This list provides a sample of the many high quality
resources available to support your professional development in the following
topics: Mathematics, How
Children Learn Math, Teaching Math, Curriculum
Texts, Web Sites, Action
Research, and Lesson Study .
However, there is considerable overlap between these categories, so you may want
to read through the whole list.
Bassarear, Tom (2000) Mathematics for elementary school teachers.
New York: Houghton Mifflin. I
like this book because it can be used as a self-study guide for elementary
mathematics. I would use it as a text if I were teaching a mathematics content
course. Bassarear emphasizes
conceptual understanding and takes a constructivist approach.
Chapin,
Suzanne H. and Johnson, Art (2000) Math Matters Grades K-6: Understanding the
math you teach. Sausalito, CA: Math Solutions Publications. Targeted
for a teacher audience, this book presents a new look at the mathematics of
elementary school. It is very user friendly in writing, content, and
size.....
Guillen, Michael. (1983).Bridges to Infinity. Los Angeles: Jeremy
P. Tarcher, Inc. A book I love, the history of mathematics in short 7 page
chapters. Sadly out of print now.
Get a copy if you can.
Kamii, C. (1999). Teaching Fractions: Fostering Children’s Own
Reasoning. Developing mathematical
reasoning in grades K-12:1999 NCTM Yearbook. (pp.82-92). NCTM:Reston.
An example of the good chapters that appear in the NCTM yearbooks.
Each yearbook is on a different theme. Here Kamii is as provocative as
ever about the problems of using
manipulatives to teach children mathematics.
Labinowicz, Ed. (1987). Children’s Right to be Wrong.
Arithmetic Teacher, December, pp. 2,21 A short article, but a
classic on the importance of letting children think and make mistakes, rather
than constantly correcting them before or after.
National
Research Council. (2001). Adding it up: Helping children learn mathematics. J.
Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study
Committee, Center for Education, Division of Behavioral and Social Sciences and
Education. Washington, DC; National Academy Press.
An extremely important report about mathematics education which reviews and
synthesizes the latest research on learning mathematics P-8. A team of
researchers representing different perspectives and expertise explores "the
mathematics children need to learn, now they learn it, and how it might be
taught to them effectively (p.xiv). They focus in detail on the mathematics of
number.
Skemp, R. (1976). Relational
Understanding and Instrumental Understanding.
Mathematics Teaching. Association
of Teachers of Mathematics, Great Britain.
December, 77, 152-163. A
classic article, widely referenced, that describes two very different ways of
thinking about mathematics. The
terms “relational” and “instrumental” are used widely to represent
“conceptual” and “procedural” understanding.
Piaget's works on children's conceptions of number, geometry etc..
Books written about Piaget's works by others may be inaccurate so be careful about
believing everything you read. However, his own writing is not very
accessible, so expect to wrestle with it. Constance Kamii studied with Piaget
for 12 years, so her writings convey an accurate understanding of his ideas.
There are
many wonderful resources available, these are just a sampling of them.
Becker,
Jerry and Shimada, Shegeru (1997) The open-ended approach: A new proposal for
teaching mathematics. Reston,VA:
NCTM. This book describes in depth
the Japanese approach to teaching mathematics using open-ended
problem-solving.
Burn, Marilyn (1992).
Math and literature (k-3) Book One. Math Solutions. Anything by
Marilyn Burns is very good.
Burns, Marilyn (1996).
50 Problem-solving lesson: Grades 1-6. Math Solutions Publications.
Fosnot, Catherine
Twomey and Dolk, Maarten (2001). Young mathematiicans at work:
Constructing number sense, addition, and subtraction. Portsmouth, NH:
Heinemann. As the title suggests book takes real examples of how
children construct mathematical concepts. A very helpful book for
developing teaching knowledge and mathematical knowledge.
Fosnot, Catherine
Twomey and Dolk, Maarten (2001). Young mathematiicans at work:
Constructing multiplication and division. Portsmouth, NH:
Heinemann. As the title suggests book takes real examples of how
children construct mathematical concepts. A very helpful book for
developing teaching knowledge and mathematical knowledge.
Jensen, Robert (1991).
Early Childhood Mathematics. Research Ideas for the Classroom
Series. New York: Macmillan. NCTM publication that summarizes research
findings about specific topics in early grades math.
Kamii
(19xx) Young children reinvent arithmetic. New York: Teachers College
Press. There are 4 books in this series ranging from grades 1-4.
They are all good, make sure you get the latest editions.
Kamii studied with Piaget, and has very detailed and clear ideas on what
constructivism is really about.
Kamii, Constance
(1982). Number in pre-school and kindergarten.
Kamii, Constance and
DeVries, Rheta (1980). Group games in early education: Implications of
Piaget’s theory.
