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Improving Seventh Grade StudentsÂ’ Learning of Ratio and Proportion using Schema-Based Instruction and Self-Monitoring
Unformatted Document Text:  Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-668). National Council of Teachers of Mathematics, Charlotte, NC: Information Age Publishing. Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). National Council of Teachers of Mathematics, Charlotte, NC: Information Age Publishing. Lesh, R., Post, T., & Behr, M. (1988). Proportional Reasoning. In J. Hiebert & M. Behr (Eds.) Number Concepts and Operations in the Middle Grades (pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics. Lester, F. K., Garofalo, J., & Kroll, D.L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeaod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 75-88). New York: Springer-Verlag. Litwiller, B., & Bright, G. (2002). Making sense of fractions, ratios, and proportions. Reston, VA: National Council of Teachers of Mathematics. Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: Author. National Mathematics Advisory Panel (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel. Washington, DC.: U.S. Department of Education. National Research Council (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Richland, L. E., Zur, O., & Holyoak, K. J. (2007). Cognitive supports for analogies in the mathematics classroom. Science, 316, 1128-1129. Rittle-Johnson, B, & Star, J.R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99, 561-574. Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287-301. Star, J., & Rittle-Johnson, B. (in press). It pays to compare: An experimental study on computational estimation. Journal of Child Experimental Psychology, doi:10.1016/j.jecp.2008.11.004. Stylianou, D. A., & Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expert-novice similarities and differences. Mathematical Thinking and Learning, 6, 353-387. Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem solving instruction on students with learning problems. Journal of Special Education, 39, 181-192.

Authors: Jitendra, Asha. and Star, Jon.
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Lamon,   S.   J.   (2007).   Rational   numbers   and   proportional   reasoning:   Toward   a   theoretical 
framework   for   research.   In   F.   K.   Lester,   Jr.   (Ed.),  Second   handbook   of   research   on 
mathematics   teaching   and   learning
  (pp.   629-668).   National   Council   of   Teachers   of 
Mathematics, Charlotte, NC: Information Age Publishing.  
Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester, Jr. (Ed.), 
Second handbook of research on mathematics teaching and learning (pp. 763-804). National 
Council of Teachers of Mathematics, Charlotte, NC: Information Age Publishing.  
Lesh, R., Post, T., & Behr, M. (1988). Proportional Reasoning. In J. Hiebert & M. Behr (Eds.) 
Number Concepts and Operations in the Middle Grades (pp. 93-118). Reston, VA: Lawrence 
Erlbaum & National Council of Teachers of Mathematics.
Lester,   F.   K.,   Garofalo,   J.,   &   Kroll,   D.L.   (1989).   Self-confidence,   interest,   beliefs,   and 
metacognition: Key influences on problem-solving behavior. In D. B. McLeaod & V. M. 
Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 75-88). New 
York: Springer-Verlag.
Litwiller, B., &  Bright, G. (2002). Making sense of fractions, ratios, and proportions. Reston, 
VA: National Council of Teachers of Mathematics.
Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.
National   Council   of   Teachers   of   Mathematics   (2000).   Principles   and   Standards   for   School 
Mathematics. Reston, VA: Author.
National   Mathematics   Advisory   Panel   (2008).  Foundations   for   Success:   The
Final   Report   of   the   National   Mathematics   Advisory   Panel.   Washington,   DC.:   U.S. 
Department of Education.
National   Research   Council   (2001).  Adding  it   up:   Helping   children   learn   mathematics
Washington, DC: National Academy Press.
Richland,  L. E., Zur, O., & Holyoak, K. J. (2007). Cognitive  supports  for analogies  in the 
mathematics classroom. Science, 316, 1128-1129.
Rittle-Johnson, B, & Star, J.R. (2007). Does comparing solution methods facilitate conceptual 
and procedural knowledge? An experimental study on learning to solve equations. Journal of 
Educational Psychology
99, 561-574.
Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. (2005). Moving 
from   rhetoric   to   praxis:   Issues   faced   by   teachers   in   having   students   consider   multiple 
solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24
Star,   J.,   &   Rittle-Johnson,   B.   (in   press).   It   pays   to   compare:   An   experimental   study   on 
computational   estimation.
 Journal   of   Child   Experimental   Psychology
Stylianou,   D.   A.,   &   Silver,   E.   A.     (2004).   The   role   of   visual   representations   in   advanced 
mathematical problem solving: An examination of expert-novice similarities and differences. 
Mathematical Thinking and Learning, 6, 353-387.
Xin, Y. P., Jitendra,  A. K., & Deatline-Buchman, A. (2005). Effects  of mathematical  word 
problem   solving   instruction   on   students   with   learning   problems.  Journal   of   Special 
, 39, 181-192.

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