**Bibliography for the Mathematics Preparation of Middle School
Teachers**

Mathematics preparation of middle school teachers was the focus of two
meetings held in the summer of 1997. The first was a meeting between
U.S. Department of Education (ED) staff and the Mathematical Association
of America's (MAA) Committee on the Mathematical Education of Teachers
(COMET), and the other, a meeting of mathematicians, mathematics
educators and teachers, was co-sponsored by ED, National Science
Foundation (NSF), and the National Aeronautics and Space Administration
(NASA). Participants in both meetings called for the various mathematics
communities to work together to provide standards or guidelines for the
undergraduate mathematics preparation of teachers.

One immediate outcome of this effort is a suggested bibliography of
recommended readings that could be used to support the undergraduate
mathematics preparation of teachers.

We hope the resources presented below are helpful to all persons who are
concerned about and who are in a position to help improve the
mathematical preparation of middle school teachers. If you have any
comments or suggestions, please contact Joe Teresa, Project Manager, at
<Joe_Teresa@ed.gov>.

####### Recommended Readings for Faculty and Students

**Geometry & Visualization**

Banchoff, Thomas F. 1996. *Beyond the Third Dimension: Geometry,
Computer Graphics, and Higher Dimensions.* New York, NY: Scientific
American Library.

Emmer, Michele. 1993. T*he Visual Mind: Art and Mathematics*. Cambridge,
MA: MIT Press, 1993.

Ferguson, Claire. 1994. *Helaman Ferguson: Mathematics in Stone and
Bronze*. Erie, PA: Meridian Creative Group.

Fischer, Gerd. 1986. *Mathematical Models from the Collections of
Universities and Museums*. Wiesbaden, DRG: Friedrich Vieweg & Sohn,
1986.

Francis, George K. *A*. 1987. *Topological Picturebook,* New York, NY:
Springer-Verlag.

Geddes, Dorothy, et al. *Geometry in the Middle Grades: Addenda Series,
Grades 5-8*. Reston, VA: National Council of Teachers of Mathematics,
1992.

Hildebrandt, Stephan. *Mathematics and Optimal Form*. New York NY:
Scientific American Library, 1995.

Loeb Arthur L. 1991. *Concepts & Images: Visual Mathematics*. Boston,
MA: Birkhäuser.

Loeb, Arthur L. 1976. *Space Structures: Their Harmony and
Counterpoint*. Reading, MA: Addison-Wesley.

Rucker, Rudy. 1984. *The Fourth Dimension: Toward a Geometry of Higher
Reality*. Boston, MA: Houghton Mifflin.

Schattschneider, Doris S. 1995. *Visions of Symmetry: Notebooks,
Periodic Drawings & Related Work of M. C. Escher*. New York, NY: W. H.
Freeman.

Weeks, Jeffrey R. 1985. *The Shape of Space: How To Visualize Surfaces.*
New York, NY: Marcel Dekker.

## Symmetry & Patterns

Grunbaum, Branko and Shephard, G.S., 1987. *Tilings and Patterns*. New
York, NY: W. H. Freeman.

Hildebrandt, Stefan and Tromba, Anthony. 1996. *The Parsimonious
Universe: Shape and Form in the Natural World*. New York, NY:
Copernicus.

Huntley, H.E. 1970. *The Divine Proportion: A Study in Mathematical
Beauty*. Mineola, NY: Dover.

McCown, Jack R. and Sequeira, Michael A. 1994. *Patterns in Mathematics:
Problem Solving from Counting to Chaos*. Boston, MA: Prindle Weber
Schmidt.

Morrison, Philip and Morrison 1982. Phylis, *Powers of Ten*. New York,
NY: Scientific American Library.

Rosen, Joseph. 1995. S*ymmetry in Science: An Introduction to the
General Theory*. New York, NY: Springer-Verlag.

Stevens, Peter S. 1974. *Patterns in Nature.* Boston, MA: Little, Brown
& Co.

Thompson, D'Arcy. 1942. *On Growth and Form*, (2 vols.) Cambridge,
England: Cambridge University Press. (Abridged Edition, 1966).

**Data Presentation & Analysis**

Brook, Hassard, and Richard J. et al. 1986. T*he Fascination of
Statistics*. New York, NY: Marcel Dekker.

Burrill, Gail, et al. 1992. *Data Analysis and Statistics Across the
Curriculum*. Reston, VA: National Council of Teachers of Mathematics.

Campbell, Stephen K. 1974. *Flaws and Fallacies in Statistical
Thinking*. Englewood Cliffs, NJ: Prentice-Hall.

Gonick, Larry and Smith, Woolcott. 1993. *The Cartoon Guide to
Statistics*. New York, NY: HarperCollins.

Huff, Darrell. 1993. *How to Lie with Statistics*. New York, NY: W.W.
Norton & Co., 3.

Landwehr, James and Watkins, Ann. 1986. *Exploring Data*. Palo Alto, CA:
Dale Seymour Publishers.

Moore, David S. 1995. *Statistics: Concepts and Controversies*, Third
Edition. New York, NY: W. H. Freeman.

Peterson, Ivars. 1998. *The Jungles of Randomness*. New York, NY: John
Wiley.

Tanur, Judith M., et al. 1989. *Statistics: A Guide to the Unknown*,
Third Edition. Laguna Hills, CA: Wadsworth.

Tufte, Edward R. 1990. *Envisioning Information*. Cheshire, CT: Graphics
Press.

Tufte, Edward R. 1983. *The Visual Display of Quantitative Information.*
Cheshire, CT: Graphics Press.

Zawjewskii, Judith S. et al. 1991. *Dealing with Data and Chance:
Addenda Series, Grades 5-8*. Reston, VA: National Council of Teachers of
Mathematics.

