Early

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Early Number Concepts
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1
10
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5
7
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6
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8
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Early Number Concepts... What is it?
Youre going to be sorry you ever asked that.
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Objectives

• Better define early number concepts.
• Compare and contrast early number concept
  theories.
• Describe how early number concepts impacts your
  teaching and your students.
• Have some good, CLEAN fun while learning.

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BIG Issues
Conceptual Knowledge Versus Procedural Knowledge
Innate Ability Versus Experience
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Only people ignorant of history and too shallow
to understand what an enormous task it is to
create anything could believe that children can
reach any serious understanding of even basic
concepts by the faddish methods of discovery
and creativity being used in public school
classrooms Most of us will never discover or
create anything significant that was not
understood. Thomas Sowell, a
senior fellow at the Hoover Institute, Stanford
University
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For instance, some critics have claimed that
instruction based on the NCTM standards is fuzzy
math. It is not clear, though, why encouraging
students to understand mathematics, use this
understanding to invent solution procedures for
challenging problems, justify and defend their
procedures and solutions, and critically analyze
others procedures and solutions is fuzzy math.
Arthur J. Baroody, Professor,
University of Illnois at Urbana-Champagin
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Agenda
PART 1 Development of Number Concepts Magnitude
of Numbers One to One Correspondence Collections I
nterlude 1 Let the Games Begin!
PART 2 Counting Number Words Operations (, -,
) Commutative Property Equality Interlude 2
More Games!!
PART 3 Advanced Early Number Concepts
Quaternions!!!
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Problems
Eliz had 8 cookies. She ate 3 of them. How many
cookies does Eliz have left? Eliz has 3 dollars
to buy cookies. How many more dollars does she
need to earn to have 8 dollars? Eliz has 3
dollars. Tom has 8 dollars. How many more dollars
does Tom have than Eliz?
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Solvin'
1. What proportion of the time do you
automatically remember the answers for simple
multiplication/addition/subtraction problems? 2.
Some people use solutions called derived facts
where they use a problem they know how to figure
out the answer for another problem. How often do
you use derived fact solutions? 3. Some people
use counting to solve addition problems. How
often do you use counting to solve addition
problems? 4. Overall, please estimate what
proportion of the time you solve simple
multiplication/addition/subtraction problems in
ways other than by automatically remembering the
answers?
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Plussin'
1 8 3 6 3 5 9 7 7 3 2 3
2 8 3 4 1 9 6 3 3 7 0 8
1 5 2 7 1 9 4 6 6 1 9 1
1 2 4 8 2 5 7 5 7 9 9 9
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Minusin'
4 6 5 2 1 9 6 8 3 3 1 6
4 6 5 2 1 9 6 8 3 7 9 4
5 2 8 6 1 6 2 9 4 0 6 0
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Equality
At Ideal University, there are six times as many
students as professors. Write an equation to
represent this situation using S to indicate the
number of students and P to indicate the number
of professors.
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The Players
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William A. Brownell
Born May 19, 1895 Died May 28, 1977 Allegheny
College A.B. 1917 University of Chicago A.M.
1923 University of Chicago Ph.D. 1926
University of Illinois Cornell University Universi
ty of Michigan George Peabody College for
Teachers Northwestern University Duke University
1930 1949 University of California at Berkeley
1950 1961
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Thomas P. Carpenter
EmeritusPh.D. University of Wisconsin,
1971Teacher Education Building Rm 476A225 N.
Mills StreetMadison, Wisconsin 53706Phone
[phone]         Email tpcarpen_at_wisc.eduW
ebsite http//www.education.wisc.edu/ci/mathed/ca
rpenter/
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Arthur J. Baroody
Professor Curriculum Instruction 310 Education
Building 1310 S. 6th St. MC 708 baroody_at_uiuc.edu 2
17 333-4791
Degrees Ph.D., Educational and Developmental
Psychology, Cornell University, 1979 B.S.,
Science Education, Cornell University, 1969
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Geoffrey B. Saxe
UC Berkeley4315 Tolman Hall Berkeley,
CAOffice [phone]saxe_at_socrates.berkeley.ed
u
EDUCATION 1976-1977   Post-doctoral Trainee,
Children's Hospital Medical Center (Harvard
University Medical School) and Boston Veteran's
Administration Hospital, Boston, Massachusetts.
Atypical cognitive development. 1976   Ph.D.,
University of California, Berkeley. Psychology.
1970   B.A., University of California, Berkeley.
Psychology
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Karen Wynn
Professor Department of Psychology Yale
University 2 Hillhouse Ave Box 208205 New Haven,
CT 06520-8205
EDUCATION Ph.D., 1990, Massachusetts Institute
of Technology B.A., 1985, McGill University
(Montreal)
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References
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Arthur J., Tiilikainen, Sirpa H., Wilkins,
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Development of Arithmetic Concepts and Skills
(2002). PP. 127-150. Baroody, Arthur Benson,
Alexis. Early Number Instruction. Teaching
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Brian, Marchesini, Moemi, Girelli, Luisa.
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Carpenter, Thomas P., Elizabeth Fenneman, Megan
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22
Gelman, R. (1978). Counting in the preschooler
What does and does not develop. In R.S. Siegler
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(pp.213-241). Hillsdale, NJ Lawrence
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Mathematics Education. Journal for Research in
Mathematics Education. Vol 8 No. 5 (Nov 1977).
PP. 382-384 Hiebert, J, Wearne, D. (1992).
Links between teaching and learning place value
with understanding in the first grade. Journal
for Research in Mathematics Education, 23, 68,
122. How People Learn Brain, Mind, Experience,
and School. Commission on Behavioral and Social
Sciences and Education, National Research
Council LeFevre, Jo-Anne. Multiple Procedures
in Adults. Development of Arithmetic Concepts
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Okamoto, Yukari. Language Supports.
Development of Arithmetic Concepts and Skills
(2002). PP. 230-236. Mix, K. (2002). The
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Piaget, J.(1952). The childs conception of
number. London Routledge and Kegan Paul. Simon,
T.J., Hespos, S.J., Rochat, P. (1995). Do
infants understand simple arithmetic? A
replication of Wynn (1992). Cognitive
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Jr., R. G. (1980). Perception of numbers by human
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(1996). Infants individuation and enumeration
of sequential actions. Psychological Science, 7,
164-169 Wynn, K. (1992). Addition and
subtraction by human infants. Nature, 358,
749-750. Wynn, K. (1990). Childrens
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