attention. If a teacher can tell the story and follow it with the true situation, the class will have something more to connect a theory to than just the numbers. It will make the math more colorful. I really like this article because it promotes relating math and mathematicians to the social and emotional world. Teachers should research the theorems they present inorder to potentially find some great information to supliment the math. Math might become more interesting to many students as a result of such efforts.
Keywords: Geometry, Puzzles,
Ref: Jamie6
Author(s): Kremer, Ron
Date: 1989
Title: Exploring with Squares and Cubes
Journal or Publisher: Dale Seymour Publications
Volume, Issue, Pages:
Reviewer: Jamie
Date of Review: March 4,1999
Ron Kremer has put together a great book for mathematics teachers from grades four through nine. He presents activities of varying difficulty some which will take a whole class period, others which would be good supplements for lessons that a teacher has all ready put together. The book begins with an activity that challenges students to discover all of the different shapes four squares can make when at least one side of each square must match with one side of another square. The students are to check that they do not repeat any shapes and they are to be given ample time to discover these shapes on their own. As a general rule for teaching these activities, Kremer states "Be sure not to over-explain a topic or provide answers when students seem to hesitate. That kind of teaching robs students of the learning moment, dampens curiosity, and prevents them from moving toward the level of independent investigation."
As you flip through his book, you'll see that Ron presents
activities that are progressively more difficult and therefore
useful for higher level geometry classes. Some topics covered in
later activities are surface area, volume, and symmetry. I
questioned the value of some of the lessons he presents, but it
would be easy to pick and choose what you find valuable for your
class. On a whole, I think that his book is worthwhile to look
through in order to find ideas for lessons.Most of the activities
are mental challenges; he presents quite a few which require
students to do puzzle solving (for example placing pentominoes
correctly in order to create a familiar figure). Kremer believes
in letting students discover mathematical concepts on their own
and therefore having ownership of their knowledge. You can see
this in the way he has created several of his lessons, and his
methods fits what research and the Standards have implied about
how math should be taught. Therefore, I would suggest looking at
Exploring with Squares and Cubes to gather resources for teaching
geometry lessons at any ability level between fourth and ninth
grade.
Keywords: Geometry, Manipulatives,
Ref: Jamie7
Author(s): Woodward, Ernest; Hamel, Thomas
Date: 1992
Title: Geometric Constructions and Investigations with a Mira
Journal or Publisher: J. Weston Walch Publishing Company
Volume, Issue, Pages:
Reviewer: Jamie
Date of Review: March 5, 1999
The authors of Geometric Constructions and Investigations with a Mira have put together 21 lessons related to symmetry, reflections, and constructing geometric shapes. They have certainly followed the suggestions of the writers of the Standards in that their lessons require that students are "doing" rather that just "knowing" the math at hand. To make this more clear, I'll explain one of their typical (but more difficult) lessons. A transparency with the definitions of a trapezoid, parallelogram, rectangle, and square is provided for the teacher to leave up through out the class period. The class should discuss the definitions, and then they are instructed to create these shapes using a Mira and worksheets which are provided. Creating these shapes helps students to understand them, their differences, and similarities.
Before a teacher attempts to incorporate Mira activities, he or she should read the introductory information concerning the Mira and how it should be used. I would also suggest practicing some of the activities to get a feel for where some difficulty may develop in class. As defined by the authors, "the Mira is piece of translucent red acrylic plastic about 9 cm by 15 cm...[it] is held upright by two ends also made of plastic...[it] sits perpendicular to the surface being examined...and it is possible to see an object on the far side of the Mira in addition to being able to see the image that is on the near side of the Mira."
I would highly recommend investing in this book and a set of Miras for a middle school geometry class. To me, they seem very valuable for enhancing student understanding geometric shapes and geometry's rules.