Zawojewski, Judith S. et al. 1991. *Dealing with Data and Chance*.
Reston, VA: National Council of Teachers of Mathematics.

**Practical Mathematics**

Adams, William J. 1996. *Get a Grip on Your Math*. Dubuques, IA:
Kendall/Hunt.

Bolt, Brian. *Mathematics Meets Technology*. New York, N.Y: Cambridge
University Press.

COMAP. 1996. *For All Practical Purposes: Introduction to Contemporary
Mathematics.* Third Edition. New York, NY: W. H. Freeman.

Courant and Robbins. c.1941. *What Is Mathematics: An Elementary
Approach to Ideas and Methods.* New York, NY: Oxford University Press.

Davis,Philip J and Hersh, Reuben. 1986. "Descartes' Dream: The World
According to Mathematics." Boston, MA: Houghton Mifflin.

Freudenthal, Hans D. 1978. *Weeding and Sowing: Preface to a Science of
Mathematical* Education. Boston MA: Reidel.

Geddes, Dorothy, et al. 1992. *Measurement in the Middle Grades: Addenda
Series, Grades 5-8*. Reston, VA: National Council of Teachers of
Mathematics.

Huff, Darrell. 1996. *The Complete How to Figure It.* New York, NY: W.W.
Norton & Co.

Jacobs, Harold R. 1982. *Mathematics, A Human Endeavor: A Book for Those
Who Think They Don't Like the Subject.* San Francisco, CA: W. H.
Freeman.

Kline, Morris. 1985. *Mathematics for the Non-Mathematician.*Mineola,
NY: Dover Press (originally, Mathematics for Liberal Arts, 1967,
Addison-Wesley).

Lord, John. 1995. *Sizes: How Big (or Little) Things Really Are*. New
York, NY: Harper Perennial.

O'Connor, Vincent. 1997. *Mission Mathematics: Linking Aerospace and the
NCTM Standards, Grades 5-8*. Reston, VA: National Council of Teachers of
Mathematics.

Rauff, James V. 1996. , *Math Matters*. New York, NY: Wiley.

Sadovskii,L. E. and Sadovskii, A. L. 1993. *Mathematics and Sports*.
Providence, RI: American Mathematical Society.

Steen, Lynn Arthur. 1997. *Why Numbers Count: Quantitative Literacy for
Tomorrow's America*. New York, NY: The College Board.

Stein, Sherman K. 1996. *Strength in Numbers: Discovering the Joy and
Power of Mathematics in Everyday Life*. New York, NY: John Wiley & Sons.

Tannenbaum, Peter, and Arnold, Robert. 1992. *Excursions in Modern
Mathematics.* Englewood Cliffs, NJ: Prentice Hall.

Wattenberg, Frank 1990. *Personal Mathematics and Computing: Tools for
the Liberal Arts*. Cambridge, MA: MIT Press.

**Numbers & Infinity**

Beckman, P. *A History of Pi*. 1971. Boulder, CO: Golem Press.

Clawson, Calvin C. 1994. *The Mathematical Traveler: Exploring the Grand
History of Numbers*. New York, NY: Plenum Press.

Conway, John Horton and Guy, Richard. 1996. *The Book of Numbers*.
Washington, DC: Mathematical Association of America. (New York, NY
Copernicus)

Curcio, Frances, et al. 1994. *Understanding Rational Numbers and
Proportions: Addenda Series, Grades 5-8*. Reston, VA: National Council
of Teachers of Mathematics.

Dantzig, Tobias. 1967. *Number: The Language of Science*, Fourth
Edition. New York, NY: Free Press.

Davis, Philip. 1961. *The Lore of Large Numbers*. New York: NY: Random
House.

Hopkins, Nigel J. 1992. *Go Figure! The Numbers You Need for Everyday
Life*. Detroit, MI. Visible Ink Press.

Humez, Alexander. 1993. *Zero to Lazy Eight: The Romance of Numbers*.
New York**,** NY: Simon & Schuster.

Ifrah, Georges. 1985. *From One to Zero: A Universal History of
Numbers*. New York, NY: Viking Penguin.

Imeson, K.R. 1989. *The Magic of Number*. Leicester, England: The
Mathematical Association.

Lines, Malcolm E. 1990. *Think of a Number: Ideas, Concepts, and
Problems*. Philadelphia, PA: I.O.P Publishing.

Maor, Eli. 1993. *The Story of a Number*. Princeton, NJ: Princeton
University Press.

Maor, Eli. 1991. *To Infinity and Beyond: A Cultural History of the
Infinite*. Princeton, NJ: Princeton University Press.

Reys, Barbara J., et al. 1991. *Developing Number Sense in the Middle
Grades: Addenda Series, Grades 5-8*. Reston, VA: National Council of
Teachers of Mathematics.

Reid, Constance. 1992. *From Zero to Infinity: What Makes Numbers
Interesting*, Fourth Edition. Washington, DC: Mathematical Association
of America.

Roberts Joseph. 1992.*The Lure of the Integers*. Washington, DC:
Mathematical Association of America.

Rucker, Rudy. 1982. *Infinity and the Mind: The Science and Philosophy
of the Infinite*. Boston, MA: Birkhauser.

Schimmel, Anne-Marie. 1993. *The Mystery of Numbers*. New York, NY:
Oxford.

Sondheimer, Ernst and Rogerson, Alan. 1981. *Numbers and Infinity: An
Historical Account of Mathematical Concepts*. New York, NY: Cambridge
University Press.

Vilenkin, N. Ya. 1995. *In Search of Infinity*. Cambridge, MA:
Birkhäuser Boston.

**Recreational Mathematics**

Bolt, Brian. 1993. *A Mathematical Pandora's Box*. Cambridge, UK:
Cambridge University Press.