Kamii, Constance and
Clarke, Faye (1997). Measurement of length: The need for a better approach to
teaching. School Science and Mathematics, 97(3), 116-121 and 299-300. If
you have ever wondered why children do not seem to be able to measure
accurately, then this fascinating and provocative article will explain the
problem and the challenge of teaching children about measurement of
length. See article by Reece and Kamii for similar findings about
measuring volume.
Kamii,
Constance. (2001). Measurement of time: Children's construction of
transitivity, unit iteration, and conservation of speed. School Science
and Mathematics, 101(3), 125-132. This is the third of Kamii's articles
on measurement. This one deals with the most challenging of the topics,
time.
Ma, Liping (1999) Knowing
and Teaching Elementary Mathematics: Teachers’ Understanding of fundamental
mathematics in China and the United States. NY: Erlbaum. Destined to become a classic, and the source
of the phrase that is reverberating around mathematics education circles, “a
profound understanding of fundamental mathematics (PUFM).”
This very important book is
already setting the agenda for mathematics education in the coming years.
Mathematics in the
Middle School. NCTM journal focused on middle grades. Comes free with
membership to NCTM. An excellent resource with short, relevant articles for the
classroom.
Mewborn, D. and
Huberty, P (1999). Questioning Your Way to the Standards.
Teaching Children Mathematics. December,
226-246. A favorite article of mine that helps to explore the
importance of the questions teachers ask in their classrooms. An example
of the quality of the NCTM journals.
Myren,
Christina (1995). Posing open-ended questions in the primary classroom
Teaching Resource Center, PO Box 82777, San Diego92138.
K-2 wonderful questions with examples of student’s work. Highly
recommended.
NCTM (1991). Professional
Standards for Teaching Mathematics. Reston, VA: Author.
One of the original three standards documents, still contains much
that is very helpful about teaching mathematics.
NCTM (2000) Principles
and Standards for School Mathematics. Reston, VA: Author. This is the
latest NCTM statement about mathematics curriculum and teaching. It
updates the three previous books of standards. It includes recommendations
for K-12 mathematics education. Every school and grade level team should
have one. The Illinois standards support and are aligned with these
standards.
Reece, Charlotte S.
and Kamii, Constance. (In press). The measurement of volume: Why do children
measure inaccurately? School Science and Mathematics. This fascinating
article follows Kamii (1997) and elaborates the problems of measurement by
looking at volume.
Richardson,
Kathy Developing number concepts series. Anything by Kathy Richardson is very good.
This is just one of many books she has published.
Rowan, T. and Robles,
J. (1998). Using questions to help
children build mathematical power. Teaching Children Mathematics. May
(4)9, 504-509. Another good article on asking questions in the
mathematics classroom.
Stein,
M. K., Smith, M. S., Henningsen, M., & Silver, E. (2000). Implementing
standards-based mathematics instruction. New York: Teachers College Press
Stenmark,
Jean Kerr, Thompson, Virginia, and Cossey, Ruth (1986) Family math. Excellent
way to include families in mathematics education.
There are several books in this series.
Stigler and Hiebert
(1999). The teaching gap. New York: Free Press. The book that reports
on the TIMSS video study, and brings to a wide audience the Japanese model for
professional development—lesson study.
Written in accessible language, this is An important book for
administrators to read.
Teaching Children
Mathematics. NCTM journal focused on early grades.
Comes free with membership to NCTM. An excellent resource with short,
relevant articles for the classroom.
Van
de Walle, John ( 2001). Elementary and middle school mathematics: Teaching
developmentally. Addison
Wesley Longman. This is the text
I use in my undergraduate courses, but it contains much in the way of
activities, methods and approaches that will provide nourishment for the
experienced teacher. Van de Walle
was involved in producing the new Principles and Standards, so this text is well
aligned with those expectations.
Wakefield,
Alice (1998) Early childhood number games. New York: Allyn Bacon.
This book relies on Kamii’s work, and provides more examples of games to use
to develop number sense.
Both of the following texts are highly regarded and have
data to prove that children from all backgrounds score well in testing.
They are both based on research into the teaching of mathematics.
Teachers who use them, and are supported by professional development,
speak highly of these series. The
authors of books like this have done much of the hard work for you, they have
selected high quality activities based on sound mathematical thinking and an
understanding of how children learn mathematics.
Everyday Mathematics. University of Chicago School Mathematics Project.
Everyday Learning Corporation. K-6 series.
This series has a reputation for expecting a higher level of
mathematical thinking from students. It
“cycles” through the curriculum, touching repeatedly on certain topics.
Investigations, in Number, Data, and Space.
Scott Foresman . K-5 series. Comes in the form of “replacement units” – 6-8
handy books on each topic that include good information to deepen the
teacher’s understanding of the mathematics they are teaching. These books need
study and thought, and some teachers find them very different from conventional
textbooks. They are black and white
with a lot of reading. Available in
SIUE library for reference.
