International Journal of Mathematics Trends and Technology
Volume 67 | Issue 7 | Year 2021 | Article Id. IJMTT-V67I7P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I7P504
This study presents the research conducted on the Greek Mathematics Primary textbooks about the notion of the sequences of rational numbers on the geometric model of the number line. In other words, which and how many representations have been used in the textbooks of primary school for the above notion. In addition, it is commenting on the frequency and kind of representations, as well their correlation with the difficulties students face, based on surveys. Results show that there is a limited scope of activities on Mathematics textbooks about the sequences of rational numbers on the geometric model of the number line in Greece.
[1] E.Avgerinos, R.Vlachou and K.Kantas, Comparing different age student abilities on the concept and manipulation of fractions, Research on Mathematical Education and Mathematics Applications. (2012) 159-169.
[2] E.Αvgerinos and R.Vlachou, Fractions and representation: A didactic approach to the concepts of number line, unit equal parts and abusive fractions,, 29th Panhellenic Conference on Mathematics Education, Mathematics: Theory - Practice – Extensions-Greek version. (2012) 135-147.
[3] E.Αvgerinos and R.Vlachou, The Perceptions of pedagogical studies students in the concepts of number line, equal parts of the unit and abusive fractions, 15th Pancyprian Conference on Mathematics Education and Science-Greek version. (2013) 189-201.
[4] E.Αvgerinos and R.Vlachou, Cognitive conflicts in the understanding of explicit numbers during the transition of students from Primary to Gymnasium and from Gymasium to High School, 30 Panhellenic Conference on Mathematics Education, Challenges and Prospects of Mathematics Education and Research in the Internationalized Network Age-Greek version. (2014).
[5] G.Boulet, Didactical implications of children's difficulties in learning the fraction concept, Focus on Learning Problems in Mathematics. 20(4) (1998) 19-34.
[6] X.Chen and Y.Li, Instructional coherence in Chinese mathematics classroom—a case study of lessons on fraction division, International Journal of Science and Mathematics Education. 8(4) (2009) 711-735.
[7] E.Deliyianni, A.Gagatsis, I.Elia and A.Panaoura, Representational flexibility and problem-solving ability in fraction and decimal number addition: A structural model, International Journal of Science and Mathematics Education. 14(2) (2016) 397-417.
[8] A.Dreher and S.Kuntze, Teachers ’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom, Educational Studies in Mathematics. 88(1) (2015) 89-114.
[9] E.Dubinsky, I.Arnon and K.Weller, Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion: The case of 0.9 and 1. Canadian Journal of Science, Mathematics and Technology Education. 13(3) (2013) 232-258.
[10] A.Gagatsis, L.Kyriakides and A.Panaoura, Assessing the cross-cultural applicability of number line in conducting arithmetic operations using structural equation modeling: A comparative study between Cyprus, Italian and Greek primary pupils. World Studies in Education. 5(1) (2004) 85-101.
[11] P.Gridos, E.Avgerinos, J.Mamona-Downs and R.Vlachou, Geometrical figure apprehension, construction of auxiliary lines, and multiple solutions in problem solving: aspects of mathematical creativity in school geometry. International Journal of Science and Mathematics Education. 19(4) (2021).
[12] A.J.Hackenberg, Units coordination and the construction of improper fractions: A revision of the splitting hypothesis, The Journal of Mathematical Behavior. 26(1) (2007) 27-47.
[13] J.Hodgen, D.Küchemann, M.Brown and R.Coe, Lower secondary school students' knowledge of fractions, Research in Mathematics Education. 12(1) (2010) 75-76.
[14] C.Howe, S.Luthman, K.Ruthven, N.Mercer, R.Hofmann, S.Ilie and P.Guardia, Rational number and proportional reasoning in early secondary school:towards principled improvement in mathematics, Research in Mathematics Education. 17(1) (2015) 38-56.
[15] C.Janvier, Translation processes in mathematics education. Problems of Representation in the Teaching and Learning of Mathematics, Hillsdale, NJ: Lawrence Erlbaum. (1987) 27-32.