# 

# Courant, R and Robbins, H. E. c. 1941. *What is Mathematics: An Elementary Approach to Ideas* *and Methods.* New York, NY: Oxford Univ. Press.

Dewdney, A. K. 1993*. 200percent of Nothing*. New York, NY: Wiley.

Dorrie, H. 1965. *100 Great Problems of Elementary Mathematics: Their
History and Solution*. New York, NY: Dover Publications.

Dudeney, H. E. 1958. Amusements in Mathematics. New York, NY: Dover
Publications.

Dudeney, H.E. and Gardner, M.ed. 1967. *536 Puzzles and Curious
Problems.* New York, NY: Scribner.

Frolichstein, J. 1962. *Mathematical Fun, Games and Puzzles* Mineola,
New York: Dover Publications.

Gamow, G. 1971. *One, Two, Three, Infinity.* Providence, NJ: Bantam
Books.

Gardiner, A. 1987. *Mathematical Puzzling*. New York, NY: Oxford
University Press.

Gardner, M. 1959-1961. *The Scientific-American Book of Math. Puzzles
and Diversions. New York, NY:* Simon and Schuster.

Gardner, M. 1961. *Science\--Good, Bad, and Bogus*. Buffalo, NY:
Prometheus.

Gardner, M. 1983. *Wheels, Life and Other Math. Amusements*. San
Francisco, CA: Freeman.

Gardner, M. 1956. *Mathematics, Magic and Mystery.* Mineola, NY: Dover
Publications*.*

Gardner, M. 1957. *Fads and Fallacies in the Name of Science*. Mineola,
N.Y: Dover Publications.

Gardner, M. 1971. *"Sixth Book of Math. Games from Scientific
American."* San Francisco, CA: Freeman.

Gardner, M. 1986. *Knotted Doughnuts (and other mathematical
entertainment*).\
San Francisco, CA: W.H. Freeman.

Gardner, M. 1996. *New Math. Diversions from Scientific American*. New
York, NY: Simon and Schuster.

Gardner, M. *M. Aha, Gotcha.* 1982. San Francisco: W.H. Freeman, 1982

Gardner, M. *More Math. 1963. Puzzles and Diversions from Scientific
American.* London, England: Bell Press.

Gardner, Martin. 1989. *Penrose Tiles and Trapdoor Ciphers*. Washington
DC: Mathematical Association of America.

Gardner, Martin. 1995. *New Mathematical Diversions From Scientific
American, Revised Edition.* Washington, DC: Mathematical Association of
America.

Gardner, Martin. 1996. *The Universe in a Handkerchief: Lewis Carroll's
Mathematical Recreations, Games, Puzzles, and Word Plays*. New York, NY:
Springer-Verlag.

### 

### Huff, Darrell. 1982*. How to Lie with Statistics*. New York, NY: W. W. Norton. 

Jacobs, Harold R. 1970. *Mathematics: A Human Endeavor. A Book for
Those* *Who Think They Don't Like the Subject.* San Francisco, CA: W. H.
Freeman.

Kordenskii, Boris. 1992. *The Moscow Mathematical Puzzles.* Mineola, NY:
Dover Publications.

Polya, G.1971. *How to Solve It,* 2nd ed. (paper), Princeton, NJ:
Princeton U. Press.

Radamacher, Hans and Toeplitz, Otto. 1990. *The Enjoyment of
Mathematics: Selections* from *Mathematics for the Amateur*. Princeton,
NJ: Princeton University Press.

Singh, J. 1972. *Great Ideas of Modern Mathematics, Their Nature and
Use*. Mineola, NY: Dover Publications.

Smullyan, R. 1992. *The Lady or the Tiger.* New York, NY: Times Books.

Stein, Sherman K. 1976. *Mathematics-The Man-Made Universe: An
Introduction to the Spirit of Mathematics.* McGraw-Hill (originally)
W.H. Freeman.

Vilenkin, Ya. 1971. *Combinatorics*. New York, NY: Academic Press.

**Algebraic Thinking**

Bednarz, Nadine; Kieran, Carolyn; and Lee, Lesley. 1996. *Approaches to
Algebra: Perspectives for Research and Teaching*. Dordrecht: Kluwer
Academic.

Gelfand, I. M. and Shen. 1993. *Algebra*. Boston, MA: Birkhauser.

Lacampagne, Carole, et al. 1995. *The Algebra Initiative Colloquium* (2
vols.). Washington, D.C: U.S. Department of Education.

Phillips, Elizabeth et al. 1991. *Patterns and Functions: Addenda
Series, Grades 5-8*. Reston, VA: National Council of Teachers of
Mathematics.

Sawyer, WW. 1978. *A Concrete Approach to Abstract Algebra*. Mineola,
NY: Dover Publications.

**Chaos & Fractals**

Barnsley, Michael F. 1988. *Fractals Everywhere*. Boston, MA: Academic
Press.

Casti, John L. 1994. *Complexification: Explaining a Paradoxical World
Through the Science of Surprise.* New York NY: Harper Collins.

Cohen, Jack and Stewart, Ian. 1995. *The Collapse of Chaos: Discovering
Simplicity in a Complex World*. New York, NY: Viking Penguin.

Ekeland, Ivar, 1988. *Mathematics and the Unexpected*. Chicago, IL:
University of Chicago Press.

Gleick, James. 1987. *Chaos: Making a New Science.* New York, NY: Viking
Press.

Hall, Nina. 1994. *Exploring Chaos: A Guide to the New Science of
Disorder*. New York NY: W. W. Norton.

Mandelbrot, Benôit. 1982. *The Fractal Geometry of Nature*. San
Francisco, CA: W. H. Freeman.

