References
- Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal 90(4), 449-466. https://doi.org/10.1086/461626
- Ball, D. L.; Hill, H. C. & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator 29(3), 14-46.
- Ball, D. L.; Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education 59(5), 389-407. doi: 10.1177/0022487108324554
- Baumert, J.; Kunter, M.; Blum, W.; Brunner, M.; Voss, T.; Jordan, A.; Klusmann, U.; Krauss, S.; Neubrand, M. & Tsai, Y. M. (2010). Teachers' mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal 47(1), 133-180. https://doi.org/10.3102/0002831209345157
- Capraro, R. M.; Capraro, M. M.; Younes, R.; Han, S. Y. & Garner, K. (2010). A longitudinal look at the equal sign through the lens of textbooks: A meta-analysis of relational symbols in K-12 textbooks. Paper presented at the annual meeting of the Southwest Educational Research Association held at New Orleans, LA; February 18, 2010.
- Cramer, K.; Behr, M.; Post, T. & Lesh, R. (1997). The rational number project: Fraction lessons for the middle grades, Level 1. Dubuque, IA: Kendall/Hunt.
- Cramer, K. & Wyberg, T. (2009). Efficacy of different concrete models for teaching the part-whole construct for fractions. Math. Think. Learn. 11(4), 226-257. ME 2011f.00421 doi:10.1080/10986060903246479
- Cramer, K. A.; Post, T. R. & delMas, R. C. (2002). Initial fraction learning by fourth- and fifthgrade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. J. Res. Math. Educ. 33(2), 111-144. ME 2002c.02128 https://doi.org/10.2307/749646
- Cumming, G. & Finch, S. (2005). Inference by eye: Confidence intervals and how to read pictures of data. American Psychologist 60(2), 170-180. Retrieved from: http://www.apastyle.org/manual/related/cumming-and-finch.pdf https://doi.org/10.1037/0003-066X.60.2.170
- Diezmann, C. & English, L. (2001). Promoting the use of diagrams as tools for thinking. In: A. Cuoco and F. Curcio (Eds.), The roles of representation in school mathematics. 2001 Yearbook of the National Council of Teachers of Mathematics (pp. 77-89). Reston, VA: National Council of Teachers of Mathematics.
- Empson, S. B. (2002). Organizing diversity in early fraction thinking. In: B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios and proportions. 2002 Yearbook of the National Council of Teachers of Mathematics (pp. 29-40). Reston, VA: National Council of Teachers of Mathematics.
- Han, S. Y.; Rosli, R.; Capraro R. M. & Capraro, M. M. (2011). The textbook analysis on probability: The case of Korea, Malaysia, and U. S. textbooks. J. Korea Soc. Math. Educ. Ser. D 15(2),127-140.
- Hill, H.; Rowan, B. & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Education Research Journal, 42(2), 371-406. Retrieved from: http://deimos3.apple.com/WebObjects/Core.woa/FeedEnclosure/tamupublic. 2117699024.02117699032.2276427372/enclosure.pdf https://doi.org/10.3102/00028312042002371
- Huck, S. W. (2008). Reading statistics and research (5th edition) Boston, MA: Pearson Education.
- Kiren, T. E. (1980). The rational number construct: Its elements and mechanisms. In: T. E. Kiren (Ed.), Recent research on number learning (pp. 125-149). Columbus, OH: Eric-SMEAC.
- Koballa, T. R.; Glynn, S. M. & Upson L. (2005). Conceptions of teaching science held by novice teachers in an alternative certification program. J. Sci. Teacher Educ. 16(4), 287-308. ME 2006e.03303 https://doi.org/10.1007/s10972-005-0192-5
- Lamon, S. J. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Erlbaum. ME 2001b.01827
- Lamon, S. J. (2001). Presenting and representing from fractions to rational numbers. In: A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics (pp. 146-165). Reston, VA: The National Council of Teachers of Mathematics.
- Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. ME1999e.02385
- Martin, S. & Sebesta, L. (2004). Fractions: Building a foundation with concrete manipulatives. Illinois Schools Journal 83(2), 2-21.
- Mewborn, D. S. (2003). Teaching, teachers' knowledge and their professional development. In: J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 45-52). Reston, VA: National Council of Teachers of Mathematics.
- Miller, S. P. & Hudson, P. J. (2006). Helping students with disabilities understand what mathematics means. Teaching Exceptional Children 39(1), 28-35. Retrieved from: http://elem-math.wiki.educ.msu.edu/file/view/12_Miller_TExcepCh06.pdf
- Naiser, E. A.; Wright, W. E. & Capraro, R. M. (2004). Teaching fractions: Strategies used for teaching fractions to middle grade students. Journal of Research in Childhood Education 18(3),193-198.
- National Assessment Educational Progress [NAEP] (2005). NAEP questions tools. Retrieved from: http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx?subject=mathematics
- National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: NCTM. ME 1999f.03937 for discussion draft (1998)
- Newton, K. J. (2008). An extensive analysis of perservice elementary teachers' knowledge of fractions. American Educational Research Journal 45(4), 1080-1110. doi: 10.3102/0002831208320851
- Patterson, J. M.; Capraro, R. M.; Kemp, G. P.; Standish, H. & Sun, Y. (2003). The divergent child: Fraction concepts from their perspective. Paper presented at the 81st annual meeting of the National Council of Teachers of Mathematics held at San Antonio, TX; April, 2003.
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher 15(2), 4-14.
- Simmons, P. E.; Emory, A.; Carter, T.; Coker, T.; Finnegan, B.; Crockett, D.; Richardson, L.; Yager, R.; Craven, J.; Tillotson, J.; Brunkhorst, H.; Twiest, M.; Hossain, K.; Gallagher, J.; Duggan- Haas, D.; Parker, J.; Cjas, R.;, Alshannag, Q.; McGlamery, S.; Krockover, J.; Adams, P.; Spector, B.; LaPorta, T.; James, B.; Rearden, K. & Labuda, K. (1999). Beginning teachers: Beliefs and classroom actions. Journal of Research in Science Teaching 36(8), 930-945. https://doi.org/10.1002/(SICI)1098-2736(199910)36:8<930::AID-TEA3>3.0.CO;2-N
- Skemp, R. (1976). Relational understanding and instrumental understanding. Math. Teaching 77(Dec.), 20-26. ME 1979l.00120 for Arith. Teacher. (1978). 26(3), 9-15. [Reprinted from Math. Teaching 77(Dec. 1976)] Retrieved from: http://www.grahamtall.co.uk/skemp/pdfs/instrumental-relational.pdf
- Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. J. Res. Math. Educ. 31(1), 5-25. ME 2000e.03419 https://doi.org/10.2307/749817
- Van de Walle, J. A.; Karp, K. S. & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Boston, MA: Pearson Allyn & Bacon.
- Vygotsky, L. (2009). Interaction between learning and development. In: M. Gauvain & M. Cole (Eds.) Readings on the development of children (pp 42-48). New York, NY: Worth. [Reprinted from M. Cole, V. John-Steiner, S. Scribner and E. Souberman (Eds.) (1978), Mind in society: The development of higher psychological processes, (pp. 71-91) Cambridge, MA: Harvard University Press]
- Wright, K. B. (2008). Assessing EC-4 preservice teachers' mathematics knowledge for teaching fractions concepts (Unpublished master's thesis). College Station, TX: Texas A&M University.
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