Keywords: Technology, Teaching Strategies,
Ref: Jamie8
Author(s): Brunner, Ann; Sheehan, Sharon
Date: 1997
Title: the Algebra Launching PAD
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 90, No.9, pages 696-701
Reviewer: Jamie
Date of Review: March 5, 1999
"The Algebra Launching PAD" summarizes a four-year sequence of courses for "low-achieving" students. The program work is mostly computer and calculator-focused because, as the authors say, "such "low-achieving" students don't lack ability, motivation, or dedication when presented with appropriate and challenging material." Therefore, 90% of class time is spent working with computers or using calculators as this technology seems useful and grabs students attention. Part One of this program covers algebra. Lessons are focused on teaching students to determine from looking at a graph if a function is linear, quadratic, exponential, or an inverse function; to recognize functions by their algebraic form; and analyzing graphs and data rather than doing paper and pencil work. The second course covers geometry. During the third and the fourth courses, students learn most of the math taught in traditional algebra, advanced algebra, and trigonometry. The goal of the program is that students develop their own particular way of seeing problem. They should move from a partial understanding of the mathematics vocabulary and ideas necessary for solving problems to a more full understanding which fosters creativity, higher level thinking, and confidence.
If you check out this article, you'll find that the authors provide a sample assignment which appears to be very beneficial to enhancing student understanding of exponential equations and the analysis of graphical information. The assignment requires students to graph a countries past, present, and future (1990-2090) population given the country's population rate of increase. They are then to analyze their results.
Student responses to the program all seem to be positive, but I
question how much they are gaining and retaining. I think that
if students are learning more from this program than a
traditional one then keep the program running. I would like to
see the benefits of this program first-hand as I'm skeptical of a
program that is so technologically-based. I think that students
miss out on some things, and the sample assignment supplementing
the article seemed incredibly straight-forward. But my mind is
open to the idea, and I believe that some modifications could be
made so that parts of this computer-calculator course could find
itself incorporated into a regular mathematics curriculum.
Depending on who and where you teach,this article and the program
it highlights may be of great interest.
Keywords: Issues, Teaching Strategies,
Keywords: Activities, Connections,
The authors of this article have put together a thorough
description of an actvity involving cryptography. The
objectives are encoding and decoding messages using linear
functions, using modular arithmetic, analyzing patterns and
making test conjectures, and finally to communicate procedures
and algorithms both orally and in writing. The goal is to
develop stronger problem-solving strategies. It's an activity
for high school students, but the level of difficulty can vary.
The lesson involves making decoder tools, giving the students
important hints for decoding, and solving various coded messages.
The article provides instructions for making the decoder tool,
helpful decoding hints, and sample messages.
This is a great activity for encouraging exploration and for
opening students eyes to some occupations that involve a lot
of mathematics. In specific, I would mention the importance of
cryptology in businesses inorder to protect corporate secrets,
in the military to protect information, and in banking in order
to secureaccounts.
Keywords: Technology, Activities,
Engebretsen and Vonder Embse suggest analyzing free throws as
a means for teaching laws of trigonometry and calculus. They
also suggest that we use one of many programs that can be
downloaded onto TI-85's or TI-92's. These programs are
incredible. The calculator screne displays the side-view of a
basketball hoop and the path the ball will take given the
parameters entered by the student. The parameters are
height of release, launch angle, and initial velocity. Before
the class actually gets into experimenting with values and
analyzing the functions they come up with, the class should
brainstorm questions relating to shooting a free throw. Some
questions to probe for are:
1. How high is the rim above the ground?
2. How far horizontally is the front of the rim from the
free-throw line?
3. How long will the ball be in the air before it reaches the
basket?
etc.
I will definately use this activity in my upper-level high
school classes. I think it provides a great incorporation
of technology and it's not just number-crunching--this is a
prime example of problem-based learning!
Keywords: Standards, ,
Standard One states, "The goal of teaching mathematics is to
help all students develop mathematical power." This is an
audacious objective to incorporate in to every lesson, but the
authors of this article think it feasible. All a teacher needs to
do is ask him or herself if the activities they plan are
worthwhile. To answer affirmatively, the following two questions
should get a "yes."