Peterson, Ivars. 1993. *Newton's Clock: Chaos in the Solar System.* New
York, NY: W. H. Freeman.

Peak, David and Frame, Michael. 1994. *Chaos Under Control: The Art and
Science of Complexity.* New York, NY: W. H. Freeman.

Peitgen, Heinz-Otto and Richter, Peter H. 1986. *The Beauty of
Fractals*. New York, NY: Springer-Verlag.

Peitgen, Heinz-Otto and Saupe, Dietmar. 1988. *The Science of Fractal
Images*. New York, NY: Springer-Verlag.

Pickover, Clifford A. 1995. *The Pattern Book: Fractals, Art, and
Nature*. River Edge, NJ: World Scientific.

Pickover, Clifford A. 1996. *Fractal Horizons: The Future Uses of
Fractals*. New York, NY: St. Martin's Press.

Ruelle, David. 1993. *Chance and Chaos.* Princeton, NJ: Princeton
University Press.

Schroeder, Manfred. 1995. *Fractals, Chaos, Power Laws: Minutes from an
Infinite Paradise*. New York, NY: W. H. Freeman.

Stewart, Ian. 1989. *Does God Play Dice? The Mathematics of Chaos.* .
Oxford, UK: Blackwell.

**History & Culture**

Albers, Donald J. and Alexanderson, G.L. 1985. *Mathematical People:
Profiles and Interviews*. Cambridge, MA: Birkhauser Boston.

Albers Donald J., et. al. 1990. *More Mathematical People: Contemporary
Conversations*. Orlando, FL: Harcourt Brace Jovanovich.

Ascher, Marcia. 1991. *Ethnomathematics: A Multicultural View of
Mathematical Ideas*. Pacific Grove, CA: Brooks Cole.

Casti. John L. 1996. *Five Golden Rules: Great Theories of 20th-Century
Mathematics and Why They Matter. New York**,** NY:* Wiley.

Crump, Thomas. 1990. *The Anthropology of Numbers*. New York, N.Y:
Cambridge University Press.

Dunham, William. 1990. *Journey Through Genius: The Great Theorems of
Mathematics.* New York, NY: John Wiley & Sons.

Gullberg, Jan. 1997. *Mathematics from the Birth of Numbers*. New York,
NY: W. W. Norton.

Hardy, G. H. 1992. *A Mathematician's Apology*. New York, NY: Cambridge
University Press.

Hofstadter, Douglas R. 1980. *Gödel, Escher, Bach: An Eternal Golden
Braid*. New York, NY: Vintage Press.

Kline, Morris. 1953. *Mathematics in Western Culture*. New York, NY:
Oxford University Press.

Knauff, Robert E. 1996. *Short Stories From the History of Mathematics*.
Burlington, NC: Carolina Biological Supply Co.

Kramer, Edna E. 1981. *The Nature and Growth of Modern Mathematics*.
Princeton, NJ: Princeton University Press.

Gheverghese, Joseph, George. 1991. *The Crest of the Peacock:
Non-European Roots of Mathematics*. New York, NY: I.B. Tauris.

McLeish, John. 1994. *The Story of Numbers: How Mathematics Has Shaped
Civilization.* New York NY: Fawcett Columbine.

Motz, Lloyd. 1993. *The Story of Mathematics*. New York, NY: Plenum.

Nelson, David, et.al. 1993. *Multicultural Mathematics*. New York, NY:
Oxford University Press.

Newman James R, 1988. *The World of Mathematics*. (4 Vols.). Redmond,
WA: Microsoft Press.

Schwartzman, Steven. 1994. *The Words of Mathematics*. Washington DC:
Mathematical Association of America.

White, Alvin. 1993. *Essays in Humanistic Mathematics*. Washington, DC:
Mathematical Association of America.

**The Mathematical Mind**

Changeux**,** Jean-Pierre and Connes**,** Alain. 1995. *Conversations on
Mind, Matter, and Mathematics*. Princeton, NJ: Princeton University
Press.

Davis, Philip J. and Hersh, Reuben. 1980. T*he Mathematical Experience.*
Boston, MA: Birkhauser.

Dehaene, Sanislas. 1997. *The Number Sense: How the Mind Creates
Mathematics*. New York, NY: Oxford University Press.

Devlin, Keith. 1997. *Goodbye, Descartes: The End of Logic and the
Search for a New Cosmology of the Mind.* New York, NY: John Wiley.

English, Lyn G. 1997. *Mathematical Reasoning: Analogies, Metaphors, and
Images*. Mahwah, NJ**:** Lawrence Earlbaum.

Guillen, Michael. 1983. *Bridges to Infinity: The Human Side of
Mathematics*. Boston, MA: Houghton Mifflin.

Hoffman, Paul. 1988. *Archimedes' Revenge: The Joys and Perils of
Mathematics*. New York, NY: W.W. Norton & Co.

Lang, Serge. 1985. *The Beauty of Doing Mathematics: Three Public
Dialogues*. New York, NY: Springer-Verlag.

Rothstein, Edward. 1995. *Emblems of Mind: The Inner Life of Music and
Mathematics*. New York, NY: Random House.

**Nature of Mathematics**

Chaitin, Gregory J. 1997. *The Limits of Mathematics*.New York, NY**:**
Springer-Verlag.

Courant, Richard and Robbins, Herbert. 1960. *What is Mathematics?* New
York: Oxford University Press.

Davis, Donald M. 1993. *The Nature and Power of Mathematics,* Princeton
NJ: Princeton University Press.

Davis, Philip J. and Hersh, Reuben. 1986. *Descartes' Dream: The World
According to Mathematics*. San Diego, CA: Harcourt Brace Jovanovich.

Devlin, Keith. 1998. L*ife by the Numbers*. New York, NY: John Wiley.

