11. Knapp, M.S., Shields, P.M., & Turnbull, B.J. (1995, June). Academic challenge in high-poverty classrooms. Phi Delta Kappan, 76, 770–776.

12. See pages 315–333 of Chapter 9 “Teaching for Mathematical Proficiency” in Adding It Up for four classroom vignettes illustrating different images of mathematics instruction.

13. See the discussion of Communities of Learners (pp. 344–345) in Chapter 9 “Teaching for Mathematical Proficiency” in Adding It Up.

14. For a fuller discussion of the research, see the section on Cooperative Groups (pp. 348–349) in Chapter 9 “Teaching for Mathematical Proficiency” in Adding It Up.

15. For a fuller discussion of the research, see the section on Grouping (pp. 346–348) in Chapter 9 “Teaching for Mathematical Proficiency” in Adding It Up.

16. See the section on Instructional Programs and Materials (pp. 36–39) in Chapter 2 “The State of School Mathematics in the United States” in Adding It Up.

17. See the section on Manipulatives (pp. 353–354) in Chapter 9 “Teaching for Mathematical Proficiency” in Adding It Up.

18. See the section on Assessments (pp. 39–44) in Chapter 2 “The State of School Mathematics in the United States” in Adding It Up.

19. See the section on Knowledge of Mathematics (pp. 372–378) in Chapter 10 “Developing Proficiency in Teaching Mathematics” in Adding It Up.

20. See the section on Programs to Develop Proficient Teaching (pp. 385–397) in Chapter 10 “Developing Proficiency in Teaching Mathematics” in Adding It Up for a description of four different approaches to professional development and teacher education.



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