بازنمایی‌های چندگانه: فرایندی مهم در یاددهی و یادگیری کسر‌ها

[1] Canterbury S.A., An investigation of conceptual knowledge: Urban African American Middle School Student’ use of fraction representations and computations in performance-based tasks, (Doctoral dissertation University of Georgia, 2006), 2007, pp. 19-80, 215. [2] Stewart V.M., Making sense of students’ understanding of fractions: An exploratory study of sixth graders’ construction of fraction concepts through the use of physical referents and real world representations, Doctoral dissertation, Florida State University, 2005. [3] Hull L., Fraction models that promote understanding for elementary students, Master's thesis, University of Central Florida, 2005. [4] Hasemann K., on difficulties with fractions. Educational Studies in Mathematics, Vol.12, 1981, pp.71-87. [5] National Council of Teachers of Mathematics, Principles and standards for school mathematics, 2000. [6] Hitt F., Working Group on Representations and Mathematics Visualization, Representation and Mathematics Visualization, 1998-2001, pp. 2 3. [7] Oylum C.A., The effects of multiple representations-based instructions on several grade students’ algebra performance, attitude toward mathematics, and representation بازنماییهای چندگانه: ... نشریه علمی پژوهشی فناوری آموزش، سال پنجم ، جلد 5 ،شماره 1 ،پاییز 1831 preference, Doctoral dissertation, Middle east technical university, 2004. [8] Gyamfi K. A., External multiple representations in mathematics teaching, Master's thesis, North Carolina State University), Available at: http://www.lib.ncsu.edu/theses/available/etd04022003-213629/, 2003, pp. 5-6. ]2 ]کریمییی عبییدالعظی ، مجموعییه سییؤالهییای علییوم و ریاضیییات تیمییز TIMSS پایییه چهییارم ابتییدایی، تهییران، پژوهشگاه موالعات آموزش و پرورش،1397 . [10] Erbilgin E., Effects of spatial visualization and achievement on students’ use of multiple representations, (Master's thesis, Florida State University), Available at: http://etd.lib.fsu.edu/theses/available/etd09172003-182500/, 2003, p.3 ]11 ]حس پور سارا، مفهوم کسر برای معلمان ابتدایی، پایان نامه کارشناسی ارشد، دانشگاه شهید باهنر کرمان، .1395 ]19 ]گویا زهیرا و حسیام عبدالیه، ندیش ویر وارههیا در شکلگیری بدفهمیهای ریاضی دانیشآمیوزان، رشید آموزش ریاضی، دوره بیست و سوم، شیماره دو، دفتیر انتشارات کمک آموزشی ،1391 ،لفحههای4-15. [13] Rider R. L., The effect of multi-representational methods on students' knowledge of function concepts in developmental college mathematics, Doctoral dissertation, North Carolina State University, Available at: http://www.lib.ncsu.edu/theses/available/etd03182004-090043/, 2004. [14] Bosse M. and Bahr D., The state of balance between procedural knowledge and conceptual understanding in mathematics teacher education, Journal for Research in Mathematics Education, Vol. 14, 2008, pp. 2-8.