Devlin, Keith. 1994. *Mathematics: The Science of Patterns.* New York,
NY: Scientific American Library.

Hersh, Reuben. 1997. *What is Mathematics Really?* New York: Oxford
University Press.

King, Jerry P. 1992. *The Art of Mathematics*. New York: Plenum Press.

Kitcher, Philip. 1983. *The Nature of Mathematical Knowledge*. New York,
NY: Oxford University Press.

Kline, Morris. 1980. *Mathematics: The Loss of Certainty**.*** New York,
NY: Oxford University Press.

Körner, T. W. 1996. *The Pleasures of Counting.* New York, NY: Cambridge
University Press.

Stein, Sherman K. 1976. *Mathematics: the Man-Made Universe*, Third
Edition. San Francisco: W.H. Freeman.

Steen, Lynn Arthur. 1990. *On the Shoulder of Giants: New Approaches to
Numeracy.* Washington, DC: National Academy Press.

Stewart, Ian. 1995. *Nature's Numbers: The Unreal Reality of
Mathematical Imagination.* New York, NY: Basic Books.

Stewart, Ian. 1997. *The Magical Maze: Seeing the World through
Mathematical Eyes.* New York, NY: John Wiley.

**Elements of Mathematics**

Barrow, John D. 1994. *Pi in the Sky: Counting, Thinking, & Being*.
Boston, MA: Little Brown & Co.

Berlinski, David. 1995. *A Tour of Calculus*. New York, NY: Pantheon.

Devlin, Keith. 1988. *Mathematics: The New Golden Age*. London, England:
Penguin.

Eigen, Manfred and Winkler, Ruthild. 1993. *Laws of the Game: How the
Principles of Nature Govern Chance*. Princeton, NJ: Princeton University
Press.

Ekeland, Ivar. 1993. *The Broken Dice and Other Mathematical Tales of
Chance*. Chicago ILL***:*** University of Chicago Press.

Guillen, Michael. 1995. *Five Equations That Changed the World: The
Power and Poetry of Mathematics*. New York NY: Hyperion.

Jacobs Konrad. 1992. *Invitation to Mathematics*. Princeton, NJ:
Princeton University Press.

Kline, Morris. 1985. *Mathematics and the Search for Knowledge*. New
York, NY: Oxford University Press.

Stewart, Ian. 1995. *Concepts of Modern Mathematics*. Mineola, NY: Dover
Publications.

**Snapshots & Vignettes**

Devlin, Keith. 1994. *All the Math That's Fit to Print: Articles from
The Manchester Guardian*. Washington, DC: The Mathematical Association
of America.

Dunham, William. 1994. *The Mathematical Universe: An Alphabetical
Journey Through the Great Proofs, Problems, and Personalities*. New
York, NY: John Wiley & Sons.

Ogilvy, C. Stanley. 1994. *Excursions in Mathematics.* New York, NY:
Dover, 1994.

Paulos. John Allen. 1991. *Beyond Numeracy: Ruminations of a Numbers
Man.* New York, NY: Alfred A. Knopf.

Pickover, Clifford A. 1995. *Keys to Infinity*. New York, NY: Wiley.

Peterson, Ivars, Islands *of Truth: A Mathematical Mystery Cruise*. New
York, NY: W. H. Freeman, 1990.

Schwartzman, Steven. 1994. T*he Words of Mathematics: An Entymological
Dictionary of Mathematical Terms in English.* Washington, DC:
Mathematical Association of America.

Steinhaus, Hugo. 1983. *Mathematical Snapshots,* Third Edition. New
York, NY: Oxford University Press.

Stewart, Ian. 1992. *The Problems of Mathematics*. Second Edition. New
York, NY: Oxford University Press.

**Frontiers of Mathematics**

Aczel, Amir D. 1996. *Fermat's Last Theorem: Unlocking the Secret of an
Ancient Mathematics Problem*. New York, NY: Four Walls Eight Windows.

Cipra, Barry. 1994-96. *What's Happening in the Mathematical Sciences?
Vols. 1-3*. Providence, RI: American Mathematical Society.

Osserman, Robert. 1996. *Poetry of the Universe: The Mathematical
Imagination and the Nature of the Cosmos.* New York, NY: Doubleday.

Penrose, Roger. 1989. *The Emperor's New Mind.* New York, NY: Oxford
University Press.

Peterson, Ivars. 1988. *The Mathematical Tourist: Snapshots of Modern
Mathematics*. New York, NY: W. H. Freeman.

Singh, Simon. 1997. *Fermat's Enigma: The Epic Quest to Solve the
World's Greatest Mathematical Problem*. New York, NY: Walker.

Steen, Lynn Arthur. 1978. *Mathematics Today: Twelve Informal Essays.*
New York, NY: Springer-Verlag.

Stewart, Ian. 1997. *Life's Other Secret: The New Mathematics of the
Living World*. New York, NY: John Wiley.

**Innumeracy & Mathematics Anxiety**

Buxton, Laurie. 1991. *Math Panic*. Portsmouth, NH: Heinemann.

Dewdney, A. K. 1993. *200percent of Nothing: An Eye -Opening Tour
through the Twists and Turns of Math Abuse and Innumeracy*. New York:
John Wiley & Sons.

Gullberg, Jan. 1997. *Mathematics: From the Birth of Numbers.* New York,
NY**:** Norton.

Kogelman, Stanley and Heller, Barbara R. 1995. *The Only Math Book
You'll Ever Need*. Revised Edition. New York NY: Harper Collins.

Motz, Lloyd, and Weaver, Jefferson Hane. 1991. *Conquering Mathematics
from Arithmetic to Calculus.* New York, NY: Plenum Press.

Paulos, John Allen. 1988. *Innumeracy: Mathematical Illiteracy and its
Consequences*. New York, NY: Vintage Books.

