Math wars 2: It's the teaching, stupid!

Phi Delta Kappan

Volumn 87, Issue 5, 2006, Pages 356-363

  Marshall, John ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32344433002     PISSN: 00317217     EISSN: None     Source Type: Journal    
DOI: 10.1177/003172170608700506     Document Type: Review

References (31)

1. Mary Baratta-Lotton, Mathematics Their Way (Menlo Park, Calif.: Addison-Wesley, 1976), p. 90.
2. Michael T. Battista, "The Mathematical Miseducation of America's Youth: Ignoring Research and Scientific Study in Education," Phi Delta Kappan, February 1999, p. 426.
3. Richard W. Copeland, How Children Learn Mathematics: Teaching Implications of Piaget's Research (New York: Macmillan, 1970), p. 32.
4. James W. Stigler and James Hiebert, The Teaching Gap (New York: Free Press, 1999), p. 85.
5. Principles and Standards for School Mathematics (Reston, Va.: National Council of Teachers of Mathematics, 2000), p. 46.
6. A. W. Bell, J. Costello, and D. Küchemann, A Review of Research in Mathematical Education (London: NFER-Nelson, 1983), p. 162.
7. Thomas Post, "The Role of Manipulative Materials in the Learning of Mathematical Concepts," in Mary Montgomery Lindquist, ed., Selected Issues in Mathematics Education (Berkeley, Calif.: McCutchan, 1980).
8. "Mathematics itself is about exact and precise ideas and 'concepts, ' about 'abstractions,' which are in our minds. Although these concepts can be applied to our real world, and things in the real world can help us to think about mathematics, the abstractions are not things we can see and touch. Mathematics is in the mind, in our thoughts." Sir Wilfred Cockcroft and John Marshall, "Educating Hannah: It's a What?," Teaching Children Mathematics, February 1999, p. 328.
9. Simon Singh, Fermat's Last Theorem (London: Fourth Estate, 1997), p. 150.
10. Mathematics in the Modern World: Readings from Scientific American (San Francisco: W. H. Freeman, 1968), p. 190.
11. Committee of Inquiry into the Teaching of Mathematics, Mathematics Counts (London: H.M.S.O., 1982), p. 71.
12. Bell, Costello, and Küchemann, p. 7.
13. If a young soccer player scores 17 goals in 20 games, then his scoring average is 0.85 goals per game. The problem is real, but the average is abstract, as one cannot score 0.85 goals in a real game.
14. Liping Ma, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Mahwah, N.J.: Erlbaum, 1999), p. xxiv.
15. MN, 1998), p. 8.
16. Committee of Inquiry into the Teaching of Mathematics, p. 68.
17. A recently published book reports that "Antell and Keating's research shows that, when each of us was just four days old, we were able to distinguish between collections of two and three objects that we saw. . . . We certainly have the beginning of a sense of twoness and threeness by the time we are six to eight months old." Kevin Devlin, The Math Instinct (New York: Thunder's Mouth Press, 2005), p. 12.
18. Principles and Standards for School Mathematics, p. 80.
19. Bell, Costello, and Küchemann, p. 98.
20. Ibid.
21. John A. Van De Walle, Elementary School Mathematics: Teaching Developmentally (New York: Longman, 1994), p. 121.
22. Research shows that "formulae and their appropriate use and retention" depend "both on earlier practical experiences and on a perceived need for and appreciation of this efficiency." Bell, Costello, and Küchemann, p. 162.
23. Stigler and Hiebert, p. 45.
24. Ibid., p. 65.
25. Cockcroft and Marshall, Elementary School Mathematics: Teaching Developmentally, op. cit.;
26. and Deirdre Oempsey and John Marshall, "Dear Verity, Now I'm Getting into Shape!," Phi Delta Kappan, April 2002, pp. 606-11.
27. Kenneth Lovell, Educational Psychology and Children (London: University of London Press, 1958), pp. 118-26;
28. H. Maddox, How to Study (London: Pan, 1976), p. 56;
29. Mathematics Counts, p. 70;
30. Lawrence F. Lowery, The Biological Basis of Thinking and Learning (Berkeley: Regents of the University of California, 1998);
31. and Principles and Standards for School Mathematics.