1. "Operations & Algebraic Thinking,"
Common Core State Standards Initiative
.
2. Dr. Fong Ho Heong, Chelvi Ramakrishnan, and Bernice Lau Pui Wah,
Math in Focus
, T4-T10.
3. Common Core State Standards Initiative.
4. Mitchell Stephens,
The Rise and Fall of the Word,
16.
5. Elizabeth Spelke as quoted on "Words,"
Radio Lab
.
6. Susan Rich Sheridan, in "Scribbles," 18.
7. Ibid.
8. Ibid.
9. "Concrete-to-Representational-to-Abstract (C-R-A) Instruction."
10.
Maulfry Worthington and Elizabeth Carruthers, "The Art of Children's Mathematics, 5.
11.
Kristine Reed Woleck, "Listen to Their Pictures," 215-27; Carole Saundry and Cynthia Nicol, "Drawing as Problem-Solving," 57-63; Stephen P. Smith, "Representation in School Mathematics," 263-74.
12. Elizabeth Carruthers and Maulfry Worthington,
Children's Mathematics
, 87.
13. Ibid., 79-82.
14. Ibid., 149-50.
15. Bernard Bagnall, "Children's Mathematical Writing."
16. Ibid., 222-24.
17. "Maximizing Student Mathematical Learning in the Early Years," 4-5.
18. Chapin, O'Conner and Anderson as quoted in "Maximizing Student Mathematical Learning in the Early Years," Ibid., 5.
19. "Bansho (Board Writing)."
20. Ibid., 205.
21. Ibid.
22. Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi, and Susan B. Empson,
Children's Mathematics
.
23. Ibid., 7-12.
24. "Efficient,"
Dictionary.com,
accessed July 1, 2014, http://dictionary.reference.com/browse/efficient.
25. Ibid.