Ruedy, Elisabeth and Nirenberg, 1992. Sue, *Where Do I Put the Decimal
Point? How to Conquer Math Anxiety & Let Numbers Work for You,* New York
NY: Avon Books.

Sons Linda R. and Nicholls, Peter J. 1992. *Mathematical Thinking in a
Quantitative World*. Dubuque, IA: Kendall/Hunt.

Tobias, Sheila. 1987. *Succeed with Math: Every Student's Guide to
Conquering Math Anxiety.* New York, NY: The College Board.

Tobias, Sheila. 1993. *Overcoming Math Anxiety*. (Revised Edition). New
York, NY: W. W. Norton.

**Number Theory**

Andrews, George, E. 1994. *Number Theory*. Mineola, NY: Dover
Publications.

Baker, Alan. 1984. *A Concise Introduction to the Theory of Numbers.*
New York, NY: Cambridge University Press.

Dickson, L. E. 1957. *Introduction to the Theory of Numbers*. Mineola,
NY: Dover Publications.

Dickson, L. E. 1969. *Theory of Numbers*. New York, NY: Chelsea
Publications (3 volumes)

Dudley, Underwood. *Elementary Number Theory.* San Francisco, CA:
Freeman Press.

Feller, vol 1. 1967. *An Introduction to Probability Theory and Its
Applications*, second edition. New York, NY: Wiley.

Friedman, Richard. 1968. *An Adventurer's Guide to Number Theory*. New
York, NY: McGraw-Hill.

Hardy, G. H. and Wright, E. M. 1979. *An Introduction to the Theory of
Numbers.* New York: NY: Oxford University Press**,** 5th Ed.

# 

# Ireland and Rosen. 1972. *Elements of Number Theory.* Tarrytown-on-Hudson, NY: Bogden & Quigley.

Menninger, Karl. 1992. *Number Words and Number Symbols: A Cultural
History* *Numbers.* New York, NY: Dover Publications.

Nagell.T. 1964. *Introduction to Number Theory.* New York, NY: Chelsea
Publications.

Niven and Zuckerman. 1956*. Introduction to Number Theory*. New York,
NY: Wiley.

Niven and Zuckerman's. 1983. *An Introduction to the Theory of Numbers*.
New York, NY**:** Wiley.

Stark, H. M. 1978. *An Introduction to Number Theory.* Cambridge, MA:
MIT Press.

Vinogradov, I. M. 1954. *Elements of Number Theory.* Mineola, NY: Dover
Publications.

**Geometry**

Abbott, E. A. 1963. Flatland: *A Romance of Many Dimensions*. Barnes &
Noble.

# Bonola, R.. 1963. *Non-Euclidean Geometry. A Critical and Historical Study of Its Development.* Mineola, NY: Dover, Publications. 

Euclid. 1956. *The Elements*, 3 volumes. Mineola, NY: Dover,
Publications.

Hilbert, D. 1971. Foundations of Geometry. Chicago, ILL: Open Court.

Hilbert and Cohn-Vossen. *Geometry and the Imagination*. New York,
NY:Chelsea

Hobson, E. W. *A treatise on Plane Trigonometry*. Mineola, NY: Dover.

Klein, F. 1956. *Famous Problems of Elementary Geometry*. Mineola, NY:
Dover, Publications.

## Public Policy and Mathematics

## Crossen, Cynthia. 1994. *Tainted Truth: The Manipulation of Fact in America.* New York NY: Simon & Schuster. Friedman, Sharon M., and Rogers, Carol L. 1991. *Environmental Risk Reporting: The Science and the Coverage*. Bethlehem, PA: Lehigh University, Dept. of Journalism.

MacNeal, Edward. 1994. *Mathsemantics: Making Numbers Talk Sense*. New
York, NY: Viking Penguin.

Paulos, John Allen. 1996. *A Mathematician Reads the Newspaper.* New
York, NY: Doubleday.

Porter, Theodore M. 1995. *Trust in Numbers: The Pursuit of Objectivity
in Science and Public Life*. Princeton, NJ: Princeton University Press.

Schwartz, Richard H. 1991. *Mathematics and Global Survival*, Second
Edition. Needham Heights, MA: Ginn Press.

Taylor, Alan D. 1995. *Mathematics and Politics: Strategy, Voting,
Power, and Proof*. New York, NY: Springer-Verlag.

**Educational Research**

Breiteig, T., Huntley, I., and Kaiser-Messmer, G. 1993. *Teaching and
Learning Mathematics in Context. New York, NY:* Ellis Horwood 1993.

Hanna, Gila. 1996. *Towards Gender Equity in Mathematics Education*.
Boston, MA (Dordrecht}: Kluwer Academic.

Noss, Richard and Hoyes, Celia, 1996. *Windows on Mathematical
Meanings*. Boston, MA (Dordrecht): Kluwer Academic.

Schmidt, William H. et al. 1997. *A Splintered Vision: An Investigation
of U.S. Science and Mathematics Education*. Boston, MA ( Dordrecht):
Kluwer Academic.

Schmidt, William H. et al. 1997. *Many Visions, Many Aims, Volume 1*.
Boston , MA (Dordrecht): Kluwer Academic.

Secada, Walter G., et al. 1995. *New Directions for Equity in
Mathematics Education*. New York, NY: Cambridge University Press.

Silver, Edward A. 1998. *Improving Mathematics in Middle School: Lessons
from TIMSS and Related Research*. Washington, DC: Office of Educational
Research and Improvement, U. S. Department of Education.

**Education Policy**

Mathematical Sciences Education Board, National Research Council.1990.
*Reshaping School Mathematics: A Philosophy and Framework for
Curriculum.* Washington, DC: National Academy Press.

