Articles Related to Math Education


About the logico-mathematical foundation of number concepts

Kamii, C., & Rummelsburg, J. (2008). Arithmetic for first graders lacking number concepts. Teaching Children Mathematics, 14(7), 389-394.

 

Kamii, C., Rummelsburg, J., & Kari, A. (2005). Teaching arithmetic to low-performing, low-SES first graders. Journal of Mathematical Behavior, 24(1), 39-50.

 

Examples of physical-knowledge activities

 

Ozaki, K., Yamamoto, N., & Kamii, C. (2008). What do children learn by trying to produce the domino effect? Young Children, 63(5), 58-64.

 

Kamii, C., Miyakawa, Y., & Kato, Y. (2004). The development of logico-mathematical knowledge in a block-building activity at ages 1-4. Journal of Research in Childhood Education, 19(1), 44-57.

 


About some games for young children

 

Kamii, C., and Nagahiro, M. (2008). The educational value of Tic-Tac-Toe for Four-to-Six-Year-Olds. Teaching Children Mathematics 14(9), 523-527.


Kato, Y., Honda, M., & Kamii, C. (2006). Kindergartners play Lining Up the Fives: A card game to encourage logico-mathematical thinking. Young Children, 61(4), 82-88.

 

Kamii, C. (2003). Modifying a board game to foster kindergartners' logico-mathematical thinking. Young Children, 58(5), 20-26.

 


About single-digit addition and subtraction


Kamii, C., & Lewis, B. A. (2003). Single-digit subtraction with fluency. Teaching Children Mathematics, 10(4), 230-236.

 

Kamii, C., Lewis, B. A., & Kirkland, L. D. (2001). Fluency in subtraction compared with addition. Journal of Mathematical Behavior, 20, 33-42.

 

Kamii, C., & Lewis, B. A. (1990). Constructivism and first-grade arithmetic. Arithmetic Teacher, 38(1), 36-37.

 

About double-digit addition and subtraction


Kamii, C., & Dominick, A. (1998). The harmful effects of algorithms in grades 1-4.  In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics: 1998 NCTM yearbook (pp. 130-140).  Reston, VA:  National Council of Teachers of Mathematics.

 

Kamii, C., & Joseph, L. (1988).  Teaching place value and double-column addition.  Arithmetic Teacher, 35(6), 48-52.

 

Kamii, C., Lewis, B. A., & Livingston, S. J. (1993).  Primary arithmetic: Children inventing their own procedures. Arithmetic Teacher, 41(4), 200-203.

 


About multiplication


Clark, F. B., & Kamii, C.  (1996).  Identification of multiplicative thinking in children in grades 1-5.  Journal for Research in Mathematics Education, 27, 41-51.

 

Kamii, C., & Anderson, C. (2003). Multiplication games: How we made them and used them. Teaching Children Mathematics, 10(3), 135-141.

 

Kamii, C.; Pritchett, M.; & Nelson, K. (1997). 52 x 8: The importance of children's initiative. The Constructivist, 12(3), 5-11.


 

About the measurement of length, volume, and time


Kamii, C. (2006). Measurement of length: How can we teach it better? Teaching Children Mathematics, 13(3), 154-158.

 

Kamii, C., & Clark, F. (1997).  Measurement of length:  The need for a better approach to teaching. School Science and Mathematics, 97, 116-121.

 

Reece, C. S., & Kamii, C. (2001). The measurement of volume: Why do young children measure inaccurately?  School Science and Mathematics, 101, 356-361.

 

Kamii, C., & Long, K. (2003). The measurement of time: Transitivity, unit iteration, and conservation of speed. In Clements, D. H., and G. Bright (Eds.), Learning and teaching measurement: 2003 NCTM Yearbook, pp. 169-180. Reston, VA: National Council of Teachers of Mathematics.

 

Long, K., & Kamii, C. (2001). The measurement of time: Children's construction of transitivity, unit iteration, and conservation of speed. School Science and Mathematics, 10(3), 1-8.


 

About why “length x width” is incomprehensible in grades 4-6 (and beyond)

 

Kamii, C., & Kysh, J. (2006). The difficulty of "length x width": Is a square the unit of measurement? Journal of Mathematical Behavior, 25, 105-115.

 


About fractions


Kamii, C., & Warrington, M. A. (1999). Teaching fractions: Fostering children's own reasoning. In Stiff, L. V., & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12: 1999 NCTM yearbook (pp. 82-92). Reston, VA:  National Council of Teachers of Mathematics.

 

Warrington, M.A., & Kamii, C. (1998). Multiplication with fractions: A Piagetian, constructivist approach. Mathematics Teaching in the Middle School, 3, 339-343.


Kamii, C., & Warrington, M. A. (1995).  Division with fractions:  A Piagetian, constructivist approach.  Hiroshima Journal of Mathematics Education, 3, 53-62.

 

Kamii, C., Clark, F. B.  (1995). Equivalent fractions:  Their difficulty and educational implications.  The Journal of Mathematical Behavior, 14, 365-378.



About the relationship between abstraction and representation

 

Kato, Y.; Kamii, C.; Ozaki, K.; & Nagahiro, M. (2002). Young children's representations of groups of objects: The relationship between abstraction and representation. Journal for Research in Mathematics Education, 33, 30-45.

 

Kamii, C., Lewis, B. A., & Booker, B. M. (1998). Instead of teaching missing addends. Teaching Children Mathematics, 4, 458-461.


 

About “manipulatives” as not always facilitating mathematical thinking

 

Kamii, C., Lewis, B. A., & Kirkland, L. D. (2001). Manipulatives: When are they useful? Journal of Mathematical Behavior, 20, 21-31.

 

Chandler, C., & Kamii, C. (2009). Giving change when payment is made with a dime: The difficulty of tens and ones. Journal for Research in Mathematics Education, 40, 97-118.

 

Williams, C., & Kamii, C. (1986).  How do children learn by handling objects?  Young Children. 42, 23-26.

 


About inventing averaging


Kamii, C., Pritchett, M., & Nelson, K. (1996).  Fourth graders invent ways of computing averages.  Teaching Children Mathematics, 3, 78-82.



Comments