1. Are your students minds engaged in critical thinking, and are
you giving them the freedom and encouragement to to explore,
conjecture, experiment, and relfect on their results?
2. Do students believe in the worth of the task? That is, have you
presented real-life contexts for learning, caught imaginations, and
tapped into their intelletual curiosity?
The authors say that an activity is good if the above
questions recieve positive answers, if the level of difficulty is
correct, and if teachers trust their students' abilities.
Educators need to refrain from jumping in and explaining things too
early. The authors say, and I agree, that "students will have more
fun and are more excited about their work when allowed to solve
problems their own way...the resulting mathematical empowerment is
priceless."
Keywords: Activities, Geometry,
Using the path of a golf ball on a mini-golf course is a great
way to teach translational geometry. The authors of this article
present an incredibly indepth project done with students using
miniature golf. Groups of two to four students worked together,
using their geometry skills, to figure out the paths balls could
take in order to get hole in one on maps on single holes from
courses. Then, they teamed up with a computer-aided design
student and one or two wood technology students for 15 days to
construct one hole of miniature golf. They also had to mark three
paths, on a print-out of the hole, that would result in a
hole-in-one. The paths had to include one with the ball
banking against one wall, a ball banking twice and a ball
banking three times. The paths also had to be turned in with a
mathematical proof of the end result.
I think that this is a great activity. If I have the time
and a few teachers in the involved departments to team up with,
I will certainly try to use it. But it can also be modified by
eliminating the construction and still useful in the classroom.
In addition, a teacher could vary the level of difficulty in
analyzing the path of the ball; for example, figuring out
equations, or just figuring out how the cooridinates change.
Keywords: Geometry, Manipulatives, Technology
This article presents a discovery lesson in which the discovery
is that if you join the centriod of a triangle to the three
vertices, the three resulting triangles have equal areas. The
fist step of this lesson is having students create a triangle and
make the centriod-vertices segments. After this is done, ask
the class if they think that the areas of the three triangles are
equal. The class will then get into some hands-on activities.
They will cut out the interior triangles and check to see if they
have equal weights using a soda-straw balance (a diagram is
provided in the article). The class should discuss the
connection between weight and area. The next step of the lesson
is to explore if this conjecture of equal area holds for all
triangles. It would be quite laborious to inspect all triangles
through the previously explained method; however, Sketchpad is
quite efficient. Students can easily manipute triangles and
employ programs which calculate the area's of their prescribed
interior triangles. In using Sketchpad, the students will realize
the valididity of the arguement. However, they still will not
understand the calculations. The authors of the article suggest
investigating the two centriod properties using the Mathcab
program which can be downlowded onto TI-85s.
I like this activity because it requires analysis. Students
aren't just given a theorem and formula's and told to memorize
them; they are presented with a theorem and then activities
which bring that theorem to life. They are also more likely
to understand the formulas if they go through this discovery
process.
This activity is suggested for tenth-grade geometry classes. The
authors also suggests that the teacher somehow incorporate the
fact that the lesson can be stretched into the fields of physics
and engineering (consider uniform density and its applications).
Keywords: Curriculum, Connections, Standards
Architecture in Mathematics is a curriculum for a summer-school
math class. It was used at an all-girls school, but could
certainly be taught in a co-educational setting. The program
involved using mathematics to create scale-models of the
classroom and then the students' dream homes. The initial project
was the classroom. The students were not told how to complete
it; they were simply provided the necessary materials (tape
measure, graph paper, architects scale, trianlge, white glue,
clear tape, basic model-buildings instructions, and a Design
and Mathematics booklet). After the models of the classroom were
complete and much discussion about their construction, the class
took what they had learned and moved on to constructing their
dream homes. One students concluded, "I never realized how
important it is to be precise. Your whole plan could be messed
up if you don't calculate right."
The program covered taking measurements and working with
angles, areas, and volumes. It served its
purpose well as a problem-based summer-school program and it held
attention because students were creating THIER dream
homes. I think that the program could also be modified and
worked into a unit during the regular academic year, and I would
check into teaming up with the Industrial Technology teacher
in order to keep construction in the plan.