After
reading Liping Ma's book, many people ask if there is a curriculum available
that is in line with her findings. In a response to an email, she and an
associate report that there is not and she is hoping to produce something, but
it will be at least five years. However, some people find aspects of the
Singapore math curriculum interesting and supportive.
Singapore
Mathematics Curriculum. http://www.singaporemath.com/
www.nctm.org.
GO here for LOTS of on-line resources, NCTM publications, and to join
the NCTM. This site links to the
ILLUMINATIONS website which has a wealth of additional resources.
If you join the NCTM, they provide a wonderful service that enables members to
search current and back issues of their excellent journals, as well as access
teaching resources via grade level links.
www.isbe.net you all know this one,
there is good stuff here, well worth checking to keep up to date with additions.
www.ictm.org This website will
tell you the dates and locations of state and
local Illinois conference where you can network with wonderful Illinois
math teachers who are doing exciting things.
Some of you could also present your work at these conferences.
www.mathematicallysane.comThis site draws together many useful materials and arguments from mathematics
educators and mathematicians to support teachers who are trying to reform their
teaching in line with NCTM expectations. It
provides a counter to www.mathematicallycorrect.com
which presents the views of a small group of very vocal and prominent
research mathematicians in California who are critical of many NCTM
recommendations
classroom.siue.edu
This site is the SIUE School of Education's online classroom, and contains links
to some classes and Special Projects like math resources used by the
Southwestern Regional Math Conference.
www.auntymath.com
This is the web site of Angela G. Andrews, who teaches in Naperville,
Illinois. She presents an excellent challenging problem every other week
for use in your K-5 classroom. Angela Andrews is a very experienced
teacher and workshop presenter. She works closely with the latest NCTM and
state recommendations for teaching mathematics.
http://carson.enc.org/reform/journals/nf_math.htm
www.gamesk-5.com
This site provides details about the games recommended by Constance Kamii in her
books applying Piaget's theory to math education. These games help children to think about
arithmetic. You may order the games from here individually or in grade
sets k-5.
http://www.stclair.k12.il.us/makethelink/mlgrid.htm
This site is part of the St. Clair County Regional Office Site. They
provide a grid that links each of the Illinois Learning Standards to sample
lessons. So if you are looking for help with a particular Illinois
Learning Standard, this site may be very useful.
http://education.ti.com/
This is Texas Instrument's site and it offers many resources and professional
development opportunities for integrating technology (guess which make?) into
your math teaching.
http://owl.english.purdue.edu/handouts/research/r_apa.html#Your%20Reference%20List
This
is just one of many web sites which offer advice on American Psychological Association
[APA] formatting for references. For Electronic
Reference Formats the APA's own web site summarizes its latest
position.
http://www.nku.edu/~mathed/gifted.html
In conjunction with mathematics educators from around the world and in response to numerous requests from teachers and parents,
this website helps mathematics educators, parents, teachers of mathematically promising, talented, gifted and creative students
as well as the students themselves.
http://www.wwshs.org/academics/mathfiles/ictmhome.php
This Making Math Fun
Web site has approximately 100 free, downloadable, interesting, fun math
activities and worksheets for middle school or high school for use in
PreAlgebra through PreCalculus.
www.lessonresearch.net
is devoted to information about the Japanese lesson study model from
researchers at Mills College. It
includes references to and copies of articles.
www.tc.columbia.edu/lessonstudy/
is devoted to information about Japanese lesson study model from the Teachers
College Columbia Lesson Study Research Group. It includes references and copies
of articles.
http://www.schoolrenewal.org/feature/lesson_study/
shares how one school in California is using lesson study for their
professional development.
http://www.gse.uci.edu/Renewal/feature/lesson_study/ls-discussion.html
This site hosts a Lesson Study Discussion Forum
The St Louis Action
Research Collaborative's web site has many helpful resources.
Including examples of teachers' projects from other institutions.
http://www.bath.ac.uk/~edsajw/
Jack Whitehead is a UK professor who has constructed an homepage with multiple
examples of student work, as well as links to other professors' home
pages, including those of McNiff, Mills (see texts recommendations below) and
many other notable authors and action researchers from around the world.
If you want to go to one web site for information, this should probably be it.
McNiff, J., Lomax, P., and Whitehead, J. (1996). You and
your action research project. New York: Routledge.
These UK authors have produced a very helpful book to
guide students through action research and report writing. You could use this
book and pair up with someone else who reads Mills (below) to broaden your
understanding of this kind of research.
Mills, G. (1999). Action research: A guide for the
teacher researchers. New York: Prentice Hall.
This is another excellent book that guides teachers
through action research projects.