NCTM. 1989. *Curriculum and Evaluation Standards for School
Mathematics*. Reston, VA: National Council of Teachers of Mathematics.

NCTM. 1991. *Professional Standards for Teaching Mathematics*. Reston,
VA: National Council of Teachers of Mathematics.

NCTM. 1995. *Assessment Standards for School Mathematics*. Reston, VA:
National Council of Teachers of Mathematics.

National Research Council. 1989. *Everybody Counts: A Report to the
Nation on Mathematics Education.* Washington, DC: National Academy
Press.

**Educational Practice**

Alan Baddeley. 1998. *Human Memory: Theory and Practice. Revised
Edition.* Boston, MA: Allyn and Bacon.

Artzt, Alice F. and Newman, Claire M. 1997. *How to Use Cooperative
Learning in the Mathematics Class.* Second Edition. Reston, VA: National
Council of Teachers of Mathematics.

Ball, D. 1990. "Prospective Elementary and Secondary Teachers'
Understanding of Division." *Journal forResearch in Mathematics
Education. 21*, 132 -144.

Behr, M., and Hiebert, J. (Eds.). 1988*. "Number Concepts and Operations
in the Middle Grades*. Reston, VA: National council of Teachers of
Mathematics.

Campbell, S., and Zazkis, R. 1994. "Distributive flaws: Latent
Conceptual Gaps in Preservice Teachers' Understanding of the Property
Relating Multiplication to Addition." *Proceedings of the Sixteenth
Annual Meeting of the North American Chapter of the International Group
for the Psychology of Mathematics Education* (Vol. 2, pp. 268-274).
Baton Rouge, LA.

Carl, Iris M. Carl. 1995. *Prospects for School Mathematics*. Reston,
VA: National Council of Teachers of Mathematics.

Cobb, P., Yackel, E., and Wood, T. 1988. "Curriculum and Teachers
Development: Psychological and Anthropological Perspectives. In E.
Fenemma, T.P. Carpenter, & S.J.

Dehaene, Stanislas. 1997. *The Number Sense-How the Mind Creates
Mathematics*. New York, NY: Oxford University Press.

deLange, Jan et al. 1993. *Innovations in Maths Education by Modelling
and Applications*. Ellis Horwood.

Edelman, Gerald. 1992. *Bright Air, Brilliant Fire Basic Books*. New
York, NY: HarperCollins.

Fuson, K.C. 1990. "Issues in Place Value and Multi-Digit Addition and
Subtraction Learning and Teaching. *Journal for Research in Mathematics
Education, 21,* 273-280.

Gordon, Ian E. 1997. *Theories of Visual Perception.* 2nd Ed .New York,
NY: Wiley.

Graeber, A., and Tirosh, D. 1988. "Multiplication and Division Involving
Decimals: Preservice Elementary Teachers' Performance and Beliefs."
*Journal of Mathematical Behavior, 7,* 263-280.

Graeber, A., Tirosh, D., and Glover, R. 1986. " Preservice Teachers'
Beliefs and Performance on Measurement and Partitive Division Problems."
In G. Lappan & R. Even (Eds.), *Proceedings of the Eighth Annual
Psychology of Mathematics Education\--North America Conference* (pp.
262-267). East Lansing, MI.

Graeber, A., Tirosh, D., and Glover, R. 1989. Preservice teachers'
misconceptions in solving verbal problems in multiplication and
division. *Journal for Research in Mathematics Education, 20,* 95-102.

Greer, B, 1992. "Multiplication and Division as Models of Situations."
In D.A. Grouws (Ed.), Handbook *of research on mathematics teaching and
learning* (pp. 276-295). New York: Macmillan.

Harel, G., and Confrey, J. (Eds.) 1994. *The Development of
Multiplicative Reasoning in the Learning of Mathematics.* Albany, NY:
SUNY Press.

Hynes, Michael C. 1996. *Ideas: NCTM Standards-Based Instruction, Grades
5-8*. Reston, VA: National Council of Teachers of Mathematics.

Jean-Pierre, Changeux,. 1997. *Neuronal Man.* Princeton, NY: Princeton
University Press.

Kodaira, Kunihiko. 1992. *Japanese Grades 7-9 Mathematics*. University
of Chicago School Mathematics Project.

Kosslyn., Stephen M. 1994. *Image and Brain*. Cambridge, MA: MIT Press.

Lakoff, George. 1987. *Women, Fire, and Dangerous Things*. Chicago, ILL:
University of Chicago Press.

Lamon (Eds.), *Integrating research on teaching and learning
mathematics* (92-131). Madison, WI: Wisconsin Center for Education
Research, University of Wisconsin.

Lappan, G. and Even, R. 1989. "L*earning to Teach: Constructing
Meaningful Understanding of Mathematical Content."* Lansing, MI:
National Center for Research on

Teacher Education, Craft Paper 89-3.

Lester, F.K., and Mau, S.M. 1993. " Teaching mathematics via problem
solving: A course for prospective elementary teachers." *For the
Learning of Mathematics, 13*(2), 8-11.

Martin, W.G., and Harel, G. 1989. "Proof frames of preservice elementary
teachers." *Journal for Research in Mathematics Education, 20*, 41-51.

Meiring, Steven P., et al. 1992. *A Core Curriculum: Making Mathematics
Count for Everyone.* Reston, VA: National Council of Teachers of
Mathematics.

Ohanian, Susan. 1992. *Garbage, Pizza, Patchwork Quilts, and Math Magic:
Stories about Teachers Who Love to Teach and Children Who Love to
Learn.* New York, NY: W. H. Freeman.

Roth, Ilona, and Bruce, Vicki. 1995. *Perception and Representation*:
Current Issues. Chicago, ILL: Open University Press.