[16] C.Jiang and B.L.Chua, Strategies for solving three fraction-related word problems on speed: a comparative study between Chinese and Singaporean students, International Journal of Science and Mathematics Education. 8(1) (2010) 73-96.
[17] Χ.Κakadiaris, Ν.Belitsou, G.Stefanidis and G.Chronopoulou, Maths in 5th grade, Workbooks and Teacher’s book, Athens-in Greek version (2006).
[18] Ο.Kassoti, P.Kliapis and Th.Oikonomou, Maths in 6th grade, Workbooks and Teacher’s book, Athens-in Greek version (2006).
[19] Χ.Lemonidis, Ε.Theodorou, Κ.Νikolantonakis, Ι.Panagakos and Α.Spanaka, Maths in 3rd grade: Maths of nature and life, Workbooks and Teavher’s book, Athens-in Greek version (2006).
[20] H.Lee and P.Sztajn, Focusing on units to support prospective elementary teachers’ understanding of division in fractional contexts, School Science and Mathematics. 108(1) (2008) 20-27.
[21] C.Y.Lin, Web-based instruction on preservice teachers’ knowledge of fraction operations, School Science and Mathematics. 110(2) (2010) 59-70.
[22] J.J.Lo, Conceptual bases of young children’s solution strategies of missing value proportional Tasks. Psychology of Mathematics Education in Proceedings of Seventeenth PME International Conference (1993) 162-177.
[23] F.Rønning, Making sense of fractions in different contexts. Research in Mathematics Education. 15(2) (2013) 201-202..
[24] O.Şahin, B.Gökkurt and Y.Soylu, Examining prospective mathematics teachers’ pedagogical content knowledge on fractions in terms of students’ mistakes, International Journal of Mathematical Education in Science and Technology. 47(4) (2016) 531-551.
[25] A.Sfard, On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin, Educational Studies in Mathematics. 22 (1)(1991)1-36.
[26] A.J.Shahbari and I.Peled, Resolving cognitive conflict in a realistic situation with modeling characteristics: coping with a changing reference in fractions, International Journal of Science and Mathematics Education. 13(4) (2015) 891-907.
[27] L.Streefland, Fractions in Realistic Mathematics Education: A paradigm of developmental research. Dordrecht:Τhe Netherlan (1991).
[28] E.Thanheiser, D.Olanoff, A.Hillen, Z.Feldman, M.J.Tobias and M.R.Welder, Reflective analysis as a tool for task redesign: The case of prospective elementary teachers solving and posing fraction comparison problems, Journal of Mathematics Teacher Education. 19(2-3) (2016) 123-148.
[29] M.J.Tobias, Prospective elementary teachers’ development of fraction language for defining the whole, Journal of Mathematics Teacher Education. 16(2)(2013) 85-103.
[30] R.Vlachou and E.Avgerinos, Visualization and understanding in mathematics education: the case of fractions, The Journal of the ISIS-The Logics of Image. (2016).
[31] R.Vlachou and E.Avgerinos, Multiple representatıons and development of students' self-confidence on rational number. Experiences of Teaching with Mathematics, Sciences and Technology. 4(2018) 567-586.
[32] R.Vlachou and E.Avgerinos, Current trend and studies on representations in mathematics: The case of fractions. International Journal of Mathematics Trends and Technology (IJMTT ). 65(2) (2019) 54-72.
[33] R.Vlachou, E.Avgerinos and P.Gridos, The Open-ended Problem as a key tool for the development of students’ mathematical ability and attitude. Mediterranean Journal for Research in Mathematics Education. 17 (2020) 53-63.
[34] I.Whitacre and D.S.Nickerson, Investigating the improvement of prospective elementary teachers’ number sense in reasoning about fraction magnitude. Journal of Mathematics Teacher Education. 19(1) (2016) 57-77.
Evgenios Avgerinos, Georgia Lazakidou, Roza Vlachou, Konstantinos Simeonidis, "The Number Line as Geometric Model for Representation of Fractions: The case of the Greek Mathematics Primary Textbooks," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 7, pp. 26-34, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I7P504
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