Keywords: Activities, ,
The Making Mathematical Connections Web site hosts a collection
of "opening" and "filler" activities for the math classroom.
Most of the activities are best-suited for younger grades, but
a few presented would work well in middle school classes.
All of the activities involve nametags that can be esily posted and
and removed fromt the board or charts. For example,
one possible opening activity is to have students place their name
in the correct position of a Venn Diagram. The diagram should
have one cicle for having one sister overlapping a second circle
which represents having one brother. Students who do not fit the
criteria of having one brother and/or one sister will palce their
nametag in the space that is the compliment to the union of the
sister circle and the brother circle. This activity should be
used to take attendance as students who are absent will be noted
because their nametags will not have been moved.
A suggested "filler" game, to be played, for example, as students
are waiting to go to lunch, is "Guess my Rule." The teacher
should explain that he or she is thinking of a secret rule and
that nametags of students following that rule will go on the
side of a chart labeled "yes" while those who are not will have
their nametags on the side labeled "no." At some point, students
should be coming up with the rules.
These are some fun activities to review concept probably
covered in class...but to do it in a game-like fashion. I am
definately planning on using activities like this in the my
classes. They serve an important purpose of keeping a class
moving and paying attention.
Keywords: Activities, Connections,
This website provides an in depth multi-day lesson on the
mathematics involved in baseball. Battisa suggests starting off
by having students write short reports about some aspect of the
game, including personal experiences, collecting cards, and also
the basic rules of baseball. The class should be broken down
into groups to discuss their papers and stay in those groups
to work through the rest of the lesson.
The baseball lesson includes studying algebraic formulas involved
in palyer statistics, the geometry behind the baseball field, an
analysis of a pitch (speed and time it takes to cross home plate),
etc.
I would highly reccommend checking this site out. The lesson is
worthwhile and it's explained thouroughly. It should be perfect
for a high school functions, statistics, and trigonometry course.
The class would do important reviewing and would be challenged by
the new mathematical processes involved.
Keywords: Teaching Strategies, Algebra, Calculus
This website explains how a Tonka truck can be used to illustrate
an application of slope in the algebra class or introduce the
derivative in a calculus class. In the algebra class, the teacher
should draw a one-dimensional vertical motion axis on the board.
Then, attach a piece of chalk to the back of a Tonka truck and
move the truck around on the board. When the truck is moving
forward, the speed is positive; when the truck is moving in
reverse, the students should be told to think about it as a
negative speed (if they have not covered velocity yet). The
activity contiues and soon student are analyzing time-position
graphs for the truck. The Tonka Truck visual can also be used in
calculus to introduce the derivative as a means for discovering
instataneous slope.
I think that this is a great visual way of presenting position
vs. time graphs and the derivative. I would guess that students
would be highly likly to remember these concepts if they had been
presented such a creative manner.
Keywords: Geometry, ,
The Wallpaper Groups website does a good job providing
examples of translations, rotations, reflections, glide
reflections, and latiices. There are several designs to study
as well as explanations of each of the previously mentioned
transformations. These explanations are posted right next to
an example design.
As I was surfing through this website, reading the author's
descriptions of the various transformations of a plane, I thought
that it might be a good idea to have a geometry class look at this
website and one or two others in order to gather information and
write their own reports about plane symmetry groups. It would
be easy to have students spend one or two days of class doing
their research (the teacher should provide a list of websites
to choose from) and then write their reports and possibly
prepare a visual to share with the class. I would suggest looking
at this website if you are doing a unit including transformations.
Keywords: Geometry, History,
It may seem difficult to tie multiculturalism into
the math class, but don't give up on trying. I found a great web-
site on Native American geometry. It's a beautiful and incredibly
interesting site. Geometry is explained as a spatial language...
so much of what we are surrounded with is directly related to
geometry: corporate logos, religious symbols, street signs, etc.
The author of Native American geometry uses many present-day
examples, but also refers to history and geometry's origins.