Silver, Edward A., et. al. 1990. *Thinking Through Mathematics:
Fostering Inquiry and Communication in Mathematics Classrooms.* New
York, NY: The College Entrance Examination Board.

Simon, M. and Blume, G. 1993. "Mathematical justification: a classroom
teaching experiment with prospective teachers." In B. Pence (Ed.),
*Proceedings of the Fifteenth Annual Meeting of the North American
Chapter of the International Group for the Psychology of Mathematics
Education* (Vol. II, pp. 110-116), Asilomar, CA.

Simon, M. and Blume, G. 1994. " Mathematical modeling as a component of
understanding ration-as-measure: A study of prospective elementary
teachers." *Journal of Mathematical Behavior, 13,* 183-187.

Simon, M.A. 1993. "Prospective elementary teachers' knowledge of
division." *Journal for Research in Mathematics Education, 24,* 233-254.

Simon, M.A., and Blume, G.W. 1994. "Building and understanding
multiplicative relationships: A study of prospective elementary
teachers." *Journal for Research in Mathematics Education, 25,* 472-494.

Sowder, Judith T. and Schappelle, Bonnie P. 1998. *Providing a
Foundation for Teaching Mathematics in the Middle Grades*. Albany, NY:
State University of New York Press.

Thiessen, Diane, and Matthias, Margaret. 1992. *The Wonderful World of
Mathematics: A Critically Annotated List of Children's Books in
Mathematics*. Reston, VA. National Council of Teachers of Mathematics.

Thompson, A. (1984). "The relationship of teachers' conceptions of
mathematics and mathematics teaching to instructional practice."
*Educational Studies in Mathematics, 15,* 105-127.

Tobias, Sheila, 1990. *They're Not Dumb, They're Different: Stalking the
Second Tier.* Tucson, AZ: Research Corp.

Wood, T., Cobb, P., Yackel, E., and Dillon, D. (Eds.). 1993. "Rethinking
elementary school mathematics: Insights and issues." *Journal for
Research in Mathematics Education Monograph series, Number 6.* Reston,
VA: National Council of Teachers of Mathematics.

Zazkis, R., and Campbell, S., 1996. " Divisibility and multiplicative
structure of natural numbers: Preservice teachers' understanding."
*Journal for Research in Mathematics Education, 27n 5,* 540-563.

Zazkis, R., and Khoury, H., 1994. " To the right of the "decimal" point:
Preservice teachers' concepts of place value and multi-digit structures.
In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in Collegiate
Mathematics Education I, CBMS Issues in Mathematics Education, vol.4,
195-224.

**History of Mathematics**

Eves, Howard. 1983. *An Introduction to the History of Mathematics.*
Philadelphia, PA: Saunders. (5th Ed )

Hogben, L. 1960. .*Mathematics in the Making.* New York, NY: Doubleday.
Galahad.

Hogben, L. 1993. *Mathematics for the Million.* New York: NY: Norton.

Lam, Lay Yong and Ang, Tian Se. 1992. Fleeting Footsteps: Tracing the
Conception of Arithmetic and Algebra in Ancient China. River Edge, NJ:
World Scientific.

Li, Yen and Du, Shiran. 1987. *Chinese Mathematics, A Concise History.*
translated by J. N. Crossley and A. W-C. Lun. Oxford, England: Clarendon
Press.

Mikami, Y. 1974. *The Development of Mathematics in China and* Japan.
Jamaica: Chelsea Publications.

Neugebauer, Otto. 1957, 1969. The Exact Sciences in Antiquity.
Providence, RI: Brown University Press. Mineola, NY: Dover Publications.

Struik, D. J. 1987. Concise History of Mathematics. Mineola: NY: Dover
Publications.

Swetz, Frank J. and Kao, T. I. 1977. *Was Pythagoras Chinese: An
Examination of the Right Triangle in Ancient China*. Pennsylvania State
Univ. Press, and NCTM, Reston, Virginia.

Van der Waerden. B.L. 1961. *Science Awakening: Egyptian, Babylonian,
and Greek Mathematics.* Oxford University Press, Paperback, New York,
NY: Wiley.

# 

#  

# **Technology**

An Education Week/Milken Exchange on Education Technology. October 1998.
"Technology Counts.". Bethesda, Maryland.

CEO Forum. October 1997. "School Technology and Readiness Report from
Pillars to Progress."

Committee for Economic Development. 1995. *Connect Students to a
Changing World: A* *Technology Strategy for Improving Mathematics and
Science Education*," Washington, DC.

*"Computers Meet Classroom: Classroom Wins."* Teachers College Record,
Vol. 95, number 2, (winter, 1993: 184-210).

Education Commission of the States. 1998. "Harnessing Technology for
Teaching and Learning," Washington, DC

Glennan, Thomas. and Melmed, Arthur. 1996*. "Fostering the Use of
Educational Technology, Elements of a National Strategy."* Rand Critical
Technology Institute.

Hart, Peter D. June 1997. "Preparing Our Young People for a Changing
World: Students,

NASA, International Society for Technology on Education. June 1998.
"National Educational Technology- Standards for Students," Washington,
DC,

North Central Educational Laboratory. 1996. "Planning for Learning
Through Use of Technology." Seattle, Washington CD-ROM..

Panel on "Educational Technology. March 1997. " Report to the President
on the Use of

Teachers and the Public Speak Out on the Role of Education Technology in
America's Classrooms." Research Associates, Inc. Milken Exchange on
Education Technology.

Technology to Strengthen K-12 Education in the United States."
President's Committee of Advisors on Science and Technology. Washington,
DC.

U.S. Office of Technology Assessment. April 1995*. "Teachers and
Technology: Making the Connection."* Washington, DC: U.S. Government
Printing Office.