For example the site includes informations about a 12-sided
Dodecagon present on Aztec calendar stones. Many other topics are
covered. Such as, an introduction to a variety of designs that
can be made from the quartered cirle, the inner and outer squares,
and the octogon. One of it's highlights is a page called "Symbolic
Secrets" where the reader is taught how to recreate some popular
corporate symbols.
I think that this is a great website. It's full of information
that I would love to incorporate into class. From looking at
it, I feel inspired to do more research on the topic--maybe
even create a unit on Native American Geometry.
Ref: Jamie9
Author(s): Al Rogers
Date: May 8, 1999
Title: Think Quest: Thinking, Learning and Technology
Journal or Publisher:
Volume, Issue, Pages:
Ref: Jamie10
Author(s): Myerscough, Dan; Plager, Don; McCarthy, Lynn; Hopper, Hallie; Fegers,Vickie
Date: 1996
Title: Cryptography: Cracking Codes
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 89, No. 9, pages 743-748
Reviewer: Jamie
Date of Review: May 14, 1999
Ref: Jamie11
Author(s): Vonder Embse, Charles; Engenbretsen, Arne
Date: 1996
Title: A Mathematical Look at a Free Throw Using Technology
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 89, No.9, pages 774-779
Reviewer: Jamie
Date of Review: May 13, 1999
Ref: Jamie12
Author(s): Alper, Lynne; Fendel, Dan; Fraser, Sherry; Resek, Diane
Date: 1995
Title: Implementing the Professional Standards for Teaching Mathematics: Was it Worth it?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 88, No. 7, pages 598-602
Reviewer: Jamie
Date of Review: May 14, 1999
Ref: Jamie13
Author(s): Norem Powell, Nancy; Anderson, Mark; Winterroth, Stanley
Date: 1994
Title: Reflections on Miniture Golf
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 87, No. 7, pages 490-495
Reviewer: Jamie
Date of Review: May 14, 1999
Ref: Jamie14
Author(s): Perham, Arnold; Perham, Bernadette; Perham, Faustine
Date: 1997
Title: Creating a Learning Environment for Geometric Reasoning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 7
Reviewer: Jamie
Date of Review: May 15, 1999
Ref: Jamie15
Author(s): Reif,Daniel
Date: 1996
Title: Archicture in Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 89 No. 6
Reviewer: Jamie
Date of Review: May 15, 1999
Ref: Jamie16
Author(s): Tischler-Welchman, Rosamond
Date:
Title: Making Mathematical Connections
Journal or Publisher:
Volume, Issue, Pages:
http://www.enc.org/classroom/lessons/docs/104923/4923_12.htm (9 pages)
Reviewer: Jamie
Date of Review: May 16, 1999
Ref: Jamie17
Author(s): Battista, Michael
Date: Vol. 86, No.4, 1993
Title: Mathematics in Baseball
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages:
http://www.enc.org/classroom/lessons/docs/103080/3080.htm (8 pages)
Reviewer: Jamie
Date of Review: May 16, 1999
Ref: Jamie18
Author(s): Borlaug, Voctoria
Date: 1993
Title: From Algebra to Calculus: a Tonka toy Tronk Does the Trick
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages:
http://www.enc.org/classroom/lessons/docs/104086/4048.htm
Reviewer: Jamie
Date of Review: May 16,1999
Ref: Jamie19
Author(s): Joyce, David
Date: 1997
Title: Wallpaper Groups
Journal or Publisher: Department of Mathematics and Computer Science Clark University
Volume, Issue, Pages:
http://aleph0.clarku.edu/~djoyce/wallpaper
Reviewer: Jamie
Date of Review: May 16, 1999
Ref: Jamie20
Author(s): Hardaker, Chris
Date: 1998
Title: Native American Geometry
Journal or Publisher: Geometric Explorations
Volume, Issue, Pages:
http://www.earthquake.com/Designs/index.html
Reviewer: Jamie
Date of Review: May 16, 1999